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ScanSAR radiometric calibration based on roll angle Estimatiru Bast, Daniel Christopher 2002

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ScanSAR Radiometric Calibration Based on Roll Angle Estimation by DANIEL CHRISTOPHER BAST B . S c , Royal Military College of Canada, 1993 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F THE REQUIREMENTS FOR T H E DEGREE OF MASTER OF APPLIED  SCIENCE  in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Electrical and Computer Engineering) We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A May 2002 © D a n i e l Christopher Bast, 2002  In presenting this thesis i n partial fulfilment o f the requirements for an advanced degree at the University o f British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying o f this thesis for scholarly purposes may be granted by the head o f my department or by his or her representatives. It is understood that copying or publication o f this thesis for financial gain shall not be allowed without my written permission.  Department o f \ : \ ^ c c \ r„>A e  G ^ c l W ^-y^^ettNK.  The University o f British Columbia Vancouver, Canada  Date  h  0 ^  Abstract Wide-area S A R imagery obtained by the R A D A R S A T - 1 ScanSAR mode can suffer from various radiometric artifacts. Some of these artifacts arise from the incorrect application of Range Dependent Gain Corrections due to insufficient knowledge of satellite roll angle. Specifically, roll angle estimation errors as small as 0.1 degrees can cause noticeable gain errors of 1 d B or more. Beam-stitching techniques exist that can reduce these errors in the beam overlap region; however, accurate roll information is required for optimum radiometric calibration across the entire range swath. Current roll angle estimation algorithms do not provide consistent results even on routine scenes. These algorithms are susceptible to uncertainties in the range beam patterns, overall scene a°, and other system variables. Currently, the Canadian Data Processing Facility does not implement an automated roll angle estimator. Compensation for range gain errors is performed in the post-processing stage. This thesis proposes a new data acquisition method, in which signal data is obtained during the beam switchover by transmitting pulses through one beam and receiving them with another beam.  This "hybrid data" is then used in a new (hybrid peak detection)  and modified (three beam) algorithm to provide a more accurate and robust roll estimate. Algorithms using this hybrid data are more tolerant to lower mean scene a°, gain uncertainty, and other variables than algorithms using normal data. As this data is not currently acquired, the algorithm is tested using simulated data.  The logistics of acquiring hybrid data are  also explored. The implementation of hybrid data acquisition on R A D A R S A T - 1 would not require any significant software changes. The effects of various roll angle estimation errors on different beam combinations are simulated. The new data and algorithms offer significant potential for improving roll estimates. Results suggest that the three beam algorithm can generally tolerate 3-4 dB lower a° and 0.2 to 0.4 d B more uncertainty in the beam pattern gain than a current algorithm, while meeting required radiometric accuracy. The hybrid peak detection algorithm did not meet stringent roll requirements, but was shown to produce consistent coarse roll estimates while remaining independent of the mean scene a° and beam gain uncertainty.  Other current  algorithms can also be modified to use the hybrid data for potentially greater accuracy.  ii  Contents Abstract  i i  List of Figures .  v l  List of Tables  i x  List of Acronyms and Abbreviations  x  List of Symbols  X 1  Acknowledgements 1  m  Synthetic Aperture Radar: Background  1  1.1  Introduction  1  1.2  Single beam SAR  2  1.3  2  x  1.2.1  Factors affecting Signal Amplitude and Phase  4  1.2.2  Signal Sampling  6  1.2.3  Physical Effects of Signal Sampling  1.2.4  Point Target Signal Strength  8  1.2.5  Range Window  9  7  ScanSAR  1 0  1.3.1  ScanSAR Calibration Errors  11  1.3.2  Factors Hindering Calibration  22  1.4  Related Compensation Strategies  25  1.5  Summary  25  Current Roll Angle Estimation Algorithms  28  2.1  Introduction  28  2.2  Goulding's Algorithm  29  2.3  Jin's Algorithm  34 iii  3  2.4  Dragosevic's Algorithm  35  2.5  Current Algorithm Summary  37  Required Roll Angle Accuracy  38  3.1  Introduction  38  3.2  Required Roll Angle Accuracy  38  3.2.1  Determining the Roll Angle Error Limit  38  3.2.2  Accuracy Results  46  3.3 4  51  P r o p o s e d A l g o r i t h m s for R o l l A n g l e E s t i m a t i o n  52  4.1  Conception of Algorithm Idea  52  4.2  Algorithm Mechanisms  54  4.2.1  Pulse Trigger Delay  60  4.2.2  Range Gate Delay Adjustment  62  4.3  4.4  4.5  4.6 5  Required Accuracy Summary  Algorithm Implementation  68  4.3.1  Data Extraction  68  4.3.2  Data Averaging  69  The Proposed Algorithms  72  4.4.1  Hybrid Peak Detection  72  4.4.2  Three Beam Overlap Ratio  75  Algorithm Pros and Cons  83  4.5.1  Pros  83  4.5.2- Cons  85  Conclusion  86  Data Simulation  87  5.1  Introduction  87  5.2  Data Simulation  87  5.2.1  87  5.3  Data Requirements  Variance  88  iv  6  5.4  Speckle  5.5  Beam-Pattern Energy  101  5.5.1  Range Gain Removal  101  5.5.2  Beam Gain Uncertainty Simulation  106  5.6  General System Parameters  5.7  Conclusion  ,  108 109  Results from Proposed A l g o r i t h m s and G o u l d i n g A l g o r i t h m  110  6.1  Introduction  HO  6.1.1  Goulding Summary  HO  6.1.2  Hybrid Peak Detection Summary  110  6.1.3  Three Beam Summary  Ill  6.2  7  94  Illustration and Explanation of Results  HI  6.2.1  HI  Result Subsets  6.3  Beam Gain Uncertainty Results  113  6.4  Noise Results  125  6.5  Tabular Results  135  6.6  Results Summary  138  Conclusions  140  7.1  Review  140  7.2  Hybrid Peak Detection Conclusions  141  7.3  Three Beam Ratio Conclusions  141  7.4  Conclusion Summary  142  7.5  Immediate Improvements  142  7.6  Future Work Bibliography  143 144  v  List of Figures 1.1  Typical single beam flight configuration  1.2  Typical ScanSAR pattern  1.3  Target azimuth bandwidth resulting from burst operations and its applicable  11  azimuth beam-pattern gain 1.4  3  13  Gain differences from an incorrect azimuth pattern correction due to Doppler centroid estimation error  15  1.5  Example of azimuth scalloping  16  1.6  ScanSAR beam configurations from payload file 25 [7]  17  1.7  Range pattern gain overlap transition point  19  1.8  Range pattern gain correction with and without roll error for W2-S5 interface  20  1.9  Range pattern gain correction with and without roll error for W1-W2 interface 21  1.10 Discontinuities in the scene due to improper RDGC application ©CSA . . .  27  2.1  The range swath consisting of beams W2 and S5 with corresponding RDGCs  31  2.2  Overlap area beam data with respective RDGCs and the corrected beams . .  32  2.3  The mean of the log ratio for several different roll angle estimates  33  2.4  Matrix notation for Dragosevic algorithm  36  3.1  W1-W2 interface discontinuity for a —0.20° roll error  40  3.2  W1-W2 interface with -0.2° to +0.2° roll error  41  3.3  Sensitivity to roll errors for each ScanSAR interface  43  3.4  Linear merging method for beam stitching  44  3.5  Linear merging method with roll error of —0.1°  45  3.6  Linear merging method with roll errors of —0.2° to 0.2°  46  vi  3.7  Visual determination of noticeable changes in grayscale background  49  3.8  W 1 - W 2 interface applied to 8 look Gaussian noise  50  4.1  Data format for one range sub-swath burst  53  4.2  Creation cf W1W2 beam from W l and W 2 patterns  54  4.3  Timing for one range data line  55  4.4  Possible hybrid data reception if transmit pulses are always O N for the S5-S6 overlap area and the P R F increases from the near to far beam  4.5  56  Possible hybrid data reception if transmit pulses are always O N for the S5-S6 overlap area and the P R F decreases from the near to far beam  58  4.6  Hybrid data reception with delay of first pulse in upcoming burst  61  4.7  Hybrid data reception with delay of first pulse in upcoming burst and R d g  adjustment  64  4.8  Current vs. proposed data acquisition for burst switching  65  4.9  Hybrid data acquired from current R A D A R S A T - 1 timing  70  4.10 A l l beam interfaces and their resultant new beam patterns for R A D A R S A T - 1  71  4.11 Polynomial fit to hybrid data for hybrid peak detection on Melfort scene  74  . .  4.12 Implementation of proposed algorithm Part 1  77  4.13 Implementation of proposed algorithm Part 2  79  4.14 A l l ScanSAR normal pattern slopes and hybrid slopes  80  4.15 Average slopes of the hybrid patterns  82  5.1  Theoretical distributions of S A R data as given by Quegan [21]  90  5.2  Actual and simulated distributions of S A R data  91  5.3  Actual data for Prince Albert scene and simulated data for Melfort scene each with range cross section of 108 averaged lines  92  5.4  Melfort Scene © C C R S / C C T 1983  95  5.5  Vancouver Scene (Optical Scene) © C C R S / C C T 1993  96  5.6  Topview Scene © u n k n o w n  97  5.7  Labrador Scene © C S A 1997  98  5.8  Toronto Scene © C S A 1996  99  vii  5.9  Virden Scene © C C R S / C C T 1995  100  5.10 Example of elevation angle to slant range conversion for the S7 beam  . . . .  