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UBC Theses and Dissertations

Reduction of Earth observation system response time using relay satellite constellations Sanad, Ibrahim Shaaban 2020

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REDUCTION OF EARTH OBSERVATION SYSTEM RESPONSE TIME USING RELAY SATELLITE CONSTELLATIONS by  Ibrahim Shaaban Sanad  B.Sc., Military Technical Colleague, Cairo Egypt, 2004 M.Sc., Military Technical Colleague, Cairo Egypt, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2020  © Ibrahim Shaaban Sanad, 2020  ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Reduction of Earth Observation System Response Time Using Relay Satellite Constellations  submitted by Ibrahim Shaaban Sanad in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering  Examining Committee: David G. Michelson, Associate Professor, Electrical and Computer Engineering, UBC Supervisor  Ryozo Nagamune, Associate Professor, Mechanical Engineering, UBC Supervisory Committee Member  Mieszko Lis, Assistant Professor, Electrical and Computer Engineering, UBC Supervisory Committee Member Nicholas C. Coops, Professor, Forestry Resources Management, UBC University Examiner Gary Hinshaw, Professor, Physics & Astronomy, UBC University Examiner     iii Abstract System Response Time (SRT) is the interval between submitting an imaging request to, and receiving imagery from, Earth Observation (EO) satellites. Reduction of SRT is especially important in natural disaster and national security situations. The use of dedicated relay communication satellite constellations (RCSCs) to significantly reduce SRT has long been recognized but often dismissed as too costly. In recent years, however, the introduction of low-cost satellite and launcher technology has rekindled interest in this approach. Here, we contribute tools, techniques, and insights that allow designers to design RCSCs for EO constellations more systematically than previously possible. First, we present a framework for designing RCSCs in support of EO constellations based on the industry-standard System Tool Kit (STK) software and demonstrate its use. Second, based on a statistical analysis of the orbital parameters for 34 remote sensing satellite constellations (RSSCs) and a thorough review of their missions, we propose nine representative classes that allow the performance of RCSCs to be broadly assessed with far less effort than testing against an exhaustive set. Third, we present a toolkit for calculating SRT for various relay network configurations and implement it as STK add-on modules. We also present a tool to design RCSCs in Medium Earth Orbit (MEO) that can achieve persistent inter-relay intersatellite links (ISLs) and thereby minimize SRT. Fourth, for cases where the RCSCs have persistent inter-relay ISLs, we use our tools to generate performance curves that show how system response is affected by changes in the orbital altitudes and inclinations of the relays, and the latitude of a ground station and thereby overcome a key limitation of previous work. We demonstrate that a Walker-Delta 4/2/1 RCSC with 4 satellites in two planes achieves much better performance at much lower cost than a Walker-Delta 3/3/0 RCSC with 3 satellites in three planes when serviced by a single ground station. This is noteworthy given that Walker-Delta 3/3/0 configuration will be used by the recently announced first commercial MEO relay satellite constellation. The results convincingly demonstrate the value of assessing the sensitivity of a given relay constellation to its design parameters. iv Lay Summary System Response Time (SRT) is the interval between submitting an imaging request to, and receiving imagery from, Earth observation satellites. Reduction of SRT is especially important in natural disaster and national security situations. The introduction of low-cost satellite and launcher technology has rekindled interest in using a constellation of dedicated relay satellites to significantly reduce SRT. We have developed design frameworks and add-on modules for the industry-standard Systems Tool Kit (STK) software that make the design of relay satellite constellations with various configurations and topologies more systematic and more efficient than was previously possible. These tools have allowed us to demonstrate that a Walker-Delta constellation with 4 relay satellites in two planes achieves much better performance at a lower cost than a constellation with 3 relay satellites in three planes. This is noteworthy given that the latter configuration will be used by the recently announced first commercial relay satellite constellation.             v Preface The work reported in this thesis is an original intellectual produce of the author, Ibrahim Sanad, under the supervision of Prof. David G. Michelson. Prof. Michelson and Mr. Sanad jointly set the research objectives, developed the research plan, and drafted the thesis outline. Mr. Sanad developed all of the software and conducted all of the computer simulations used to generate the results. Prof. Michelson and Mr. Sanad jointly interpreted the results and drew conclusions. Mr. Sanad drafted most of the text, but the final version contains many editorial contributions from Prof. Michelson and Dr. Zahra Vali provided helpful advice and feedback during the latter stages of the work.  Portions of Chapters 1 and 2 have been published: I. Sanad and D. G. Michelson, “Application of Earth-space path loss as a constraint in the design of LEO satellite constellations,” in Proc. 2017 USNC-URSI Radio Science Meeting, San Diego, CA, and I. Sanad and D. G. Michelson, “Evolving goals and techniques of satellite constellation design for navigation, communications, and remote sensing: 1958-2018,” in Proc. 2018 USNC-URSI Radio Science Meeting, Boston, MA. I conducted all the numerical simulations and prepared most of the slides of these presentations under the supervision of Prof. Michelson. A version of Chapter 3 has been published: I. Sanad and D. G. Michelson, “A framework for heterogeneous satellite constellation design for rapid response Earth observations,” in Proceedings of the 2019 IEEE Aerospace Conference, Big Sky, MT, USA, pp. 1-10. I conducted all the computer simulations & the numerical analysis and wrote most of the manuscript under supervision of Prof. Michelson.  vi A version of Chapter 4 has been published: I. Sanad, Z. Vali, and D. G. Michelson, “Statistical classification of remote sensing satellite constellations,” in Proceedings of the 2020 IEEE Aerospace Conference, Big Sky, MT, USA, pp. 1-15. I conducted all the computer simulations & the numerical analysis and wrote most of the manuscript. The final version contains many editorial contributions from Prof. Michelson and Dr. Zahra Vali.   vii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ........................................................................................................................ vii List of Tables ............................................................................................................................... xii List of Figures ............................................................................................................................. xiii List of Abbreviations ................................................................................................................. xvi Acknowledgments .................................................................................................................... xviii Dedication ................................................................................................................................... xix Chapter 1: Introduction ................................................................................................................1 1.1 Overview ......................................................................................................................... 1 1.2 Motivation ....................................................................................................................... 3 1.3 Problem Statement .......................................................................................................... 5 1.4 Objectives ....................................................................................................................... 6 1.5 Thesis Outline ................................................................................................................. 7 Chapter 2: Literature Survey .....................................................................................................10 2.1 Satellite Constellation Design – A Short Survey .......................................................... 10 2.1.1 Figures of Merit for Early Design Earth Observation Constellations....................... 13 2.1.1.1 Coverage ........................................................................................................... 13 2.1.1.2 Ground Sampling Distance ............................................................................... 15 2.1.1.3 Cost ................................................................................................................... 16 2.1.2 System Response Time ............................................................................................. 18 2.2 Related Literature.......................................................................................................... 19 viii 2.2.1 Satellite Constellation Design Optimization ............................................................. 21 2.2.1.1 Revisit Time Minimization ............................................................................... 21 2.2.1.2 Access Time Maximization .............................................................................. 24 2.2.2 Planning and Scheduling Optimization .................................................................... 26 2.2.3 Ground Station Networks ......................................................................................... 28 2.2.4 Relay Satellite Systems ............................................................................................. 29 2.2.4.1 GEO Relays ...................................................................................................... 29 2.2.4.2 Non-GEO Relays .............................................................................................. 30 2.3 Summary ....................................................................................................................... 33 Chapter 3: A Framework for Heterogeneous Satellite Constellation Design for Rapid Response Earth Observations .....................................................................................................35 3.1 Introduction ................................................................................................................... 35 3.2 Parametric Study Tool for Heterogeneous Satellite Constellation Design ................... 36 3.3 Proposed Framework .................................................................................................... 38 3.3.1 Imaging Constellation Design................................................................................... 39 3.3.2 Relay Constellation Design....................................................................................... 42 3.4 Selected Results from a Case Study.............................................................................. 44 3.5 Discussion ..................................................................................................................... 51 Chapter 4: Reference Configurations for Remote Sensing Satellite Constellations ..............53 4.1 Introduction ................................................................................................................... 53 4.2 A Representative List of Remote Sensing Satellite Constellation Missions ................ 56 4.2.1 SAR Constellations ................................................................................................... 58 4.2.1.1 RADARSAT ..................................................................................................... 58 4.2.1.2 ICEYE ............................................................................................................... 59 ix 4.2.1.3 XpressSAR ........................................................................................................ 59 4.2.1.4 OptiSAR ............................................................................................................ 60 4.2.2 Optical Constellations ............................................................................................... 61 4.2.2.1 RapidEye ........................................................................................................... 61 4.2.2.2 PlanetScope (PS) ............................................................................................... 61 4.2.2.3 Digital-Globe (DG) ........................................................................................... 62 4.2.3 Weather and Scientific Constellations ...................................................................... 63 4.2.3.1 FORMOSAT-3/COSMIC ................................................................................. 63 4.2.3.2 NASA’s CYGNSS ............................................................................................ 64 4.2.3.3 CICERO ............................................................................................................ 65 4.3 Methodology ................................................................................................................. 66 4.3.1 Data Sources ............................................................................................................. 66 4.3.2 Statistical Analysis Reductions ................................................................................. 66 4.4 Results and Discussion ................................................................................................. 69 4.4.1 Analysis of Satellites in CelesTrak Groups .............................................................. 69 4.4.2 Analysis of Satellite Constellation Groups ............................................................... 73 4.4.3 Previously Proposed RCSCs in MEO ....................................................................... 81 4.5 Summary ....................................................................................................................... 83 Chapter 5: SRT Calculations for EO Satellites Supported by Various Relay Network Configurations ..........................................................................................................85 5.1 Introduction ................................................................................................................... 85 5.2 SRT Calculations .......................................................................................................... 90 5.2.1 SRT and Performance-related Metrics...................................................................... 90 5.2.2 Relay Network Configurations ................................................................................. 93 x 5.2.3 SRT Calculation Algorithm ...................................................................................... 96 5.3 Relay Constellations with Persistent ISLs .................................................................... 97 5.3.1 Intra Orbit ISLs ......................................................................................................... 98 5.3.2 Inter Orbit ISLs of Walker Relay Constellations .................................................... 102 5.3.3 Algorithm for Configuring Relay Constellations with Persistent ISLs .................. 104 5.4 Implementation ........................................................................................................... 105 5.4.1 MATLAB/STK Interface ........................................................................................ 105 5.4.2 MATLAB/STK Integrated Toolkit for SRT Calculations ...................................... 106 5.4.2.1 Toolkit Initialization and Set-up ..................................................................... 107 5.4.2.2 High Fidelity Object Models from STK ......................................................... 109 5.4.2.3 SRT Calculations Modules in MATLAB ....................................................... 110 5.4.3 Configuring Walker Relay Constellations with Persistent ISLs using STK ........... 112 5.5 Results ......................................................................................................................... 114 5.5.1 SRT Calculations – A Case Study .......................................................................... 114 5.5.1.1 Computational Performance Evaluation ......................................................... 118 5.5.2 Walker Constellations with Persistent ISLs ............................................................ 120 5.6 Discussion ................................................................................................................... 126 Chapter 6: Sensitivity Analysis of Walker-Delta Constellations Used as Relay Satellites ..128 6.1 Introduction ................................................................................................................. 128 6.2 Case Studies ................................................................................................................ 131 6.3 Representative Configuration for Remote Sensing Satellite Constellations ............... 133 6.4 Parametric Study Framework ..................................................................................... 134 6.5 Trends and Patterns ..................................................................................................... 136 6.5.1 Case Study 1 – Walker-Delta 3/3/0 Constellation Configuration ........................... 136 xi 6.5.2 Case Study 2 – Walker-Delta 4/2/1 Constellation Configuration ........................... 139 6.6 Discussion ................................................................................................................... 143 Chapter 7: Conclusions and Recommendations .....................................................................146 7.1 Conclusions ................................................................................................................. 146 7.2 Recommendations for Future Work............................................................................ 148 References ...................................................................................................................................149 xii List of Tables Table 2-1 – Previous efforts to reduce SRT.................................................................................. 20 Table 4-1 – DMC3 satellite data from TLEs. ............................................................................... 68 Table 4-2 – Weather monitoring constellations. ........................................................................... 76 Table 4-3 – Optical constellations. ............................................................................................... 77 Table 4-4 – SAR constellations. ................................................................................................... 78 Table 4-5 – Hybrid-sensors (Optical and SAR) constellations. .................................................... 79 Table 4-6 – Representative classes of RSSCs............................................................................... 80 Table 4-7 – Previously proposed single instances of MEO RCSCs. ............................................ 81 Table 4-8 – Major RCSCs in MEO............................................................................................... 81 Table 5-1 – Pros and Cons of various network configurations under study. ................................ 95 Table 5-2 – Coverage computation process and method in different relay network  configurations............................................................................................................ 96 Table 5-3 – Pseudo-code of the main program used for SRT calculations. .................................. 97 Table 5-4 – Pseudo-code of the main program used for configuring walker RCSCs with persistent ISLs .......................................................................................................... 104 Table 5-5 – Simulation input parameters and their ranges. ........................................................ 113 Table 6-1 – Constellation parameters used for the reference RSSC in simulations. .................. 133  xiii List of Figures Figure 1-1 – Satellite mission activities. ......................................................................................... 1 Figure 1-2 – An overview of the thesis chapters and contributions. .............................................. 9 Figure 2-1 – Design processes of RSSC missions. ....................................................................... 13 Figure 2-2 – System Response Time and its components. ........................................................... 18 Figure 2-3 – Relevant literature survey. ....................................................................................... 21 Figure 2-4 – Concept of multiobjective optimization and Pareto front. ....................................... 24 Figure 3-1 – Data flow of the trade analysis process and defining various DVs and MOPs used in simulations.................................................................................................................... 37 Figure 3-2 – Rectangular sensor parameters (Source: AGI-STK). ............................................... 40 Figure 3-3 – SW vs. h at different sensor FOVs. .......................................................................... 40 Figure 3-4 – SSO altitude and daylight global coverage at a different number of satellites. Each satellite has a rectangular sensor with 20o FOV. .......................................................... 45 Figure 3-5 – Daylight global coverage vs sensor FOV of SSO constellation at 600 km altitude for different numbers of satellites. ..................................................................................... 45 Figure 3-6 – Optimized f required to achieve 5m GSD using 1 μm sensor DP. The global coverage percentage achieved by SSO constellation of 4 satellites at h = 600 km. ..... 47 Figure 3-7 – Optimized f required to achieve 0.5m GSD using 1 μm sensor DP. The global coverage percentage achieved by SSO constellation of 4 satellites at h = 600 km. ..... 47 Figure 3-8 – MIO constellation altitude and MIOSats and their effects to improve coverage with the SSO constellation. .................................................................................................. 48 Figure 3-9 – Daily coverage percentage vs GS latitude for an equatorial constellation at 8,000 km altitude. ......................................................................................................................... 49 Figure 3-10 – Heterogeneous satellite constellation configuration. ............................................. 50 Figure 3-11 – Heterogeneous constellation performance. ............................................................ 50 Figure 4-1 – Visualization of DMC3 satellite constellation using STK and its Standard Object database. ....................................................................................................................... 68 Figure 4-2 – Histograms of all satellites in the Disaster Monitoring group on CelesTrak. .......... 71 Figure 4-3 – Histograms of all satellites in the Earth resources group on CelesTrak. ................. 71 Figure 4-4 – Histograms of all satellites in the Planet group on CelesTrak. ................................ 72 Figure 4-5 – Histograms of all satellites in the Spire group on CelesTrak. .................................. 72 xiv Figure 4-6 – Histograms of all satellites in the Weather and NOAA groups on CelesTrak. ........ 73 Figure 4-7 – Distribution histograms of RSSCs groups. .............................................................. 75 Figure 4-8 – Correlation matrix of the constellation group parameters........................................ 80 Figure 4-9 – Relay #1 (red), Relay #2 (white), and Relay #6 (yellow). ....................................... 82 Figure 4-10 – Relays that use 2 planes. Relay #3 (blue green), Relay #4 (green), and Relay #5 (white). ......................................................................................................................... 82 Figure 5-1 – Top: Example of gaps and accesses intervals of a particular point on the Earth grid. Bottom: Example of the correspondent mean response time. ...................................... 91 Figure 5-2 – Access time intervals between system objects over time......................................... 92 Figure 5-3 – Various network configurations of relay satellite constellations. ............................ 95 Figure 5-4 – ISL Geometry in the constellation. .......................................................................... 98 Figure 5-5 – Geometry for intra-orbit ISL. ................................................................................... 98 Figure 5-6 – Geometry of intra-orbit ISL with minimum shadowing radius of Earth. ................ 99 Figure 5-7 – α and ψ vs Nsp  in intra-OISLs................................................................................ 100 Figure 5-8 – h vs Nsp  in intra-OISLs. ......................................................................................... 101 Figure 5-9 – D vs Nsp  for different h. ......................................................................................... 101 Figure 5-10 – MATLAB/STK integrated toolkit and its modules for SRT calculations ............ 107 Figure 5-11 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a Walker relay constellation 25o: 3/3/0 at hrelay = 14,000 km & 𝝀𝑮= 5o. ........... 116 Figure 5-12 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a Walker relay constellation 25o: 3/3/0 at hrelay = 8,000 km & 𝝀𝑮𝑺= 5o. ........... 117 Figure 5-13 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a Walker relay constellation 25o: 3/3/0 at hrelay = 14,000 km & 𝝀𝑮𝑺= 35o. ....... 117 Figure 5-14 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a Walker relay constellation 25o: 3/3/0 at hrelay = 8,000 km & 𝝀𝑮𝑺= 35o. ......... 118 Figure 5-15 – Execution time comparison for one-day simulation. ........................................... 119 Figure 5-16 – Valid MEO RCSC for P = 2, Nsp  = 1, 2, 3, and 4 and f = 0 and 1. ..................... 121 Figure 5-17 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 1. ................................... 121 Figure 5-18 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 2. ................................... 122 Figure 5-19 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 3. ................................... 122 Figure 5-20 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 4. ................................... 123 xv Figure 5-21 – Valid Walker RCSCs for P = 2. ........................................................................... 123 Figure 5-22 – Valid Walker RCSC for P = 3, Nsp  = 1&2. ......................................................... 124 Figure 5-23 – Valid Walker RCSC for P = 3, Nsp  = 3&4 .......................................................... 124 Figure 5-24 – Variation of relative elevation and distance between pairs of relay satellites from the two relay configurations (altitude 8,000 km and inclination 45 degrees). ........... 125 Figure 6-1 – Walker-Delta 3/3/0 constellation. .......................................................................... 131 Figure 6-2 – Walker-Delta 4/2/1 constellation. .......................................................................... 132 Figure 6-3 – Visualization of the reference RSSC...................................................................... 134 Figure 6-4 – Parametric study framework. ................................................................................. 135 Figure 6-5 – Mean values of TAG between imaging and relay satellites of Walker-Delta 3/3/0 constellation vs hrelay at different irelay values. ............................................................ 137 Figure 6-6 – Coverage properties between Walker-Delta 5o:3/3/0 vs λGS at different values  hrelay. ........................................................................................................................... 138 Figure 6-7 – Coverage properties between Walker-Delta 15o:3/3/0 vs λGS at different values hrelay. ........................................................................................................................... 138 Figure 6-8 – Coverage properties between Walker-Delta 25o:3/3/0 vs λGS at different values hrelay. ........................................................................................................................... 139 Figure 6-9 – Mean values of TAG between imaging and relay satellites of Walker-Delta 4/2/1 constellation vs hrelay at different irelay values. ............................................................ 140 Figure 6-10 – Coverage properties between Walker-Delta 5o:4/2/1 vs λGS at different values hrelay. ........................................................................................................................... 141 Figure 6-11 – Coverage properties between Walker-Delta 15o:4/2/1 vs λGS at different values hrelay. ........................................................................................................................... 142 Figure 6-12 – Coverage properties between Walker-Delta 25o:4/2/1 vs λGS at different values hrelay. ............................................................................................................................ 142   xvi List of Abbreviations AGI Analytical Graphics, Inc AoI Area of Interest AWB Analysis Workbench DLSN Double Layer Satellite Network DMC Disaster Monitoring Constellation DP Detector Pitch DRM Disaster Risk Management DRR Disaster Risk Reduction DRS Data Relay System DV Design Variable EDRS European Data Relay System EO Earth Observation EOS Earth Observation Satellites FCC Federal Communications Commission FOM Figure of Merit FOV Field of View GD Gap Duration GEO Geostationary Earth Orbit GPS Global Positioning System GS Ground Station GSD Ground Sampling Distance GSN Ground Station Network HHA Horizontal Half Angle HSC Heterogeneous Satellite Constellation HSCD Heterogeneous Satellite Constellation Design IGSO Inclined Geosynchronous Orbit IRT Intrinsic Response Time ISL Intersatellite Link ISS International Space Station LEO Low Earth Orbit LOS Line of Sight MEO Medium Earth Orbit MIO Mid-Inclination Orbit MOP Measure of Performance MRT Mean Response Time RAAN Right Ascension of Ascending Node RCSC Relay Communication Satellite Constellation RGT Repeating Ground Track xvii RSSC Remote Sensing Satellite Constellation RT Revisit Time SAR Synthetic Aperture Radar SCD Satellite Constellation Design SRT System Response Time SSO Sun-Synchronous Orbit STK Systems Tool Kit SW Swath Width TAG Time Average Gap TDRSS Tracking and Data Relay Satellite System TLE Two Line Elements TT&C Telemetry, Tracking, and Control VHA Vertical Half Angle   xviii Acknowledgments First and foremost, I would like to thank God (Allah), the most merciful and the most compassionate, for His help and blessings. “All praise and thanks are for Allah, the One who, by His blessing and favor, perfected good works are accomplished” Prophet Mohammed (Peace be upon him) I would like to express my sincere gratitude to my supervisor, Prof. David G. Michelson, for his professional supervision, critical discussions, continuous support, encouragement, coaching, and guidance throughout my studies. I look forward to collaborating with him in the future. I wish to express my thanks to all my colleagues in the Radio Science Lab for their nice companionship through the time of my research. Thanks to Dr. Zahra Vali for her valuable comments on my work and practice talks. I would like to take the moment to recognize and praise the unconditional support that I never imagined someone could ever have the capacity to give. I would like to thank my parents, for their continuous and unlimited moral support. They have been a constant source of love, encouragement, and inspiration. My brothers and sisters are also thanked for their support. I am also so grateful to my lovely wife, Hager and my children, Mostafa and Maryam for their patience, support, and continuous encouragement, without your support I would never be able to finish my research. Finally, I would like to express my most profound gratitude to my beloved country, Egypt, for supporting and funding my research. xix Dedication  To My Beloved Family, My Parents, My Lovely Wife, My Children, My Brothers, My Sisters,  My Mother-in-Law, and My Father-in-Law  (Thank You So Much)             1 Chapter 1: Introduction 1.1 Overview The design of satellite constellations for Earth Observation (EO) missions is entering a new phase as designers seek to accommodate an important and emerging class of users that require fast data delivery in order to satisfy disaster relief and national security requirements.  