102  5.11 Comparison of payload file a) original 2-Way gains, b) as in (a) but with R~  3  gain correction, and c) same as (b) but converted to slant range  103  5.12 Geometry affecting slant range  104  5.13 Geometric model used in simulation  105  5.14 Beam uncertainty model used in simulation on S5 beam  106  5.15 Gain uncertainty applied to S5 beam  107  6.1  Overall results from beam gain uncertainty and individual beam combinations with three beam method  6.2  114  Individual beam combinations with Goulding and hybrid peak detection methods  117  6.3  Results from Vancouver and Labrador scenes with all three methods  120  6.4  Results from Melfort and Topview scenes with all three methods  121  6.5  Results from Virden and Toronto scenes with all three methods  122  6.6  Gain uncertainty results with and without W2S5 combination for Vancouver scene and overall results  6.7  124  Overall results from noise and individual beam combinations with three beam method  6.8  6.9  127  Individual beam combinations with Goulding and hybrid peak detection methods  128  Results from Vancouver and Labrador scenes with all three methods  130  6.10 Results from Melfort and Topview scenes with all three methods  131  6.11 Results from Virden and Toronto scenes with all three methods  132  6.12 Noise results with/without W2S5 combination for Vancouver scene and overall results  133  6.13 Conversion of gain uncertainty from a percentage to dB  137  6.14 Roll accuracy vs number of average range lines  138  viii  List of Tables 1.1  RADARSAT-1 imaging modes and available beams  1.2  RADARSAT-l's ScanSAR combinations  3.1  Roll estimation accuracy requirements based on beam pattern and stitching  2 18  method  51  4.1  ScanSAR timing parameters for SCNB from the Prince Albert scene  55  4.2  Actual RADARSAT-1 ScanSAR timing parameters from Prince Albert scene  67  4.3  RADARSAT-1 -3 dB beam-widths for standard and wide beams used in ScanSAR mode  83  6.1  Beam accuracy requirements  112  6.2  Beam accuracy requirements  135  6.3  Tabular results for all beams (including W2S5), all methods  136  ix  List of Acronyms and Abbreviations ADC  Analog to Digital Conversion  AGC  Automatic Gain Control  CCRS  Canada Center for Remote Sensing  CDPF  Canadian Data Processing Facility  CSA  Canadian Space Agency  EM  Electro-Magnetic  FM  Frequency Modulation  I  In-phase Component of Complex Signal  LMS  Least Mean Squares  max  maximum  MATLAB ™  Registered trademark of Mathworks Inc.  MDA  MacDonald Dettwiler and Associates L t d .  min  minimum  Nadir  Surface point directly below satellite  PRF  Pulse Repetition Frequency  Q  Quadrature Component of Complex Signal  RCM  Range Cell Migration  RCS  Radar Cross Section  RDGC  Range Dependent Gain Correction  Rx  Receive(r)  SI through S7  R A D A R S A T - 1 standard beams 1 through 7  SAR  Synthetic Aperture Radar  ScanSAR  Scanning Synthetic Aperture Radar  SNR  Signal to Noise Ratio  Tx  Transmit (ter)  W l through W 3  R A D A R S A T - 1 wide beams 1 through 3  List of Symbols a  R a d a r Cross Section ( R C S )  a°  R C S / u n i t ground area  (7°  d B representation  (7°  a v e r a g e s c e n e o~°  P°  reflectivity per unit slant  7  speckle  v  chirp length  T  fast  e  elevation  angle  incidence  angle  estimated  roll  l  o  e  1 0  R C S / u n i t ground  range  noise  T  e  10 * l o g  time  angle  M9  m e a n l o g r a t i o f o r r o l l a n g l e A;  9sq  squint  <t>  azimuth  A  carrier  k  angle angle  frequency  a  pulse taper  a-hs  aperture taper factor  B  receiver b a n d w i d t h  b  factor  BW  azimuth bandwidth  BWi  a z i m u t h b a n d w i d t h per b e a m  Cl  c o r r e c t e d d a t a for b e a m 1  C2  c o r r e c t e d d a t a for b e a m 2  Co  speed of light  D  antenna width  a  D  delay  F  receiver noise  h  doppler  t  time figure  frequency  xi  List of Symbols C o n t ' d G(6, (f)  antenna gain in elevation and azimuth  Hi  gain offset between beams  I  signal intensity = o~°  k  Boltzmann's constant  L  antenna length  n  azimuth time  n  azimuth time at closest approach  Nf,  # of beam patterns  P  average transmitted power  R i  Range Gate Delay  R  range to target (also known as slant range)  r  across track range resolution  2  s  0  t  g<  y  r  slant range at closest approach  Si  sample interval  t  slow time  Tshift  time shift of hybrid data in memory  v  relative satellite to target velocity  0  W  azimuth beam pattern  W  range beam pattern  Wj  antenna pattern converted to slant range cell j  W  window receive time  a  r  t  xii  Acknowledgements T o b e g i n , I w o u l d l i k e t o t h a n k m y w i f e , T a m m y , for p r o v i d i n g s u p p o r t a n d  encouragement  d u r i n g m a n y h o u r s spent b l a n k l y s t a r i n g at a c o m p u t e r screen a n d / o r p u n c h i n g a w a y lessly at the k e y b o a r d . a b o u t this?"  H e r responses to m y endless requests to  " p r o o f r e a d this" or  end"How  d u r i n g t y p i n g this thesis were greatly a p p r e c i a t e d .  I w o u l d also like to t h a n k m y advisor, D r .  Ian C u m m i n g ,  for p r o v i d i n g g u i d a n c e  advice i n p e r f o r m i n g this research a n d giving feedback d u r i n g the w r i t i n g process. provided encouragement  and  H e also  to complete a n d present this work at M D A , U B C , a n d I G A R S S ' 0 2 .  . T h e r e are several people at M D A w h o c o n t r i b u t e d k n o w l e d g e regarding R A D A R S A T - 1  systems.  Specifically,  thanks  goes to:  a n d suffered m y questions Martie  G o u l d i n g (whose  a l g o r i t h m I u s e d for c o m p a r i s o n a n d w h o r e v i e w e d t h i s m a n u s c r i p t ) , C a t h y V i g n e r o n ( w h o s e brain  I picked o n several  occasions  for v e r y specific  u p w i t h the original idea used in roll estimation  details),  algorithms),  Tony  Luscombe  and Bernd Scheuchl  A u s t r i a n v i e w o n life a n d S A R a p p l i c a t i o n s a l w a y s s e e m e d t o c l a r i f y t h e I w o u l d also like to t h a n k B o b H a w k i n s at  CCRS  (who  for t a k i n g t h e  came (whose  situation).  time  m a n u s c r i p t a n d p r o v i d e d significant feedback that was greatly appreciated.  to  review  this  I hope I could  answer most of his points properly. F i n a l l y , I w o u l d like to t h a n k the L o r d ,  J e s u s C h r i s t , for p r o v i d i n g s u c h a u n i q u e  and  useful r e m o t e sensing t o o l t h a t will h o p e f u l l y keep m e , a n d several others, o c c u p i e d for m a n y years to  come.  xiii  Chapter 1  Synthetic Aperture Radar: Background 1.1 Introduction Synthetic tions.  Aperture Radar  ( S A R ) is a n i n v a l u a b l e t o o l f o r m a n y  remote  sensing  applica-  T h e ability to actively gather i n f o r m a t i o n a b o u t the earth's surface, night or day, a n d  i r r e g a r d l e s s o f w e a t h e r c o n d i t i o n s , is e x t r e m e l y i m p o r t a n t f o r s e a - i c e m o n i t o r i n g [1],  cartog-  r a p h y , a g r i c u l t u r e , f o r e s t r y , c o a s t a l s u r v e i l l a n c e , a n d s o f o r t h . E a c h a p p l i c a t i o n h a s its particular needs in terms  of r e q u i r e d resolution,  tion, a n d other radar parameters.  coverage  Canada's  first  area, frequency b a n d , polariza-  I n p a r t i c u l a r , t h e r e q u i r e d a r e a o f c o v e r a g e is a p r i m a r y  consideration, a n d some recent S A R systems a c c o m m o d a t e imaging modes.  own  this by h a v i n g several  r a d a r satellite, R A D A R S A T - 1 ,  different  is a n e x c e l l e n t e x a m p l e  of  such a versatile satellite. R A D A R S A T - 1 h a s t w o m a i n i m a g i n g m o d e s , s i n g l e b e a m a n d S c a n S A R [2], e a c h o f w h i c h is c o m p r i s e d o f s e v e r a l b e a m s as g i v e n i n T a b l e 1.1. single b e a m i m a g i n g i n t h a t it sacrifices  S c a n S A R i m a g i n g differs f r o m c o m m o n  a z i m u t h r e s o l u t i o n for w i d e - s w a t h  m e t h o d b y w h i c h t h i s s a c r i f i c e is a c c o m p l i s h e d is b e s t e x p l a i n e d t h r o u g h  first  single b e a m S A R a n d t h e n c a r r y i n g that u n d e r s t a n d i n g over to S c a n S A R  1  coverage.  The  understanding  imaging.  Mode  Beam Name  Abbr.  Width  Unit  Single Beam  Standard  S1-S7  100  km  Single Beam  Extended Low/High Incidence  E L I , EH1-EH6  75/170  km  Single Beam  Fine  F1-F5  50  km  Single Beam  Wide  W1-W3  150  km  ScanSAR  Wide A  SCWA  500  km  ScanSAR  Wide B  SCWB  450  km  ScanSAR  Narrow A  SCNA  300  km  ScanSAR  Narrow B  SCNB  300  km  Table 1.1: RADARSAT-1 imaging modes and available beams  1.2  Single beam S A R  S i n g l e b e a m S A R is t h e i m a g i n g o f a c o n t i n u o u s s t r i p o f t h e e a r t h ' s s u r f a c e f o r a period. and  A s the satellite m o v e s i n its o r b i t a r o u n d t h e e a r t h , the satellite a n t e n n a  receives  signals  from within a  fixed  boundary.  far edges c o r r e s p o n d to the  the a n t e n n a b e a m pattern. of a single  image.  configuration. elevation, also  r  p  figure,  and m a x i m u m (max)  T h e m i n a n d m a x elevation  F i g u r e 1.1,  In this  m i n i m u m (min)  transmits  T h i s b o u n d a r y is d e f i n e d as a s t r i p o f  the earth's surface t h a t has a n e a r a n d far edge ( w i t h respect to the satellite). and  specified  angles are  These  near  elevation angles of  fixed  for the d u r a t i o n  o n the following page, depicts a s t a n d a r d single b e a m S A R  L is t h e a n t e n n a l e n g t h i n a z i m u t h , D is t h e a n t e n n a w i d t h i n  is t h e c h i r p d u r a t i o n a n d t h e i n t e r - p u l s e p e r i o d ( d e t e r m i n e d f r o m  1/PRF)  is  shown.  T h e s i g n a l t r a n s m i t t e d f r o m t h e a n t e n n a is a l i n e a r F M c h i r p o f fixed d u r a t i o n , b a n d w i d t h , a n d power. defines 1900  It is t r a n s m i t t e d a t fixed i n t e r v a l s for a s p e c i f i c i m a g e o n a c a r r i e r f r e q u e n c y w h i c h  t h e r a d a r b a n d (i.e.  k m ) f r o m the satellite  X , C , etc).  T h e signal travels a l o n g distance  to the surface a n d back; hence,  (approximately  the received signal strength  q u i t e l o w a n d r e c e i v e r t i m i n g b e c o m e s c r i t i c a l t o e n s u r e t h a t t h e c o r r e c t s i g n a l is and  r e c o r d e d . T h e r e c e i v e d s i g n a l is r e c o r d e d b y t h e s a t e l l i t e i n c o m p l e x f o r m .  s i g n a l h a s a r e a l i n - p h a s e (I) c o m p o n e n t , a n d a n i m a g i n a r y o r q u a d r a t u r e ( Q )  A  is  observed complex  component.  /L  Figure 1.1: Typical single beam S A R flight configuration. The satellite moves along the track at the top while illuminating an elevation swath of varying widths, according to Table 1.1  3  1.2.1  Factors affecting Signal Amplitude and Phase  S o m e m a i n f a c t o r s w h i c h a f f e c t t h e a m p l i t u d e , \JP  •  R a n g e to  target  dependent  ( a l s o k n o w n as  o n range.  R  =  slant  + Q,  range),  range to target  2  a r e t h e s e [3]:  E M wave  energy  in general a n d r  Q  =  strength  is  strongly  range at the  closest  approach.  •  T r a n s m i t t e r power,  P  •  A n t e n n a g a i n p a t t e r n s , G(9,  t  (j>), a l l a n t e n n a s h a v e a b e a m p a t t e r n w i t h n u l l s a n d l o b e s  w h i c h is d e p e n d e n t o n t h e e l e v a t i o n a n g l e 6 a n d t h e a z i m u t h a n g l e (f>.  •  T a r g e t r e f l e c t i v i t y , a, a n d t a r g e t i n c i d e n c e a n g l e ,  T h e a m o u n t of E M energy reflected  f r o m a target d e p e n d s o n its characteristics a n d i n c i d e n c e angle. T h e r e are several t e r m s t h a t m a y v a r y f r o m text to text, u s e d i n reference to  target  reflectivity:  — t a r g e t r a d a r c r o s s s e c t i o n ( R C S ) , o r a, is d e f i n e d as t h e s i z e o f a u n i f o r m l y r e f l e c t i n g s p h e r e t h a t r e t u r n s t h e s a m e a m o u n t o f E M e n e r g y as t h e t a r g e t , g i v e n i n m . 2  — a  0  is d e f i n e d as t h e f r a c t i o n a l p o r t i o n o f t h e e n e r g y r e f l e c t e d f r o m t h e t a r g e t , w h i c h  is a l s o s t a t e d a s t h e R C S / u n i t g r o u n d a r e a . — a°  is f u r t h e r d e f i n e d a s t h e d B r e p r e s e n t a t i o n o f c ° , n o r m a l i z e d t o p i x e l a r e a b y  a" = 10 x  l o g  1  0  3  ^ .  — (5° is t h e r e f l e c t i v i t y p e r u n i t s l a n t r a n g e ( d B ) , a n d is r e l a t e d t o a  0  10 x l o g  1 0  (sin(^))  b y (3° =  cr° —  [4].  S i g n a l p h a s e t a n ( Q / J ) h o w e v e r , is p r i m a r i l y a f f e c t e d b y :  •  range to target  (R)  •  t a r g e t s c a t t e r i n g m e c h a n i s m s w i t h i n a s i n g l e r a n g e c e l l , for e x a m p l e p e n e t r a t i o n d e p t h , s i g n a l i n t e r f e r e n c e p a t t e r n s , a n d so f o r t h .  A l l o f t h e s e f a c t o r s c o m b i n e t o g i v e t h e S A R f o r m o f t h e r a d a r e q u a t i o n [5]:  P G\B t  S  N  R  ~  </>) X a 3  eU  hs  2(i*)*R*kT Fva 0  4  B  a°r  y  '  '  where A is the carrier wavelength, au  is a n aperture-taper factor ( a ^ =  s  1 for u n i f o r m  i l l u m i n a t i o n ) , r is the across-track (range) resolution, k is B o l t z m a n n ' s constant = 1.38e—23, y  T  0  is the reference temperature, F is the receiver noise figure, v is the relative sensor-target  velocity, a n d a s is a pulse taper factor. F r o m (1.1), it can be seen that the S N R is strongly dependent on gain, frequency, a n d range. T h e frequency and range are t y p i c a l l y well k n o w n ; however, the gain pattern is based u p o n elevation angle, w h i c h is not. It is this u n c e r t a i n relationship of signal strength based on b e a m gain t h a t gives rise to the p r o b l e m addressed i n this thesis. O v e r a l l , scene S N R is affected b y proper r a d i o m e t r i c beam calibration. T h i s S A R version of the radar equation has several different forms. A d d i n g i n a r e l a t i o n chirp length T , a n d receiver  for S N R to the P R F , incidence angle 0j, squint angle 6 , sq  p  b a n d w i d t h B, gives another useful form: QNR =  P  '  G  (  2  2(4TT)  Interestingly, the range t e r m is R  3  *)  e ' »  g  A  v R  3  (cW2)<7°PRF  '  (fe T  3  B)  0  and not R , 4  sin  6,  sin  8  n  2 [  sq  '  , ]  as w o u l d be expected from the two-way  p r o p a g a t i o n of a n E M wave from a n isotropic source, and reflected from a perfect, u n i f o r m sphere back to the source. T h i s is given thus:  I (R)  = P /(4n  S  where I  s  t  R) 2  (1.3)  2  is the received intensity back at the source. For a real aperture radar, (1.3) does  hold true. However, a S A R coherently adds signal pulses so that the received signal voltage is a function of the number of s u m m e d pulses. T h i s coherent a d d i t i o n significantly affects signal d a t a b u t not noise, as seen below:  V  ,  aignal  N  (VLse,N)  =  NV,  (1.4)  =  N(V?)  (1.5)  V  2  SNR;v  =  ,yT ' = al N  )  N  S  N  R  i  ( ) L 6  \ noise,N/  where the subscript 1 implies the signal and S N R for a single pulse. T h e number of pulses t h a t are to be coherently added is a function of the radar p l a t f o r m parameters, a n d is given thus: N = £ 2r v ip a  1-7  w h e r e t h e p a r a m e t e r s a r e as p r e v i o u s l y d e s c r i b e d . U p o n s u b s t i t u t i o n o f (1.7)  i n t o (1.3), a n  R t e r m is r e m o v e d , r e s u l t i n g i n t h e r a d a r e q u a t i o n ( 1 . 1 ) .  1.2.2 The As  Signal Sampling  t r a n s m i t t e d F M c h i r p is r e c e i v e d a n d s t o r e d i n m e m o r y i n a r a n g e / a z i m u t h f o r m a t . the  chirp pulse  bounces  off e v e r y  target  in the  antenna, all of the factors m e n t i o n e d in subsection  satellite  1.2.1  footprint  a n d returns to  act o n the signal.  S i g n a l t i m i n g is  c r i t i c a l i n d e t e r m i n i n g h o w t h i s s i g n a l is s a m p l e d a n d r e c o r d e d . T h e r e a r e t w o d i f f e r e n t measurements  t h a t affect a S A R s y s t e m :  fast t i m e a n d s l o w  the  time  time.  Fast T i m e T h e s a t e l l i t e is t y p i c a l l y p r o g r a m m e d t o m a i n t a i n c o v e r a g e o f t h e s a m e m i n a n d m a x e l e v a t i o n angles t h r o u g h o u t the d u r a t i o n of the image.  Since the earth's radius depends o n latitude,  t h e n e a r a n d f a r r a n g e s w i l l c h a n g e as t h e s a t e l l i t e m o v e s .  T i m i n g p a r a m e t e r s a r e a d j u s t e d as  r e q u i r e d to m a i n t a i n the correct elevation angles; however, the n u m b e r of s a m p l e s r e c o r d e d per r a n g e line does n o t often c h a n g e d u r i n g a scene. In t e r m s of d a t a r e c o r d i n g , the near a n d far e d g e s of t h e s w a t h c a n t h e r e f o r e be c o n s i d e r e d  fixed  f r o m pulse to pulse, w h i c h  means  t h a t e a c h range line has the s a m e w i n d o w of o p p o r t u n i t y to receive a s i g n a l f r o m targets the  swath. This window  is q u i t e s h o r t , t y p i c a l l y <  a p p r o x i m a t e l y 3 meters.  0.4  ms, d u r i n g w h i c h t i m e the satellite  moves  S i n c e t h e r a n g e t o t a r g e t is a p p r o x i m a t e l y 8 0 0 - 9 0 0 k m , t h i s 3  s a t e l l i t e m o v e m e n t is c o n s i d e r e d i n s i g n i f i c a n t f o r t h i s o n e w i n d o w . for  in  m  A l l recorded signal d a t a  e a c h r a n g e l i n e is b a s e d e n t i r e l y o n t i m i n g i n t h e r a n g e d i r e c t i o n .  In a  RADARSAT-1  s i n g l e s t a n d a r d b e a m , o n e r a n g e s w a t h c a n c o v e r u p t o 100 k r n , a n d m a y h a v e a r a n g e c e l l s p a c i n g o f 12 m ; t h i s r e s u l t s i n a p p r o x i m a t e l y 8 0 0 0 r a n g e c e l l s p e r r a n g e l i n e b e i n g r e c o r d e d i n less t h a n 0.4 m s .  T h e r e f o r e , the sufficient s a m p l i n g a n d r e c o r d i n g i n t o r a n g e cells of o n e  t r a n s m i t t e d c h i r p p u l s e , r e f l e c t e d f r o m m a n y t a r g e t s , is s a i d t o b e o p e r a t i n g i n "fast  time",  T. T h e r e a r e s e v e r a l f a c t o r s w h i c h affect  received signal strength, a n d hence the ability to  s h a p e t h e a n t e n n a b e a m p a t t e r n t o fit t h e r e c e i v e w i n d o w is a n e c e s s a r y r e q u i r e m e n t o f a n y radar system.  T h e range b e a m pattern, W,  is t y p i c a l l y d e f i n e d i n t e r m s o f a n t e n n a  r  6  gain  ( d B ) a n d satellite elevation angle. into account,  w i t h the  JR~  3  It is c a r e f u l l y d e s i g n e d t o t a k e t h e f a c t o r s i n S e c t i o n  t e r m b e i n g one  of the  most  significant.  Hence,  two  1.2.1  identical  targets differing o n l y i n r a n g e will p r o d u c e slightly different returns, d e p e n d i n g o n  which  p o r t i o n of the b e a m p a t t e r n the signal passes t h r o u g h .  Slow T i m e In  order to p r o d u c e a n image  r a n g e , i t is n e c e s s a r y  that  has adequate  d a t a s a m p l i n g i n a z i m u t h , as w e l l as  t o t r a n s m i t a s e r i e s o f c h i r p p u l s e s as t h e s a t e l l i t e m o v e s i n i t s o r b i t .  