The Revisit Time or RT of a single satellite is the time elapsed between two successive observations of the same point on the surface of the Earth [1]. System Response Time (SRT) is the interval between submitting a user observation request and receiving the image product or the observation data directly, as depicted in Figure 1-1. It is the key metric in assessing the timeliness of EO imagery. For disaster monitoring missions, SRT is a more important performance parameter than RT, where the objectives are dictated by user requests, the time it takes for the final distribution of the data to the end-user has much more impact on overall mission performance, rather than the time interval between target revisits. It accounts for the time required for: 1) data collection requests to reach the imaging satellites, 2) the imaging satellite to reach the target, and 3) data (imagery) to reach the ground station.        Figure 1-1 – Satellite mission activities.  2 System Response Time can be reduced by one or more of the following methods [2]: 1) Increasing the number of available ground stations for download and/or controlling the imaging satellite payload. 2) Using one or more ground stations located in the polar regions (as observation satellites have typically a high inclination orbit). 3) Using planning and scheduling technology to generate optimal operation schedules. 4) Increasing the number of observation satellites: small-satellite constellations in Low Earth Orbit (LEO) allow observations with high repetition rates and medium to high image resolutions. 5) Using Geostationary Earth Orbit (GEO) relay satellite systems for tracking and data relay. 6) Using non-GEO relay satellite systems for tracking and data relay. These methods may not be practical either due to an increase in mission costs (1,4,5), technological risk (3), or political reasons and cost constraints (2,5). The communication delay components of the SRT can be reduced (and possibly eliminated) by deploying relay satellite constellation networks in Medium Earth Orbit (MEO), that are dedicated to command delivery from Earth stations to the imaging satellites and data (images) relay back to Earth sites. This thesis focuses on the design and performance analysis of such heterogeneous EO satellite constellations that use intersatellite links (ISLs) between two different functional constellations, an EO satellite constellation dedicated to imaging and a communication satellite constellation dedicated to command delivery from Earth stations to the imaging satellites and data (images) relay back to Earth sites in order to reduce the SRT.    3 1.2 Motivation In recent years, there has been considerable interest in reducing the SRT of EO satellites in order to achieve rapid response in case of natural or man-made disasters [3], [4] or matters involving defense and national security [5]. In the space industry, new approaches for achieving real-time data availability are frequently required to fulfill customer needs [6]. Recently, Audacy, a California-based start-up firm, has begun to establish the first commercial intersatellite data relay network designed to offer uninterrupted access to small commercial satellites including EO satellites. They received the required licenses from the U.S. Federal Communications Commission (FCC) in June 2018 [7], [8]. EO satellites are very useful during both the response and recovery phases of the disaster management cycle [9] because they can provide accurate, frequent and almost instantaneous data for large stricken areas anywhere in the world. For disaster preparedness and risk management, e.g., when hurricanes and cyclones approach to land and the risk of flooding increases, specific EO satellites can be tasked to provide high resolution and up-to-date imagery of the areas at risk [10]. Timeliness is critical to an effective disaster response because the primary goal is to search for and rescue survivors. Analysis and assessment of disaster damage provide authorities and decision-makers with the necessary key information for emergency measures to be undertaken in the recovery phase [11]. The significant investment in space-based Earth observation infrastructure has not yet been fully exploited for Disaster Risk Reduction (DRR) [3]. However, a number of international coordination efforts have been pioneering the establishment of the necessary connections between data providers, information developers, and end-users to ensure that decision-makers in the Disaster Risk Management (DRM) community are able to benefit from satellite EO. The International Charter on Space and Major Disasters [12] is the main global mechanism by which countries can access satellite EO data in support  4 of their disaster response activities. With a collaboration of 17 worldwide members, the Charter is able to provide rapid access to data from a virtual constellation of satellites, both optical and radar, and thereby support disaster management centers during relief actions. The Disaster Monitoring Constellation for International Imaging (DMCii), which became operational with the launch of four microsatellites in 2002-3 [13], is the first dedicated constellation for this purpose. At the start, it provided daily global coverage of the Earth at moderate resolution (32 m). It successfully supported responses to many disasters including the Indian Ocean tsunami in 2003 and Hurricane Katrina in 2005. The second-generation DMCii was deployed in 2005-11. It provides data continuity and offers enhanced imaging capability to cover larger areas at higher spatial resolution. DMC-3, also referred to as TripleSat constellation, is the latest generation of DMC series and has provided daily imaging capacity at 1-m very high resolution (VHR) since 2015. That SRT can be significantly reduced by using constellations of dedicated relay satellites has long been recognized but often dismissed as too costly to be practical. However, the introduction of low-cost satellite and launcher technology in recent years has dramatically increased the feasibility of this approach. The significantly reduced cost of space launch provided from commercial launch systems makes space access more affordable and provides opportunities for more ambitious space missions [14], [15]. Moreover, new space-to-ground link technologies such as the use of Ka-band [16] and optical intersatellite communication [17] provide much higher capacity methods to downlink EO imagery than conventional X-band technologies. Furthermore, the development of new techniques for onboard data processing using machine learning [18] and the recent methods for optimizing the compression of EO image data with automatic selection of the compression parameters based on the type of image [19].  5 1.3 Problem Statement Acceptable SRT can be achieved only by EO satellite constellations in LEO as they allow observations of ground targets with high repetition rates [2]. Satellite constellations are able to revisit and photograph huge swathes of the planet as often as several times each day at any weather condition, a frequency much higher than that achieved by previous EO satellites [20]. Nevertheless, the key problem still in the limited period during which the EO satellite can communicate with a given ground station (GS). Reduction of SRT depends on the configuration of imaging constellation (number of satellites, number of planes and constellation orbital parameters), the distribution and locations of a number of GSs, and the time scheduling of the system. Previous work has focused on reducing SRT through minimizing the RT of the imaging constellation [21]–[25], using ground station networks (GSNs) [26]–[30] and improved algorithms for scheduling the imaging satellites considering their constraints and resources [2], [22], [31]–[36]. However, these approaches cannot significantly reduce the gaps in connectivity between Earth stations and imaging satellites which generally contribute greatly to SRT. Ultimately, improving SRT requires a space-based solution to relay commands to imaging satellites and, possibly, relay data back to the receiving GS using ISL capabilities between the relay satellites. Previous work in this category focused on using GEO communication satellites for tracking and data relay since the mid-1970s [37]–[43] and recently has focused on data relay satellite networks using non-GEO systems, namely LEO [2], [44]–[48] and MEO systems [2], [46], [49]–[51]. We have selected satellite systems in MEO for servicing imaging satellites in LEO for several reasons. They have the advantages of the characteristics of both GEO and LEO systems [52]. They are frequently proposed in multilayer satellite networks for global satellite communication systems [53]–[57] because they have shorter round trip delays and lower transmission power requirements [58]. From  6 another perspective, with the accumulating space debris, future collisions between large fragmentation debris and other intact objects are less probable in MEO region, due to the existing lower levels of spatial densities, than if the same breakup occurred in LEO region, particularly with the recent proposals of deploying thousands of telecommunication satellites expected to orbit Earth in the near future in LEO. Based on the literature survey and the limitations in previous work, we have identified gaps in using data relay networks in MEO layer to improve the SRT of imaging satellite constellations in LEO layer. Previous design methods for Heterogeneous Satellite Constellation Design (HSCD) to support rapid EOs were ad hoc and not systematic. Further, only single instances have been proposed and simulated in the previous work. Their performance has not been analyzed for realistic remote sensing satellite constellations (RSSCs) nor has their sensitivity to deviations from the specified orbital parameters been considered or discussed. Moreover, previous work has not addressed, nor can industry-standard design tools such as Systems Took Kit (STK) predict, the manner in which system performance improves when different relay satellite configurations are introduced, and the relaying strategies become more sophisticated. 1.4 Objectives The primary objective of this thesis is to develop tools and techniques that allow heterogeneous satellite constellations that provide simultaneous connectivity between LEO satellites and the ground using relay satellites in MEO to be designed and evaluated in a more systematic way.       7 In particular, we seek to: 1. Go beyond the previously proposed isolated instances of relay constellations in MEO. 2. Evaluate the performance of the heterogeneous constellation systems in terms of the system response time. 3. Use realistic and representative configurations of RSSCs that help to explore the trade-space of relay satellite constellations when they are used for serving these configurations. 4. Predict the SRT when ISLs between satellites are involved. 5. Analyze the improvement of the system performance as ISLs between the relay satellites are introduced and become more sophisticated. 6. Generate design curves that show the relationship between the design variables (DVs) and SRT or its related measures of performance to demonstrate the sensitivity analysis of the DVs and allow designers to perform appropriate trade-offs. Although the details of the communications technology used to implement the intersatellite and Earth-satellite links and the intersatellite network are important considerations [61], [62], the work described here is based almost completely on the prediction of intersatellite and satellite-to-ground visibility as dictated by orbital mechanics. Consideration of the implications of link budgets and routing protocols is a logical next step beyond the work described in this thesis.  1.5 Thesis Outline The thesis is organized into seven chapters. A brief summary of the thesis chapters is given below: Chapter 1 provides the context for the thesis construction with a focus on the motivation of this work, thesis objectives and contributions. Moreover, this chapter outlines the overall scope and objectives.  8 Chapter 2 gives a short survey of satellite constellation design that shows how the constellation design methods for remote sensing applications have been developed and why they are different compared to the constellations of communication and navigation applications. Further, this chapter gives a review of figures of merit (FOMs) commonly used in EO orbit design with a detailed description of SRT, the FOM of interest in this research. Moreover, introduces the line of reasoning of thesis theme by introducing a comprehensive survey of the related literature. Chapter 3 introduces a general framework to design heterogeneous satellite constellations for rapid response Earth observations. This framework provides us with the general guidelines for configuring such constellation systems and shows the challenges in designing and evaluating the performance of these systems. Chapter 4 proposes reference configurations for EO satellite constellations in LEO and summarizes the previously proposed relay constellations in MEO using the available Two-Line Element (TLE) data of the operational remote sensing satellites and a literature survey of the operational and underdevelopment remote sensing missions and the related previous work. Chapter 5 focuses on our methodology for SRT calculations in different network configurations based on the relay satellites capabilities and the availability of ISLs between relay satellites. This chapter presents detailed descriptions of the MATLAB/STK integrated model and its algorithms required for trade-space analysis. In addition, this chapter provides an algorithm for configuring the relay satellite constellations that can achieve persistent inter-relay ISLs. Chapters 6 demonstrates how we can use the tools we developed for SRT calculation to get different solutions to the relay communication satellite constellations (RCSCs) by investigating the coverage properties between different RCSCs and the imaging satellites and between the RCSCs and a GS.  9 Finally, Chapter 7 summarizes the findings and contributions of the thesis, both on the methodology side and on the applications, discusses the main limitations of the analysis, and highlights opportunities for future work. The relationship between the thesis chapters and the contributions are depicted in Figure 1-2.  Figure 1-2 – An overview of the thesis chapters and contributions.         10 Chapter 2: Literature Survey This chapter presents an overview of satellite constellation design (SCD) and system response time reduction. The first part of this chapter introduces a short survey of SCD design phases of development, the motivation of using heterogeneous satellite constellations in remote sensing applications, and a review of figures of merit (FOMs) commonly used in EO orbit design with a detailed description of SRT, the FOM of interest in this research. The second part of this chapter presents a comprehensive survey of the related literature of the previous efforts to improve the SRT of the imaging satellites in LEO. A summary of the major findings in this survey is introduced in the last part of the chapter. 2.1 Satellite Constellation Design – A Short Survey The idea of satellite constellations is to deploy multiple satellites into coordinated orbits and operate them to achieve common goals, typically related to providing global coverage, low latency, or low revisit time communications or imaging services. The concept was first proposed in the late 1950’s and more fully developed in the 1960’s [59]. Thus, along with cost considerations, the mission planners’ primary aim is to design a constellation composed of the smallest number of satellites to achieve specific mission requirements. Weather forecasting was an area of particularly fast development early on, as several series of incrementally improved satellites were launched in short periods. These series could be considered as predecessors of modern constellations because the lifetime of some of those assets overlapped. The first of these series was the Television Infrared Observation Satellite (TIROS) program, which began in the early 1960s with over about 44 satellites launched until now [60]. However, the full power of constellations involving a large number of satellites working simultaneously (as opposed to  11 sequentially) did not appear until the 1970s, with the first constellations for navigation purposes, and reached maturity in the satellite communications industry [59]. The first eight satellites of the Global Positioning System (GPS) constellation were launched into an inclined orbit (55o) at an altitude of ~ 20,000 km between February 1978 and April 1980 [61]. The GPS program currently maintains a constellation of 24–32 satellites generating signals at multiple frequencies in the L band. The Russian Global Navigation Satellite System (GLONASS) was launched a few years later (first launch in 1982), with similar parameters as GPS (24 satellites, ∼19,000 km, L band) except for the inclination, which was set to 64.8o to provide better coverage of high-latitude regions [62]. The European Galileo was designed to consist of 30 satellites several years after GPS and GLONASS, but the parameters were also quite similar (23,616 km, 56o inclination, L band) [63]. Although the design of most navigation constellations converged on an optimal value of 20–30 satellites in MEOs, some designs of constellations for communications purposes in LEO often had many more satellites. Indeed, although small constellations of satellites in GEO for communications purposes, such as the Tracking and Data Relay Satellite System (TDRSS) [38], were planned in the 1970s, the use of a large number of satellites in LEO constellations were explored during the late 1980s because they offered advantages in terms of power requirements and latency. The first LEO constellations for communications purposes, Iridium [64] and Globalstar [65], consisted of 66 and 48 satellites, respectively, and they were deployed 20 years after the first GPS launch. Another similar example is the Orbcomm satellite constellation (50 satellites in LEO) [66]. Traditional satellite constellation design methods are associated with global or zonal, continuous (single or manifold) coverage under the typical assumption that payload field of view (FOV) is a wide circular cone whose axis is along with the satellite local vertical. These methods are typically used for  12 navigation and communication applications where these assumptions are justified [67]. On the other hand, remote sensing sensor apertures are typically much smaller, and their FOVs are shaped differently, e.g., Synthetic Aperture Radars (SARs) use a side-looking imaging geometry. Moreover, optical and SAR sensors need to pass over the imaged areas, while navigation and communication payloads access all of the conical FOV at the same time. Thus, traditional constellation design methods are not applicable to remote sensing missions and, in any case, lead to a huge number of required satellites when high-resolution images and continuous global coverage are considered. That is why remote sensing constellations have been proposed and implemented only later and most of them have different configurations and different orbital parameters and number of satellites compared to communication or navigation constellations. The process of remote sensing constellation design starts from establishing mission objectives and constraints according to mission requirements. Therefore, objectives and constraints of remote sensing missions are the main drivers of development remote sensing sensors, evolving the missions’ FOMs, and selection constellation orbital configurations and the number of satellites based on simulation methods and orbital mechanics laws as shown in Figure 2-1. Selection of orbital parameters for the constellation mission is the most important factor for the fulfillment of the space mission requirements. Practically, straightforward approach for selection of these parameters does not exist. Consequently, it is necessary to follow a complex process that requires trade-offs among the different parameters and the corresponding FOMs such as coverage, revisit time, sensor resolutions (spatial, spectral, and temporal), the capacity of data collected, swath width, spectral ranges of interest for every application, and, of course, the system response time.  13  Figure 2-1 – Design processes of RSSC missions. 2.1.1 Figures of Merit for Early Design Earth Observation Constellations 2.1.1.1 Coverage The performance analysis is intended to validate the constellation design solution, that is, to verify that the proposed constellation will meet the mission requirements over a given period of time. For satellite constellations, the coverage metrics quantify how well the constellation “covers” the surface of the Earth with its observations. Coverage figures of merit (FOMs) are usually calculated on a grid of points on the surface of the Earth, by propagating the different spacecrafts that compose the constellation for a certain simulation time considering the most important perturbations [68]. These FOMs are derived by evaluating the data collected during the propagation and computing the statistics over the Earth zones of interest (global, zonal, or regional). The coverage of the satellite system is usually described from two dimensions of space and time. The spatial coverage of the satellite system can be used to characterize the spatial observation ability of a satellite system in a given period of time, and the time coverage of the satellite system can be used to characterize the time domain capability of the satellite system in a given period of time. For example,  14 the space coverage efficiency such as percentage of coverage while the time coverage efficiency such as mean coverage gap, maximum coverage gap, time average gap, and mean response time [68]–[70]. 1. Percentage of coverage The percentage of coverage for any point on the grid is simply the number of times that point was covered by one or more satellites divided by the total number of simulation time steps. The advantage of percent coverage is that it shows directly how much of the time a given point or region on the ground is covered. However, it does not provide any information about the distribution of gaps in that coverage [68]. 2. Mean coverage gap The mean coverage gap is the average length of breaks in coverage for a given point on the simulation grid. This FOM also is known as mean revisit time, which is the most common metric used in coverage analysis by far. 3. Maximum coverage gap The maximum coverage gap is simply the longest of the coverage gaps encountered for an individual point. This FOM is also known as maximum revisit time or maximum gap time, which is popular as it provides worst-case information. However, it is considered a poor FOM because it incorrectly ranks constellations because a single point or a small number of points determines the results. 4. Time Average Gap The time average gap is the mean gap duration averaged over time. Alternatively, it is the average length of the gap we would find if we randomly sampled the grid points. It represents the size of the coverage gap that you would expect to fall into if you selected a random moment in time. It is constructed as a weighted average of the existing gap durations where the weight for each gap is defined  15 as the likelihood that you will select a time within that gap. This FOM is very similar to mean response time. 5. Mean Response Time The mean response time is the average time from when we receive a random request to observe a point until we can observe it. If a satellite is within view of the point at a given time step, the response time at that step will be 0. If the point in question is in a coverage gap, then the response time would be the time until the end of the coverage gap. This FOM takes into account both coverage and gap statistics in trying to determine the whole system's responsiveness. Therefore, it is the best coverage FOM for evaluating overall system responsiveness. One major advantage of mean response time as a FOM is that delays in processing or communications (for both data requests and responses) can be directly added to the coverage response time. This results in total response time or System Response Time (SRT), which gives the total time from when users request data until they receive it. We can also evaluate minimum, mean, and maximum total response times which have much more operational meaning than simple gap statistics. 2.1.1.2 Ground Sampling Distance The ground sampling distance (GSD) is the distance of the center of neighboring pixels projected to the ground. GSD is the key FOM of the spatial resolution, which is highly dependent on the coverage FOMs described above (temporal resolution). Detecting short time scale changes is generally done with coarser spatial resolution. Likewise, detailed observations of a region with small scale features require longer intervals of time between observations [71].  16 2.1.1.3 Cost The coverage of a constellation is traded against a number of satellites, the required number of launches for constellation deployment and ultimately cost. The cost can be considered as an objective to be minimized, or as a constraint to satisfy. Access to Earth orbit for small satellites and specifically the cost and availability of launch services is still a big problem nowadays and arguably the most significant threat to the growth of concepts based on large constellations of small satellites [72]. While ideally, one would like to incorporate cost in these trades, the cost is very challenging to estimate, especially during Pre-Phase A studies where there is a lot of uncertainty. Hence, proxies are often used instead of cost. Wertz [73] uses the mission ΔV budget to define the Orbit Cost Function (OCF), which allows us to estimate the relative cost of putting a spacecraft into a given orbit relative to the cost of putting it into a 185 km circular LEO. Specifically, the OCF is defined as the ratio of the mass delivered in a 185 km altitude circular orbit to the mass delivered in mission orbit. It can be seen as a multiplier to obtain the cost of putting a spacecraft into its mission orbit from the cost of putting the spacecraft in LEO, which can be estimated using historical launch vehicle cost data. The cost model used in this work tries to capture the effect in cost of the main design decisions such as the altitude, inclination, the number of satellites in the constellation, and the way these satellites are distributed among one or several planes. The total cost of the mission is composed of constellation cost and launch cost, 𝐶𝑜𝑠𝑡 =  𝐶𝐿𝑎𝑢𝑛𝑐ℎ + 𝐶𝐶𝑜𝑛𝑠𝑡𝑒𝑙𝑙𝑎𝑡𝑖𝑜𝑛  .                                            (2.1) The constellation cost is computed multiplying the number of total satellites by the cost of a single satellite, 𝐶𝐶𝑜𝑛𝑠𝑡𝑒𝑙𝑙𝑎𝑡𝑖𝑜𝑛 =  𝑛𝑆𝑎𝑡 ∗  𝐶𝑆𝑎𝑡 .                                             (2.2)  17 The launch cost is calculated multiplying the cost of a single launch by the number of planes in the constellation as, 𝐶𝐿𝑎𝑢𝑛𝑐ℎ = 𝑛𝑃𝑙𝑎𝑛𝑒𝑠 ∗  𝐶𝐿𝑉  .                                                (2.3) In doing so, it is assumed that an extra launch vehicle is required for every additional plane in the architecture. This is a reasonable assumption given that many small satellites do not have propulsion capabilities to do expensive out-of-plane orbit maneuvers such as changing Right Ascension of Ascending Node (RAAN) [74]. A possibility not considered in this work is the ability of the upper stage of the launch vehicle to make plane changes and deliver satellites to multiple planes. We assume that a single launch vehicle can only deliver payloads to a given orbital plane. Another proxy used for launch cost is the cost of the propellant needed to put the spacecraft into the desired mission orbit [69] since it is difficult to obtain accurate pricing information for launch services, which also depends on purely commercial considerations. In this model, two launch options are considered, the dedicated launch and the rideshare/piggyback. Dedicated launches provide more freedom to the customer to select the destination orbit and the launch date but are more costly than ridesharing/piggybacking options, which often used for CubeSats and provide less (or no) flexibility in choosing orbits and mission schedule. For instance, the rideshare option availability highly depends on the destination orbit; while there are more opportunities to launch small satellites as secondary payloads to the International Space Station (ISS) orbit, SSO or Geostationary transfer orbit (GTO) while it is very difficult to find these launch services for other inclinations such as 30o [69]. In this work, the amount of propellant needed is computed in several steps: 1) The ΔV required to go from the launch site to specific altitude h and inclination i, which is assumed to be a known constant.  18 2) The ΔV required to go from this specific h to the desired altitude, which is computed using a Hohmann transfer [75]. 3) The ΔV required to go from this specific i to the desired inclination. Finally, it is important to note that the goal of cost models for early system design phases is not to provide accurate absolute cost estimates, but rather to provide accurate relative cost assessments while showing enough sensitivity in cost to the major other mission FOMs and design variables. 2.1.2 System Response Time SRT is the time between a request of imaging of a point and the time at when data from imaging satellites is available at the GS. It is a key metric in assessing the timeliness of EO imagery and accounts for the waits for: 1) data collection requests to reach the imaging satellites, 2) the imaging satellite to reach the target, and 3) data (imagery) to reach the GS. An illustration of SRT and the delay time components is shown in Figure 2-2 [35], [76]. We have modified this figure for more clarifications to the definition of SRT in our case study.  Figure 2-2 – System Response Time and its components.  19 The definitions of each time component in Figure 2-2 are as follows: 1. T1 is the command preparation time (Fixed time) which specifies the amount of time required to generate collection commands prior to the uplink of the commands from GS to imaging satellites  2. T2 is the command uplink delay time (Dynamic time), which is the time delay until access between imaging satellite and the command GS will occur for command delivery.  3. T3 is the commanding time (Fixed), which specifies the amount of time required to uplink generated collection commands from the command GS to the imaging satellite, and the pre-collection time, which specifies the amount of time required to configure access time of the targets after the collection command has been received. 4. T4 is the Intrinsic Response Time (IRT) (Dynamic), which is the time between a request of coverage of a point and the time at which coverage is achieved. This time completely depends on the revisit time of the imaging constellation. 5. T5 is the collection time (Fixed), which is the amount of time required for an imaging satellite to perform a collection of image for the assigned target, and the post-collection time (Fixed time), which is the time required to configure a receiving GS for downlink. 6. T6 is the data downlink delay time (Dynamic), which is the time delay until access between imaging satellite and the receiving GS will be occurred to start data downlink. 7. T7 is the downlink time (fixed), which specifies the amount of time required to downlink generated data. The following section presents a comprehensive survey of the related literature of the previous efforts to improve SRT of the imaging satellites in LEO. 2.2 Related Literature Reduction of SRT depends on the configuration of imaging constellation (number of satellites, number of planes and constellation orbital parameters), distribution and locations of a number of GSs, and on  20 the time scheduling of the system. Previous work has focused on reducing SRT by minimizing the RT of the imaging constellation [21]–[25], using GSNs [26]–[30] and improved algorithms for scheduling the imaging satellites considering their constraints and resources [2], [22], [31]–[36]. These approaches, despite their limitations, cannot significantly reduce gaps in connectivity between Earth stations and imaging satellites, which are the root cause of increasing SRT. The majority of satellite missions in LEO adopt a store-and-forward approach to communications, where payload data is collected over the target area of interest (AoI) and successively downloaded to GSs along with telemetry [77]. Since the key problem is still the limited period during which the imaging satellite has contact with the GSs, other approaches have been proposed and used to increase the visibility windows between imaging satellites and GS in order to improve SRT. Table 2-1 shows the pros and cons of different efforts to improve these visibility windows in order to reduce SRT. Figure 2-1 summarizes the relevant literature survey of the area of interest, which confirms that the problem is of current and continuing interest. Table 2-1 – Previous efforts to reduce SRT. Approach Pros Cons Satellite constellations using Store and Forward - Reduce RT - Simple communication architecture - Limited access times - Long system response time - EO satellites are very expensive - Cost of storing large amounts of EO imagery More Earth Stations - Increase connection times with LEO satellites - Many regulatory challenges (Political, strategic, and cost constraints) - No way to achieve continuous communications GEO Relays - Maintain real-time access - Very expensive (Building and Launch) - Requires costlier and heavier LEOs - Existing GEOs (such as TDRSS and EDRS) are NOT designed for commercial use MEO Relays - Lower launch costs and shorter link distances - Complex network architecture based on relay satellite capabilities and the network topology   21  Figure 2-3 – Relevant literature survey. 2.2.1 Satellite Constellation Design Optimization Optimization methods of EO satellite constellations focus either on minimizing the revisit time (RT), where satellites do not achieve continuous coverage of an area on the Earth’s surface [78], or maximizing the contact opportunities (access time) between satellites and GSs. Several studies have dealt with implementing these optimization methods in satellite constellation design for EO missions, which can be found in the literature. 2.2.1.1 Revisit Time Minimization Constellations of multiple LEO satellites for EO missions are required to have a design that provides frequent revisits for high-performance operations [79]. A lot of research has been done on optimizing constellations for continuous and regional coverage of the Earth to minimize revisit time (RT). The genetic algorithm (GA) is known for its robustness in obtaining a global optimum solution for nonlinear  22 multivariable problems through its stochastic and heuristic search algorithms [80]. In their thesis, Pegher and Parish [81] tried to compare the coverage optimization and the RT optimization of sparse military satellite constellations using traditional approaches and GA. Another method of hybrid satellite constellation design called Genetic Satellite Constellation (GSC) was proposed in [82] by using single GA optimization. A study on Simulated Annealing and GA approaches to satellite constellation design for coverage of a limited latitude region was conducted in [83], where in both methods outperformed the conventional Walker approach at low Earth central angles. In some EO missions, designers use propulsion systems, mounted onboard the satellite, to maneuver the satellite continuously between the areas of interest (AoIs) to improve the RT [84]. An optimal control algorithm was developed in [85] to sort the AoIs in an optimal sense and then maneuver the satellite between them. The results of this study show that the thrusters have to work continuously throughout the mission lifetime. In some other works, a method to design natural orbits, which visit the AoIs using the natural gravitational forces and without the use of propulsion, was developed in [84]. A satellite, in a natural orbit, needs to be as close as possible to the Earth when visiting a ground site to achieve high resolution. A synchronization is needed, between the Earth rotational motion and the satellite motion, to guarantee visiting all the AoIs. To find these natural orbits, two approaches were developed. In the first approach, the problem is formulated as an optimization problem. Stochastic optimization methods were used as an attractive alternative for optimizing space orbits design [86], [87]. The cost functions for this type of problem usually have numerous local minima. The second approach adopted a semi analytical method to reduce the number of unknowns and then perform numerical search or stochastic optimization [88]. Nevertheless, the two methods suffer from the following weaknesses: (1) both methods assume a two-body model for the satellite motion; (2) both  23 methods assume zero FOV for the satellite instrument. These assumptions limit the number of solutions to the problem. EO missions usually use repeating ground track (RGT) orbits, which allow specific and repeated observations for the AoIs to be scheduled at certain time intervals or with the same observing conditions during the orbit repeat cycle [22]. Most of the previous work uses RGT orbits for designing single and multi-plane satellite constellations for supporting specific targets as opposed to providing global coverage [23]–[25]. Flower constellations were studied for use in the EO in [21], where four satellites were used at an altitude of 740 km for RT of six days. However, RGT is not necessary in the case of the constellation, which consists of a large group of satellites in order to provide global coverage. Constellation designers are rarely concerned with optimizing performance with respect to a single objective. Rather, multiple competing requirements drive the design, resulting in a configuration that reflects a compromise between two or more metrics. Multiple objective evolutionary algorithms (MOEAs) provide the decision maker with a tool to characterize the trade-off between several conflicting objectives by finding a set of nondominated or Pareto-optimal designs. In mathematical terms, the multiobjective problem can be written as [89]: min [𝑓1(?⃗?), 𝑓2(?⃗?), … , 𝑓𝑛(?⃗?)]𝑇     𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 {𝑔(?⃗?) ≤ 0𝑘(?⃗?) = 0?⃗?𝑙 ≤ ?⃗? ≤ ?⃗?𝑢  ,                                 (2.4) where 𝑓𝑖  is the ith objective function; g and k are the inequality and equality constraints, respectively; and ?⃗? is the input vector of optimization or decision variables. In such a case, there is usually no single optimal solution, but a set of alternatives with different trade-offs, called Pareto optimal solutions (Pareto front), noninferior solutions, or nondominated solutions. Consider Figure 2-4 where both 𝑓1 and  24 𝑓2 are to be minimized. Because both objectives are important, there cannot be a single solution that optimizes 𝑓1 and 𝑓2, rather a set of optimal solutions exists which depict a trade-off [89].  Figure 2-4 – Concept of multiobjective optimization and Pareto front.  Based on this concept, a class of fast and elite MOEA was introduced in [90]. In this work, an open-source MOEA called the nondominated sorting genetic algorithm 2 (NSGA-2) is used to approximate the Pareto fronts for several multiple-objective constellation design trade-offs. An efficient MOEA has been developed in [89]. In this paper, the considered key parameters were the satellite’s revisit time and the off-nadir resolution, and the satellite’s orbital lifetime. 2.2.1.2 Access Time Maximization EO Satellites on LEO have usually scarce opportunities to contact GSs due to their proximity to the Earth’s surface. The resulting contact windows depend on the satellite’s orbit parameters and the GSs distribution on Earth’s surface, which can be defined as satellite access times [91]. To maximize access times, deploying EO satellite constellations with a careful selection of their orbital elements and/or GSs placement are needed. Deploying a large number of EO satellites on different planes certainly can  25 increase the access times, improve the global coverage by minimizing the RT, and consequently improve SRT. Nevertheless, every operational satellite requires licensing that costs millions and takes years. The EO satellites themselves are very expensive due to their high-cost payloads. For example, the RapidEye satellite constellation costs around USD 136 million for five microsatellites including launch [92]. In comparison with communication satellites, a French company is starting a $139 million effort to build, launch and operate a constellation of 20 small satellites for connecting Internet of Things (IoT) devices at sea and elsewhere [93]. Sky and Space Global (UK) Ltd company is planning a constellation of 200 nanosatellites in equatorial LEO for narrowband communications that it expects will cost $160 million or less to complete in total [94]. Relay satellite networks can provide a solution for maximizing access time. Nevertheless, very few researchers have dealt with this as an optimization problem. When an optimization technique is used to explore a specific problem, it is wise to begin with a baseline test problem of a similar type, provided that one exists. This serves two primary purposes: the objective function construction may be tested and validated, and ideal algorithmic parameter settings may be established before proceeding to an original problem. In what follows, a baseline satellite constellation design problem found in the literature was discussed in [91]. In that paper, an example of a cost function was defined using the total access time from a ground station to a LEO satellite via indirect real-time link through the relay satellite network with the ultimate goal of maximizing the defined cost function. That paper can be considered in a related future work to minimize SRT of an EO satellite constellation supported by relay satellites after understanding this system, which is the main goal of this thesis.   26 2.2.2 Planning and Scheduling Optimization EO satellites image some regions of Earth at the request of customers. Each photograph generates a profit but, due to the presence of several constraints, not all requests can be satisfied. Typically, the number of requests exceeds what can feasibly be accommodated during a specific time or an orbit cycle. The scheduling problem is to select a subset of requests yielding a maximal profit for a given orbit, subject to operational constraints [95] and harmonize the operations necessary to acquire the images of an area of interest with the operations needed to transmit the images to GSs. Data downloading from EO satellites to a GS takes time and must be performed within limited visibility windows between satellite and a receiving GS. In the best case, when using a high-latitude GS such as Svalbard satellite Earth station (78o latitude), the total connection time with an imaging satellite on a Sun-Synchronous Orbit (SSO) at 600 km is about 2.5 hours during a day, nearly 10 % of the total time. When using a GS at 45o latitude, the total visibility duration becomes nearly one hour only during a day, nearly 4% of the total time, with a maximum gap duration of approximately 10 hours. New satellites hosting advanced optical and radar instruments are now orbiting our planet in LEO constellations to provide a better temporal, spectral, and spatial resolution of derived images [96]. The capabilities of these sensors have increased dramatically, reaching levels that exceed the capacity of current space-to-ground communications technologies [16]. For rapid response to natural disasters, the large quantities of the collected data from these sensors require efficient planning and scheduling algorithms to acquire images of large stricken areas and transmit it back to Earth in a very short time during the limited visibility windows between satellites and GSs. The scheduling problem of EO satellite constellation is to specify the start times and duration  27 of the observation activities to acquire the requested images of the Earth surface, as well as to specify the start times and duration of the download activities to transmit the images back to GSs. A scheduling problem of multi-satellite, multi-orbit, and multi-user scenarios was studied in [95]. Similarly, a planning and scheduling algorithm was proposed for COSMO-SkyMed constellation in [89] and [97]. A proposed model for the multi-request mission planning problem including download windows to a set of GSs is proposed in [98] and provides a mathematical formulation and heuristic solution method for the scheduling problem of EO satellites. The main objective of these algorithms and models is to maximize the number of images taken (rewards of images) and transmitted back to Earth using several GSs for communicating with the satellites for both uploadings the operational commands to satellites and receiving back the image files. With the rapidly growing demand for environmental monitoring and disaster warning, the satellite data transmission-scheduling problem has attracted a great deal of attention [34], [36]. An optimization algorithm is proposed in [35], which is based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) for optimal scheduling of a SAR constellation. The constellation is a Walker-Delta configuration compromises of 4 satellites distributed on 2 planes at 47o inclination to minimize the RT of the mid-latitude regions. The objective of the optimization problem is to minimize the SRT by a frequent revisit of a target area for collection of ISR (Intelligence, Surveillance, and Reconnaissance) information. The scientific literature on planning and scheduling of EO satellite constellations discussed the scheduling optimization problem for maximizing the amount of data (images) taken and transmitted back to Earth in a short time. Although these efforts in previous work of scheduling remote sensing satellites for rapid response to natural disasters, it can be considered an insufficient improvement regarding SRT reduction. They optimize the start times and duration of both images acquisition and  28 download activities based on mission constraints and satellite resources and could not significantly reduce gaps in connectivity between Earth stations and imaging satellites, the main cause of excessive SRT. The key problem is the satellite line of sight with GSs. LEO satellite complete one orbit every 90 minutes (depending on satellite altitude). To communicate with the satellite, for example, to bring down imagery to the Earth site, we need a clear line of sight from the ground antenna to the LEO satellite. But the window of visibility during a given pass may last only ten minutes or so. It could be many hours before the satellite flies overhead again. 2.2.3 Ground Station Networks One way to solve this problem would be to install a more complex Ground Station Network (GSN) around the world to increase the space-to-ground communication time windows [16]. This infrastructure enables the space assets to conduct their mission successfully, provides high bandwidth and high accessibility data link for EO satellite constellations [28]–[30]. Nevertheless, GSN cannot fully resolve the problem. 71% of the Earth is covered by water so there is no way to achieve continuous communications with LEO satellites from a GSN no matter how many ground stations could be built. Moreover, GSN has many challenges and constraints. There is a cost constraint in deploying multiple GSs around the world. The ongoing cost of only ground control accounts for around 5% of the spacecraft cost per year due to the significant resources needed by the GS staff, even for the relatively simple architecture currently used [27].  Other potential drivers include politics, environment, infrastructure, and requirements for availability and survivability. For example, some locations that provide good Line-of-Sight (LOS) and accessibility might be prone to earthquakes or hurricanes. Tracking stations in foreign territory would require  29 diplomatic agreements, and those in remote locations might require additional facility security or a high level of automation. Automation can add a layer of complexity and risk, since not all anomalies or events can be predicted in advance, and redundancy can add another layer of cost [26]. 2.2.4 Relay Satellite Systems The space-based relay infrastructure is quickly evolving into a global standard because it comes to enable mission operators to communicate with remote sensing satellites to achieve high-level goals and offer fast data delivery to end-users, instead of just depending on the limited access intervals between imaging satellites and Earth stations. Relay satellite systems are capable of relaying user data in near-real-time at an unprecedented data rate. We can classify these systems into two major groups based on the orbit types, GEO and non-GEO relay systems. 2.2.4.1 GEO Relays GEO constellations place relay satellites at zero or near zero inclined circular orbits at an altitude of 35,786 km. Full-time coverage for LEO spacecraft can be achieved through only three ≈ 120 deg separated satellites with a 25o to 35o FOV [46]. The first proposals for using relay satellites to support EO satellites for Telemetry, Tracking, and Control (TT&C) employed GEO communication satellites [39]. GEO data relay systems such as European Data Relay System (EDRS) [37] and NASA Tracking and Data Relay Satellite System (TDRSS) [38] can maintain real-time access to LEO satellites and a number of the current and upcoming small satellite missions lean to these systems for communications [40], [43]. NASA TDRSS operates 6 active GEO satellites that can each relay communications between LEOs and the Earth. The satellites are positioned at 3 strategic longitudes to maximize global LEO coverage. The first EDRS (EDRS-A) launched on the 29th of January 2016 is revolutionizing satellite communications as Europe’s first optical space communication network, capable of relaying user data  30 in near-real-time at 1.8 Gbit/s. On March 31, 2019, China positioned a GEO relay satellite to support its human spaceflight efforts [99]. With Europe and India working on similar efforts, the space-based relay is quickly evolving into a global standard. GEO relay systems are regularly attributed with a number of advantages over ground station networks for the purposes of telemetry, command, and data download to and from satellites in LEO [41]. Nevertheless, traditional GEO communications satellites are as big as trucks, take years to build, typically cost $100 million or more without launching cost [100]. Moreover, they are not an appealing solution for small satellites, which become of more importance to the scientific and engineering community, or for spacecrafts that not equipped for long-range communications because they require high power and specific antenna size onboard LEO satellites [42]. On the other hand, NASA TDRSS time is used primarily by NASA missions in LEO, including the ISS [101] and it is not designed to serve the growing commercial space industry, which includes dozens of companies planning to launch thousands of communications and Earth-imaging satellites into LEO in the next decade. 2.2.4.2 Non-GEO Relays Non-GEO infrastructure, namely LEO and MEO systems, is a desirable option due to lower launch costs and shorter link distances than GEO systems. Data relay networks in LEO is composed of a large number of satellites flying in polar or inclined circular orbits. They achieve global coverage by coordinately spacing the satellites so that when a satellite loses line of sight there is at least another one that comes into view. The main advantage of LEO constellations is their limited distance to the Earth surface, from 160 km to 2,000 km. This decreases the power requirements for space to ground links, minimizes the communication propagation delays and reduces the launch costs. Nevertheless, the small orbital periods (from 90 to 130 min approximately) limit the contact windows between the relay  31 satellites and the GSs to 10-15 min thus reducing the volume of data that can be successfully returned. Similarly, a relay system based on LEO satellites would suffer from short satellite-to-satellite contact windows and would require complex tracking and acquisition mechanisms [46]. The concept of using relay satellites in LEO for servicing only a single imaging satellite (user satellite) was introduced in [44] where a proposed constellation of 7 to 9 small satellites evenly distributed in the same orbit as the user satellite to relay data from the user satellite via intraorbital ISLs, which connect satellites in the same orbital plane, and then to the ground. LEO constellation consists of 6 satellites at 70o inclination and 750 km altitude has been proposed in [45] and [47] as relay satellites to transport the collected data from two EO constellation types in LEO, each has 9 satellites, to a GS. The objective of this work is to evaluate the network performance rather than optimize the relay configuration for servicing imaging satellites. A network of LEO imaging satellites has been proposed in [48] to minimize the mean response time (MRT), which is the average time from when a satellite receive a random request to observe a point until it can observe it - data downlink is not accounted for. Solving the optimization problem in that paper finds the optimal 2-D Lattice Flower Constellation [102] parameters of 44 satellites in circular orbits that minimize MRT with global continuous connectivity. The results show that the optimized constellation can drastically reduce MRT. However, the optimized constellation compromises of 44 satellites distributed on 4 circular orbital planes at 1477.97 km altitude and 57.88o inclination, which is clearly an excessive number of imaging satellites. Moreover, this is a very high altitude, which is not appropriate for good spatial resolutions of Earth images. We select satellite systems in MEO layer for servicing imaging satellites in LEO for many reasons. They have the advantages of the characteristics of both GEO and LEO systems [52]. They are frequently proposed in multilayer satellite networks for global satellite communication systems [53]– 32 [57] because they have shorter round trip delays and lower transmission power requirements [58]. From another perspective, with the accumulating space debris, future collisions between large fragmentation debris and other intact objects are less probable in MEO region, due to the existing lower levels of spatial densities, than if the same breakup occurred in LEO region  particularly with the recent proposals of deploying thousands of telecommunication satellites expected to orbit Earth in the near future in LEO region. A theoretical concept of using a tracking and data relay system for China is introduced in [49]. This system consists of MEO satellite constellation with ISLs and terrestrial gateway station. The proposed MEO constellation in this work was previously designed for mobile communication for China [103] and is called a common-track constellation because of all its satellites follow the same track on the Earth surface. The coverage performances of 4 different MEO constellations, Rosette, Polar, Equatorial, and common-track, are compared in [50]. The constellations have the same altitude and total satellite number (6 satellites). The constellation parameters of Rosette and Polar are taken from [104] and [105], respectively, with only change in altitude for the sake of fair comparison. Coverage performance in this work was performed to examine the coverage percentage of a celestial sphere at 300 km altitude, as a lower limit for most existing LEO spacecrafts and to examine the coverage of nine terrestrial GSs distributed in China area. Another comparison is discussed among different constellation configurations to serve as relay satellites is introduced in [51]. Visibility outages of a single LEO satellite were analyzed and compared in case of using three different relay constellation configurations, which are the three layers of BeiDou triple-layer navigation system. Nevertheless, this is a questionable comparison because the constellations are using different orbit types and have a different number of satellites and a different number of planes.  33 The first promising evaluation study that uses relay satellites in specific LEO and MEO constellation configurations (Walker-Delta) to reduce system response time is described in [2]. However, the goal of that paper was not to find the optimal configuration of this scheme but to explore its potential performance enhancement. Moreover, only one level of ISL routing has been considered, a telecommand can be bridged only by one relay from a GS to an imaging satellite.  2.3 Summary The development of satellite constellations design in various applications passed through two different phases. The first phase of traditional satellite constellation design methods is associated with global or zonal, continuous (single or manifold) coverage under the typical assumption that payload FOV is a wide circular cone whose axis is along with the satellite local vertical. These methods are typically used for navigation and communication applications, which justify these assumptions. In this phase, constellation design focus on methods for deploying multiple satellites in a manner that guarantees minimum position uncertainty (for navigation) and continuous Earth-space or intersatellite coverage (for communications). These methods generated constellations of homogenous (identical) satellites in terms of their function and have uniform constellation configurations. The second phase is dedicated for remote sensing constellations, which have been proposed and implemented later because of the remote sensing sensor apertures are typically much smaller and their FOV are shaped differently. In this phase, traditional constellation design methods are not applicable to remote sensing missions and there is no straightforward approach in designing satellite constellations as they are mainly derived by different mission objectives and goals. Constellations in this phase are homogeneous in terms of their function even satellites in the same constellation could carry different types of remote sensing sensors. Some of the orbital configurations of these constellations are uniform  34 and others are non-uniform. However, the majority of these constellations are using SSOs. Therefore, reference configurations of the remote sensing constellations do not exist. Since timeliness is valuable, rapid response for EOs and the need for fast data delivery to end-users lead to a new level of complexity and opportunity into satellite constellation design, which is the phase of heterogeneous (nonhomogeneous) constellations that uses ISLs between two different functional constellations, remote sensing constellation for imaging and a constellation of small satellites dedicated for command delivery and relay data back to Earth sites. The use of communication satellite networks comes to enable mission operators to communicate with remote sensing satellites to achieve high-level goals and fast data delivery, instead of just depending on the limited access intervals. The main objective of these constellations is the reduction of SRT - the key FOM for assessing the timeliness of EO imagery. Previous work has focused on reducing SRT through improved planning scheduling algorithms (insufficient improvement), using RGT orbits for RT minimization (opposed to providing global coverage), using GSNs (many cost and political constraints), and deploying a large number of EO satellites (too expensive). Recently, the space-based relay satellite systems are quickly evolving into a global standard for solving the communication gaps between LEO satellites and Earth sites. GEO relay satellites have some disadvantages. Ultimately, building non-GEO relay communication infrastructure could be the best option for SRT reduction to provide real-time communication services for the small satellite constellations.      35 Chapter 3: A Framework for Heterogeneous Satellite Constellation Design for Rapid Response Earth Observations  3.1 Introduction Natural disasters and military conflicts have demonstrated a need for rapid response EOs using heterogeneous constellations where two different functional constellations are cross-linked. One is mainly for imaging and the other is a communication constellation that is dedicated to relaying commands from Earth stations to imaging satellites and data collection back to Earth. This scheme has been proposed in previous work to explore its potential enhancement of the system performance [2], [49]–[51], or to evaluate the network performances by comparing candidate relay constellations for servicing remote sensing satellites [45], [47]. However, previous design methods for heterogeneous satellite constellation design (HSCD) to support rapid response EOs were ad hoc and not systematic. Therefore, the objective of this chapter is to develop a systematic design procedure for HSCD to reduce SRT. Since the best heterogeneous configuration may require studying several constellation combinations, our objective here is to establish a framework capable of generating thousands of heterogeneous constellation configurations from ranges of predefined design variables (DVs) and sizing those configurations in terms of the corresponding predefined measures of performance (MoPs). This framework introduces the design/performance curves that can provide solutions to designers to configure both the imaging and relay constellations of the heterogeneous constellation systems that can achieve specific objectives and improve the overall system performance by reducing the average value of maximum SRT.  36 One of these solutions is an imaging constellation of 8 satellites equally distributed in 2 different planes, SSO that is a commonly used orbit for EO missions and a Mid-Inclination Orbit (MIO) with a ~45 deg inclination to provide high revisit in mid-latitude regions of the Earth. We select this imaging constellation based on daily global coverage percentage, the main parameter to analyze the performance of the constellation, GSD as a key measure of spatial resolution, and a trade-off analysis between these two MOPs and satellite optical payload parameters, FOV and focal length f. This constellation can achieve 98.75% daily global coverage with specific payload parameters that achieve a 0.5 m GSD. For the relay constellation, we select a constellation on MEO in the Equatorial plane and a location of a GS as a receiving and transmitting Earth site. This relay constellation can reduce the maximum SRT by nearly 20 hours in case of using a GS at 35o latitude. The remainder of this chapter is organized as follows. Section 3.2 introduces a parametric study tool for HSCD of remote sensing missions. Section 3.3 introduces the proposed framework of the methodology used to design the heterogeneous constellations. Section 3.4 presents and discusses selected results from a case study using the proposed framework. Discussions of the results and the main findings of this chapter are presented in Section 3.5. 3.2 Parametric Study Tool for Heterogeneous Satellite Constellation Design Our approach in supporting control (command delivery) and data recovery of the LEO remote sensing systems is well suited for STK’s analytical capability, which is developed by Analytical Graphics, Inc. (AGI). We use STK software with some of its modules such as Coverage, Analysis Workbench (AWB) and STK Analyzer, which is used for STK automation, to run a series of parametric studies. For each parametric study, one or two DVs will be run through a sweep of values and at each value, MOP statistics will be collected. Through our analysis, we will see how changing each of these DVs affects  37 the correlated MOPs. A chart shows the trade analysis process is represented in Figure 3-1 and also define different DVs and MOPs used in this parametric study.  Figure 3-1 – Data flow of the trade analysis process and defining various DVs and MOPs used in simulations. We present a flow of trade-off design curves to configure heterogeneous satellite constellations for remote sensing missions. Our objectives are to design an optical imaging constellation that achieves daily global coverage, specify their payload parameters required for achieving specific spatial resolution, find the best relay satellite constellation on an Equatorial plane to reduce SRT, and the location of a GS to be a receiving and transmitting Earth site. Ranges of multiple DVs and their relevant MOPs are determined to find out the solutions of each constellation in this configuration that meet the mission requirements. Among all solutions, designers can find out the optimal/suboptimal configuration parameters.  