A s p r e v i o u s l y m e n t i o n e d , e a c h t r a n s m i t t e d p u l s e r e q u i r e s less t h a n 0.4 m s , w h i c h m e a n s t h e s a t e l l i t e c o u l d t r a n s m i t a c h i r p a t i n t e r v a l s s l i g h t l y g r e a t e r t h a n 0.4 m s .  t h e r e a r e 8 t o 10 p u l s e s " i n t h e a i r " a t a n y o n e  large,  nadir  T h e s e a l l p l a y a r o l e i n s e l e c t i n g t h e P R F . F o r R A D A R S A T - 1 , t h e P R F is u s u a l l y  b e t w e e n 1200-1400 H z . W h e n t a k i n g satellite-earth  The  that  T h e r e are other  l i m i t a t i o n s as w e l l , i n c l u d i n g r a n g e t i m i n g , c h i r p d u r a t i o n , m e m o r y l i m i t a t i o n s , a n d returns.  in  a n t e n n a f o o t p r i n t for a single  g e o m e t r y into account, this m e a n s  that  time.  b e a m o n the surface of the  3-5 k m i n a z i m u t h a n d u p t o 150 k m i n r a n g e .  e a r t h is g e n e r a l l y  quite  Since the satellite only moves a  few  m e t e r s b e t w e e n p u l s e s , o n e t a r g e t m a y b e v i s i b l e to t h e a n t e n n a for 1000 different p u l s e s .  As  the satellite continues  t r a n s m i t t i n g a n d r e c e i v i n g , t h e r e c o r d e d d a t a is s t o r e d  b y r a n g e l i n e i n w h a t is c a l l e d "slow t i m e " , o r  sequentially  t.  T h e a z i m u t h b e a m p a t t e r n also has v a r y i n g g a i n b a s e d o n the a z i m u t h p o s i t i o n , m u c h like the range b e a m p a t t e r n has v a r y i n g g a i n b a s e d o n the elevation angle.  However, whereas the  r a n g e b e a m p a t t e r n was s p e c i f i c a l l y d e s i g n e d (in t h e o r y ) to a c c o u n t for s e v e r a l different g a i n factors, t h e a z i m u t h b e a m p a t t e r n uses u n i f o r m w e i g h t i n g , quite similar to a sine f u n c t i o n ( the range w i n d o w pattern, W, r  § 1  ^).  a n d hence,  its b e a m p a t t e r n  O t h e r t h a n their shapes, the m a i n difference  a n d the a z i m u t h window pattern, W , a  is  between  is t h e a s p e c t r a t i o o f  the footprint.  1.2.3  P h y s i c a l Effects of S i g n a l S a m p l i n g  O b s e r v i n g a n d r e c o r d i n g t h e s i g n a l d a t a i n a r a n g e / a z i m u t h f o r m a t a l l o w s for t h e d a t a be  correlated i n order to construct  appropriately matched  filter,  a radar image.  as d e r i v e d f r o m  7  the  E a c h r a n g e l i n e is c o r r e l a t e d w i t h transmitted  chirp parameters.  to an  During  t h i s c o r r e l a t i o n , k n o w n as r a n g e c o m p r e s s i o n , t h e d a t a t r a n s f o r m s f r o m noisy, or u n c o r r e -  cted  d a t a , to d a t a t h a t now has characteristics based o n a s u m of g r o u n d targets t h a t  are  e q u i d i s t a n t f r o m t h e s a t e l l i t e f o r e a c h p a r t i c u l a r r a n g e l i n e [3]. In o r d e r to d i s t i n g u i s h a m o n g s t m a n y t a r g e t s of e q u i d i s t a n c e for a single r a n g e cell, S A R s y s t e m s also correlate the d a t a i n the a z i m u t h d i r e c t i o n . phase difference  t h a t o c c u r s for each target,  T h i s c o r r e l a t i o n is b a s e d o n  in azimuth, due to a change  in the  the  satellite  p o s i t i o n for e a c h r a n g e line. A l t h o u g h t a r g e t s s e p a r a t e d i n a z i m u t h m a y c o n s t i t u t e a single range cell,  the  a z i m u t h phase  h i s t o r y of e a c h target  over a series of r a n g e lines  may  be  sufficient, so t h a t t h e a z i m u t h c o r r e l a t i o n or c o m p r e s s i o n w i l l b e a b l e t o d i s t i n g u i s h t h e m . D e p e n d i n g o n s y s t e m p a r a m e t e r s , a n o t h e r effect t h a t m a y h a v e t o b e c o r r e c t e d f o r is R C M . R C M  o c c u r s w h e n its r a n g e r e c e p t i o n t i m e varies m o r e t h a n o n e r e s o l u t i o n cell  defined  b y the  inverse  of the  range  s a m p l i n g rate)  over  a target's  exposure  (typically  time.  This  m i g r a t i o n is a w e l l - k n o w n f u n c t i o n o f s l o w t i m e , t, a n d t a r g e t d i s t a n c e , r , a n d is w r i t t e n as G  r(t,r ). 0  1.2.4  Point Target Signal Strength  O n c e a l l t h e p r e v i o u s c o n s i d e r a t i o n s a r e t a k e n i n t o a c c o u n t , R a n e y [6] d e f i n e s t h e r e c e i v e d a n d d e m o d u l a t e d (to b a s e b a n d ) s i g n a l s t r e n g t h f r o m a single p o i n t target, a s s u m i n g a — as  AxAy,  follows:  .(*,r.r.) = W.  W  W (r - ^ r  ) exp U  (r -  ^  )  exp  47T  .  .  -j—r{t,r  0/  (1. where  c  D  clear that  is t h e  speed  of light,  a n d A is t h e  signal carrier wavelength.  there are four m a i n factors d e a l i n g w i t h signal strength.  The  From first  (1.8), two  it  is  factors  are a m p l i t u d e factors a n d deal w i t h the a z i m u t h a n d range windows; the t h i r d a n d f o u r t h factors  are phase  factors.  T h e t h i r d factor represents  the  c h i r p for a specific  range  t h e f o u r t h d e a l s w i t h t h e D o p p l e r m o d u l a t i o n n e c e s s a r y for a z i m u t h c o m p r e s s i o n . second factor, W  r  and  It is t h e  t h e r a n g e w i n d o w a m p l i t u d e , w h i c h is t h e p r i m a r y f o c u s o f t h i s r e s e a r c h .  1.2.5 The  Range Window  range window  b e a m p a t t e r n , or range b e a m  a t t r i b u t e s of the r a d a r a n t e n n a . R A D A R S A T - 1  pattern,  is d e t e r m i n e d b y t h e  physical  was t h e first satellite t o h a v e s e v e r a l a v a i l a b l e  b e a m p a t t e r n s w h i c h c a n be selected based o n the scene i m a g i n g geometry.  Basic  antenna  d e s i g n t h e o r y f o r a flat a n t e n n a d i c t a t e s t h a t a n i n c r e a s e i n s i z e h a s t w o m a i n e f f e c t s o n  the  range b e a m pattern:  •  T h e m a i n b e a m lobe becomes more concentrated.  •  T h e g a i n is i n c r e a s e d .  SAR  antennas are specifically designed to be l o n g i n the d i r e c t i o n of travel, or a z i m u t h  direction,  a n d narrow in the  p o i n t i n g , or range direction.  This  results  in a range  beam  p a t t e r n t h a t is s i g n i f i c a n t l y l a r g e r t h a n t h e a z i m u t h b e a m p a t t e r n . T h e r a n g e b e a m p a t t e r n i n single b e a m m o d e c a n cover 8000 r a n g e cells, w h i l e the a z i m u t h b e a m p a t t e r n m a y cover o n l y 1000 a z i m u t h s a m p l e s . S i n c e t h e r a n g e b e a m p a t t e r n is b a s e d o n e l e v a t i o n a n g l e a n d c o n v e r t e d t o a s l a n t r a n g e , any  errors that o c c u r while correcting the range b e a m p a t t e r n will also be based o n elevation  angle, or slant range. and  T h i s c o n v e r s i o n is n e c e s s a r y b e c a u s e  not elevation angle.  have  the  same  the radar measures slant  I n a z i m u t h , t h e b e a m p a t t e r n is b a s e d o n f r e q u e n c y .  D o p p l e r frequency b a n d w i d t h ; thus,  targets  range  A l l targets  are t r a n s m i t t e d a n d  received  through the same azimuth b e a m pattern. The  axes o n the  final  single  b e a m scene however,  are based  o n slant  range  (which  is  n o r m a l l y converted to a g r o u n d range) a n d a z i m u t h time, not a z i m u t h frequency. T h e r e f o r e , range b e a m - p a t t e r n errors resulting f r o m the  application of the  wrong R D G C  appear  as  constant gain variations in the a z i m u t h direction that vary in intensity in the range direction. H o w e v e r , e r r o r s i n t h e a z i m u t h b e a m - p a t t e r n c o r r e c t i o n affect t h e a z i m u t h f r e q u e n c y o f t h e s c e n e , a n d a r e n o t as v i s i b l e t o t h e e y e s i n c e t h e e r r o r s e q u a l l y affect a l l t a r g e t s . scene content,  incidence angle dependence,  A G C e r r o r s , a n d o t h e r effects, m a y  However, contribute  m o r e t h a n b e a m - p a t t e r n errors (in either range or a z i m u t h ) to the a m p l i t u d e d a t a . Since range errors resulting from a n incorrect range R D G C  application cause  d e f e c t s i n t h e i m a g e , i t is i m p o r t a n t t h a t t h e c o r r e c t R D G C b e u s e d .  9  obvious  T h i s requires accurate  knowledge  of the  satellite attitude,  mainly, the  roll angle.  Unfortunately,  does not provide very accurate roll angle d a t a f r o m o n - b o a r d attitude down-link.  A s i m p l e d e s c r i p t i o n o f t h e p r o b l e m is t h a t  RADARSAT-1  sensors i n the  RADARSAT-1  has very  r a n g e t i m i n g , b u t less a c c u r a t e a n t e n n a p o i n t i n g i n f o r m a t i o n , a n d b a s e d o n by  data  accurate  measurements  C S A , roll control m a y only be w i t h i n ± 0 . 3 ° . D e p e n d i n g o n the selected b e a m , scene r a d i o m e t r y , a n d other factors, single b e a m S A R  is n o t as s e n s i t i v e t o i n c o r r e c t R D G C a p p l i c a t i o n s as S c a n S A R . T h i s is b e c a u s e r a d i o m e t r i c errors v a r y slowly t h r o u g h o u t the scene. errors in R D G C 0.2  t o 0.3  S c a n S A R imagery, however,  corrections, since s m a l l g a i n differences  d B a r e e a s i l y n o t i c e d as d i s c o n t i n u i t i e s  i n target  is s e n s i t i v e t o  small  brightness greater  i n t h e s c e n e [7].  