38 3.3 Proposed Framework We use 3 different orbital types; the first 2 types are used for the imaging constellation and the third type is for the relay constellation: 1. Sun Synchronous Orbit (SSO) on LEO 2. Mid Inclined Orbit (MIO) on LEO 3. Circular MEO on an Equatorial plane Our framework can be summarized in the following steps: 1. The first design/performance curve is for designing a constellation on SSO based on its global coverage percentage, the main MOP to analyze the performance of the constellation, using different values of DVs such as a number of satellites per plane, orbital altitude, and the payload FOV. 2. The second design/performance curve is to specify the optical payload f at a specific Detector Pitch (DP) value based on their effects on coverage percentage and GSD as a key measure of spatial resolution. 3. Coverage analysis by ground target latitude (MOP) of the SSO constellation to see how adding imaging satellites on MIO can improve the constellation coverage percentage. 4. The third design/performance curve is to determine the number of satellites in MIO (DV) and the required altitude (DV) based on the global coverage percentage (MOP). 5. The fourth design/performance curve is for designing the relay constellation. We determine the minimum number of relay satellites (DV) at 8,000 km required for achieving continuous coverage to a GS and specify its available latitude range/s (DV). Then, using this number of satellites, we  39 determine the maximum gap duration between relay and imaging satellites (MOP), which is considered the maximum value of T2 and T6 in SRT computation. 3.3.1 Imaging Constellation Design For some remote sensing payloads, the satellite altitude plays a large role in determining the details of information obtained and the total area imaged by the sensor based on its FOV. Sensors at high altitudes typically view a larger area but cannot provide good spatial resolution. Therefore, our aim is to generate the design curves for SSO constellations in order to provide designers with some quantitative information about the relationships between orbital altitude, number of satellites, payload FOV and their effects on Earth global coverage. Then, we discussed the sensor parameters impacts on coverage and spatial resolution. From these design curves, we can select SSO constellation altitude, a number of satellites and the sensor parameters that achieve a daily global coverage with 0.5 m GSD as a measure of spatial resolution. In the beginning, we used a satellite sensor with a fixed rectangular FOV = 20o, which is defined according to specified vertical half-angle (VHA) and horizontal half-angle (HHA) as shown in Figure 3-2 [76]. These sensor types are typically used with satellites or aircraft for modeling the FOV of instruments such as push-broom sensors and star trackers. Sensor FOV is independent of orbital altitude (h) while the swath width (SW), which is the ground-projected FOV, depends on it. Increasing the sensor FOV increases SW at the same altitude. At a fixed FOV, increasing orbital altitude increases SW according to 𝑆𝑊 = 2 ∗ ℎ ∗ tan (𝐹𝑂𝑉2)  ,    (3.1)  as shown in Figure 3-3.                                                              40  Figure 3-2 – Rectangular sensor parameters (Source: AGI-STK).  Figure 3-3 – SW vs. h at different sensor FOVs.  41 We know that for SSO imaging constellation, increasing both the orbit altitude and the sensor FOV will improve coverage capabilities until we run up against the GSD constraint for the sensor. Fortunately, we can change sensor parameters to permit greater viewing capabilities at higher altitudes. The ground sampling distance, 𝐺𝑆𝐷 =𝐷𝑃∗𝑟𝑓∗ √sin (𝑒𝑙𝑒𝑣)  ,                                                                   (3.2) is a function of both sensor f and DP. For our next step, we will see how changing the f will impact coverage for a 2 different sensor FOV to achieve specific GSD resolutions for an imaging constellation on SSO. We select the sensor DP to be 1 μm. To define the resolution of an optical sensor, we must specify the focal constants shown in Figure 3-2, f and DP. These parameters and the satellite altitude are used in the computations of the GSD in (3.2) where r is the sensor range and elev is the elevation angle. The low GSD values are better image resolutions. Therefore, increasing f and decreasing DP will improve GSD. We started with the default values in STK sensor resolution parameters with a sensor FOV=20o to study the effects of orbital altitude, a number of satellites and the FOV on the constellation coverage. Then, we will optimize the sensor parameters to get the required spatial resolution. We will show the design curves associated with the process of determining if an optical sensor will achieve the required coverage and spatial resolution. Once that is accomplished, the next big step is to decide the best imager parameters that serve mission purposes. Then, we can select the orbital altitude and the number of satellites of a constellation. Since the orbit track spacing varies with latitude, the revisit rate is significantly greater at higher latitudes than at the equator. After setting the SSO constellation parameter, we analyzed its coverage. Results will show that the mid-latitude regions have the most uncovered portions. Therefore, we show through simulations how many MIO satellites and their altitudes required to improve the global coverage and revisit time of these mid-latitude regions.  42 By this step, we can select the imaging constellation altitude, number of satellites/plane and sensor parameters. The following step is to select the relay satellite constellation to improve the SRT. 3.3.2 Relay Constellation Design The heterogeneous system configuration and the constellation details have a significant impact on system availability. The availabilities are dependent on the LEO & MEO constellation characteristics, e.g., altitudes, number of orbital planes & types, number of satellites per plane, etc. The best configuration of a heterogeneous system requires studying several constellation combinations. In this chapter, we design MEO satellite constellation that can deliver commands from a GS to an observing satellite, collect data and storage from an observing satellite, and download it to a GS. It means that a bidirectional inter-layer ISLs are involved in our network scheme. We propose using relay satellites on an Equatorial plane for the relay constellation at the minimum altitude of MEO range, which is 8,000 km. Thus, the unknown parameter of the relay configurations will be the number of satellites. Moreover, we select the latitude of the GS, which will be used as a transmitting and receiving Earth site. STK can compute the Intrinsic Response Time (IRT) for an imaging constellation based on the Time Average Gap (TAG), which is the average length of the coverage gap found if the timeline for target points is sampled randomly [76]. STK can also compute the SRT for the imaging constellations by selecting a command and receiver GS and providing values for the fixed intervals listed in the appendix. However, STK does not have the option for SRT computations when using relay satellites either for command delivery or for collecting data back from imaging satellites. Therefore, we divide SRT into 3 major dynamic time components, T2 due to coverage gaps between command GS and imaging satellites, IRT that depends on the revisit time of the imaging satellite constellation itself, and T6 due to the coverage gaps between imaging satellites and the receiving GS.   43 In case of no relay satellites used, the max values of T2 and T6 are equal to the Maximum Gap Duration (Max GD) between the GS and the imaging satellites. This is the worst case where the maximum SRT occurs when the GS has to wait for a Max GD to uplink its command to the imaging satellite and again the imaging satellite has to wait for the same period, Max GD, to download its data to a GS. Max SRT, in this case, depends on the number of imaging satellites, the GS location, and the target locations. Although the high latitudes ground sits are effective and can improve SRT, these stations contact the satellite in each revolution, though the transmission time is limited to a few minutes per orbit, which is too small to accommodate all the acquired data. Therefore, we use MEO relay satellites to increase the connectivity durations for data download and to decrease the maximum SRT.  When using relay satellites, the max T2 will be equal to the max GD between a GS and a relay plus the max GD between the relay and the imaging satellite. The same for downlink, the max T6 will be equal to the max GD between the imaging satellite and a relay plus the max GD between the relay and GS. Thus, we first perform multiple simulations in order to find the minimum number of relay satellites at a minimum MEO altitude (8,000 km) that achieve continuous coverage to a GS. In this case, the daily coverage percentage of a GS is the MOP, which is depending on the two inputs of STK-Analyzer, the latitude of the GS and the number of relay satellites. A minimum 10o elevation angle is applied to the GS as an elevation angle constraint in order to avoid obstacles caused by natural barriers at low elevation [2]. First, we can select the number of relay satellites at 8,000 km altitude and a GS latitude, which has continuous daily coverage. Therefore, max 𝑇2 𝑎𝑛𝑑 max 𝑇6 will be based on the gap durations between relay satellites and the imaging satellites themselves. Second, using STK access tool, we compute the average of both max 𝑇2  and max 𝑇6 for 𝑀𝑎𝑥 𝑆𝑅𝑇̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅  , given by 𝑀𝑎𝑥 𝑆𝑅𝑇̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ = 𝐼𝑅𝑇̅̅ ̅̅ ̅ + max 𝑇2̅̅ ̅̅ ̅̅ ̅̅ ̅̅ +  max 𝑇6̅̅ ̅̅ ̅̅ ̅̅ ̅̅ + 𝑇1 + 𝑇3 + 𝑇5 + 𝑇7     .                      (3.3)  44 3.4 Selected Results from a Case Study We performed multiple simulations to generate several thousand constellations at altitudes ranging from 200 km to 1200 km with a step size of 5 km (to improve the resolution of the results we obtained) for a number of imaging satellites from 2 to 6. The global coverage percentage is the MOP in this case while SSO altitude, hSSO, and a number of satellites, SSOSats, are the DVs. Since we are using an optical sensor, a daylight constraint is applied to the coverage definition object in STK scenario before the global coverage evaluation. These simulations are based on a sensor FOV of 20o. Figure 3-4 shows that increasing hSSO and SSOSats increase the global coverage percentage during daylight imaging. It also shows that the greater number of satellites, the better global coverage % achieved at a specific altitude.  From Figure 3-4, we can see that SSO constellation of 4 satellites at an altitude 600 km can achieve about 46% global coverage percentage when using 20o sensor FOV. To show the effects on the coverage when changing sensor FOV at a different number of satellites, we select an orbital altitude at 600 km as a case study. For a range of a sensor FOV, we analyze how increasing the sensor FOV and the number of satellites affects the daily global coverage percentage during daylight as shown in Figure 3-5. We can observe the increase of the coverage percentage to be 81.4% by simply increase sensor FOV from 20o to be 40o using the same number of satellites at the same altitude. Nevertheless, this will be at the expense of the spatial resolution and the optical payload parameters. Therefore, our objective in the next step is to specify the sensor focal length, f, and the sensor detector pitch, DP, values in two different values of FOVs, 20o and 40o, where they can achieve the required global coverage % and the required ground sampling distance (GSD) as a MOP for the spatial resolution.  45  Figure 3-4 – SSO altitude and daylight global coverage at a different number of satellites. Each satellite has a rectangular sensor with 20o FOV.  Figure 3-5 – Daylight global coverage vs sensor FOV of SSO constellation at 600 km altitude for different numbers of satellites.  46 We ran simulations using a SSO constellation of 4 satellites at 600 km altitude to show the effects of changing sensor FOV and f on coverage and on GSD. From these simulations, we can specify f that met the required GSD when using two sensors with FOVs, 20o and 40o. We selected the sensor DP to be 1 μm. Figure 3-6 and 3-7 show that increasing f increases the coverage percentage of the SSO constellation until it reaches the maximum global coverage percentage that can be achieved by this constellation. From Figure 3-6, we can optimize the minimum f required to achieve 5 m GSD images while from figure 3-7, we can get the optimized f to achieve 0.5 m GSD. Below these values, this constellation will achieve the same resolution but will reduce its coverage percentage. Results in both figures show that there is no need to increase f, as they will improve neither coverage time nor GSD. Based on the previous results, we select an SSO constellation consisting of 4 satellites, each with a 40o sensor FOV. The maximum global coverage percentage of this constellation is 81.41%. Among the available solutions, an SSO constellation of 6 satellites at h = 1,200 km, and each has a 20o FOV sensor. This constellation will increase coverage percentage to be 96%. Nevertheless, this constellation needs a very big increase in the sensor parameters. In this case, we need a sensor f = 2.5 m to achieve 0.5 m GSD, which is not practical. From coverage analysis of the SSO constellation, we concluded that most of the uncovered portions of Earth are in mid-latitudes region (from -50o to +50o latitude). The other portions are very small portions on Polar Regions. Based on this analysis, we propose another imaging constellation on MIO (i = 45o) to overcome the coverage limits of the SSO constellation and increase the revisit time of the mid-latitude regions where the bulk of the world’s population reside. This constellation will have the same sensor parameters as the SSO constellation.   47  Figure 3-6 – Optimized f required to achieve 5m GSD using 1 μm sensor DP. The global coverage percentage achieved by SSO constellation of 4 satellites at h = 600 km.  Figure 3-7 – Optimized f required to achieve 0.5m GSD using 1 μm sensor DP. The global coverage percentage achieved by SSO constellation of 4 satellites at h = 600 km.   48 The objective of the next step from simulations is to know the number of MIO satellites (MIOsats) and the altitude of this constellation that improves the daylight global coverage percentage with the proposed SSO constellation. As shown in Figure 10, MIO constellation of 4 satellites at 575 km altitude with the same sensor parameters as the SSO constellation can improve the coverage percentage to be 98.75%. We applied 0.5 m GSD as a constraint to the coverage definition during these simulations. Therefore, we can see that increasing MIO orbital altitude (hmio) will not improve the coverage due to this applied constraint.  Figure 3-8 – MIO constellation altitude and MIOSats and their effects to improve coverage with the SSO constellation. To design a relay constellation, we started by deriving design curves that help to answer the following questions: 1. What is the number of satellites on an Equatorial plan at 8,000 km altitude that can achieve continuous coverage of a GS?  49 2. What is the GS latitude? 3. What will be the effect of using this MEO constellation with its GS on the maximum SRT?  We can find the answers to the first 2 questions in Figure 3-9. Any GS at latitude from 0o to 34o has a continuous coverage from MEO constellations consists of a number of satellites Ns = 4, 5, or 6 satellites. We select the minimum number of relay satellites Ns = 4 satellites and a GS at 30o latitude from these simulations. The configuration of the heterogeneous satellite constellation and the location of the GS are shown in Figure 3-10. Analysis of the heterogonous constellation performance in terms of SRT compared with the performance of the imaging constellation is shown in Figure 3-11. This heterogeneous system can reduce the maximum SRT by nearly 20 hours in case of using a GS at 35o latitude.  Figure 3-9 – Daily coverage percentage vs GS latitude for an equatorial constellation at 8,000 km altitude.  50  Figure 3-10 – Heterogeneous satellite constellation configuration.  Figure 3-11 – Heterogeneous constellation performance.  51 3.5 Discussion This chapter provides the rationale for using heterogeneous constellations to EOs and data return. The main objective of this chapter is to provide a systematic approach to design a heterogeneous constellation to support the rapid response of EOs. We introduced a framework to design an imaging constellation that can achieve a complete global coverage each day that reduces RT and a relay constellation for serving this imaging constellation to reduce SRT. Previous work on heterogeneous constellations has focused on communication constellations and specific design cases; little treatment of performance trends or optimal solutions or applications to EOs. The heterogeneous system configuration and the constellation details have a significant impact on system availability. The availabilities are dependent on the imaging and relay constellation characteristics, e.g., altitudes, number of orbital planes & types, number of satellites per plane, etc. The best configuration of a heterogeneous system requires studying several constellation combinations. Since there are many different configurations of the RSSCs, correct selection of reference observation and relay constellations is likely key to reduce the solution space of HSCD. The goal of this work was not to find an optimal configuration of the relay communication constellation in MEO for servicing an EO constellation in LEO but to explore the potential performance enhancement brought by this heterogeneous constellation configuration. We found that the simulation results are promising. The selected results from the case study discussed in Section 3.4 showed that when relay satellites are involved in the scheme, the maximum SRT can be reduced by nearly 20 hours if compared with the imaging constellation only without relay satellites. The parametric study presented in this chapter has revealed the limitations of STK-Analyzer in STK automation and the limitation of STK software in SRT computations when relay satellites are involved.  52 Therefore, the following next steps could be performed in order to cover the limitation of this framework and the simulation tool: 1. Develop a methodology for SRT calculation considering the different capabilities of relay satellites and the existing type of ISLs. 2. Develop an alternative way to automate STK to support trade-space exploration in HSCD. The most likely way to do that is using MATLAB for STK automation due to its widespread use, simple implementation of certain data constructions and the availability to interface with STK.         53 Chapter 4: Reference Configurations for Remote Sensing Satellite Constellations 4.1 Introduction Recent technological advances spurred the exploration of problems that require multiple spacecraft operating in a synchronized manner, promoting research and development activities in innovative distributed space system concepts including constellations for Earth Observations. Satellite constellations were the first successful implementation of distributed satellite systems, which respond to a functional need such as global coverage with high repetition rates (short RT) [2]. SRT, the more important performance parameter than RT for disaster monitoring missions, is the key metric for assessing the timeliness of EO imagery in disaster response, can be significantly reduced by using dedicated relay satellites that can reduce (and possibly eliminating) the communication delay components of SRT for EO constellations. This heterogeneous constellation architecture has been proposed before in previous work to explore the potential enhancement of the system performance [2], [49]–[51] or to evaluate the network performances by comparing candidate relay constellations for servicing remote sensing satellites [45], [47]. Nevertheless, previous progress in this area has been hampered because designing and evaluating the performance of these heterogeneous systems are difficult due to the large size of the solution space, which depends on: 1. Various configuration parameters of the EO satellite constellations 2. Payload types and aperture parameters of EO sensors 3. Relay satellite constellation parameters 4. Capabilities of the relay satellites and the existing type of ISLs   54 The heterogeneous system configuration and the constellation details have a significant impact on system availability. The availabilities are dependent on the RSSC & RCSC characteristics, e.g., orbital altitudes, inclinations, number of orbital planes & types, number of satellites per plane, etc. The best configuration of a heterogeneous system requires studying several constellation combinations of imaging and relay constellations. In some cases, multiple candidate relay constellations could be appropriate for servicing the same remote sensing constellation. As we discussed before, the related previous work uses isolated instances of relay satellite constellations in MEO [2], [49]–[51]. Furthermore, two ways are used to represent the remote sensing constellation in LEOs, a celestial sphere at specific altitude as a lower limit for the existing LEO satellites [49], [50], which is unrealistic representation, and a random configuration such as a constellation of 5 satellites in 3 planes on SSO, which was used in [2], where capabilities of relay satellites have not been fully exploited in this work. This requires a unified classification of the configurations of EO satellite constellations and summarizes the basic possible configurations of relay constellations to get representative and realistic constellation configurations when designing a relay constellation for servicing LEO satellite constellations. Most of the previous work and survey papers have focused on categorizing and classifying the remote sensing satellites based on their mission application or the remote sensor type [96], [107], [108]. An extensive and compendium survey in [60] has covered the Earth Observation on a global scale. This book introduces a survey of space EO missions and sensors (past, present, and future). Nevertheless, they did not introduce a classification or grouping to the configurations of the remote sensing constellations.  55 Ulybyshev presented in [109] a short historical survey of the constellation design methods of global continuous coverage using circular and elliptic orbits. He classified the satellite constellations into two major types, homogeneous and nonhomogeneous. Homogeneous constellations are that included a number of orbit planes with an equal number of satellites in each plane and same inclination and altitude while he classified the nonhomogeneous satellite constellations into two subgroups: 1) constellations in different inclinations and equal altitudes 2) constellations in different inclinations and altitudes. This survey was based on the traditional constellation design methods such as Streets Of Coverage (SOC) [110]–[113], Walker [114], Draim [115], and Flower constellations [116], which are not applicable to the remote sensing missions as explained in Section 2.1. TS Kelso’s CelesTrak website [117] provides Two-Line Elements (TLEs) [118] for use with the Simplified General Perturbations - 4 (SGP4) orbital propagator [119]. They group satellites with common purposes, like weather, Earth resources, disaster monitoring, and the Planet and Spire constellations (due to their sizes). These TLEs are classified by common mission rather than orbit or sensor types and there is no classification or grouping to the remote sensing constellations based on the configuration type. The objective of this chapter is to provide representative configurations of the RSSCs instead of using random or unrealistic configurations as used before. These configurations are useful for the current and future simulation-based studies in designing and evaluating the performances of the heterogeneous satellite constellations by proposing realistic and representative RSSCs configurations. Based on a statistical analysis of the NORAD TLEs for 34 RSSCs and a thorough review of their missions, we propose nine representative classes that allow the performance of RCSCs to be broadly assessed with far less effort than testing against an exhaustive set. These classes are based upon orbital inclination (three categories) and the number of planes & different altitudes (three categories) although only seven  56 of these classes are actually populated by actual RSSCs. The actual number of planes, orbital altitudes, and orbital inclinations are represented by simple distributions. This chapter also summarizes the major configurations of RCSCs in MEO, which will be useful when conducting simulation-based studies for system performance of RSSCs. In this chapter, Section 4.2 presents a review of what already known about the constellation configurations and orbit types used for RSSC missions by introducing a representative list of the RSSC missions. The data sources and the methodology used in the statistical analysis of these data are discussed in Section 4.3. In Section 4.4, we discuss the main observations in the results from the statistical analysis of the collected data, introduce the proposed representative classes for RSSCs configurations, and summarize the previously proposed relay constellations in MEO. Finally, a summary of this chapter is in Section 4.5. 4.2 A Representative List of Remote Sensing Satellite Constellation Missions Traditional satellite systems for EO missions have the following key limitations that can impact their utility [120]: 1. Most current systems consist of a single satellite, or a small constellation with 3-5 assets, resulting in limited coverage and the revisit performance will be of the order of days. 2. The majority of imaging satellites are in high inclination polar orbits which are optimized for global coverage at the expense of revisit times. 3. Optical imaging satellites are generally in sun-synchronous orbits with fixed imaging local time of ~10.30 am to maximize illumination conditions and minimize cloud cover, resulting in minimal coverage at different times of the day.  57 4. SAR imaging satellites are generally in sun-synchronous orbits with a fixed imaging local time of ~06:00 am as the satellites' solar panels can always see the Sun, without being shadowed by the Earth. These limitations can be overcome by a moderately sized constellation of small satellites in different orbit types and inclinations, which can provide multiple observations throughout the day. Satellite constellations provide a number of advantages including: 1. Enable activity monitoring and change detection with near persistent observation being potentially achievable using large constellations that can improve the temporal resolution (revisit time). 2. Easy replacement of a satellite within a constellation due to the relatively low costs of a single satellite. 3. Soft degradation of the system performance caused by the malfunction of one satellite. Nevertheless, the constellation design process for RSSC missions is a complex trade-off between: 1. Overall mission cost, which is a function of launch cost, the total number of satellites, number of planes, and the satellite size and mass. 2. Providing high-resolution images. 3. Providing fast imaging delivery. In this section, a representative list of different RSSC configurations in different missions and applications is introduced to show how the constellation and orbital parameters are selected to overcome the mission limitations and to achieve the mission requirements. We introduce some examples of RSSCs based on the sensor type, which can be classified into 3 categories: SAR, optical, and weather & scientific constellations. The following examples of RSSC missions are given in order  58 to show that different remote sensing applications need different approaches for cost-effective missions and different constellation configurations and parameters. Moreover, they reflect what we have already known about the general trends of configurations and orbital parameters for RSSCs. 4.2.1 SAR Constellations 4.2.1.1 RADARSAT Synthetic-aperture (SAR) sensors, with huge mass and power requirements, have been flown by large satellites such as the RADARSAT satellite constellation (RCM), Canada’s new generation of EO satellites. RCM is a three-spacecraft fleet operated by the Canadian Space Agency launched on 12 June 2019. The primary goal of RCM is to provide continuous C-band SAR data to RADARSAT-2 users, as SAR imagery at a high temporal resolution is required by several users in the Canadian government. Other improvements include more frequent area coverage of Canada and reduced risk of a service interruption. Its SAR sensors have a mass of 400 kg each and a high resolution of 1 × 3 m. There is also a secondary payload, an Automatic Identification System (AIS) for ships, that will be used independently or in conjunction with the SAR [121]. The primary areas of interest of RCM are the landmass of Canada and its surrounding Arctic, Pacific and Atlantic maritime areas. RCM is a trio of EO satellites in one SSO plane spaced apart by 120o at a mean altitude of 593 km at 97.74o inclination. Its 12-day repeat cycle provides a coherent change detection period of 4 days (taking into account three satellites) and optimizes uniformity of repeat coverage to the areas of interest while maintaining global access with each satellite [122]. RCM orbit selection was based on trading off several considerations: 1) important considerations for the nominal altitude are power and fuel 2) secondary considerations when choosing the orbit altitude include GS contact time, link margin, and incidence angle variation across the imaged swath 3) given an approximate range of altitudes, orbit selection needs to take into account repeat cycle considerations.  59 4.2.1.2 ICEYE Active microwave payloads such as SAR sensors have been typically associated with large and expensive platforms, mainly due to their mass and required power [123]. However, while in markets timeliness is valuable, ICEYE is making trade-offs between providing high-resolution SAR images and fast image delivery. Finland’s Aalto University plans to provide data with a constellation of six SAR satellites focused on Earth’s Arctic regions and build up to a constellation of 18 space-based radars in collaboration with the European Space Agency (ESA) to offer customers the ability to acquire data on any area of the globe within a couple of hours of a request [124]. Compared to existing SAR constellations, ICEYE large number of satellite units distributed on multiple orbital planes (6 SSOs at ~500 km altitude) enable shorter response time from data acquisition request to delivery on the scale of 2-3 hours in the arctic latitudes. To reduce the size and cost of the ICEEYE satellites and thus enable a large number of satellites in the constellation, it is necessary to have a small imaging payload, which is an X-band SAR designed by ICEYE. The instrument is built with several trade-offs focusing mostly on low unit mass and cost so that the high temporal resolution can be realized in a commercially feasible way but with an image resolution of 10 × 10 m  [125]. ICEYE-X1 was the first satellite under 100 kilograms to carry a SAR sensor launched on January 2018. The second satellite, ICEYE-X2 was launched into orbit on December 2018. The ICEYE-X3 radar payload failed shortly into the mission. The fourth and fifth satellite, ICEYE-X4 and ICEYE-X5 were launched July 2019. 4.2.1.3 XpressSAR Unlike the most SAR satellites, XpressSAR Inc., an American owned and operated company, will launch and operate a high-resolution X-Band SAR constellation that will consist of four identical  60 satellites in two orbit planes with a 35° inclination and altitude 425 km. XpressSAR constellation (with a planned launch in 2022) is optimized to provide revisit performance in the cloud-persistent regions of the globe between 45°N and 45°S. XpressSAR will have a mean revisit of one to four hours depending on the target latitude [126]. 