T h i s is b e c a u s e  b e a m S A R is b a s e d o n o n e b e a m , w h i l e S c a n S A R m u s t s t i t c h t o g e t h e r t w o o r m o r e  than single  beams.  In t h e o v e r l a p r e g i o n , e a c h b e a m h a s its o w n , a n d u s u a l l y o p p o s i t e , g a i n e r r o r s w h i c h  create  a d i s c o n t i n u i t y i n i m a g e intensity at the s t i t c h i n g p o i n t .  1.3  ScanSAR  S c a n S A R w a s d e v e l o p e d p r i m a r i l y for t h e p u r p o s e of i n c r e a s i n g t h e c o v e r a g e a r e a o f a S A R system,  at  the  expense of a z i m u t h resolution,  f r o m a n o r m a l s i n g l e b e a m S A R [5].  and without  significant  hardware  changes  T h i s is a c h i e v e d b y u s i n g a t l e a s t t w o d i f f e r e n t  range  swaths a n d r e d u c i n g the a m o u n t of time spent i m a g i n g each. Instead of focusing o n a single i m a g e strip, S c a n S A R switches b e t w e e n strips of different ranges. necessarily  affected,  as  the  range sampling parameters  do not  R a n g e r e s o l u t i o n is  change;  however,  not  azimuth  r e s o l u t i o n is d e g r a d e d a c c o r d i n g t o t h e l o w e r b a n d w i d t h a v a i l a b l e for f o r m i n g a n i m a g e  in  each different range strip. In the R A D A R S A T - 1  S c a n S A R system,  a p p r o x i m a t e l y 57-120 pulses are t r a n s m i t t e d  e a c h s t r i p before the s y s t e m switches to the n e x t strip.  T h i s g r o u p of pulses,  a i m e d at  at the  s a m e s t r i p , is c a l l e d a b u r s t . A s p r e v i o u s l y m e n t i o n e d , P R F ' s v a r y f r o m 1 2 0 0 - 1 4 0 0 H z , w h i c h means  t h a t t h e s y s t e m h a s a p p r o x i m a t e l y 12 t o 15 b u r s t s p e r s e c o n d .  t y p i c a l S c a n S A R i m a g i n g p a t t e r n , p l e a s e refer t o F i g u r e  F o r a n e x a m p l e of a  1.2.  A l t h o u g h F i g u r e 1.2 s h o w s n o o v e r l a p b e t w e e n d i f f e r e n t r a n g e s t r i p s , i n r e a l i t y t h e r e be significant  overlap (in b o t h range a n d azimuth)  10  f r o m a few  h u n d r e d o f cells to  a  can few  Azimuth Figure 1.2: Typical ScanSAR pattern consisting of four beams. Each beam is illuminated in blocks known as bursts. Each burst for a specific beam has the same bandwidth. thousand. R D G C  L u s c o m b e [8] s u g g e s t s t h e u s e o f t h e r a n g e o v e r l a p a r e a s t o i m p r o v e t h e o v e r a l l  corrections.  Since targets  near the s w a t h b o u n d a r i e s are i m a g e d b y two  different  r a n g e b e a m s at t h e s a m e i n c i d e n c e angles, differences b e t w e e n t h e r e c e i v e d s i g n a l e n e r g y for the s a m e target c a n t h e n b e a t t r i b u t e d to g a i n differences i n the S A R s y s t e m patterns). in P R F s ,  (i.e.  T h i s a s s u m e s t h a t a l l o t h e r f a c t o r s h a v e b e e n a c c o u n t e d f o r , s u c h as t r a n s m i t energy,  a n d so o n .  T h e knowledge gained f r o m analyzing the  antenna  differences resulting  g a i n differences c a n t h e n be d i r e c t l y a p p l i e d to i m p r o v i n g the overall s w a t h c a l i b r a t i o n .  1.3.1  S c a n S A R Calibration Errors  T h e r e are two m a i n errors t h a t result f r o m u n c e r t a i n t y i n satellite orientation: a z i m u t h g a i n errors a n d range gain errors.  A l t h o u g h b o t h occur due to i m p r o p e r application of  c o r r e c t i o n p a t t e r n s , t h e r e s u l t o f e i t h e r e r r o r is s i g n i f i c a n t l y d i f f e r e n t .  11  beam  A z i m u t h Calibration Errors In the  a z i m u t h direction, the  moves.  T h e range to target  range  to  target  or slant  is d e f i n e d b y E q u a t i o n (1.9)  r a n g e a t c l o s e s t a p p r o a c h , v is s a t e l l i t e v e l o c i t y , closest a p p r o a c h , n . 0  range,  R,  for a  c h a n g e s as  flat  the  earth, where  satellite r  0  is  the  a n d n is a z i m u t h t i m e f r o m t h e t i m e  of  A s s u m e t h e e a r t h is s t a t i o n a r y a n d t h e s a t e l l i t e is m o v i n g i n a s t r a i g h t  line, otherwise v represents the relative satellite-target  velocity.  2  R(n) = Vr + v (v-rj ) 2  2  0  2  0  ~ r + ^-(r,  -  0  T h e r a n g e r a t e o f c h a n g e is t h e d e r i v a t i v e o f (1.9) f r e q u e n c y c a n b e c a l c u l a t e d as  4 r? ) 0  2  -  ^ ( r ? -  a n d is g i v e n as R.  V o  )  4  + ...  (1.9)  F r o m this, the D o p p l e r  follows:  f * = ™  (1-10)  T a r g e t altitude, target range, satellite/earth geometry, satellite orientation, a n t e n n a b e a m p a t t e r n , a n d e a r t h r o t a t i o n a l l affect t h e t a r g e t g e o m e t r y f o r a s i n g l e t a r g e t o n o n e r a n g e - l i n e in R A D A R S A T - 1 .  I n t e r m s o f a z i m u t h p a t t e r n c a l i b r a t i o n , t h i s w o u l d n o t b e as s i g n i f i c a n t a  p r o b l e m as i f t h e e n t i r e s c e n e w a s a z i m u t h c o m p r e s s e d i n o n e s t a g e , t h a t is n o m u l t i - l o o k i n g . H o w e v e r , a z i m u t h c o m p r e s s i o n is a l m o s t a l w a y s a c h i e v e d i n a m u l t i - l o o k i n g o p e r a t i o n  across  t h e s c e n e . H e n c e , t h e effects o f D o p p l e r e r r o r s c a n b e s i g n i f i c a n t f o r b o t h a z i m u t h c o m p r e s sion a n d a z i m u t h beam-pattern calibration. T h e a z i m u t h b e a m p a t t e r n varies w i t h a z i m u t h frequency.  M o r e specifically, the a z i m u t h  b e a m p a t t e r n moves over targets f r o m a m i n i m u m gain to a m a x i m u m gain a n d back a m i n i m u m g a i n w i t h r a n g e a n d f r e q u e n c y r e l a t e d b y (1.9) S c a n S A R , h o w e v e r , t h e t o t a l a z i m u t h b a n d w i d t h BW  a  s o t h a t t h e b a n d w i d t h p e r b e a m is n o w BW  t  N  0  is t h e n u m b e r o f b e a m s .  =  a n d (1.10).  In  RADARSAT-1  must be d i v i d e d between each where i represents  to  beam  the i t h b e a m  and  S i n c e t h e a z i m u t h b e a m p a t t e r n is b a s e d o n a z i m u t h f r e q u e n c y ,  there are gaps i n each S c a n S A R target's D o p p l e r history, whereas single b e a m m o d e has  a  m o r e c o m p l e t e D o p p l e r history. T h e s e gaps are regions i n the a z i m u t h b e a m p a t t e r n t h r o u g h w h i c h a t a r g e t is n o t i m a g e d f o r a p a r t i c u l a r b e a m . b e a m a n d S c a n S A R a z i m u t h D o p p l e r histories.  12  S e e F i g u r e 1.3 f o r a c o m p a r i s o n o f s i n g l e  Each T a r g e t has a d i f f e r e n t Bandwidth and C e n t e r F r e q u e n c y b a s e d on A z i m u t h P o s i t i o n  Azimuth Beam-Pattern  Figure 1.3: Target azimuth bandwidth resulting from burst operations and its applicable azimuth beampattern gain. A single ScanSAR target will NOT have a complete azimuth spectral history as compared to a single beam target. Each ScanSAR target has a different centre frequency from its closest neighbours. Improper azimuth pattern correction increases the gain of some azimuth frequencies and lowers others. This produces a scalloping effect. When applying the correct azimuth beam-pattern correction, it is critical to know the Doppler centre frequency (Doppler centroid), as this corresponds to the centre of the azimuth beam pattern [9]. Beam-pattern correction is required so that each azimuth frequency receives the correct uniform weighting in the final image. Targets separated in azimuth are imaged through different portions of the beam pattern; thus, the beam-pattern corrections for each are based on their respective frequencies. If the Doppler centroid is not known to 13  sufficient  a c c u r a c y , t h e n targets w i l l receive the w r o n g corrections.  H e n c e , for e a c h  look, targets t h a t otherwise have a u n i f o r m R C S a p p e a r to have intensity o n frequency.  vice versa.  Note  A s time  that  targets increase  progresses,  the  in frequency  towards  the  target's D o p p l e r frequency  azimuth  variations  t o p o f F i g u r e 1.3  decreases.  If t h e  at  In the  final  S c a n S A R image,  a n d t h e o p p o s i t e is t r u e f o r a n e g a t i v e these v a r i a t i o n s r e m a i n after  different  T h i s does not  D o p p l e r frequencies  beam-pattern corrections.  h o l d t r u e for single b e a m  for e a c h target  transforming the  T h e r a m p w i d t h is b a s e d  range  line  thousands  l i n e i s less n o t i c e a b l e ,  of range lines instead of just  r a m p i n the scene rather t h a n several.  the  azimuth  azimuth  s a m e g a i n difference  hundred.  In other words,  spreads  14  one  clearly  compensation  H e n c e , the usual r a m p has b e e n replaced b y a n absolute v a l u e d sine-like pattern.  across  t h e r e is o n l y  F i g u r e 1.5 [10] i l l u s t r a t e s a s c a l l o p i n g e x a m p l e  due to the m a i n - l o b e of the a z i m u t h b e a m  as  i n one stage, t h e n the g a i n v a r i a t i o n f r o m  since the  a few  is k n o w n  in each  s h o w i n g i t s p e r i o d i c n a t u r e ; h o w e v e r , i n t h i s c a s e t h e r e is n o a z i m u t h p a t t e r n at all.  illustrates  ramp,  o n the a z i m u t h w i d t h of d a t a used  If t h e e n t i r e s c e n e is a z i m u t h c o m p r e s s e d range  incomplete  frequency.  