4.2.1.4 OptiSAR  The OptiSAR constellation comprises eight tandem pairs of SAR and optical satellites divided into two orbit planes. The four tandem pairs will be equispaced around an orbit plane, where each tandem pair consists of a leading SAR satellite, which uses UrtheCast’s SAR-XL technology that provides a dual-band (X-band and L-band) SAR instrument, and a trailing optical satellite that is following approximately 2 minutes behind the SAR satellite. The first orbit plane is a SSO with a 10:30 a.m. equator crossing time that is a commonly used orbit for EO missions, and the second plane is a Mid-Inclination Orbit (MIO) with a ~45o inclination. The MIO is used to provide ultra-high revisit in mid-latitude regions of the Earth where the bulk of the world’s population resides. Both orbit planes have a satellite altitude of 450 km [127]. Traditionally, the power-hungry nature of SAR sensors combined with their day and night imaging ability have driven SAR satellites to fly in dawn-dusk orbits to maximize power generation and the payload duty cycle. This, however, hasn't been the case for optical satellites due to the less than optimal ground illumination conditions in such orbits. A key feature of the OptiSAR constellation is the cross-cueing capabilities between the SAR and optical satellites which enables the system to have a wide swath surveillance mode with the SAR satellite. Using onboard processing, it is capable to detect, classify objects of interest (e.g., ships), and then automatically task the optical satellite to take a high-resolution image or video of the selected objects [127].   61 4.2.2 Optical Constellations 4.2.2.1 RapidEye RapidEye is a commercial multispectral EO mission that includes a constellation of five minisatellites that have been launched on a single Russian Dnepr rocket from the Baikonur Cosmodrome in Kazakhstan in August of 2008 [128]. They are deployed in orbits at an altitude of 630km. The satellites are placed equally spaced in a single SSO to ensure consistent imaging conditions and short RT. The satellites follow each other in their orbital plane at about 19 min intervals. The constellation approach in a single orbital plane permits a cumulative swath to be built up (the spacecraft view adjacent regions of the ground, with image capture times, separated by only a few minutes). A RT of one day can be obtained anywhere in the world (± 70o latitudes) with body pointing techniques. The average coverage repeat period over mid-latitude regions (e.g., Europe and North America) is 5.5 days at nadir. The RapidEye system can access any area on Earth within one day and cover the entire agricultural areas of North America and Europe within five days. The uplink and downlink capability are provided by reception stations located at Svalbard (Norway) and operated by Kongsberg Satellite Services (KSAT) [129]. 4.2.2.2 PlanetScope (PS) The standardized CubeSat concept [130] has offered a cost-effective solution to revolutionize the EO potential. This concept uses compact and light-weight (<1.33 kg) single-unit (1U; 10×10×11.35 cm) building blocks as the modular basis for forming larger satellite configurations (i.e., 3U, 6U, 12U) for a variety of application fields [131]. As CubeSats are comprised largely of commercial off-the-shelf components and deployed as a secondary payload on reusable rockets, the changing economics of EO has made it feasible to launch CubeSats in flocks at an unprecedented rate.  62 PS is a satellite constellation consisting of 170+ CubeSats (“Doves”) operated by Planet Labs, an American commercial Earth-imaging company based in San Francisco, CA. Their goal is to image the entirety of the planet daily to monitor changes and pinpoint trends. Each Dove satellite is a 3U CubeSat. The number of CubeSats in this constellation is still increasing. The majority of CubeSats are in SSOs (~475 km altitude) with a midmorning equatorial overpass time (9:30–11:30 a.m., local solar time) and a nadir GSD between 3.5–4 m. Smaller flocks of PS satellites still operate in the International Space Station (ISS) orbit (~400 km altitude), which results in a variable equatorial overpass time and a GSD of ~3 m. Doves form the largest satellite constellation in the world and provide a complete image of Earth once per day. The constellation is constantly "on" and does not require ordering or acquisition planning [132]. 4.2.2.3 Digital-Globe (DG) DG is a Maxar technologies company headquartered in Westminster, Colorado, that has five very high-resolution Earth-imaging satellites (GeoEye-1, WorldView-1, WorldView-2, WorldView-3, WorldView-4). With this fleet of agile satellites and large telescopes for Very High resolution (VHR) imagery, DG offers today the sharpest imagery worldwide (up to 30 cm GSD with WorldView-3 and WorldView-4 launched in November 2016) [20]. The constellation consists of 5 satellites distributed nonuniformly on four different SSO planes. In January 2019, Maxar reported that WorldView-4 satellite experienced a failure in its CMGs (Control Moment Gyros), preventing the satellite from collecting imagery due to the loss of an axis of stability [133]. Each satellite in the constellation has its own plane with different altitudes with a nonuniform phasing crossing the Equator. WorldView-Legion is DG's next generation of EO satellites that consists of six satellites planned to be launched in 2021 into a mix of SSO and mid-latitude orbits. These satellites will replace imaging  63 capability currently provided by WorldView-1, WorldView-2, and GeoEye-1. The initial constellation is to be orbited with two satellites going to SSOs and four to 45° orbits [134]. Unlike PS constellation that can provide a complete image of Earth once per day, DG constellation can capture the earth’s landmass in 60 days. However, DG is the only commercial company with a 30-centimeter product on the market to extract detailed information from phenomena that the smaller satellites can image only provide low-resolution images. 4.2.3 Weather and Scientific Constellations  4.2.3.1 FORMOSAT-3/COSMIC FORMOSAT-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) is a joint mission of Taiwan and U.S. The mission consists of six identical LEO satellites. The constellation was launched on April 15, 2006, into the same orbit plane of a designated circular parking orbit, at an altitude of 516 km. This was being followed by a 13-months constellation deployment/distribution sequence until the distribution of six orbit planes was achieved. Currently, each satellite has its own plane non-uniformly distributed around the Equator (orbits are phased ~30o apart in ascending node and 52.5o apart in Argument of Latitude) at ~793 km altitude and 72o inclination [135]. Until the launch of FormoSat-3/COSMIC, there had been little GPS radio occultation (GPS-RO) data, which is a remote sensing technique that relies on the change detection of GPS radio signals as it passes through Earth’s atmosphere for measuring its physical properties and performing weather forecasting and monitoring climate change. The major source had been the German CHAMP satellite (launch July 15, 2000), which has delivered 150-200 profiles per day globally. COSMIC’s six satellites have generated a total of more than 2,500 RO data per day. The retrieved RO data have been assimilated  64 into numerical weather prediction models by many major weather forecast centers and research institutes [135]. NOAA and Taiwan’s National Space Organization (NSPO) intend to jointly develop and launch COSMIC-2, a high-reliability next generation follow-on system. FormoSat-7/COSMIC-2 will provide the next generation of global navigation satellite system GNSS-RO data to users. This constellation is expected to be a much-improved constellation system consisting of 12 satellites, 6 satellites at 72o inclination, and 6 satellites at 24o inclination (currently operational), which will enhance observations in the equatorial region over what is currently being collected with the COSMIC mission. This constellation configuration was chosen because it provides the most uniform global coverage to collect a large amount of atmospheric and ionospheric data. This constellation will produce more than 8,000 soundings per day, compared to the approximate 2,500 soundings per day currently produced by COSMIC due to COSMIC-2’s ability to track three navigation systems’ signals versus COSMIC’s ability to track one [136]. 4.2.3.2 NASA’s CYGNSS Cyclone Global Navigation Satellite System (CYGNSS) is a constellation of eight microsatellites launched into low inclination LEO over the tropics on December 15, 2016, non-uniform distributed on a circular inclined orbit at altitude 450 km. The 34o orbit inclination was selected to maximize the dwell time over latitudes at which hurricanes are most likely to occur. This configuration will make frequent measurements of ocean surface winds in the tropics, with a primary objective of monitoring the location, intensity, size, and development of tropical cyclones. Successive spacecraft in the constellation observed Enawo over a period of several hours just before it made landfall on Madagascar on March 6, 2017 [137].   65 4.2.3.3 CICERO Community Initiative for Continuing Earth Radio Occultation (CICERO) constellation is developed by GeoOptics Inc. of Pasadena, CA. The precise number of satellites (~26 of 6U CubeSats in total) and the timeline for their deployment will depend on customer demands. The first four operational RO satellites are currently on four different SSOs at altitudes 493 and 497 km. The next phase will compromise of 10 satellites and occupy circular orbits at 500-700 km at inclinations above 65°. These cells are collecting GPS and Glonass RO profiles to return 500 - 1,000 profiles per day. Later launches will introduce cells at lower inclinations to densify coverage of the mid-latitudes and tropics. They will add Galileo and BeiDou tracks, doubling the per-cell data return. The constellation orbital parameters are optimized to maximize the number and the distribution of atmospheric soundings that maximize global distribution of occultation events [138]. In summary, there are many different configurations RSSCs because there are many factors driving the orbital parameters, number of satellites, the number of planes and their distribution. The design of general-purpose RCSC that serves a range of RSSCs is complicated by the many different RSSCs configurations that have been deployed to date and the effort required to test the performance of a candidate RCSC against each one. Accordingly, we have sought to determine whether a pattern in RSSCs exist that would allow us to represent the greater population by a much smaller set of representative classes.   66 4.3 Methodology 4.3.1 Data Sources We performed a statistical analysis of the data sets of the Weather & Earth Resources Satellites groups provided from CelesTrak for the remote sensing satellites in LEO. This analysis is based on the TLEs data available mainly from the CelesTrak website with the help of the data available from the Space Track website [139]. We grouped these satellites into constellations using different sources 1) analysis of the orbital elements data extracted from TLE data sets 2) orbit visualization of these data sets using AGI’s STK standard object database and Cesium, which available on CelesTrak website 3) literature survey of the remote sensing constellation missions. The TLE data for CelesTrak comes from Space Track, although on CelesTrak, they perform a variety of additional checks and provide supplemental TLEs that Space Track does not. In general, CelesTrak is easier to use (e.g., not need to register and log in) and does not place restrictions on the use of the data. Additionally, they provide an improved Satellite Catalog (SATCAT), which includes data not included on Space Track, such as operational status, Radar Cross Section (RCS) values (up until recent years), along with more timely and accurate identifications of new launches. Moreover, they provide groups of satellites for common purposes, like the Earth Resources list, which contains TLE data for a large group of operational remote sensing satellites, weather, disaster monitoring, and the Planet and Spire constellations (due to their sizes), none of which is on Space Track. 4.3.2 Statistical Analysis Reductions We collected the TLE files of all remote sensing satellites provided from CelesTrak groups that are currently operational. Using MATLAB, we convert the data string of NORAD TLEs of these groups  67 into a data structure in order to get all the data provided in TLEs for each satellite. We focus to get these information data from TLEs: 1. Keplerian orbital elements (Semi-major axis (a) from satellite mean motion, inclination (i), eccentricity (e), Right Ascension of Ascending Node (RAAN), Argument of Perigee (ω), Mean Anomaly) 2. Object ID (satellite name) 3. Launch Year (a part of the international designator) 4. Launch Number Statistical analysis of the remote sensing satellites in each group gives us some general and commonly known information about the remote sensing satellites, e.g., most of the satellites are on circular or near-circular orbits and the majority of these satellites are on high inclinations, definitely, SSOs. Since this information does not reveal anything about the constellation configurations, grouping satellites into constellations is required for the statistical analysis of the RSSCs. In order to group these satellites, we have to know which ones are in which constellation. In many cases, we use the satellite’s name (e.g., FLOCK or LEMUR) to tell which constellation they are in, but that’s not always the case. Therefore, we have to do a survey on each constellation mission to confirm that all these satellites are in one constellation mission and add the missing satellites that have different names while they already belong to the same constellation. For example, the GeoEye-1 satellite belongs to the DG satellite constellation while the other 4 satellites are WorldView 1 – 4. We also analyzed the launch year and launch number in the year of all of these satellites as a way to know whether the satellites are in the same plane or not. For example, all 5 RapidEye satellites have the same launch number, 40, in the same year, 2008. So, all of them should be on the same plane. However, we find that while it is typical to maintain all satellites from a particular launch in the same orbital plane, but again that is not always the case.  68 The best way to test whether satellites are in the same plane is to calculate the RAAN from the TLE orbital data. As an example, the data from Disaster Monitoring Constellation (DMC) satellites indicate that RAAN values of DMC3-FM1, DMC3-FM2, and DMC3-FM3 are slightly different while the three satellites are in the same orbit (almost the same altitude and inclination), refer to Table 4-1. In such cases, we use the AGI STK standard object database to visualize these satellites to confirm the data we have. Figure 4-1 shows the three DMC3 satellites which are almost in virtually the same plane, but not exactly the same. Here, where FM1, FM2, and FM3’s orbits are in red, white, and green, respectively. The RAAN is quite close for FM1 and FM2, but off a bit for FM3, which are in accordance with values in Table 4-1.  Figure 4-1 – Visualization of DMC3 satellite constellation using STK and its Standard Object database. Table 4-1 – DMC3 satellite data from TLEs. Satellite name Launch year Launch number a (km) e (deg) mean altitude (km) i (deg) RAAN (deg) DMC3-FM1 2015 32 7025.9117 0.0015855 647.771727 98.0089 26.3471 DMC3-FM2 2015 32 7025.897 0.0012957 647.757015 98.0108 26.5179 DMC3-FM3 2015 32 7025.927 0.0016872 647.786953 98.0096 27.2491  69 After processing and analysis of the TLE data from CelesTrak, we created satellite groups of different RSSCs that are currently operational. Some other under development constellations were added from a literature survey of RSSC missions such as CICERO, Vivid-i, OptiSAR, NovaSAR, XpressSAR, MicroSAR, and ICEYE to identify the configurations of 34 RSSCs with 348 satellites, which represent the majority of the RSSCs to date and near future. We grouped the remote sensing satellites into constellations using different sources: 1) the orbital elements data extracted from TLE data sets, 2) orbit visualization of these data sets using AGI’s STK standard object database and Cesium, which is available on CelesTrak website, and 3) literature survey of the remote sensing constellation missions. Statistical analysis of the constellation parameters of these constellations is performed. In the analysis of these constellation configurations, we obtained the histograms of the total number of satellites, number of planes, average orbital altitude, average eccentricity, average inclination, and the uniformity of satellite distributions for each constellation. Then, we generated a correlation matrix between these variables to see patterns that help in classification the RSSCs. Finally, we summarized all the single instances of MEO relay constellations that have been previously proposed in the literature for servicing LEO satellites. We only excluded the constellations that have 6 planes in order to keep the system cost as low as possible. 4.4 Results and Discussion 4.4.1 Analysis of Satellites in CelesTrak Groups In this section, histograms for all of the LEO satellites in separate lists of CelesTrack including weather, Earth resources, disaster monitoring, and the Planet and Spire constellations are presented. These histograms represent the distribution of satellites’ orbital parameters, altitude, eccentricity, RAAN, and inclination. This analysis was performed based on the TLE data obtained on July 28, 2019. We analyzed  70 these satellite groups to check if there is any pattern among constellation parameters that may help in the RSSC classification. Figure 4-2 shows the distribution histograms of 10 satellites listed in the disaster monitoring group on CelesTrak. Figure 4-3 shows 162 satellites listed in the Earth resources group on CelesTrak. Orbits of these satellites are circular or near-circular. The majority of these satellites are using SSOs in the altitude range from 500 km to 800 km. Very few of these satellites are using inclined orbits such as the Chinese commercial satellites, Zhuhai-1 01 and Zhuhai-1 02, which are using 43o inclination to provide data services for areas including agriculture, land and water resources, environmental protection and transport in China [140]. Figure 4-4 represents the distribution histograms of 237 satellites listed in the Planet group on CelesTrak. This group includes all the FLOCK satellites in the SSO besides RapidEye and SKYSAT constellations. Figure 4-5 shows the distribution histograms of 84 satellites listed in the Spire group on CelesTrak. These satellites are using circular orbits with multiple different altitudes and inclinations including the ISS and near-equatorial inclinations. Figure 4-6 shows the distribution histograms of 56 weather satellites listed in both weather and NOAA groups on CelesTrak. The majority of these satellites are using high inclination (~100o), near-circular orbits, and high LEO altitude ranges from 780 km to 850 km and from 1,446 to 1,520 km. Statistical analysis of the remote sensing satellites in each group gives us some general and commonly known information about remote sensing satellites such as SSO is the most widely used orbit type and most of them are circular or near-circular orbits. Although we could not use these histograms to classify the configurations of RSSCs, they helped us to group the remote sensing satellites into constellations.   71  Figure 4-2 – Histograms of all satellites in the Disaster Monitoring group on CelesTrak.  Figure 4-3 – Histograms of all satellites in the Earth resources group on CelesTrak.   72  Figure 4-4 – Histograms of all satellites in the Planet group on CelesTrak.  Figure 4-5 – Histograms of all satellites in the Spire group on CelesTrak.  73  Figure 4-6 – Histograms of all satellites in the Weather and NOAA groups on CelesTrak. 4.4.2 Analysis of Satellite Constellation Groups A comprehensive survey of the constellation configurations for RSSC missions, currently operational and under-development, are provided. This survey is based on the analysis of the orbital parameters provided in the NORAD TLEs with the help of two other methods for the sake of verifications, interactive visualization provided by the CelesTrak website, and STK standard object database. From the literature survey of these constellation missions, we classified these constellations into four groups based on sensor type. Table 4-2 summarizes the weather monitoring constellations. Table 4-3 summarizes RSSCs that are using optical sensors. Table 4-4 summarizes RSSCs that are using SAR sensors and Table 4-5 for satellite constellations that have both optical and SAR sensors. These tables summarize the information on the constellation configuration, their operational status, and the available  74 locations of Payload Ground Segment (PGS), which is responsible for the management and receiving the payload data of the constellation satellites. The constellation parameters of the constellation groups are collected from Tables 2 to 5. Figure 4-7 shows the histograms of these parameters i.e., the total number of satellites, the number of planes, the average orbital altitude, average eccentricity, average inclination, and the uniformity of satellite distributions in each constellation. Note that the uniformity distribution in this figure, 1 indicates uniformity of the satellites’ distribution in a constellation while 0 refers to non-uniformity distribution. From these histograms, we obtained the major RSSC parameters and their range of values as:  1. The number of planes: from 1 to 6 planes. 2. The total number of satellites: from 4 to 20 satellites. 3. Orbital altitude: from 400 km to 800 km. 4. Inclinations: from 97o to 100o (based on SSO altitude), ISS inclination (~51o), mid-inclinations such as (34o and 45o), and finally 70o. The correlation coefficients between each pair of the parameters shown in Figure 4-7 is presented in Figure 4-8 in order to find out any patterns among these parameters that help in RSSC classification. It is concluded that these variables are almost independent. The reason is that for each RSSC mission, the objectives and constraints are the main drivers in constellation design process and every constellation mission has its specific objectives and constraints and there is no straightforward approach for selecting their constellation parameters. From these combinations of observations, we propose a heuristic classification of the RSSCs. This classification introduces a nine-class solution based upon orbital inclination including SSO, inclined  75 orbit and hybrid and the number of planes and different altitudes including same plane-same altitude, different plane-same altitude and different planes-different altitude although only seven of these classes are populated by actual RSSCs. Table 4-6 summarizes these solutions given representative constellation missions for each class.  Figure 4-7 – Distribution histograms of RSSCs groups.  76 Table 4-2 – Weather monitoring constellations. Mission # Sats # Orbits & type Constellation configuration comments Operational status PGS FormoSat-3/ COSMIC (FS-3/C) 6 6 circular inclined 6 non-uniform distributed orbit planes. All satellites have the same altitude 793 km and inclination 72o 2006 Operational ground station network (4 GSs) FormoSat-7 / COSMIC-2 (FS-7/C2)   12 12 near-circular inclined orbits Two sets of six satellites. An initial, known as COSMIC-2A, operating in low-inclination orbits 24º inclination and altitude of ~ 520-550 km. The second set is known as COSMIC-2B that would operate in highly inclined orbits (72o) and altitude of ~ 720 km for replacement of the original FormoSat-3/COSMIC constellation, launched into in 2006. Under development Planned 8 equatorial ground stations Lemur Nanosatellite Constellation of Spire Global  57  SSO, ISS, and various circular inclined orbits Non-uniform distribution. Using many CubeSats at many different orbits for reducing the revisit time. Operational Distributed GSs in China NASA’s CYGNSS (Cyclone Global Navigation Satellite System) 8 Circular inclined single plane. Non-uniform satellite distribution. Satellites have the same altitude (520 km) and the same inclination (35o) but crossing the equator at different RAAN. Operational -- CICERO By GeoOptics   26  SSO and mixture of inclined orbits Non-uniform distribution. The precise number of satellites and the timeline for their deployment will depend on customer demands. The first two operational RO satellites are currently on two different SSOs at altitudes 493 and 497 km. The first 14 CICERO satellites will occupy circular orbits at 500-700 km at inclinations above 65°. Later launches will introduce cells at lower inclinations to densify coverage of the mid-latitudes and tropics.  Under development over the following three years 2 satellites only are operational  Proposed a worldwide license for universal data access NOAA 20 20 Polar orbits. Each satellite has its own orbit Operational Svalbard NASA TROPICS [141] 6 3 inclined orbits Six 6.0 kg 3U CubeSats spread across three 550 km altitude, 30o inclination orbital planes Launch readiness is projected for late 2019 --      77 Table 4-3 – Optical constellations. Mission # Sats # Orbits & type Constellation configuration comments Operational status PGS RapidEye 5 1  & SSO Uniformly distributed on a single SSO at the same altitude (627.3 km) and same inclination ( 97.8o) 2008 Operational Svalbard 78o N Norway DMC 8 6  & SSO Non-uniform distributed. BEIJING 1 is the remaining satellite of 5, which formed the DMC first generation (DMC-1) at altitude 687 km and inclination 97.9o. Second-generation (DMC-2) in orbit since mid-2009. Deimos-1 and UK-DMC-2 are on different SSOs at the same altitude 655 km and the same inclination 97.8o. Nigeria-2 and NigeriaSat-X were launched in 2011 into orbits with slight differences in altitude & inclination. Three third-generation satellites, (DMC3-FM1, FM2, and FM3) are uniformly distributed in the same orbit 120° apart at altitude 648 km and inclination 98o.   8 Operational out of 12 launched satellites  (2005-2015)  Ground Station Network Flock 1C 11 1  & SSO Non-uniform distributed on the same orbit (597 km altitude and 97.9o inclination with slight differences in RAAN) Only 5 are operational Planet Lab Inc. ground station network   Flock 3P 88 1  & SSO Nearly uniform distributed. Same altitude (489.7 km) and same inclination (97.45o). Operational Since 2017 Flock 3M 4 1  & SSO Non-uniform distributed. Same altitude (506 km) and same inclination (97.35o). Operational Since 2017 Flock 3P' 4 1  & SSO Non-uniform distributed. Same altitude (496.2 km) and same inclination (97.53o). Operational Since 2018 Flock 2K 47 1  & SSO Nearly uniform distributed. Same altitude (454.25 km) and same inclination (96.98o). Operational Since 2017 Flock 2e 12 1 & ISS Non-uniform distributed. Same altitude (318 km) and same inclination (51.6o).  Decayed Flock 2e' 20 1  & ISS Non-uniform distributed. Same altitude (318 km) and same inclination (51.6o). Decayed Flock 2P 12 1  & SSO Non-uniform distributed. Same altitude (489.8 km) and same inclination (97.4o). Operational Since 2016 Flock 3R 15 1 & SSO Non-uniform distributed. Same altitude (482 km) and same inclination (97.48o). Operational Since 2018 SkySat TerraBella 13 4  & SSO Non-uniform distributed. Skysat-1 on a single orbit at altitude 568.2 km and 97.7o inclination. Skysat-2 on a single orbit at altitude 626 km and 98.4o inclination. SkySat-C series is 11 satellites distributed in two planes. From Skysat-C1 to Skysat-C5 were launched in 2016 and distributed equally on a single SSO at altitude 494 km and 97.35o inclination. From Skysat-C6 to Skysat-C11 were launched in 2017 and distributed equally on another SSO at altitude 498 km and inclination 97.4o. Operational (2013-2017)  -- Digital-Globe 5 4  & SSO Non-uniform distributed. 3 satellites each on a separate plane, GEOEye1 (678.5 km altitude), WorldView-1 (489 km altitude), and WorldView-2 (766 km altitude). WorldView-3 and WorldView-4 are equally distributed on a single plane with a slight difference in altitude (611.5 km altitude) between them due to altitude decay of WV-3. 2008-2016 Operational 8 Remote Ground Terminals Vivid-i 15 3 & SSO The planned Vivid-i constellation will be launched in batches of five. The first five satellites will be launched in 2019 into SSO of 500 km altitude. CARBONITE-2 was launched in 2018 for a technology demonstration of this constellation at on SSO altitude 505 km. Announced in May 2017 Under development Appointed to be Norway's KSAT   78 Table 4-4 – SAR constellations. Mission # Sats # Orbits & type Constellation configuration comments Operational status PGS COSMO-SkyMed 4 1 & SSO Dawn-Dusk X-band SAR Systems. Uniform distributed on a single SSO at altitude 620 km and inclination 97.9o. During nominal operation, all satellites operate on the same orbital plane with 90 deg equal-spaced. During Tandem interferometric configuration, they are working in different two orbital planes. 2007-2010 Operational Multi-center architecture geographically distributed over a wide territory. 3 GSs in Italy, one in Sweden, and one in Spain COSMO-SkyMed (Second Generation –CSG) 2 1 & SSO Dawn-Dusk X-band SAR Systems. Same orbit as COSMO-SkyMed. Two satellites that will integrate and finally replace the current operational COSMO-SkyMed satellites will compose CSG. CSG-1 will be launched in 2018. CSG-2 a year later RADARSAT (RCM) 3 1 & SSO Dawn-Dusk C-band SAR Systems. Equally spaced 3 satellites around the orbit plane at altitude 592.7 km and inclination 97.74o (with a potential to increase the number to six). Launched in June 2019 Gatineau, Prince Albert, Inuvik and one foreign station in Svalbard SAR-Lupe 5 5 X-band SAR Systems for the German military to achieve Ground Sampling Distance < 1m. Non-uniform distribution. Each satellite in a single orbit (apogees at 505 km and perigees at 468 km) at inclination 98.2º. 2006-2008 Operational Single Ground Station in Gelsdorf NovaSAR  4 SSO or low inclination Equatorial orbit S-band SAR Systems. Non-uniform distributed. Altitude 580 km and designed for multiple orbits: SSO (LTAN 10:30) or a dawn-dusk orbit (LTAN 6:00) and an Equatorial orbit at a minimum 15o inclination. Planned to launch in 2018 Astrium network  XpressSAR  4 2 inclined orbits X-band radar systems. 4 satellites in two orbit planes with a 35° inclination at altitude 425 km. Planned to launch in 2020 Miami, Florida MicroSAR System  10  2 inclined orbits (TBD) C-Band radar transmitter and onboard AIS receiver at 500 km orbital altitude. Deployed in 2019 Svalbard (Norway) ICEYE 18 6 SSOs X-band radar systems. 70 kg ICEYE-X1 satellite was launched in January 2018 to SSO at altitude 500 km - the first of multiple spacecraft that will go up in the coming years. 9 satellites will be launched by the end of 2019 TBD      79 Table 4-5 – Hybrid-sensors (Optical and SAR) constellations. Mission # Sats # Orbits & type Constellation configuration comments Operational status PGS KOMPSAT (Earth-i) 4 3 SSOs 4 satellites each in a single orbit. 2 Optical satellites in the same plane but in different altitudes KOMPSAT 2 at and KOMPSAT 3. An optical one on a single plane, SSO at altitude 528 km (KOMPSAT 3A). The fourth KOMPSAT 5 on SSO dawn-dusk at altitude 550 km. Operational Korea Aerospace Research Institute (KARI) Ground Station Copernicus program (Sentinels) 7 4 SSOs  Non-uniform distribution although every two identical pairs is equally spaced in the same orbit. SENTINEL-1A and 1B are identical SAR satellites on the same SSO orbit equally spaced at altitude 695 km and inclination 98.18o. SENTINEL-2A and 2B are identical high-resolution optical satellites on the same SSO orbit equally spaced at altitude 789.8 km and inclination 98.56o. SENTINEL-3A and 3B same SSO orbit plane at inclination 98.62o but at slightly different altitudes, 804 km and 814 respectively. They have two types of payloads (optical payload, topographic payload) to provide data for services relevant to the ocean and land. SENTINEL-5P on a single SSO at inclination 98.73o. Operational GEO relay by optical communication Airbus Defence and Space Constellation  7 3 SSOs Non-uniform distribution. 3 SAR satellites and 4 optical.  TANDEM-X and TERRASAR-X fly in formation just a few hundred meters apart and are joined by PAZ satellite in 2018. These SAR satellites non-uniformly distributed in the same dawn-dusk SSO at 505 km altitude.  PLEIADES 1A and PLEIADES 1B are uniformly distributed in the same SSO at 694 km altitude. SPOT 6 and 7 are uniformly distributed on a single SSO at altitude 694 km. The four optical satellites are virtually 90° apart. 2007-2014 Operational Astrium network  Nearly 40 Direct Receiving Stations (DRS) OptiSAR 16 2 orbits, SSO and MIO The constellation is formed of 8 optical satellites and 8 SAR satellites at an altitude 450 km split across two orbital planes: SSO and Mid-Inclination Orbit (MIO) at inclination 45o. The satellites are equally distributed in each plane, with SAR satellite flying one to two minutes ahead of an optical satellite, which equipped with a high-resolution multispectral sensor. Under development ---   80  Figure 4-8 – Correlation matrix of the constellation group parameters. Table 4-6 – Representative classes of RSSCs.            