i n this case a n intensity  look.  to  back  I n t h e b o t t o m p o r t i o n , t h e a z i m u t h p o s i t i o n a x i s is i n t o t h e p a g e  r e s u l t i n g p e r i o d i c or c y c l i c a l artifact,  scalloping.  S A R . F i g u r e 1.4  data  along w i t h the correct a n d incorrect  a s t a r g e t s 1-4 d i f f e r i n a z i m u t h p o s i t i o n as w e l l as The  passed  frequency.  f r o m a z i m u t h f r e q u e n c y to a z i m u t h t i m e b e c a u s e each target has a different a n d D o p p l e r history.  and  azimuth  a m b i g u i t y n u m b e r is z e r o , t h e n a p o s i t i v e f r e q u e n c y r e f e r s t o a t a r g e t t h a t h a s n o t the r a n g e of closest a p p r o a c h , r  based  function,  -Azimuth Frequency-  Azimuth Gain  T a r g e t s that d i f f e r i n frequency now have a v a r y i n g i n t e n s i t y a c r o s s azimuth look  this  Figure 1.4: Gain differences from an incorrect azimuth pattern correction due to Doppler centroid estimation error. Target 1 and target 4 should have the same amplitude; however, the wrong pattern correction was used and now target 1 is lower than target 4.  15  Range  •  Figure 1.5: Example of azimuth scalloping. This is an image of Venus and no azimuth pattern correction is used [10]. Each azimuth look has a noticeable sine pattern in the amplitude data.  Range Calibration Errors Application  of the  wrong R D G C  is t y p i c a l l y c a u s e d  variations in the range b e a m pattern. the processed amplitude.  imagery),  In single  errors will v a r y slowly  with  S A R this range.  imaged is n o t  b y two  from one swath  beam patterns,  usually a significant  However,  in S c a n S A R  stitching together two or m o r e b e a m range swaths. same target  final  scene.  Hi  the  to have  a  p r o b l e m since final  scene  T h u s , a n y g a i n differences  t o t h e n e x t is q u i t e n o t i c e a b l e  parallel to the a z i m u t h axis, in the  an u n k n o w n roll angle  A n y error in the gain corrections cause a target  independently  beam  b y either  a n d a p p e a r as  or (in  different any  gain  is c r e a t e d  by  between  the  discontinuities,  R A D A R S A T - 1 has several different beams for varying purposes.  Its standard beams  are all approximately 100 km wide and are labelled S i through S7. The beams increase in elevation angle (or slant range) starting with S i and ending with S7. There are also three beams, approximately 150 k m wide, labelled W l through W 3 . These wide beams also increase in elevation angle (or slant range), starting with W l and ending with W 3 . R A D A R S A T - 1 has a unique ScanSAR mode which uses a combination of its standard and wide beams. R A D A R S A T - 1 has four ScanSAR beam modes, each of which utilizes different beam patterns and different combinations of beam patterns. These four ScanSAR beam modes are illustrated in Figure 1.6 based on their elevation angle and gain [7].  The  SCWB  j  i  -20  20  0  W  SCNA  rG  W2\^  Wl \  ^ -1 0 •H  F o u r RADARSAT ScanSAR  L  i  20  15  -1 0 -20 15  -i  J  25  30  1  1  \  CN  0  A  i  35 1  , i  \k-  S6  40 —i  45  40 1  45  Wl^*—^-^>  3-10 -20  Combinations  1  SCNB  i / 25 i W2  W2  ^ 35  30 1  1 —  \ 20  J i / 25 30 Elevation  s s  S6 \  t 35  40  45  Angle  Figure 1.6: ScanSAR beam configurations from payload file 25  [7]  The patterns show the dB gain variations from payload file 25 (effective starting time = 2000/109/23:00:17.000). The payload file [11] data is initially provided in one-way dB gain versus elevation angle; however, in Figure 1.6 the patterns are converted to the two-way gains. From Figure 1.6, it can be seen that the overlap area differs significantly from beam  17  to b e a m .  T h e W 1 - W 2 o v e r l a p is t h e s m a l l e s t ,  a p p r o x i m a t e l y 2 ° , w h i l e t h e W 2 - S 5 o v e r l a p is  the largest, a p p r o x i m a t e l y 6 ° . In  RADARSAT-1,  six different b e a m s , is d e f i n e d as t h e interface  may  there  are four different  ScanSAR  combinations  use  w h i c h r e s u l t s i n a t o t a l o f five d i f f e r e n t b e a m i n t e r f a c e s .  t r a n s i t i o n p o i n t f r o m one b e a m to a n o t h e r .  be  that  based  on  the  c a l i b r a t e d to have equal gains. of the b e a m interfaces.  elevation  angle  at  An  of  interface  T h e desired l o c a t i o n of  which both  R e f e r t o F i g u r e s 1.7,  a total  beam  patterns  have  1.8, a n d 1.9 f o r a n i l l u s t r a t e d  the been  example  However, other factors m a y be used to choose the interface, such  as  a Nadir ambiguity. D u r i n g s c e n e p r o c e s s i n g , t h e i n t e r f a c e is t h e p o i n t a t w h i c h d a t a f r o m t h e n e a r b e a m r e p l a c e d b y d a t a f r o m the far b e a m to c o m p l e t e  the range line.  In simple b e a m  is  stitching  a l g o r i t h m s , n o d a t a is a v e r a g e d i n t h e f i n a l s c e n e , e v e n t h o u g h e a c h b e a m m a y i m a g e  the  s a m e a r e a . S i n c e t h e i n t e r f a c e p o i n t is b a s e d o n e l e v a t i o n a n g l e a n d b e a m - p a t t e r n g a i n s ,  any  change  i n either of these factors d u r i n g the a c t u a l image  g a i n difference  i n the scene.  T h i s g a i n difference  appears at the s a m e elevation  s e v e r a l h u n d r e d r a n g e l i n e s d u r i n g t h e s c e n e a n d is e a s i l y Mittermayer 0.02  acquisition will cause an abrupt  discontinuity.  for  noticed.  [12] h a s s u g g e s t e d , i n s i m u l a t i o n , t h a t e r r o r s i n t h e e s t i m a t e d  degrees c a n cause a noticeable  angle  roll angle  M a r t i n et a l . [13] r e p o r t t h a t 0.1  of  degree  e r r o r is t h e r e q u i r e d l i m i t f o r 1 d B c a l i b r a t i o n a c r o s s t h e s c e n e . L a t e r , i n C h a p t e r 3, t h i s i s s u e is e x p l o r e d i n a n a t t e m p t t o h e l p d e f i n e w h a t t h e a c t u a l a c c u r a c y r e q u i r e m e n t i s a n d h o w i t affects R A D A R S A T - 1  S c a n S A R . F i g u r e 1.10 is a n e x a m p l e o f t h e r a n g e b e a m p a t t e r n s  t h e r e s u l t i n g e r r o r i n a t y p i c a l final S c a n S A R s c e n e .  ScanSAR Beam  Abbr.  Beam 1  Beam 2  Beam 3  ScanSAR ScanSAR ScanSAR ScanSAR  SCWA SCWA SCNA SCNB  Wl Wl Wl W2  W2 W2 W2 S5  W3 S5  Wide A Wide B Narrow A Narrow B  S6  Beam 4 • S7 S6  Swath (km) 500 450 300 300  Table 1.2: RADARSAT-1's ScanSAR combinations 18  Inc Angles (min-max Degs) 20-51 20-49 20-39 31-49  and  0  R o l l Angle E s t i m a t i o n E r r o r R e s u l t i n g i n a Discontinuity 1  1  1  1  T  T r a n s i t i o n Point ^ (Interface)  -5  RDGC 2  -10  -15  -20  34  36  38  Beam E l e v a t i o n Angle (degs)  id o a) «  s  -201—L  Figure 1.7: Range pattern gain overlap transition point  In Figure 1.7, beams 1 and 2 represent the signal strength for each beam. Both beams are created using a roll angle of 1° above the nominal one. The R D G C s used for their correction, however, assume that the roll angle is nominal (i.e no roll angle estimation error). The top portion shows the entire beam pattern while the bottom portion focuses on the beam patterns used to create the final scene. If these R D G C s are applied to the data, beam 1 gets overcorrected while beam 2 gets under-corrected. The resulting discontinuity is indicated by an arrow and is the sum of gain errors for each beam at the interface. In Figures 1.8 and 1.9, a —0.2° roll error is assigned to two different interfaces, the W2S5 and W 1 W 2 interface respectively. The top portion of each figure is the incorrect R D G C application (—0.2°), while the bottom represents the correct R D G C application.  19  P r o p e r and Improper RDGC A p p l i c a t i o n t o W2S5 40 i  1  1  1  28  29  30  1—i  1  Interface  1  1  1-  33  34  35  CQ T3  a  -H O  27  31  32  E l e v a t i o n Angle  (Degs)  Figure 1.8: Range pattern gain correction with and without roll error for W2-S5 interface  Figure 1.8 illustrates both the right and wrong R D G C application to the un-corrected signal data. The un-corrected data is the data line in the middle. The top portion represents the improperly corrected signal data. There are gain variations throughout this line and a discontinuity (approximately 1 dB) is present at the interface point. The bottom portion clearly shows the right corrected uniform range line with no variations or discontinuities present. The wrong and right corrections are shown with a +20 d B and -20 d B offset, respectively, for display purposes only.  20  Proper and Improper RDGC A p p l i c a t i o n t o W1W2  E l e v a t i o n Angle  Interface  (Degs)  Figure 1.9: Range pattern gain correction with and without roll error for W1-W2 interface Again, Figure 1.9 shows a uniform result for the correct R D G C , in the bottom portion, and an incorrect R D G C application in the top portion produces a discontinuity. The size and shape of the discontinuity present (approximately 1.5 dB) in the W 1 W 2 overlap is different from the W2S5 overlap. Note also that the gain variations throughout the range line are smaller. The differences between the W2S5 and W 1 W 2 interfaces are due to the varying slopes present in the R D G C s for each particular beam combination. Hence, every beam combination will produce different errors, even though they may all be subject to the same roll estimation error.  21  These  •  figures  help illustrate two  points:  N o t o n l y d o discontinuities result f r o m a n incorrect R D G C ,  b u t there are clearly g a i n  v a r i a t i o n s across the entire s w a t h w i t h e x t r e m e differences f o u n d at either e n d .  •  A  E a c h interface w i l l have a different response to the s a m e roll error.  h u m a n o b s e r v e r l o o k i n g a t F i g u r e 1.10  may  variations a distraction a n d a nuisance; however, sification  a l g o r i t h m will find  processing  to a S c a n S A R  them  find  this discontinuity  a n d the  other  gain  a n y a u t o m a t e d target r e c o g n i t i o n or clas-  downright confusing.  s c e n e , s u c h as c l a s s i f i c a t i o n ,  Also,  i n order to  apply  this c a l i b r a t i o n issue m u s t  further first  be  solved.  1.3.2  Factors H i n d e r i n g Calibration  Proper R D G C  a p p l i c a t i o n , as d e p i c t e d a t t h e t o p o f F i g u r e s 1.8 a n d 1.9, s h o u l d r e d u c e  v a r i a t i o n s i n the final i m a g e so t h a t a u n i f o r m target a r e a a p p e a r s a t a c o n s t a n t in the  final scene.  calibration.  However,  there  are other factors  besides roll angle  L u s c o m b e [8] h i g h l i g h t s s o m e o f t h e s e as t h e  •  E r r o r s in the shape of the  •  E r r o r s i n the overall gain of the R D G C  any  intensity  errors w h i c h  affect  following:  RDGC,  (for e a c h r e s p e c t i v e  beam).  F o r applications based o n the C a n a d i a n Space A g e n c y ' s R A D A R S A T - 1 satellite imagery, these b e a m  patterns  via payload  files.  P a y l o a d files a r e u p d a t e d e v e r y 6-9 m o n t h s a n d c o n t a i n t h e l a t e s t s a t e l l i t e p a r a m e t e r s ,  such  as a n t e n n a e l e v a t i o n  have  been  assumed  to be c a l i b r a t e d a n d u p d a t e d ,  a n d a z i m u t h b e a m patterns.  R e c e n t o b s e r v a t i o n has s h o w n that  the  p a y l o a d c a l i b r a t i o n files m a y n o t b e s u f f i c i e n t l y a c c u r a t e ; t h u s , t h e s e a d d i t i o n a l e r r o r s s h o u l d b e a c c o u n t e d for i n a n y c a l i b r a t i o n a l g o r i t h m . L e s s s i g n i f i c a n t s o u r c e s o f e r r o r a l s o e x i s t , a s h i g h l i g h t e d b y L a n c a s h i r e [14], s u c h a s following:  •  A D C saturation,  •  Errors based on  ambiguities,  22  the  •  E r r o r s b a s e d o n differing S N R levels between  beams,  •  E r r o r s b a s e d o n s u r f a c e h e i g h t a n d c o n t o u r effects, a s i g n i f i c a n t p o r t i o n o f w h i c h r e s u l t s f r o m u n k n o w n incidence angle based variations i n scattered signal strength.  O f t h e s e , a n a l o g t o d i g i t a l c o n v e r s i o n ( A D C ) s a t u r a t i o n is t h e m o s t c o m m o n a n d s i g n i f i cant s y s t e m error.  T y p i c a l l y , the a u t o m a t i c gain correction ( A G C ) a t t e m p t s to m a i n t a i n a  c o n s t a n t r e c e i v e d s i g n a l s t r e n g t h f o r t h e A D C w i t h i n a n o m i n a l r a n g e o f v a l u e s (4 b i t s f o r RADARSAT-1  [15]).  It d o e s t h i s b y s a m p l i n g t h e a v e r a g e e n e r g y p e r r a n g e l i n e , f r o m  the  first q u a r t e r o f t h e s w a t h , for eight r a n g e lines at a t i m e . T h e A G C s y s t e m a d j u s t s t h e A G C g a i n f a c t o r for t h e n e x t eight r a n g e lines a c c o r d i n g l y . A few c o m m o n r e a s o n s for A G C e r r o r s are the following:  1. U n d e s i r e d s i g n a l s t r e n g t h d u e t o n a d i r r e t u r n s .  N a d i r r e t u r n s are signals w h i c h are  reflected f r o m the earth's surface d i r e c t l y below the satellite. allows  for h i g h l y reflective  scattering from  the surface;  T h e zero angle of incidence  however,  appropriate timing  selection c a n u s u a l l y place this r a d a r r e t u r n outside the receive w i n d o w .  2. I n S c a n S A R  specifically,  there  are  s e v e r a l b l a n k r a n g e lines t h a t result f r o m t h e t i m e r e q u i r e d for a p u l s e t o t r a v e l to  the  surface a n d return.  as t h e  antenna switches between  b e a m patterns,  S i n c e t h e A G C is o n d u r i n g t h i s p e r i o d , i t a s s u m e s t h a t t h e s i g n a l  s t r e n g t h is s i m p l y l o w e r t h a n n o r m a l a n d a t t e m p t s t o c o r r e c t i t b y i n c r e a s i n g t h e g a i n . U n f o r t u n a t e l y , a l m o s t as s o o n as t h i s f a l s e c o r r e c t i o n is m a d e , t h e r e f l e c t e d p u l s e s b e g i n r e t u r n i n g a n d are s a m p l e d w i t h t o o h i g h a g a i n ; after sufficient pulses  the A G C setting  is t h e n c o r r e c t .  c o r r e s p o n d i n g to a single swath, the  s a m p l i n g of regular  T h e e n d effect is t h a t f o r e a c h set  first  of  pulses  8-10 a r e i n v a l i d , t h e n e x t 8-10 h a v e t o o h i g h  a g a i n , a n d the r e m a i n d e r are c o r r e c t l y s a m p l e d .  3. T h e g a i n e s t i m a t e s a r e d e r i v e d f r o m t h e e n e r g y i n t h e first q u a r t e r o f t h e s w a t h ;  hence,  there c a n also b e errors if this q u a r t e r significantly d e v i a t e s f r o m t h e r e m a i n d e r of the swath.  U n l i k e r o l l a n g l e e r r o r s , A G C e r r o r s effect t h e e n t i r e s w a t h i n t h e s a m e m a n n e r . T h e y c a n b e c o r r e c t e d b y a c o n s t a n t g a i n c h a n g e to the entire line w i t h o u t significant error a d d i t i o n ,  23  unless d a t a has  been  lost t h r o u g h s a t u r a t i o n at  s a t u r a t i o n h a s o c c u r r e d t h e n t h e r e is n o m e t h o d c o n s i d e r e d lost, d e p e n d i n g o n the severity.  either  end of the  4 bit range.  If s e v e r e  to recover the d a t a a n d the line m a y  A G C errors m a y differ f r o m o n e  b e a m to  be the  n e x t , a n d as s u c h , a n y A G C e r r o r m a y c o n t r i b u t e t o c r e a t i n g g a i n e r r o r s i n c o r r e c t e d d a t a . Differences i n A G C settings s h o u l d be i n c l u d e d into the R D G C  application to help  reduce  t h e s e effects. The  other  errors noted  by Lancashire, ambiguity,  S N R a n d surface  height  effects,  are  t y p i c a l l y n o t as s i g n i f i c a n t o r c o m m o n f o r m o s t s c e n e s . M o s t a m b i g u i t i e s a r e l i m i t e d i n s i z e a n d strength; however,  a m b i g u i t i e s c a u s e d b y n a d i r r e t u r n s m a y s i g n i f i c a n t l y affect  s i g n a l s t r e n g t h e v e n if t h e y d o n o t cause p r o b l e m s w i t h A G C settings.  overall  S o l u t i o n s for n a d i r  r e t u r n s a r e d i f f i c u l t a n d t h e p r o b l e m is b e s t r e s o l v e d b y a g a i n p r o p e r l y s e l e c t i n g b e a m t i m i n g p a r a m e t e r s so t h a t n a d i r r e t u r n s o c c u r o u t s i d e the receive The •  final  window.  c a l i b r a t i o n e r r o r s , n o t e d b y G o u l d i n g [16], a r e t h e  T h e elevation  b e a m c e n t r e a n g l e for e a c h r a n g e b e a m p a t t e r n c a n n o t  remain constant  — A s time  following:  relative to each other.  passes,  variations  in the  centers t o shift i n d e p e n d e n t l y . time (months)  be assumed  T h e r e a r e t w o m a i n r e a s o n s for this:  beam  patterns  may  cause the  elevation  beam  T h i s s h i f t i n g p r o b a b l y o c c u r s o v e r l o n g p e r i o d s of  a n d c a n b e a s s u m e d to b e fixed for a single scene b u t n o t for scenes  t a k e n a few m o n t h s  apart.  — R a n g e b e a m c a l i b r a t i o n is b a s e d o n a s i n g l e b e a m c a l i b r a t i o n p r o c e s s . that while each range b e a m pattern m a y be calibrated w i t h respect i t s n o m i n a l c e n t r e e l e v a t i o n a n g l e , t h e r e is n o g u a r a n t e e  T h e b e a m patterns  This  t h e m s e l v e s are n o t w e l l - k n o w n i n t h e i r respective  means  to itself  that each beam's  elevation angle has been p r o p e r l y m e a s u r e d w i t h respect to the other  •  to  and  centre  beams.  low gain  areas  n e a r t h e b e a m e d g e s . T h i s is p o t e n t i a l l y a s i g n i f i c a n t s o u r c e o f e r r o r i n e s t i m a t i n g r o l l a n g l e a n d is f u r t h e r e x p l o r e d i n t h i s t h e s i s .  It is h e n c e f o r t h r e f e r r e d t o as  the  "beam  gain uncertainty".  Therefore,  any calibration strategy  should take into account  centers a n d u n c e r t a i n low g a i n areas.  24  these possibly shifting  beam  1.4  Related Compensation Strategies  RADARSAT-1  h a r d w a r e d e s i g n is f i x e d , a n d as s u c h , r o l l a n g l e e s t i m a t e s m u s t b e  o n received signal radiometric strength.  G i v e n t h e r e q u i r e m e n t for precise satellite  based  attitude  i n f o r m a t i o n , o t h e r techniques c a n b e i n c o r p o r a t e d into f u t u r e designs s u c h as a c c u r a t e d i r e c t roll m e a s u r e m e n t s f r o m o n - b o a r d sensors or m o r e s u i t a b l e (flatter) r a n g e b e a m p a t t e r n s . t h e s i s f o c u s e s o n t h e p r o b l e m o f r o l l a n g l e e s t i m a t i o n f r o m t h e s i g n a l d a t a itself, u s i n g new h a r d w a r e or s y s t e m designs.  without  T h i s knowledge can then be used o n other systems  w i t h m i n i m a l h a r d w a r e or software design  1.5  This  changes.  Summary  S c a n S A R is a n effective  t o o l for m o n i t o r i n g large areas u s i n g m i c r o w a v e r e m o t e  O n e o f t h e m a i n p u r p o s e s o f S A R is t o d e t e r m i n e a r e l a t i v e , o r a b s o l u t e , for e a c h p i x e l i n t h e final scene.  