Inclination # of planes and altitude Sun Synchronous Orbit (SSO) Inclined orbit Hybrid Same plane Same altitude Class # 1  RapidEye, RADARSAT, COSMO-SkyMed (1st & 2nd generations), and Dove satellites (Flock-1C, Flock-3P, Flock-3M, Flock-3P', Flock-2K, Flock-2P, Flock-3R) Class # 2  Flock 2e (51.6o), Flock 2e' (51.6o), and NASA’s CYGNSS (35o)   --- Different planes Same altitude Class # 3  Vivid-I, SAR-Lupe, and ICEYE Class # 4  XpressSAR, MicroSAR, and FormoSat-3 Class # 5  OptiSAR and NovaSAR Different planes Different altitude Class # 6  Disaster Monitoring Constellation (DMC), SkySat constellation, Digital-Globe, KOMPSAT, Copernicus (Sentinels), and Airbus --- Class # 7  Lemur-2 Constellation of Spire Global, FormoSat-7, and CICERO   81 4.4.3 Previously Proposed RCSCs in MEO Based on the literature survey, we summarized the single instances of MEO relay constellations that have been previously proposed for servicing LEO satellites as shown in Table 4-7. Relay constellations could be on either a single plane or multiple planes. We exclude the constellations that have 6 satellites in 6 planes because of keeping the cost low as much as we can is the main driver in space mission implementations. Then, we propose the major possible configurations of relay constellations as summarized in Table 4-8. In this table, we defined the known parameters in each configuration under study. These configurations help us to define the input design parameters of MEO relay constellations that will be used in our next simulation-based studies. Figures 4-9 and 4-10 represent the 3D graphics of these relays using STK. Table 4-7 – Previously proposed single instances of MEO RCSCs.  Table 4-8 – Major RCSCs in MEO.   Configuration  Equatorial [50] Polar and Equatorial [56] Polar [50] Walker-Delta (f = 0) [2] Walker-Delta (f= 4) [50] Common track [49] # of planes 1 2 2 3 6 6 # Sats/plane 6 3 3 2 1 1 Total # of Sats 6 6 6 6 6 6 Orbital alt. (km) 13892 10354 13892 14622 13892 13892 Orbital inc. (deg) 0 0 & 90 90 45 53.1 55 Relay type Single Plane Multiple Planes Configuration Equatorial Polar Polar and Equatorial Walker-Star Walker-Delta Walker-Delta Relay number Relay#1 Relay#2 Relay#3 Relay#4 Relay#5 Relay#6 # of planes 1 1 2 2 2 3 Orbital inc. (deg) 0 90 0 & 90 90 45 45  82  Figure 4-9 – Relay #1 (red), Relay #2 (white), and Relay #6 (yellow).  Figure 4-10 – Relays that use 2 planes. Relay #3 (blue green), Relay #4 (green), and Relay #5 (white).  83 4.5 Summary In recent years, heterogeneous satellite constellations that use ISLs between two different functional constellations, a RSSC dedicated to EOs and a RCSC dedicated to command delivery and relay data back to Earth, have attracted considerable interest. The design of general-purpose RCSCs that serve a range of RSSCs is complicated by the many different RSSCs that have been deployed to date and the effort required to test the performance of a candidate RCSC against each one. Multiple candidate configurations of RCSCs may be appropriate for servicing the same RSSC given the coverage requirements of its configuration. Consequently, to find out the optimum configuration of a heterogeneous constellation, it is necessary to study several constellation combinations. Previous progress in this area has been hampered because of the large size of the solution space. This necessitates a classification for the RSSCs configurations to reduce the solution space. Previous work in this field has focused on categorizing the remote sensing satellites based on their mission application or sensor type. However, they did not introduce a classification to the configurations of RSSCs. Accordingly, we have sought to determine whether a pattern in RSSCs exists that would allow us to represent the greater population by a much smaller set of representative classes. Based on a statistical analysis of NORAD TLEs for 34 RSSCs and a thorough review of their missions, we propose a nine-class solution based upon orbital inclination (three categories) and a number of planes and different altitudes (three categories) although only seven of these classes are populated by actual RSSCs. The actual number of planes, orbital altitudes, and orbital inclinations are represented by simple distributions. Moreover, we obtained the major RSSC parameters and their range of values where a combination of these parameters can be used for forming representative configurations of RSSCs. The results allow the performance of RCSCs to be tested against a broad and representative set  84 of RSSCs with far less effort than testing against an exhaustive set and far more confidently than against a random set. Finally, this chapter has presented two major outcomes: 1. Identification of nine-class representative configurations, which are useful when conducting any related simulation-based studies. 2. Presentation of the major RSSC parameters and their range of values where a combination of these parameters can be used for forming representative configurations of RSSCs.  85 Chapter 5: SRT Calculations for EO Satellites Supported by Various Relay Network Configurations  5.1 Introduction One of the key components of the framework for heterogeneous satellite constellations design is the assessment of SRT for EO satellite constellations when supported by relay communication satellite constellation (RCSC) considering various network configurations. The revisit time (RT) of a satellite is the time elapsed between two successive observations of the same ground point on Earth [142]. SRT is the key metric in assessing the timeliness of EO imagery. In practice, SRT is a more important performance parameter than RT for disaster monitoring missions. Where the objectives are dictated by user requests, the time it takes for the final distribution of the data to the end-user (SRT) has much more impact on overall mission performance rather than the time interval between target revisits (revisit time) [143]. In heterogeneous satellite constellations, calculation of the SRT can be quite complex because it considers several important factors such as: 1. The readiness of the imaging satellite and imaging readiness time. 2. Relay constellation configuration and its orbital parameters. 3. Communication capabilities of the relay satellites based on the existing type of ISLs. 4. Communication technology used by the relay satellites. 5. Number and location of the receiving/transmitting ground stations. SRT calculations are very important in the preliminary mission design and analysis phase for such heterogeneous space systems considering various relay network configurations. Systems Tool Kit (STK) software, the most widely used software for aerospace mission design, does not have the option for SRT calculations for RSSC when relay satellites are involved in the scheme and ISLs between the relay satellites are introduced and become more sophisticated. The existing literature discusses  86 solutions for SRT calculations using scheduling algorithms by allocating tasks to each satellite in a mission for the goal of effectively utilizing the satellite's resource and minimizing SRT. However, these solutions can only be found for isolated instances of imaging constellations and relay satellites, which are not applicable for different configurations of heterogeneous satellite constellations.  A simple heuristic method used for SRT calculation is introduced in [2], based on a weighted assignment of the priorities to the possible scheduled operations, the method that has been previously proposed for optimization in [33]. Numerical simulations without scheduling optimization method have been performed for a SAR satellite constellation in LEO serviced by a small-satellite constellation in different geometrical configurations and altitudes. The goal of this paper was not to find the optimal configuration of this scheme but to explore its potential performance enhancement of remote sensing constellation. Only one level of ISL routing has been considered between layers (a telecommand can be bridged only by one relay from a GS to an imaging satellite). However, a promising improvement of 2 hours in terms of SRT was found by using relay constellations composed by 6 satellites distributed on 3 LEO or MEO planes. It is depicting potential for future analysis to evaluate the advantages afforded by the relay satellites when exploited in their full capabilities in communication with imaging satellites. With the rapidly growing demand for environmental monitoring and disaster warning, the satellite data transmission-scheduling problem has attracted a great deal of attention. An integrated solution to the obtained data and download scheduling problem of rapid-response Earth-imaging satellites has been proposed in [34]. The proposed algorithm in this work simulates 10 single satellites with different resolutions and randomly generated ground targets and GSs. Then, a sample of data sets was picked up from both the observation and downlink windows to compute the SRT. They also analyze the improvement of the data transmission delay time to the GS when using a single TDRSS satellite. The  87 results in that paper verified that the effect of TDRSS satellites for improving the time of data transmission is extraordinary. An optimization algorithm was developed in [35] to minimize the SRT with a different definition for the EO satellite constellations. The definition of SRT was based on selected types of the operational modes of the proposed SAR satellites. They define SRT as the time it takes from the stripmap mode to repeatedly scan the Area of Interest (AoI) and identify any abnormal activities to the final high-resolution data generation resulting from the spotlight mode scanning of the point target identified from the strip-map mode. Moreover, relay satellites are not involved in this work. One of the most fundamental considerations in the design of a space backbone network is the physical topology of the backbone satellite constellation [144]. The primary goal of a backbone constellation, i.e., the relay constellation, is to provide the coverage as required by the users, the imaging satellites. These coverage requirements depend on the network topology of the relay satellite constellation, which is defined by the relay constellation configuration and parameters, communication technology used by the relay satellites, and their capabilities based on the existing type of ISLs [2]. Previous works of this scheme focused on using Geostationary Earth Orbit (GEO) communication satellites for tracking and data relay since the mid-1970s [37], [38], [40], [42], [43], [145] and recently have focused on data relay satellite networks using non-GEO systems, namely LEO and MEO systems. Based on current literature, few papers have discussed using RCSCs in LEO [2], [44], [45], [47], [48] or in MEO [49]–[51], [55], [56]. In these works, only single instances of RCSCs have been proposed and simulated. Moreover, the connectivity analysis between relay satellites has not been introduced in order to assess the availability of persistent inter-relay ISLs in the RCSC. Persistent ISLs between relay satellites in the non-GEO RCSCs helps to improve SRT of the EO satellite constellations where a contact opportunity between the EO satellite and a relay satellite is valid  88 if the relay satellite is in view to either a ground station (GS) or another relay satellite that can redirect the information to and from the GS [2]. Consequently, connectivity analysis between relay satellites is very important in the preliminary mission design and analysis phase to assess the availability of persistent inter-relay ISLs in the non-GEO RCSCs for a careful selection of the RCSC configuration and its orbital parameters. Walker type satellite constellation in its two patterns, delta, and star  [146], has been frequently proposed as RCSCs. The coverage properties of four different MEO RCSCs, Walker delta in 6 planes, Walker star in 2 planes, Equatorial, and common-track in 6 planes, were compared in [50]. These constellations have the same altitude and the total number of satellites (6 satellites). The constellation parameters of Walker delta and Walker star are taken from [7] and [147], respectively, with the only change in altitude for the sake of fair comparison (13, 892 km). Simulation results indicated that the Walker delta and common-track constellations are suitable for the implementation of MEO RCSCs, which is intuitively obvious because their satellites are uniformly distributed on six orbital planes. A Walker delta constellation composed of 6 satellites distributed on 3 orbital planes either in LEO or MEO showed data quality improvement of EO satellites in terms of the mean response time as discussed in [2]. In this paper, only one level of ISL routing was considered where a telecommand can be bridged only by one relay satellite from a GS to an EO satellite. Although Walker type satellite constellation has been frequently proposed as RCSCs in previous works, the connectivity analysis between the relay communication satellites has not been addressed. Moreover, they have not defined the Walker constellation configurations with persistent inter-relay ISLs. The objectives of this chapter are: 1) Develop an algorithm for SRT calculations for EO satellites supported by RCSCs. Three relay network configurations of the RCSCs are investigated based on the relay satellites' capabilities,  89 the existence of ISLs between relay satellites, and the communication technology used to relay the data. 2) Implement this algorithm as STK add-on modules using interactive and modular MATLAB/STK toolkit to extend STK capabilities using MATLAB/STK interface. This toolkit performs SRT calculations in an automation manner much more efficiently and faster than STK-Analyzer. 3) Demonstrates the performance enhancement of SRT for EO satellite constellations supported by RCSCs and the efficiency of the algorithm by providing the execution time over a range of reasonable conditions. 4) Develop an algorithm to analyze connectivity between relay communication satellites to assess when persistent inter-relay ISLs are available. 5) Implement this algorithm using MATLAB/STK interface to design Walker relay constellations with persistent inter-relay ISLs. 6) Define the valid configurations of Walker type constellation that achieve this criterion and their orbital parameters presented in a group of design curves. In this chapter, we extend STK capabilities using MATLAB/STK interface by devising algorithms to calculate SRT for three different network configurations. The MATLAB codes, which are used for SRT computations, are very specific to our problem and enable us to count and compute all the access and gap durations between space segments and between space and ground segments in a much more effective and faster way than STK-Analyzer does. One of these configurations is a relay constellation with persistent ISLs between its satellites. The connectivity between relay satellites is analyzed in an automated manner using MATLAB/STK to assess the persistent paths between satellites. Then, we define the constellation parameters that can achieve 100% link availability using the minimum number of satellites per plane and the minimum number of planes.  90 This chapter is organized as follows: In Section 5.2, SRT and its performance-related metrics, specific RCSC network configurations, and the proposed algorithm for SRT calculations are introduced. Section 5.3 introduces the concept of relay constellation with persistent ISLs and the proposed algorithm for configuring RCSCs with persistent ISLs. Section 5.4 describes in detail the methodology of the algorithm’s implementation using MATLAB/STK interface, SRT calculation toolkit, and configuring relay constellations with persistent ISLs using MATLAB/STK add-on module. The results are presented and discussed in Section 5.5. Finally, the outcomes are summarized in Section 5.6. 5.2 SRT Calculations 5.2.1 SRT and Performance-related Metrics SRT is the interval between EO request submission and the availability of the image product. It depends mainly on the geometrical configuration of the system e.g., orbit type & parameters, access area, and distribution & locations of GSs [5]. It accounts for delays in getting data collection requests to reach the EO satellites, the EO satellite to reach the target and delays in transmitting collected data to reach the GS and a number of fixed duration delays in between, which are in orders of seconds or few minutes. An illustration of SRT is shown in Figure 2-2 and its delay time components is discussed in Section 2.1.2 [148]. Most traditional RSSCs design methods focus on minimizing the revisit time which is the gap duration in coverage access between targets over a given region [24], [149]–[151]. However, SRT calculations are still a fundamental problem due to the two dynamic delay times, command uplink delay time (T2) and data downlink delay time (T6) especially when relay satellites are involved and become more complicated. The intrinsic response time (IRT), a time component of SRT as depicted in Figure 2-2, is a coverage figure of merit (FOM) which is defined as the time from when a random request is received at the EO  91 satellite to observe a grid point k on Earth until the constellation can actually observe it [68]. IRT considers both coverage and gap statistics in the whole system’s responsiveness. Therefore, it is the best coverage FOM for evaluating the overall responsiveness of EO satellites [68]. Besides, delays in processing or communications (for both requests and responses) can be directly added to it, which results in the total SRT [68]. As shown in Figure 5-1, if at a given time t and a given access number n, the grid point k is being accessed by the constellation, i.e., 𝑡𝑠𝑘,𝑛 ≤ 𝑡 ≤ 𝑡𝑒𝑘,𝑛 then the 𝐼𝑅𝑇𝑘̅̅ ̅̅ ̅̅ (𝑡) is zero [152]. 𝑡𝑠𝑘,𝑛 and 𝑡𝑒𝑘,𝑛 are the start and end time of nth access between the point k and any satellite in the constellation, respectively. If the point k is in a coverage gap at a time 𝑡 (𝑡𝑒𝑘,𝑛 ≤ 𝑡 ≤ 𝑡𝑠𝑘,𝑛+1), then the IRT is defined until the point is accessed again or the time until the end of that gap (𝐼𝑅𝑇𝑘(𝑡) =𝑡𝑠𝑘,𝑛+1 − 𝑡). 𝐼𝑅𝑇𝑘̅̅ ̅̅ ̅̅  is computed from 𝐼𝑅𝑇𝑘̅̅ ̅̅ ̅̅ =1𝑇∫ 𝐼𝑅𝑇𝑘 (𝑡)𝑑𝑡 =  ∑ 𝑡𝑔𝑘,𝑛2𝑛2𝑇𝑠𝑖𝑚     ,                                          (5.1) where 𝑇𝑠𝑖𝑚 is the total simulation time and the term 𝑡𝑔𝑛,𝑘2  comes from the integration of 𝐼𝑅𝑇𝑘(𝑡), refer to Figure 5-1 [152].  Figure 5-1 – Top: Example of gaps and accesses intervals of a particular point on the Earth grid. Bottom: Example of the correspondent mean response time.  92 The dynamic value of SRT can be equal to IRT, only if all delay components are set to zero, which is almost predicted in case of using an ideal RCSC. This can be achieved by using a RCSC with persistent ISLs between each satellite in order to achieve 100% link availability in the constellation network. Moreover, this RCSC must provide continuous coverage to both the EO satellites and the transmitting/receiving GS. This data relay network is very important to enable near-immediate tasking for taking images of the Earth at any time from the EO satellites. In this case, a contact opportunity between EO and relay satellites is valid if the relay satellite is in view of either a GS or another relay that can redirect the information to and from the GS. The time average gap (TAG) is an important evaluation FOM of the coverage effectiveness that is used in SRT calculations. It is defined as the mean gap duration averaged over time. Alternatively, it is the average length of the gap we would find if we randomly sampled the grid points. It is constructed as a weighted average of the existing gap durations where the weight for each gap is defined as the likelihood that you will select a time within that gap. The static value of TAG can be calculated from 𝑇𝐴𝐺 =∑ (𝑡𝑖𝑛𝑖+1−𝑡𝑜𝑢𝑡𝑖 )2+(𝑡𝑖𝑛1 −𝑡𝑏𝑒𝑔𝑖𝑛)2+(𝑡𝑒𝑛𝑑−𝑡𝑜𝑢𝑡𝑛 )2𝑛−1𝑖=1(𝑡𝑒𝑛𝑑−𝑡𝑏𝑒𝑔𝑖𝑛)          ,                          (5.2)  as represented in Figure 5-2 [153].  Figure 5-2 – Access time intervals between system objects over time.   93 Finally, 𝑆𝑅𝑇̅̅ ̅̅ ̅ of an EO satellite constellation is given by 𝑆𝑅𝑇̅̅ ̅̅ ?̅? = 𝑇𝐴𝐺̅̅ ̅̅ ̅̅ 𝑝 +  𝐼𝑅𝑇̅̅ ̅̅ ̅ + 𝑇𝐴𝐺̅̅ ̅̅ ̅̅ 𝑝      ,                                               (5.3) where p = 1, 2, and 3 refers to the RCSC network configuration. SRT values are different because of TAG values are different in each type of constellation network configurations as discussed later in Section 5.2.3. 5.2.2 Relay Network Configurations Determination of the various relay network configurations is based on the communication technology used by the relay satellites and the existing type of ISLs between satellites. The communication technology used by the relay satellites could be either bent pipe or store-and-forward. The bent pipe system relays messages directly between one host to another without any onboard processing, while the store-and-forward approach means that a satellite receives data from a GS or an imaging satellite, stores it in onboard memory, continues on its orbit, and releases the information to the next appropriate destination, another intermediate station or a satellite [154]. On the other hand, in multiple-layer satellite networks, there are 3 different types of ISLs [48], [50]: 1) Intra-Orbit ISLs (Intra-OISLs), which are the links between satellites in the same orbit and in the same layer. 2) Inter-Orbit ISLs (Inter-OISLs), which are the links connecting satellites in adjacent orbits in the same layer and it can be also called Intra-Layer ISLs (Intra-LISLs). 3) Inter-Layer ISLs (Inter-LISLs), which are connecting satellites in orbits at different layers. Based on these types of ISLs, the relay satellites can have one of the following capabilities in serving the LEO satellite [2]:  94 1) Command delivery from a GS to an imaging satellite. 2) Data collection and storage from an imaging satellite and download to a GS. 3) Command delivery from another relay to an imaging satellite. 4) Data collection and storage from another relay and download to a GS. 5) A feasible combination of 1, 2, 3 and 4. Based on the communication technology used by the relay satellites and the existing type of ISLs, we have identified the possible network configurations of RCSC as depicted in Figure 5-3. Table 5-1 summarizes the pros and cons of the following four configurations: 1) The relay satellites use bent-pipe technology and neither Intra-OISLs nor Inter-OISLs exists between them: A contact opportunity between the imaging satellite and a relay satellite is valid only if that relay satellite is in view and connected to a GS. 2) The relay satellites use store-and-forward technology and neither Intra-OISLs nor Inter-OISLs exists between them: A relay satellite can collect and store data from a GS and relay it to the imaging satellite besides data collection and storage from an imaging satellite and download it to a GS. 3) The relay satellites use bent-pipe technology and have persistent Inter-OISLs between them. A contact opportunity between the imaging satellite and a relay satellite is valid only if that relay satellite is in view to either a GS or another relay that can redirect the information to and from the GS. Due to the relay constellation configuration, the satellites can achieve persistent links between each other. 4) The relay satellites use store-and-forward technology and have persistent Inter-OISLs between them. But, due to the constellation configuration and parameters, relay satellites cannot see each other continuously. No value is added from the study of this topology regarding constellation configurations with persistent ISLs, thus this topology is out of our scope.  95  Figure 5-3 – Various network configurations of relay satellite constellations.  Table 5-1 – Pros and Cons of various network configurations under study. Network Topology Pros Cons (1) Bent pipe without inter-relay Inter-OISLs - Small satellites can be used (e.g., CubeSats) - Simple architecture - No onboard signal processing - Routing carried out at the GSs - Large no. of satellites required for real-time coverage (2) Store-and-Forward without inter-relay Inter-OISLs - Onboard signal processing  - Medium satellites (500 - 1000 kg) - Routing carried out at GSs - Large no. of satellites required for real-time coverage (3) Bent pipe with persistent inter-relay Inter-OISLs - Onboard signal processing and routing - Real-time coverage - No onboard signal processing - Routing carried out at the GSs - Large no. of satellites required for real-time coverage (4) Store and Forward with intermittent inter-relay Inter-OISLs - Onboard signal processing and routing  - Larger medium satellites - Complex network architecture - No real-time coverage    96 5.2.3 SRT Calculation Algorithm Given the input parameters of the heterogeneous system and the network configuration type, the quality of coverage for an object is evaluated by choosing the process and the method for evaluating object/s coverage [73]. Table 5-2 summarizes the coverage computation process and method for different cases of the three network configurations. Although they use the same method for coverage evaluation, the process is different in each case. SRT calculations algorithm of EO satellite constellations supported by RCSCs in various relay network configurations is shown in Table 5-3. The goal of this pseudo code is to explain what exactly each line of the program should do and arrange the sequence of tasks that helps in the algorithm implementation using MATLAB/STK.  Table 5-2 – Coverage computation process and method in different relay network configurations. Network configuration Process Method Object to be covered Assets to achieve coverage (1) Bent pipe without inter-relay Inter-OISLs Each EO satellite in a constellation (a process in a loop) Chain access between GSs and RCSC TAG (2) Store-and-Forward without inter-relay Inter-OISLs GSs RCSC (All satellites) TAG Each EO satellite in the constellation (a process in a loop) Each relay satellite in the RCSC (a process in a loop) (3) Bent pipe with persistent inter-relay Inter-OISLs GSs RCSC (All satellites) TAG Each EO satellite in the constellation (a process in a loop) RCSC (All satellites)    97 Table 5-3 – Pseudo-code of the main program used for SRT calculations. SRT calculation algorithm for various relay network configurations 1 Input the total simulation analysis time (𝑇𝑠𝑖𝑚) 2 Input relay satellites constellation & orbital parameters 3 Input the receiving/transmitting GSs parameters (latitude, longitude, and height) 4 Input GS constraints e.g., elevation angle  5 Input EO satellites constellation & orbital parameters 6 Input imaging sensor type, parameters, and constraints 7 Define the area of interest and its grid points 8 Compute 𝐼𝑅𝑇̅̅ ̅̅ ̅ by grid point k using equation (5.1) 9 Pull out the individual data sets for each k 10 Choose the RCSC network configuration 11 Loop for i=1:1: number of EO satellites 12 Assign TAG as a metric for coverage evaluation 13 Assign the corresponding assets based on the relay network configuration from Table 5-2 14 Extract all gap durations from access data between objects and assets 15 Compute TAG from the equation (5.2) 16 End loop 17 Compute 𝑆𝑅𝑇̅̅ ̅̅ ?̅? from equation (5.3) 18 Display 𝑆𝑅𝑇̅̅ ̅̅ ?̅? for each grid point k 5.3 Relay Constellations with Persistent ISLs The space segment configuration of the communication architecture networks defines how the network nodes are distributed in one or more constellations around the Earth [155]. Therefore, the first step to model a space relay network is understanding the movement of satellites over a representative period of time. This information is needed so as to define the contact opportunities between them and therefore assess when a particular path between the space segments is available. In multiple-layer satellite networks, there are three different types of ISLs [48], [50]: 1. Intra-Orbit ISLs (Intra-OISLs), which are the links between satellites in the same orbit and in the same layer.  98 2. Inter-Orbit ISLs (Inter-OISLs), which are the links connecting satellites in adjacent orbits in the same layer and it can be also called Intra-Layer ISLs (Intra-LISLs). 3. Inter-Layer ISLs (Inter-LISLs), which are connecting satellites in orbits at different layers. 5.3.1 Intra Orbit ISLs The establishment of ISL between satellites is mainly affected by the azimuth angle, elevation angle and transmission distance between satellites. The smaller the ranges of azimuth angle, elevation angle and transmission distance of ISL, the better the performance of ISL [48]. Obviously, the ISL in the same orbital plane is more stable than those between adjacent orbital planes. An example of ISL geometry is given in Figure 5-4. Sat i and Sat j are defined as two satellites in the orbit I and Sat k denotes the satellite in the orbit II. R denotes the orbit radius of satellites [48].   Figure 5-4 – ISL Geometry in the constellation.  Figure 5-5 – Geometry for intra-orbit ISL.  The geometry of an intraorbit ISL is illustrated in Figure 5-5. Considering isosceles triangle ΔOSiSj, the intraorbit ISL angle α is related to the angle between two adjacent satellites, Si and Sj, and is given by [48]  99 2𝛼 = 𝜋 − (𝛽 + 𝛽′)  ,                                                                 (5.4) where (𝛽 + 𝛽′) is the angle between two adjacent satellites and is given by 𝛽 + 𝛽′ =  2𝜋𝑁𝑠𝑝   ,                                                                    (5.5) and Nsp is the number of satellites per plane. Then α becomes 𝛼 =𝜋2−𝜋𝑁𝑠𝑝  .                                                                     (5.6) To achieve the Intra-OISLs, the Line-Of-Sight (LOS) of any two adjacent satellites in the same plane must be met in the constellation neither to be obstructed by the earth nor traveled through the denser layers of the atmosphere. Therefore, according to Figure 5-6, the LOS path between any two adjacent satellites should be at least above the altitude of Rmin, which is the minimum shadowing radius of earth and is usually assumed as the earth's radius (RE) plus the atmosphere's altitude Lmin  [156]. It is assumed Lmin = 100 km, which is the Karman line that often used as the border between the atmosphere and outer space. O is the Earth center, RE is earth radius, h is the satellite orbital altitude, Dij is the intraorbital distance between two adjacent satellites and ψ = 𝛽 + 𝛽′ is the Earth central angle.  Figure 5-6 – Geometry of intra-orbit ISL with minimum shadowing radius of Earth.  100 Figure 5-7 represents how α and ψ values change as a function of Nsp These angles are independent of the orbital altitude. When ψ =180o, there is no link between the two satellites. Therefore, Nsp = 3 satellites are the minimum number of satellites per plane that can achieve persistent Intra-OISLs by avoiding Earth shadowing, though this number depends on the h. As inferred from min 𝛼 = sin−1 (𝑅𝐸+𝐿𝑚𝑖𝑛𝑅𝐸+ℎ)   ,                                                     (5.7) and depicted in Figure 5-8, decreasing h leads to increasing the minimum required Nsp while increasing h enhances the Dij between two adjacent satellites at the same Nsp as shown in Figure 5-9 and obtained from 𝐷𝑖𝑗 = √2 (𝑅𝐸 + ℎ)√1 − cos (2𝜋𝑁𝑠𝑝)     .                                            (5.8)  Figure 5-7 – α and ψ vs Nsp in intra-OISLs.  101  Figure 5-8 – h vs Nsp in intra-OISLs.  Figure 5-9 – D vs Nsp for different h.  102 It is inferred from Figure 5-8 that starting from h = 6,571 km and higher, the min Nsp = 3. Below this altitude, we need to increase the minimum required Nsp, which implies the establishment of relay satellites in more than one plane. However, the establishment of ISL between satellites is mainly affected by the azimuth angle, elevation angle and transmission distance between satellites. Although the ISL in the same orbital plane is more stable than those between adjacent orbital planes, we may need to increase the Nsp or decrease h, which is affecting the area of the earth that can be covered and increase the number of required nodes to relay the data in different planes. Therefore, the satellite connectivity analysis of the inter-OISLs is required to understand the movement of the relay satellites in different planes. Then, we can define the MEO constellation configurations and its parameters that can achieve 100% link availability between its satellites. 5.3.2 Inter Orbit ISLs of Walker Relay Constellations Walker [157] developed a notation for labeling orbits that is commonly used in the orbit design community and frequently used as a starting point for constellation design [68]. Specifically, the Walker constellation pattern contains a total of T satellites with Nsp satellites evenly distributed in each of P orbit planes. All the orbit planes are assumed to be at the same inclination, i, relative to a reference plane (typically the Earth's equator). The ascending nodes of the P orbit planes in a Walker delta pattern are uniformly distributed around the equator at intervals of 360o/P while in a Walker star pattern are uniformly distributed around the equator at intervals of 180o/P. Within each orbit plane the Nsp satellites are uniformly distributed at intervals of 360o/ Nsp. Satellites in Walker type constellation have identical semi-major axis (a), eccentricity (e), argument of perigee (ω = 0o), evenly distributed in right ascension of ascending node (Ω), and Nsp satellites per plane, evenly distributed in the mean anomaly (ν) [68]. The only remaining issue is to specify the relative phase between the satellites in adjacent orbit planes. To do this we define the phase difference, ∆𝜑 in a constellation as the angle in the direction of motion  103 from the ascending node to the nearest satellite at a time when a satellite in the next most westerly plane is at its ascending node. For all the orbit planes to have the same relationship to each other, ∆𝜑, must be an integral multiple, f, of 360 deg/T, where f can be any integer from 0 to P −1. So long as this condition holds, each orbit will bear the same relationship to the next orbit in the pattern. The pattern is fully specified by giving the inclination and the three parameters, T, P, f. Usually such a constellation will be written in the shorthand notation of i: T/P/f. One of the main problems in configuring the relay constellation is how to avoid collision between satellites with appropriately choosing a phasing factor, f. There is an equal number of evenly spaced satellites in each orbital plane i.e., Nsp = T /P. When P is an odd number, there is no collision. But, when P is an even number collision occurs when both Nsp and f are odd or both numbers are even [158]. For the polar/near polar orbits (i ≈ 90o), we use the Walker star configuration where the satellites are in near-polar circular orbits across approximately 180o traveling north on one side of the Earth and south on the other. To avoid satellite collisions for these polar orbits and for any value of 𝑁𝑠𝑝 and f cannot be zero at any number of planes. All these cases should be considered to generate realistic constellation configurations. The analysis of the inter-OISLs is required to understand the movement of the relay satellites in different planes to define the RCSC configurations with 100% link availability between its satellites. The communication time for inter-OISLs and its related geometry is well discussed in [18]. This time is calculated between pairs of the satellite constellation nodes in different planes. These are parsed into a three-dimensional binary matrix C ∈ MNxNxTsim where N indicates the number of network nodes and 𝑇𝑠𝑖𝑚 the total simulation time. CijTsim = 1 indicates that node i is in line of sight with node j during Tsim.  104 5.3.3 Algorithm for Configuring Relay Constellations with Persistent ISLs The Pseudo-code of the algorithm used for configuring Walker RCSCs with persistent ISLs is presented in Table 5-4. Table 5-4 – Pseudo-code of the main program used for configuring walker RCSCs with persistent ISLs Algorithm for configuring Walker RCSCs with persistent inter-OISLs 1 Input the total simulation analysis time (𝑇𝑠𝑖𝑚) 2 Set initial orbital parameters for a seed relay satellite (a, e, i, ω, Ω, and ν) for Walker constellation 3 Input satellite constellation parameters (T, P, f) 4 Calculate number of satellites per plane, Nsp 5 Set the type of Walker constellation (Delta or Star) 6 If Walker star or (i = 90o) 7 Calculate Pattern unit ( 𝑃𝑈 = 𝜋/𝑇) 8 Else Calculate Pattern unit ( 𝑃𝑈 = 2𝜋/𝑇) 9 End if 10 Calculate In-plane spacing between satellites (∆= 𝑃𝑈 ∗ 𝑃) 11 Calculate phase difference between planes (∆𝜑 = 𝑃𝑈 ∗ 𝑓) 12 Input the orbital parameters ranges and step size  13 Loop1 through the input parameters, create Walker constellation, and calculate the orbital elements 14 15 16 17 18 19 20 21 Pick the appropriate phasing factor, f, based on P and Nsp to avoid satellite collisions If (P is odd)  f = 0: 1: P-1 Elseif (Nsp is odd)     f = 0: 2: P-2        Else      f = 1: 2: P-1 End if 22 Get all the satellites orbital parameters per a constellation 23 24 25 Loop2 through each satellite pairs to determine the visibility Compute communication time between each pair of the constellation nodes [18] Check CijT for each network node 26 End loop2 27 28 End loop1 Display various outputs of the valid constellation configurations   105 5.4 Implementation 5.4.1 MATLAB/STK Interface The MATLAB/STK interface allows overall simulation parameters, satellite orbital parameters & constraints, and different system models related to STK to be defined in MATLAB. With the integration of MATLAB and STK, both of them can operate through each other to access the capabilities of both tools without switching between application sessions [159]. To automate STK from MATLAB, STK/Integration license is required to open the connection between MATLAB and STK that can be done through a COM connection or TCP/IP connectors. STK can be commanded by a select number of mexConnect commands via TCP/IP connectors, which are a limited subset of core MATLAB/STK interface commands that can be found by exploring the MATLAB help menu and all of them are prefixed with stk [159]. A COM connection is used here to automate STK and pull data back into MATLAB. The COM interface is the preferred method since it is very reliable, works for any combination of STK and MATLAB, and does not require any additional installations. The COM interface open application programming interface (API) for programming, which is a set of subroutine definitions, communication protocols, and tools for building or tasking software [76]. Using MATLAB/STK interface, we implemented the algorithm developed in Section 5.3.3 to define the contact opportunities between relay satellites and therefore assess when persistent paths between them are available. This algorithm enables us to assign the valid constellation parameters (number of planes, number of satellites per plane, orbital altitude, and inclination) of Walker constellation for configuring the RSSC in MEO with persistent links between them. Implementation of this algorithm enables us defining the valid Walker constellation configurations of relay satellite constellations that have persistent ISLs.  106 5.4.2 MATLAB/STK Integrated Toolkit for SRT Calculations Our approach in supporting payload control and data recovery of the LEO remote sensing systems is well suited for AGI STK’s analytical capability [160]. Systems Tool Kit (STK) software is a simulation tool that is widely used for space defense industries and the academic research in aerospace applications [161]. Although STK can directly compute SRT for imaging satellite constellations (without relays) by simply specifying the receiving and transmitting GSs, it does not provide an option for SRT computations when ISLs between satellites are involved [162]. Consequently, an efficient way is required for SRT calculations when relay satellites are involved considering different relay satellite capabilities and different types of ISLs between satellites.  The design of satellite constellations is a complicated and time-consuming simulation optimization problem [163]. An automated process is required for such a space system architecture design. STK-Analyzer is an integrated add-on module that helps automate and analyze STK in order to perform parametric studies easily without involving programming or scripting. Though, it is a time-consuming manner for STK automation, due to the manual system setup for building the model, and an error-prone process, due to the intermediate steps of data collection and analysis using Excel or MATLAB. To overcome these limitations, we have extended STK capabilities using MATLAB/STK interface by devising algorithms for SRT calculation in the previous three mentioned network configurations.  Figure 5-10 depicts the main elements of the SRT calculation MATLAB/STK integrated toolkit as 1) simulation setup and initialization in MATLAB, 2) high fidelity object models from STK, 3) SRT calculation modules in MATLAB, and 4) demonstration and saving the results in MATLAB. This section introduces in detail these elements separately.  107  Figure 5-10 – MATLAB/STK integrated toolkit and its modules for SRT calculations 5.4.2.1 Toolkit Initialization and Set-up Both the initialization and STK control are completely performed using MATLAB commands. After establishing a connection between MATLAB and STK, the first step is usually to open a new STK scenario and ensure that any previous scenarios are closed. MATLAB commands and initializes STK to load all the input object models required by the developed toolkit for SRT calculations e.g., satellite, GS, constellation, and chain objects. Multiple-satellite simulations require several satellites to be created and propagated. MATLAB controls STK to propagate the satellite orbits based on the initialization input parameters including the orbit propagator type and satellite orbit parameters [68]. In the toolkit initialization step, we have considered these main issues before running the related simulations for SRT calculations [152]: 1. The number and the distribution of the points in the coverage grid: The greater the number of points, the better the spatial resolution of the results but, the longer the simulation time. Also, failing to choose an adequate distribution of the grid points may lead to biased results. For instance,  108 creating a grid with constant granularity in both latitude and longitude degrees would place many more points per unit surface area in the poles than near the equator. 2. The simulation time (𝑻𝒔𝒊𝒎): It must be long enough to capture at least several orbits of different satellites so that the obtained results represent the mission. 3. The time step of the propagation: It should be a small fraction of the orbital period and selected according to the coverage grid resolution and the sensor FOV. Specifically, the time step should be chosen so that there are no spatial gaps in sensor footprint between two consecutive time steps since that could lead to artificially missing grid point accesses. 4. Fidelity of the propagation: The simulations can be run using models of various complexity and fidelity. Logically, the more complex the model, the longer the simulation time. For satellite propagation, Keplerian, J2, J4, and high-precision numerical models can be considered. The Keplerian propagator only considers the symmetric central body force. The J2 propagator adds to the Keplerian model the J2 zonal harmonic coefficient contribution to account for Earth’s oblateness, which allows to model Sun-synchronous orbit (SSO) among other orbit types. J4 is approximately 1000 times smaller than J2 and is a result of Earth’s oblateness. Since the second order J2 and the first order J4 secular effects are very small, the difference between the orbits generated by the two propagators is not significant. None of these propagators model atmospheric drag, solar radiation pressure or third body gravity; they only account for a few terms of a full gravity field model. These propagators are often used in early studies (where vehicle data is usually unavailable for producing more accurate ephemeris) to perform trending analysis for short analyses (days or weeks). Therefore, the J2 orbit propagator model is used for the EO and relay satellites in the simulations of this work.  109 5.4.2.2 High Fidelity Object Models from STK The main challenge in designing a satellite constellation is specifying the constellation configuration parameters that can achieve better coverage performances (e.g., revisit time, response time, and information age). The difficulty in the heterogeneous constellation architecture is that there are many variables of interest including the Keplerian orbital parameters, the constellation parameters of both the imaging constellation and the relay constellation, payload parameters such as field of view (FOV) or field of regard (FOR), which add constraints on the coverage performance of the imaging satellites [164], [165], and , number, locations, and the elevation angle constraints of the GSs. Furthermore, the capability of relay satellites based on the involved type of ISLs [2] and the communication technology used to relay data [166] are two important parameters in relay constellation configuration design process and the performance of the heterogeneous constellation system.  Developing stand-alone orbit propagations and space object models of the heterogeneous constellation architecture are not reasonable due to their low-fidelity in case of using simple models with specific assumptions or due to their complexity if high-fidelity models are required [167]. Moreover, these models would increase the algorithm complexity, which affects the algorithm efficiency and increases computational running-time. Analytical Graphics Incorporated (AGI) STK provides high fidelity models and orbits propagators to engineers, mission analysts, operators, and decision-makers from more than 700 global organizations. STK offers a wide range of capabilities that are relevant to the heterogeneous system structure e.g., high fidelity models of the EO satellites, RCSC, and GSs. Therefore, the best way is to use the integration between MATLAB and STK to build tools that control STK functionality leverage the two-way communications pathway between STK and MATLAB.  110 5.4.2.3 SRT Calculations Modules in MATLAB  The developed MATLAB/STK integrated toolkit contains modules to evaluate the performance of heterogeneous constellations in terms of SRT for three specific relay network configurations as represented in Figure 5-10. One of the main challenges in SRT calculations is the integration between different object models of each heterogeneous constellation configurations. This is critical to our ability to properly explore the improvement of SRT in the tradespace analysis. To integrate these models, automate STK, and develop the SRT calculation modules, MATLAB software is selected due to its widespread use, simple implementation of certain data constructions and the availability to interface with STK. SRT calculations of EO satellites for each relay network configuration are implemented using a single MATLAB m-file that computes elements of the design structure specific to that network configuration. Using MATLAB for STK automation and model integration makes our approach fits the overall research design. The developed integrated toolkit has several advantages: 1. Interactivity with the toolkit by changing the input variables and the method used for each relay network configuration. 2. It is a parametric approach, allowing the user to simulate a range of possible RCSC architectures that span many different types of input variables. 3. It is modular, allowing the user to add different topologies, change or modify the properties of each model in the system. The algorithm implementation process is passed through various subsystem modules, which conduct the required relevant analysis and call STK to simulate orbit- and constellation- dependent effects (coverage, access, etc.). The fundamental data representing a single realization of the heterogeneous constellation system is a MATLAB structure containing all the system parameters. This structure is initialized with inputs of interest to the user, then is passed through the integrated toolkit, which  111 populates the output fields sequentially. Entire families of heterogeneous configurations and their parameters are passed through the toolkit, resulting in SRT calculations based on the assigned relay network configuration. The MATLAB codes, which are used for SRT computations, are very specific to our problem and enable us to count and compute all the access and gap durations between space segments and between space and ground segments in a much more effective and faster way than STK-Analyzer does. The core of the developed MATLAB/STK toolkit is the coverage module as illustrated in Figure 5-10. Given the design input parameters of the heterogeneous system, the quality of coverage for an object (either an EO satellite or a GS) is evaluated by choosing both the process and the method for computing coverage, which is performed using the coverage module. In the coverage computation process, we need to assign an object model to be covered and then assign one or several objects as assets to this object model. This process is different in the three relay network configurations under study, refer to Table 5-2. For example, in bent pipe, each EO satellite is used as an object model, separately, and its coverage is evaluated by using a chain object model that contains the GS/GSs and the RCSC. This is because a contact opportunity between EO and relay satellites is valid only if that relay satellite is in view and connected to a GS. Although the coverage computation process is different in the three relay network configurations, the coverage computation method is the same in all of them.  TAG is used as a coverage computation method for evaluating the coverage effectiveness of the assigned object model. Consequently, TAG is the output of the developed coverage module and the input of the SRT calculation module. SRT is calculated in the SRT calculation module for two cases, with and without relay communication satellites. We use STK directly to compute the 𝑆𝑅𝑇̅̅ ̅̅ ̅ of the EO satellite constellations without relay satellites by selecting the transmitting and receiving GS [148] [162]. For SRT calculations when relay  112 satellites are involved, MATLAB performs an automated call of SRT computation module to compute both the 𝐼𝑅𝑇̅̅ ̅̅ ̅ and 𝑆𝑅𝑇̅̅ ̅̅ ̅ for the EO satellite constellations for the various relay network configurations using equation (3).  In this equation, 𝑇𝐴𝐺̅̅ ̅̅ ̅̅ 𝑝 is obtained from the developed coverage module. It is important to mention that the minimum value of 𝑆𝑅𝑇̅̅ ̅̅ ̅ equals to the 𝐼𝑅𝑇̅̅ ̅̅ ̅, which depends on the revisit time of the EO satellite constellation, if, and only if, the gap durations between the relay and EO satellites and also between the relay satellites and GSs can be set to zero. 5.4.3 Configuring Walker Relay Constellations with Persistent ISLs using STK Using MATLAB/STK interface, we implemented the developed algorithm to define the contact opportunities between relay satellites and therefore assess when persistent paths between them are available. The Pseudo-code of this algorithm is shown in Table 5-4. This algorithm enables us to assign the valid constellation parameters (number of planes, number of satellites per plane, orbital altitude, and inclination) of Walker constellation for configuring the RSSC with persistent links between them. We analyzed the inter-OISLs, which are the links connecting relay satellites in adjacent orbits with different constellation configurations. Based on this analysis, we defined the valid configurations of relay satellite constellations that have persistent ISLs. With the integration of MATLAB and STK, both of them can operate through each other to access the capabilities of both tools without switching between application sessions. We used the Walker tool in STK to generate the constellations. STK uses a seed satellite, the original satellite that is used to create the Walker constellation while the satellites generated using the Walker tool are referred to as children. We assume relay constellations of P planes of identical semi-major axis (a), eccentricity (e), inclination (i), argument of perigee (ω = 0o), evenly distributed in Right Ascension of Ascending Node (Ω), and Nsp satellites per plane, evenly distributed in the mean anomaly (ν). For the purpose of this analysis, only 2 ≤ 𝑃 ≤ 3 and 1 ≤ 𝑁𝑠𝑝 ≤ 4 are considered.  113 STK simulates the movement of the relay satellites. It combines the data inputs, shown in Table 5-5, to create a simplified constellation of equally spaced satellites both in latitude and longitude. The output of the STK simulation is a set of reports that indicate the contact times between pairs of network nodes in different planes. These are parsed into a three-dimensional binary matrix C ∈ MNxNxT where N indicates the number of network nodes and 𝑇𝑠𝑖𝑚 the total simulation time. CijT = 1 indicates that node i is in line of sight with node j during 𝑇𝑠𝑖𝑚. We use data in C to calculate the number of available inter-orbit crosslinks (Ncross) of each satellite in the constellation during 𝑇𝑠𝑖𝑚. The output of this simulation tool is the minimum number of inter-orbit crosslinks (min Ncross). The constellation configuration that satisfies the condition in equation (5.9) is considered a valid constellation, i.e., a constellation with continuous inter-orbit ISLs between all satellites. E.g.  P = 2 and Nsp = 4 results in a constellation with min Ncross = 4 which means that each satellite in the first plane has a continuous link to the other four satellites in the second plane.  min (𝑁𝑐𝑟𝑜𝑠𝑠) =  𝑁𝑠𝑝 ∗ (𝑃 − 1)                                                            (5.9)                   Table 5-5 – Simulation input parameters and their ranges. Input parameter Range Number of planes (P) 2 ≤ 𝑃 ≤ 3 Number of satellites per plane (Nsp) 1 ≤ 𝑁𝑠𝑝 ≤ 4 Orbital relay altitude (hrelay) 8,000 𝑘𝑚 ≤ ℎ𝑟𝑒𝑙𝑎𝑦 ≤ 24,000 𝑘𝑚,  (Δℎ𝑟𝑒𝑙𝑎𝑦 = 100 𝑘𝑚) Orbital relay inclination (irelay) 10𝑜 ≤ 𝑖𝑟𝑒𝑙𝑎𝑦 ≤ 90𝑜, (Δ𝑖𝑟𝑒𝑙𝑎𝑦 = 10𝑜) Walker phasing factor (f) 0 ≤ 𝑓 ≤ 𝑃 − 1   114 5.5 Results 5.5.1 SRT Calculations – A Case Study Using the developed toolkit, we demonstrate the performance enhancement of SRT for EO satellite constellations supported by RCSCs in the three defined network configurations. In this section, SRT calculations of an EO satellite constellation with and without relay communication satellites are presented. The following specific input parameters of a heterogeneous constellation system are used in the simulations: • RapidEye satellite constellation is used as the imaging constellation. This constellation is a uniformly distributed five satellites on a single SSO at h = 627.3 km and i = 97.8o. This constellation represents a major milestone in the EO industry. It is the first fully commercial operational class EO system using a constellation of 5 satellites that provides unparalleled performance [168]. Nevertheless, the main reason for choosing this constellation system is that RapidEye image data is downlinked via an X-band receiving station, owned and operated by KSAT (Kongsberg Satellite Services) in Svalbard, Norway. The geographical location of this reception facility, with a latitude of 78º, allows for downlinking image data on every orbit by which the best SRT performance without using relay satellites can be achieved. We showed here how using RCSC can enhance the system performance in terms of SRT to eliminate the need for such “expensive and complex” polar ground stations [41]. • A rectangular FOV is used to model the imaging concept of the payload. We used the rectangular sensor field of regard (FOR) parameters of RapidEye sensor from STK standard object database (Vertical Half Angle = 28.5o and Horizontal Half Angle = 3o).  115 • The simulation time for each scenario is set to 10 days which is enough to capture about 148 orbital periods for the RapidEye satellite orbit altitude and capture 50 and 30 orbital periods for relay orbital altitude 8,000 km and 14,000 km, respectively. • A Coverage Definition Object in STK bounded between - 80o latitude and 80o latitude is used to represent the coverage area of interest (AoI). A grid of 5o granularity in latitude results in a grid of 1,673 points around the AoI surface in our simulation scenario. The coverage definition in STK chooses the number of points at each λ to be proportional to the cos (λ) to obtain equal horizontal distances between points. Therefore, fewer points are placed in higher latitudes to avoid statistically weighting more the high latitudes coverage metrics. • We used Walker-Delta 3/3/0 constellation to be the RCSC. This is the constellation with the minimum Nsp with persistent ISLs between its satellites, which has been selected in the previous section. This constellation configuration is the same as Audacy constellation, the first proposed commercial intersatellite data relay network in MEO designed to offer simultaneous access to small commercial EO satellites in LEO [8]. However, Audacy satellites have the ability to continue in contact with each other, we will present how the system performance would be when other network configurations can be used. We present the following cases in our results to reveal how SRT is affected by changing ℎ𝑟𝑒𝑙𝑎𝑦 and 𝜆𝐺𝑆 while we use 𝑖𝑟𝑒𝑙𝑎𝑦=25o (from Audacy configuration): 1. ℎ𝑟𝑒𝑙𝑎𝑦 = 14,000 km and 𝜆𝐺𝑆 = 5o 2. ℎ𝑟𝑒𝑙𝑎𝑦 = 8,000 km and 𝜆𝐺𝑆 = 5o 3. ℎ𝑟𝑒𝑙𝑎𝑦 = 14,000 km and 𝜆𝐺𝑆 = 35o 4. ℎ𝑟𝑒𝑙𝑎𝑦 = 8,000 km and 𝜆𝐺𝑆 = 35o Figures 5-11 to 5-14 represent the results of the four above-mentioned cases, respectively. We present these results in terms of the distribution ratio 𝐼𝑅𝑇̅̅ ̅̅ ̅ 𝑆𝑅𝑇̅̅ ̅̅ ̅⁄ . The average values of these times were computed by the grid point latitudes (latitude of targets). When this ratio tends to one, it means a  116 reduction of the SRT as a result of eliminating gap durations between imaging satellites and GSs. As shown in these figures, the best performance can be obtained from using Walker-Delta 25o: 3/3/0 at h = 14,000 km using 5o latitude GS. Reducing h from 14,000 km to 8,000 km leads to decreasing the distribution ratio 𝐼𝑅𝑇̅̅ ̅̅ ̅ 𝑆𝑅𝑇̅̅ ̅̅ ̅⁄  that means increases in 𝑆𝑅𝑇̅̅ ̅̅ ̅, The performance when using RCSC with persistent ISLs is better than the other two configurations. This configuration reduces the uplink delay time and the downlink delay times tend to be zero where the SRT becomes dependent only on the RT of the imaging constellation. Moreover, we can draw the following conclusions: 1. A relay constellation with persistent ISLs has a dominant performance relative to the other two network configurations without ISLs, Bent pipe and Store & Forward. 2. Increasing ℎ𝑟𝑒𝑙𝑎𝑦 reduces SRT at the same 𝑖𝑟𝑒𝑙𝑎𝑦 for all network configurations. However, this improvement is constrained by λ𝐺𝑆.  Figure 5-11 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a relay constellation, Walker-Delta 25o: 3/3/0 at hrelay = 14,000 km & 𝝀𝑮𝑺= 5o.  117  Figure 5-12 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a relay constellation, Walker-Delta 25o: 3/3/0 at hrelay = 8,000 km & 𝝀𝑮𝑺= 5o.  Figure 5-13 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a relay constellation, Walker-Delta 25o: 3/3/0 at hrelay = 14,000 km & 𝝀𝑮𝑺= 35o.  118  Figure 5-14 – SRT calculation for RapidEye constellation using Svalbard GS without relay and with a relay constellation, Walker-Delta 25o: 3/3/0 at hrelay = 8,000 km & 𝝀𝑮𝑺= 35o.  5.5.1.1 Computational Performance Evaluation In this section, the computational performance of the developed SRT calculation toolkit is evaluated compared to STK-Analyzer to demonstrate the efficiency of the algorithm. STK-Analyzer is an integrated add-on module that helps automate and analyze STK in order to perform parameter studies easily without involving programming or scripting. Using this module, the simulation initialization and data analysis should be prepared manually so that one can use and vary the appropriate input variable through a range of values and gets one or more output variables. The output data is exported to Excel as an intermediate step for data reduction and processing then to MATLAB for further calculations and generating the design curves. Although using STK-Analyzer for automation helps to understand the space system design process, it is still a time-consuming manner for STK automation and an error-prone process due to manual system setup and the intermediate data handling and processing step.  119 Figure 5-15 illustrates the execution time of the developed MATLAB/STK algorithm for the three relay network configurations compared with the execution time when STK-Analyzer is used. These simulations are conducted for one-day orbit propagation with the same simulation conditions on a quad-core Intel Core i7-8565 with 8 GB RAM. The presented execution times include the time of access and gap duration computations between different objects in the relay network configuration, extracting the required data, and SRT calculation for only one iteration of the simulation input parameters used for a heterogeneous constellation system to compute SRT when a single ground target was selected. These results show that the developed toolkit enables us to count and compute all the access and gap durations between space segments and between space and ground segments in a much more effective and faster way than STK-Analyzer does.  Figure 5-15 – Execution time comparison for one-day simulation.   120 5.5.2 Walker Constellations with Persistent ISLs In this section, the contact opportunities between relay satellites in different constellation configurations are investigated. Considering only the input parameters P and Nsp with the ranges reported in Table 5-5, eight constellation options have resulted (four options for P = 2 and four options for P = 3). Nevertheless, considering the other input parameters such as Walker phasing, f, Walker type, Δℎ𝑟𝑒𝑙𝑎𝑦, and Δ𝑖𝑟𝑒𝑙𝑎𝑦, we have investigated a total of 11,520 different configurations of RCSCs in MEO. This number can be changed based on the incremental steps used for ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦.  For every iteration, the output of the algorithm which is the valid configuration returns the constellation parameters, i.e., 𝑃, 𝑁𝑠𝑝, 𝑓, ℎ𝑟𝑒𝑙𝑎𝑦 , 𝑎𝑛𝑑 𝑖𝑟𝑒𝑙𝑎𝑦. The valid configurations for P = 2 are summarized in Figure 5-16. Figures 5-17 to 5-20 show the valid configurations for P = 3 and Nsp  = 1, 2, 3 and 4, respectively. Figures from 5-21 to 5-23 summarize the minimum ℎ𝑟𝑒𝑙𝑎𝑦 and its corresponding 𝑖𝑟𝑒𝑙𝑎𝑦 for each constellation configuration that achieve persistent ISLs. From these figures, the valid relay configurations with persistent ISLs and their parameters can be obtained. As it is clear from these figures, all the input simulation parameters are contributed to forming the valid configurations while increasing the Nsp reduces the probability of achieving valid configurations with persistent inter-relay ISLs. We have identified the constellation configurations and their parameters with minimum Nsp  and the minimum P, and their phasing factor, f, which are: 1. Walker-Delta 4/2/1, a constellation with a number of planes, P = 2 and Nsp  = 2. The ranges of the orbital altitudes and the inclinations are provided in Figure 5-16. 2. Walker-Delta 3/3/0, a constellation with the minimum number of satellites per plane Nsp  = 1. We use f = 0 for this configuration because it gives uniformity to the configuration that increases the available ranges of altitudes and inclinations, which are provided in Figure 5-17.  121  Figure 5-16 – Valid MEO RCSC for P = 2, Nsp  = 1, 2, 3, and 4 and f = 0 and 1.  Figure 5-17 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 1.  122  Figure 5-18 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 2.  Figure 5-19 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 3.  123  Figure 5-20 – Valid MEO RCSC for P = 3, f = 0, 1, and 2 and Nsp  = 4.  Figure 5-21 – Valid Walker RCSCs for P = 2.  124  Figure 5-22 – Valid Walker RCSC for P = 3, Nsp  = 1&2.  Figure 5-23 – Valid Walker RCSC for P = 3, Nsp  = 3&4  125 Unlike constellations with many nodes (satellites), Walker-Delta 3/3/0 and Walker-Delta 4/2/1 configurations require a maximum of only two hops for any LEO satellite to connect to GS, which minimizes latency and maximizes total system reliability. We performed an analysis on certain pairs of MEO satellites in adjacent planes in each configuration that represent performances of the inter-OISLs between relay satellites of these two configurations. The variations of the relative elevation angle and the relative distance are presented in Figure 5-24. The (maximum, minimum) pairs for the elevation and distance of Walker 4/2/1 satellites are (-30 deg, -60 deg) and (14,400 km, 24,900 km), respectively. The (maximum, minimum) pairs for the elevation and distance of Walker 3/3/0 satellites are (-38 deg, -60 deg) and (17,700 km, 24,900 km), respectively. Although the maximum range of the two configurations is the same, Walker 3/3/0 has shorter ranges of both the relative elevation and the relative distance that guarantee more stable inter-OISLs due to the simpler pointing and tracking systems required to establish the inter-relay ISLs [169].  Figure 5-24 – Variation of relative elevation and distance between pairs of relay satellites from the two relay configurations (altitude 8,000 km and inclination 45 degrees).    126 5.6 Discussion The previous work has not addressed, nor can industry-standard design tools such as STK predict, the manner in which system response time (SRT) of EO satellite constellations, improves when relay satellites are involved and become more complicated. The first developed algorithm in this chapter addresses this gap and performs SRT calculations for EO satellite constellations supported by relay satellite networks. Three various relay network configurations were investigated based on the communication technology used by relay satellites and different relay satellite capabilities. Using MATLAB/STK interface, this algorithm was implemented as STK add-on modules. The performance enhancement of SRT for EO satellite constellations supported by RCSCs was demonstrated for three specific relay network configurations. The results illustrated that this enhancement depends on the relay network configuration, the orbital parameters of the RCSC, and the latitude of the ground station. The MATLAB/STK integrated toolkit provides a new important feature to STK that will greatly benefit the satellite constellation design society. It is efficient for exploring the tradespace solutions of the heterogeneous satellite constellation during the preliminary mission design and performance analysis phases. The developed toolkit provides interactivity by changing the input variables and the method used for each relay network configuration. Besides, it is modular, allowing the user to add, change and modify the properties of each module in the space system based on its requirements and constraints. The execution time of the algorithm presented its functionality compared to the STK-Analyzer. In future work, an improvement of the computational performances of the developed SRT calculation modules can be achieved by using the No-Graphics mode of STK graphical user interface. This can be done by creating an STK/Engine application that requires additional STK licenses. On the other hand,  127 future users could use the developed algorithm and the implemented toolkit in this work to perform design optimization of the relay satellite constellations. Relay satellite constellations with persistent intersatellite links (ISLs) extremely reduce the connectivity gaps between EO satellites and ground stations enabling control of the EO satellites and get the data back rapidly. Walker constellations were used for providing ground coverage for communication applications without the investigation of persistent inter-relay ISLs. The second developed algorithm in this chapter provides a method for connectivity analysis between relay satellites in Walker constellations. Using MATLAB/STK interface, we implemented this algorithm to define the valid Walker constellation configurations and their orbital parameters presented in a group of design curves. We found that increasing the total number of satellites decreases the possibility to form a constellation configuration with persistent ISLs. Using this tool, we have identified two major constellation Walker configurations in MEO and their orbital parameters where the relay satellites are in the line-of-sight of each other continuously, which are: (1) Walker 3/3/0, a constellation with the minimum number of satellites per plane, and (2) Walker 4/2/1 using additional one more satellite but distributed in less number of planes. Unlike constellations with many nodes, these two configurations require a maximum of only two hops for any EO satellite in LEO to communicate with the GS, which minimizes latency and maximizes total system reliability.   128 Chapter 6: Sensitivity Analysis of Walker-Delta Constellations Used as Relay Satellites  6.1 Introduction When designing complex space systems, like satellite constellation networks, particular attention must be paid to the chosen network architecture. During the conceptual design or architecting phase, the design space of such systems is explored using a simulation process over a range of design variables including orbital altitude, inclination, constellation type, and other parameters. These quantities all represent important design decisions that must be made during the conceptual design of a complex development project [170]. Unfortunately, there is a lack in the current literature discussing the conceptual design methods for relay communication satellite constellations (RCSCs) in MEO for servicing remote sensing satellite constellations (RSSCs) in LEO. A theoretical concept of using a tracking and data relay system for China is introduced in [49]. This system consists of MEO satellite constellation with ISLs and terrestrial gateway stations. The proposed MEO constellation in this work was previously designed for mobile communication for China [103] and is called a common-track constellation because of all its satellites follow the same track on the Earth surface. The coverage performances of 4 different MEO constellations, Walker-Delta (also known as the Ballard Rosette [104]), Polar, Equatorial, and common-track, are compared in [50]. The constellations have the same altitude and the total number of satellites (6 satellites). The constellation parameters of Rosette and Polar are taken from Refs. [104] and [105], respectively, with only change in altitude for the sake of fair comparison. Coverage performance in this work was performed to examine the coverage  129 percentage of a celestial sphere at 300 km altitude, as a lower limit for most existing LEO spacecrafts (as assumed in this work) and to examine the coverage of nine terrestrial GSs distributed in China area.  A comparison of different constellation configurations to serve as relay satellites is introduced in [51]. Visibility outages of a single LEO satellite were analyzed and compared in case of using three different relay constellation configurations, which are the three layers of BeiDou triple-layer navigation system (5 satellites in GEO without ISLs, 27 satellites in MEO with ISLs, and 3 satellites in inclined geosynchronous orbit (IGSO) without ISLs). Nevertheless, this is a questionable comparison because the constellations are using different orbit types and have a different number of satellites and a different number of planes. Another comparison is performed in [2] between specific instances of LEO and MEO Walker-Delta type constellations to explore the potential enhancement of the system performance when these RCSCs are used for servicing a randomly selected RSSC configuration. However, only one level of ISL routing has been considered in this work where a telecommand can be bridged only by one relay from a GS to an imaging satellite. Although comparisons between RCSCs are usually used to see which constellation can achieve better performance, only single instances of RCSCs are involved in these comparisons. Their performance has not been analyzed for realistic RSSCs nor their sensitivity to deviations from the specified orbital parameters has been considered or discussed. Recently, Audacy, a California-based space start-up firm, has begun to establish the first commercial intersatellite data relay network designed to offer simultaneous access to small commercial satellites including EO satellites. They received the required license from the U.S. FCC in June 2018 [7], [8]. Audacy uses Walker-Delta constellation 25o:3/3/0 for their MEO relay network at ~14,000 km altitude. These constellation parameters will be among many other constellations with the same constellation  130 configuration, Walker-Delta 3/3/0, and other constellations using Walker-Delta 4/2/1 configuration. These are the two major Walker-Delta configurations we have got and described in detail in Section 5.5.2. Therefore, the objectives of this chapter are to: 1. Identify a representative RSSC configuration to be used in the simulation-based process for performance evaluation of the RCSCs. 2. Show how the tools we developed can be used to design and analyze the performance of RCSCs by comparing the coverage performance of two case studies: i. Case study 1 – Walker-Delta 4/2/1, the configuration with the minimum number of planes that can achieve persistent inter-relay ISLs. ii. Case study 2 – Walker-Delta 3/3/0, the configuration with the minimum number of satellites per plane that can achieve persistent inter-relay ISLs, the configuration that will be used by Audacy. 3. Generate the design curves that show the relationship between two sets of parameters, the major design variables (DVs) and the corresponding measures of performance (MoPs). These curves demonstrate the sensitivity analysis of these parameters and allow us to perform appropriate trade-offs. Thousands of potential constellations were enumerated, simulated using STK software, and compared with one another across multiple dimensions, focusing on the results of coverage considerations. We used the MATLAB/STK modules that we have developed, which are parts of the integrated model (described in Chapter 5) between STK software (for providing high fidelity models of space and ground objects) and MATLAB for STK automation, data processing, and visualization. This approach facilitates changing the input DVs and allows us to simulate a range of possible RCSCs that span the different types of DVs in order to analyze the sensitivity of the corresponding MoPs.  131 This chapter is organized as follows: In Section 6.2, we introduce the two case studies we are using for performance evaluation and analysis and define the major DVs and MoPs for our simulations. We identify the representative RSSC used in our simulations in Section 6.3. In Section 6.4, we describe in brief the framework and the methodology of this parametric study. The trends and patterns concluded from results are introduced in Section 6.5. Finally, a discussion and interpretation of the results we obtained are summarized in Section 6.6. 6.2 Case Studies We have demonstrated in Chapter 5 that RCSCs with persistent ISLs between relay satellites (inter-relay ISLS) have a dominant performance (in terms of SRT) compared to the other two network configurations without ISLs, bent-pipe, and store-and-forward. We also have identified two major RCSCs, Walker-Delta 3/3/0 that has a minimum Nsp and Walker-Delta 4/2/1 that has a minimum P, which each can achieve continuous visibility between their satellites in MEO region. These two configurations are the case studies we use for performance evaluation and analysis. Visualizations of the two constellations, Walker 3/3/0 and Walker 4/2/1 are shown in Figures 6-1 and 6-2, respectively.  Figure 6-1 – Walker-Delta 3/3/0 constellation.  132  Figure 6-2 – Walker-Delta 4/2/1 constellation. The main challenge in designing a satellite constellation is specifying the constellation configuration parameters that can achieve better performance. The difficulty in heterogeneous constellation architecture is that there are many DVs of interest such as the Keplerian orbital parameters and the constellation parameters of both the RSSC and the RCSC. The capabilities of relay satellites based on the involved type of ISLs [2] and the communication technology used to relay data [166] are two important parameters in the design process of relay constellations and the performance of the heterogeneous constellation system. Furthermore, the number, locations, and the elevation angle constraint of the GSs are also significant DVs that affect the heterogeneous constellation performance. In Chapters 4 and 5 in this thesis, we reduced this large number of DVs by providing reference configurations for RSSCs, demonstrating that RCSCs with persistent inter-relay ISLs have dominant performance over the other two network configurations, and defined these two major configurations of Walker-Delta type constellations in MEO that can achieve persistent inter-relay ISLs. This effort has reduced the DVs into four major parameters, orbital relay altitude (ℎ𝑟𝑒𝑙𝑎𝑦), orbital relay inclination (𝑖𝑟𝑒𝑙𝑎𝑦), number and location of GS/GSs.  133 6.3 Representative Configuration for Remote Sensing Satellite Constellations In Chapter 4, we concluded that the major ranges of values of the constellation parameters for RSSCs are: 1. The number of planes (P): from 1 to 6 planes. 2. Total number of satellites: from 4 to 20 satellites 3. Orbital altitude (h): from 400 km to 900 km 4. Inclinations (i): from 97o to 100o (based on SSO altitude), ISS inclination (~51o), mid-inclinations such as (34o and 45o), and finally 70o. From these values, we can pick a combination of these parameters to be used for the RSSC in our simulations for performance evaluation and analysis of the case studies. This combination can form a realistic RSSC that can be considered a representative constellation of all RSSCs, which are currently operational and under-development as discussed before in Chapter 4. Table 6-1 summarizes different orbital and constellation parameters of the reference RSSC. This constellation consists of 50 satellites in 10 planes at different altitudes and inclinations. Satellites in the same orbit are uniformly distributed in their plane but the planes are non-uniformly distributed around the Equator. Figure 6-3 represents the visualization of the RSSC obtained from the 3-D graphics window in STK. Table 6-1 – Constellation parameters used for the reference RSSC in simulations. Orbit type and inclination (i) # of planes (P) # of satellites/plane (Nsp) Altitude h (km) RAAN (deg) SSO 6 5 400 to 900 Δh = 100 km 0, 60, 120, 180, 240, 300 34o 1 5 400 30 45o 1 5 500 90 51o 1 5 600 150 70o 1 5 700 210  134  Figure 6-3 – Visualization of the reference RSSC. 6.4 Parametric Study Framework The first step in performing sensitivity analysis or a parametric study is to define the important DVs of the system or architecture under study and the MoPs that quantify the mission or the purpose of any system of assets. SRT is the major FOM for assessing the performance of a RCSC when used for servicing a RSSC. We have demonstrated previously in Chapter 5 that SRT is mainly depending on the coverage quality between 1) the relay and imaging satellites and 2) the relay satellites and the ground stations. Accordingly, we have analyzed the coverage properties from two aspects. In the first one, we analyzed the connectivity properties between the relay and imaging satellites where ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦 are the two major DVs. We used the time average gap (TAG) as a FOM to analyze the coverage properties between satellites. In the second aspect, we analyzed the connectivity properties between the relay satellites and  135 GS where ℎ𝑟𝑒𝑙𝑎𝑦, 𝑖𝑟𝑒𝑙𝑎𝑦, and the latitude of GS, 𝜆𝐺𝑆, are the DVs and we used the percentage of coverage for a GS to be the FOM in order to analyze the coverage quality. We did not discuss the number of GSs as a DV in this chapter as we only used a single GS in our simulations. A minimum elevation angle of 10o has been applied to the GS in our simulations in order to avoid obstacles caused by natural barriers at low elevation to guarantee reliable ground communications [171]. We used the MATLAB/STK modules we developed (previously discussed in detail in Chapter 5) to present a flow of trade-off design curves for our case studies in a systematic approach. These tools are capable of generating thousands of constellation configurations based on pre-defined DV ranges and sizing those configurations in terms of pre-defined MoPs as shown in Figure 6-4. The goal of these design curves is to reveal the relationship between the DVs and the MoPs.  Figure 6-4 – Parametric study framework.  136 6.5 Trends and Patterns In this section, we present the design curves that show the relationship between the predefined DVs and MoPs in two case studies of RCSCs, Walker-Delta 3/3/0 and Walker-Delta 4/2/1 configurations. This allows us to identify the DVs that most affect the MoPs and are therefore most important. 6.5.1 Case Study 1 – Walker-Delta 3/3/0 Constellation Configuration The Walker-Delta 3/3/0 configuration is the relay satellite constellation in MEO that has the minimum number of satellites per plane, Nsp = 1, that can achieve persistent inter-relay ISLs between its satellites. This constellation configuration is used by Audacy constellation, the first proposed commercial intersatellite data relay network in MEO designed to offer simultaneous access to small commercial EO satellites in LEO [8]. Audacy uses Walker-Delta 25o:3/3/0 at ~14,000 km altitude. These constellation parameters will be among thousands of constellation configurations that were assessed using the tools we developed. We started by providing the input parameters of the RSSC, propagate its satellites using STK, and for each LEO satellite, the coverage was evaluated using the RCSC as an asset while the TAG is the method used for evaluating the coverage. Ranges of ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦 have been used to initiate loops for inserting different RCSCs. In each iteration, the coverage properties between RCSCs and RSSC satellites are analyzed and TAG was computed. Figure 6-5 represents the sensitivity of TAG to the increase of  ℎ𝑟𝑒𝑙𝑎𝑦 and changing 𝑖𝑟𝑒𝑙𝑎𝑦. It is shown that the TAG is very sensitive to the changing of both ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦. Increasing the altitude decreases TAG that means an improvement in the coverage performance of Walker 3/3/0 to the imaging satellites. However, to get the best performances from this configuration, lower inclinations should be used such as 5o and 15o.  137  Figure 6-5 – Mean values of TAG between imaging and relay satellites of Walker-Delta 3/3/0 constellation vs hrelay at different irelay values.  In the same manner, we analyzed the coverage properties between the relay satellites and a single GS. In this case, we have an additional DV besides ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦, which is 𝜆𝐺𝑆. We used in these simulations a single GS then we changed its latitude at every iteration when a RCSC is inserted to STK scenario. The coverage properties of a RCSC were analyzed in each iteration when the 𝜆𝐺𝑆 of a single GS changes. The percentage of coverage (in one-day simulation time) is the method we used to evaluate the coverage properties in each iteration. We had to show how the changing of both ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦 affect the daily coverage% of a GS. Figures from 6-6 to 6-8 show the trends and pattern of changing the three DVs used in these simulations. The general trend in GS coverage properties is that the percentage of coverage achieved by the RCSC to the GS increases as the relay inclination approaches the GS latitude. It means that relay orbits with  138 low inclinations are only visible from equatorial or near-equatorial GS. Consequently, the range of latitudes with zero coverage and also the range of latitudes with 100% decrease by approximately 10o with the increase in orbital relay inclination by nearly 10o (the same range of increment).  Figure 6-6 – Coverage properties between Walker-Delta 5o:3/3/0 vs λGS at different values hrelay.  Figure 6-7 – Coverage properties between Walker-Delta 15o:3/3/0 vs λGS at different values hrelay.  139  Figure 6-8 – Coverage properties between Walker-Delta 25o:3/3/0 vs λGS at different values hrelay.  6.5.2 Case Study 2 – Walker-Delta 4/2/1 Constellation Configuration The Walker-Delta 4/2/1 configuration is the relay satellite constellation in MEO that uses the minimum number of planes, P = 2, where the relay satellites have persistent inter-relay ISLs. In the same manner, as the previous case study, we have analyzed the two aforementioned aspects of the coverage performance. Figure 6-9 shows the relationship between TAG and ℎ𝑟𝑒𝑙𝑎𝑦 at different values of 𝑖𝑟𝑒𝑙𝑎𝑦. In general, increasing the relay orbital altitude reduces the gaps between relay and imaging satellites. However, the main observation from these results is that Walker-Delta 4/2/1 can achieve much better coverage to the RSSC satellites than Walker-Delta 3/3/0 because the TAG values obtained from Walker 4/2/1 configuration are much lower compared with Walker 3/3/0 case. We also found that Walker-Delta 4/2/1 with higher inclinations (i.e., 25o, 35o and 45o) can achieve better coverage to the imaging satellites than lower inclinations (i.e., 5o and 15o), which is the opposite to what can be achieved using Walker-Delta 3/3/0.   140  Figure 6-9 – Mean values of TAG between imaging and relay satellites of Walker-Delta 4/2/1 constellation vs hrelay at different irelay values.  For the coverage properties to GS, we performed similar tests to the Walker-Delta 3/3/0 constellation by varying the 𝜆𝐺𝑆 for different ℎ𝑟𝑒𝑙𝑎𝑦 and specific 𝑖𝑟𝑒𝑙𝑎𝑦 values. The results are shown in Figures 6-10, 6-11, and 6-12 for three specific 𝑖𝑟𝑒𝑙𝑎𝑦 values, 5o, 15o, 25o, respectively. The percentage of coverage (in one-day simulation time) is the method we used to evaluate the coverage properties at each iteration. The general trend in GS coverage is that the percentage of RCSC coverage to the GS increases as the relay inclination approaches the GS latitude. We can also see that the performance degrades as the 𝑖𝑟𝑒𝑙𝑎𝑦 increases from 5o to 25o. These results give an idea of how the constellation can be compared using the metrics stated in this chapter. It can be seen from the design curves that how the coverage properties are highly sensitive to  141 these major DVs, ℎ𝑟𝑒𝑙𝑎𝑦 , 𝑖𝑟𝑒𝑙𝑎𝑦, and 𝜆𝐺𝑆. From the design curves we introduced in this chapter, we can select some possible solutions to the RCSCs by defining ℎ𝑟𝑒𝑙𝑎𝑦 and 𝑖𝑟𝑒𝑙𝑎𝑦 that can achieve zero TAG between relay and imaging satellites. This selection should be followed by a tradeoff with the available latitude range where we can locate a GS that has continuous visibility with at least one of the relay satellites.  Figure 6-10 – Coverage properties between Walker-Delta 5o:4/2/1 vs λGS at different values hrelay.  142  Figure 6-11 – Coverage properties between Walker-Delta 15o:4/2/1 vs λGS at different values hrelay.  Figure 6-12 – Coverage properties between Walker-Delta 25o:4/2/1 vs λGS at different values hrelay.   143 6.6 Discussion We have demonstrated the ability of the tools that we developed to get different solutions to the RCSCs by investigating the coverage quality: 1) between the relay and imaging satellites and 2) between the relay satellites and a ground station. Two different FOMs are used to evaluate the quality of coverage, the time average gap for the first aspect and the percentage of coverage for the second one. Moreover, we have generated the design curves that illustrate the sensitivity of changing different constellations parameters on the coverage performance. These design curves allow us to show some of the significant trade-offs between the major design parameters in RCSCs. Walker relay satellite constellations have been introduced in the literature by performing comparisons between single instances with specific orbital parameters. Walker 4/2/1 is an interesting constellation configuration that can achieve persistent ISLs between relay satellites at specific altitudes and inclinations such as Walker 3/3/0, which will be used by the recently announced first commercial RCSC in MEO Walker. However, it has not been introduced or analyzed in the literature and the advantages of Walker-Delta 4/2/1 over Walker-Delta 3/3/0 with a single ground station (GS) is not generally recognized. Using MATLAB/STK interface, we generated performance curves that allow us to compare the performance of the Walker 3/3/0 and 4/2/1 configurations. The latter provides some advantages in the coverage performance between the relay satellites and the EO satellites in terms of time average gap (TAG), a related coverage performance metric. On the other hand, Walker 4/2/1 shows better performances in the connectivity analysis with a single GS than Walker 3/3/0 constellation. Walker 4/2/1 increases the available latitude range to locate a GS with less TAG while it is on the contrary for Walker 3/3/0.  144 In general, increasing the relay orbital altitude of the two Walker configurations reduces the gap durations, represented in TAG, between the relay and imaging satellites. In the baseline trade-off, it was shown that the TAG metric is highly sensitive to small changes in the orbital altitude and inclination of the RCSCs in the two case studies. The severity of the sensitivity decreases as the total number of satellites increases from three satellites in Walker-Delta 3/3/0 to four satellites in Walker-Delta 4/2/1. The TAG values decline gradually until certain combinations of the relay orbital altitude and inclination values where TAG becomes in-sensitive (independent) to changes in these parameters. These combinations can be used as solutions for the RCSCs because these constellation parameters provide continuous coverage to the imaging satellites where TAG = 0. From the analysis of the design curves of the two case studies, we can find that Walker-Delta 4/2/1 configuration can provide much more solutions than Walker-Delta 3/3/0 configuration. Furthermore, Walker-Delta 4/2/1 configuration can provide much better performance than Walker-Delta 3/3/0 configuration. Although it uses more satellites, they are distributed in fewer planes (two planes). Consequently, at these high altitudes, we can conclude that the number of satellites has a greater effect on the coverage properties between relay and imaging satellites rather than does the number of planes. TAG is sensitive to the changing of the relay orbital inclination as well but it differs in the two Walker configurations. In Walker-Delta 3/3/0, low inclinations (i.e., 5o and 15o) can achieve better coverage to the imaging satellites than higher inclinations (i.e., 25o, 35o and 45o). In contrast, in Walker-Delta 4/2/1, higher inclinations (i.e., 25o, 35o and 45o) can achieve better coverage to the imaging satellites than lower inclinations (i.e., 5o and 15o). The general trend in the coverage properties between the relay satellites and the GS is that the percentage coverage to the GS increases as the relay inclinations approaches the GS latitude. It means that relay orbits with low inclinations are only visible from equatorial or near-equatorial GSs.  145 Consequently, the range of latitudes with zero coverage and also the range of latitudes with 100% decrease by approximately 10o with the increase in orbital relay inclination by nearly 10o (the same range of increment). The percentage of coverage is not sensitive only to the relay inclination but also to the relay altitude. The percentage of coverage curves generally shift towards greater latitudes with the increasing of orbital altitude at the same relay inclination. From the analysis of the design curves of the coverage properties between the relay satellites and the GS, we found that Walker-Delta 4/2/1 configuration shows better performance also in the coverage analysis to GS than Walker-Delta 3/3/0 configuration. This has been concluded from increasing the available latitudes to locate a GS that has continuous coverage with the relay satellites in Walker-Delta 4/2/1. For example, at 8,000 km altitude, we can locate a GS at these ranges from 0o to 30o or from 0o to 23o or from 0o to 15o with a continuous coverage achieved by 5o:4/2/1, 15o:4/2/1, and 25o:4/2/1, respectively. Nevertheless, at the same altitude, the maximum percentage of coverage by Walker-Delta 3/3/0 is ~90% for a GS located between 0o to 5o latitudes. To improve this FOM in Walker 3/3/0 configuration, we have to use a higher relay altitude starting from 12,000 km. Finally, the selection of the orbital altitude and inclination of the RCSC is highly constrained in case of using a single GS. The severity of these constraints is likely to be decreased when using two GSs separated by 180o longitude. However, we defer further study of this issue to future work.      146 Chapter 7: Conclusions and Recommendations 7.1 Conclusions The system response time (SRT) of Earth Observation (EO) satellites can be significantly reduced by using dedicated relay communication satellite constellations (RCSCs) in Medium Earth Orbit (MEO).  The overarching goal of this work is to develop tools and techniques to support systematic design and evaluation of RCSCs in MEO that provide simultaneous connectivity between EO satellites in Low Earth Orbit (LEO) and the ground and thereby improve SRT.  This work has contributed to the design of relay constellations for EO missions by: 1. Proposing a framework for heterogeneous satellite constellation design for rapid response Earth Observations.  Significance: Based on the industry-standard Systems Tool Kit (STK) software, this framework provides a systematic alternative to the ad hoc approaches described previously in the literature. 2. Defining a representative set of reference configurations for both the most common observation satellite constellations in LEO and the most common communication relay satellite constellations in MEO.  Significance: These reference configurations makes it possible to conduct performance assessments against the constellation design tradespace more efficiently and with greater confidence using either random samples or an exhaustive set of catalogued satellite constellations. 3. Extending STK’s capabilities (using the MATLAB/STK interface) to calculate system response time for the EO satellite constellations supported by relay constellations that use:   147 a) Bent-pipe technology without intersatellite links (ISLs) between relays where a contact opportunity between the imaging satellite and a relay satellite is valid only if that relay satellite is in view and connected to a ground station (GS). b) Store-and-forward technology without ISLs between relays where a relay satellite can collect and store data from a GS and relay it to the imaging satellite besides data collection and storage from an imaging satellite and download it to a GS. c) Bent-pipe technology with persistent ISLs between relays where a contact opportunity between the imaging satellite and a relay satellite is valid only if that relay satellite is in view to either a GS or another relay that can redirect the information to and from the GS. Significance: The algorithms implemented in these add-on modules provide important new capabilities that are useful to constellation designers but not currently implemented in STK.  4. Devising an algorithm for designing relay satellite constellations that have persistent ISLs between the relays.   Significance: Relay constellations with persistent inter-relay links are much more useful than those that do not. This technique provides a convenient way to design them. 5. Demonstrating the value of assessing the sensitivity of a given relay constellation to its design parameters (e.g., orbital inclination, altitude, and the location of ground station) through a case study that compares Walker-Delta 4/2/1, a constellation with the minimum number of planes, P = 2, and Walker-Delta 3/3/0, a constellation with the minimum number of satellites per plane Nsp = 1. The results demonstrate that Walker-Delta 4/2/1 is far less sensitive to variations in design parameters than Walker-Delta 3/3/0 when a single ground station is used.  148 Significance: The advantages of Walker-Delta 4/2/1 over Walker-Delta 3/3/0 when a single ground station is used is not generally recognized. This is noteworthy given that Walker-Delta 3/3/0 will be used by the recently announced first commercial MEO relay satellite constellation. The results convincingly demonstrate the value of assessing the sensitivity of a given relay constellation to its design parameters. 7.2 Recommendations for Future Work The results presented here (and summarized in Section 7.1) have been based almost completely on assessment of intersatellite and satellite-to-ground visibility as dictated by orbital mechanics.  The scheduling problem of Earth observation is to specify the start times and durations of both the imaging activities and the image download process. In previous work, much effort has been devoted to the scheduling of Earth observation by both individual satellites and satellite constellations and a variety of strategies have been developed (see Section 2.2.2). However, the implications of adding relays to reduce SRT for planning and scheduling of Earth observations by satellite constellations have not been well explored. A logical next step is to extend these previous studies and account for Earth observation scenarios where relays have been deployed.   In this work, the details of the communications technology used to implement the intersatellite and Earth-satellite links or the routing protocols used to implement the network were not accounted for. In particular, constraints imposed by path loss, antenna gains, transmit power and receiver sensitivity were not considered. 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