radar  sensing.  brightness  Y e t , t h e v e r y m a n n e r i n w h i c h d a t a is g a t h e r e d c r e a t e s  a  difficult challenge for this r a d i o m e t r i c c a l i b r a t i o n . T h i s c h a p t e r has h i g h l i g h t e d S A R basics, a n d s p e c i f i c a l l y , h o w S c a n S A R o p e r a t e s i n c l u d i n g its m o s t c o m m o n r a d i o m e t r i c c a l i b r a t i o n errors. E r r o r s i n t h e e s t i m a t i o n of t h e satellite roll angle are p a r t i c u l a r l y t r o u b l i n g for S c a n S A R s c e n e s as t h e y usefulness  manifest  as o b v i o u s  and annoying discontinuities  in the  final  scene.  The  o f S c a n S A R i m a g i n g is d e g r a d e d i f t h e s c e n e c a n n o t b e c o n s i d e r e d a t l e a s t r e l a -  t i v e l y c a l i b r a t e d . C u r r e n t l y , t h e m a i n m e t h o d f o r c o r r e c t i n g r o l l a n g l e e s t i m a t i o n e r r o r s is a m a n u a l , p o s t - p r o c e s s i n g a p p r o a c h . O n e s u c h a p p r o a c h is t o b l e n d b e a m s t o g e t h e r a linear merge technique.  using  T h i s a p p r o a c h does p r o d u c e scenes w h i c h have r e d u c e d g a i n dis-  c o n t i n u i t i e s ; h o w e v e r , s c e n e c a l i b r a t i o n m a y b e c o n s i d e r e d t o b e e v e n less a c c u r a t e after t h i s process.  T h e ability to accurately d e t e r m i n e the satellite roll angle d u r i n g scene processing  will h e l p ensure the c a l i b r a t i o n a c c u r a c y , while at the s a m e t i m e r e d u c e a n y visible errors. T h e a i m o f t h i s t h e s i s is t o c o r r e c t t h e r o o t c a l i b r a t i o n p r o b l e m w i t h a n a c c u r a t e i n i t i a l r o l l angle d e t e r m i n a t i o n . I n c h a p t e r t w o , f o c u s is p l a c e d o n c u r r e n t r o l l a n g l e e s t i m a t i o n t e c h n i q u e s .  T h e manner  is w h i c h t h e y o p e r a t e is e x p l o r e d , a s w e l l a s t h e p r o s a n d c o n s o f e a c h a p p r o a c h . T h e r e a r e  25  three m a i n algorithms  discussed.  I n c h a p t e r t h r e e , a n a n a l y s i s o f R A D A R S A T - l ' s S c a n S A R b e a m i n t e r f a c e s is g i v e n .  This  a n a l y s i s p r o v i d e s i n s i g h t i n t o t h e r e q u i r e d r o l l a n g l e a c c u r a c y for r e l a t i v e scene c a l i b r a t i o n . A  s i m p l e g e o m e t r i c a l m o d e l is u s e d , b u t t h e r e s u l t s c a n b e c o n s i d e r e d a c c u r a t e e n o u g h  real R A D A R S A T - 1  for  interfaces.  In c h a p t e r four, two a l g o r i t h m s ( H y b r i d P e a k D e t e c t i o n a n d T h r e e B e a m ) are p r o p o s e d that  attempt  to i m p r o v e current algorithms b y o v e r c o m i n g some of their weakness.  is d o n e b y e m p l o y i n g a n e w s i g n a l a c q u i s i t i o n t e c h n i q u e .  This  O p e r a t i o n of the algorithms are  d e f i n e d as w e l l as t h e p h y s i c a l p a r a m e t e r s r e q u i r e d f o r i t s i n t r o d u c t i o n t o R A D A R S A T - 1 o r  2. C h a p t e r five e x p l o r e s t h e m a n n e r i n w h i c h d a t a a r e s i m u l a t e d f o r t h e p r o p o s e d a l g o r i t h m . T h e m o d e l s for d a t a s i m u l a t i o n are e x p l a i n e d a n d r e l a t i o n s h i p s to r e a l S A R d a t a are g i v e n . C h a p t e r six illustrates the results of the p r o p o s e d a l g o r i t h m s a n d c o m p a r e s  t h e m to  a  c u r r e n t a l g o r i t h m . A d i s c u s s i o n o f t h e r e s u l t s is i n c l u d e d , a n d t h e f i n a l c o n c l u s i o n s a r e g i v e n in chapter seven.  26  RADARSAT ScanSAR Wide B Beams Wl W2 S5 S6 Scene L o c a t i o n 52 41'00.22" -103 33'48.39" A s c e n d i n g Pass Date A c q u i r e d = APRIL 15 1996 E a s t e r n Saskatchewan and Western Manitoba Image P r o v i d e d by RSI  Figure 1.10: Discontinuities in the scene due to improper R D G C application © C S A  27  Chapter 2  Current R o l l Angle Estimation Algorithms 2.1  Introduction  T h e r e have b e e n several different a l g o r i t h m s p r o p o s e d to a c c u r a t e l y e s t i m a t e the roll angle for S c a n S A R scenes.  satellite  A s m e n t i o n e d i n C h a p t e r 1, a r t i f a c t s i n a S c a n S A R  scene  c a u s e d b y a n error i n satellite roll angle e s t i m a t i o n are d u e to i n a c c u r a t e energy, or power, calibration. polarization.  T h e r e is l i t t l e , i f a n y , r e l a t i o n b e t w e e n t h e s e e r r o r s a n d s i g n a l p h a s e  or signal  T h e r e f o r e , a n y a l g o r i t h m s s h o u l d be, a n d i n d e e d are, b a s e d o n a n a t t e m p t  to  relate the b e a m p a t t e r n s to the o b s e r v e d energy, or power, v a r i a t i o n s i n the scene. L u s c o m b e [8] w a s t h e  first  to elucidate the i n t e r b e a m s e a m p r o b l e m a n d p o i n t out  characteristics w h i c h m i g h t be a p p l i e d to ameliorate  the problems.  T h e idea of using  o v e r l a p r e g i o n s t o d e t e r m i n e t h e r o l l e r r o r w a s e x p a n d e d u p o n b y B a m l e r [17], b u t t r i e d a c t u a l i m p l e m e n t a t i o n of their ideas.  Goulding  [16]  some  implemented  the  neither  s e v e r a l v a r i a n t s of  the ideas put forward b y L u s c o m b e a n d B a m l e r a n d settled o n one p a r t i c u l a r a p p r o a c h that used a direct c o m p a r i s o n of signal energy  i n the overlap area.  J i n [9] a l s o u s e d  a similar  a p p r o a c h , b u t c o m p u t e d a correlation between the log ratio of the range d a t a a n d a kernel derived f r o m the k n o w n a n t e n n a patterns, whereas B a m l e r suggested a n estimate based a l i n e a r fit o f t h e l o g r a t i o .  M i t t e r m a y e r [12]  w a s a b l e t o s h o w t h a t a l i n e a r fit w a s  e f f e c t i v e t h a n J i n ' s c o r r e l a t i o n . D r a g o s e v i c [18] p r e s e n t e d a n a l g o r i t h m t h a t  on  more  simultaneously  solves t h e r o l l e s t i m a t e for a l l t h e r a n g e b e a m s u s i n g a n L M S s o l u t i o n to a n o v e r - d e t e r m i n e d s y s t e m of equations.  T h i s chapter will explore Goulding's, Jin's, a n d Dragosevic's algorithms,  28  h i g h l i g h t i n g the p r o s a n d cons of each.  2.2  Goulding's Algorithm  I n u s i n g t h e o v e r l a p a r e a , G o u l d i n g [16] i n v e s t i g a t e d mentation.  s e v e r a l a p p r o a c h e s for s u i t a b l e  imple-  A m o n g t h e s e w e r e B a m l e r ' s l i n e a r fit o f t h e r e l a t i v e r a t i o f u n c t i o n f o r e a c h  range  l i n e . T h e r e l a t i v e r a t i o f u n c t i o n is s i m p l y a l o g a r i t h m i c r a n g e l i n e r a t i o , p o i n t b y p o i n t , f r o m e a c h b e a m i n t h e o v e r l a p a r e a . T h i s a p p r o a c h is g i v e n as ( n o t e t h a t t h e s y m b o l 9 r e p r e s e n t s the t e r m "such that") i n order to find the best estimate  9 = e?  w h e r e Me  =  M  k  e  6k  e  M )\)  min(|(l -  (2.1)  6i  is:  {  . =  Me  C  n  C  where j  6:  9ij  =  ±y^l  (2.2)  W ^ - R D G C ^ .  (2.3)  L = I- i W  (-)  HDG(  24  is t h e r a n g e c e l l n u m b e r i n t h e o v e r l a p a r e a f o r e a c h c o r r e c t i o n o f l e n g t h  t h e t o t a l n u m b e r o f r o l l a n g l e s o f w h i c h t h e s e a r c h s p a c e is c o m p r i s e d . and  far, R D G C ' ,  and  RDGCs  are used to correct the near b e a m ,  are the c o r r e c t e d d a t a for the near a n d far b e a m s , G o u l d i n g ' s a l g o r i t h m is a n i t e r a t i v e a p p r o a c h as  1. C a l c u l a t e t h e x c o r r e s p o n d i n g R D G C b e a m s i n v o l v e d so t h a t data.  there  W, n  T h e near,  Wf.  b a s e d o n v a r y i n g roll angles, for over the  are available f r o m the p r o p e r p a y l o a d  as t h e  collected  satellite/earth  2. A  fixed  that  geometry  angles.  Knowledge  of the  is e s s e n t i a l , w i t h t h e u n k n o w n v a r i a b l e b e i n g t h e r o l l  n u m b e r of range  an accurate  not  cells are r a n g e  representation  of the  compressed  and  averaged  available.  29  The  range, correct  angle.  in azimuth,  b e a m pattern, not i n d i v i d u a l target  the  range  file.  is c a l c u l a t e d b y c o n v e r t i n g t h e b e a m p a t t e r n e l e v a t i o n a n g l e s t o a s l a n t range,  C™  follows:  functions,  o n slant  is  respectively.  R D G C  d a t a is b a s e d  x  h  RDGC™,  a n d far b e a m ,  are m a n y s a m p l e s w h i c h c a n b e shifted  T h e appropriate b e a m patterns  N.  such  energy,  is  3. T h e r e s p e c t i v e  R D G C s  are t h e n a p p l i e d to the averaged d a t a a n d the p o i n t b y  point  log ratios of the b e a m s are calculated.  4. T h e m e a n o f t h i s r a t i o is f o u n d , a n d b a s e d o n i t s v a l u e , different  r o l l offset i n t h e  R D G C  application.  A  s t e p 3)  is r e p e a t e d  m e a n o f less t h a n o n e  n e g a t i v e offset; a m e a n o f g r e a t e r t h a n o n e r e s u l t s i n a p o s i t i v e offset. a p p l i c a t i o n occurs w h e n the m e a n equals  5. T h i s  is f i r s t p e r f o r m e d f o r t h e  outer b e a m pattern.  inner  with  results  Ideally,  in  proper  (closest to  sensor)  beam  pattern  and  then  If m o r e t h a n t h r e e b e a m s a r e i n v o l v e d , t h e n t h e w h o l e  the  algorithm  beams.  A l t h o u g h e a c h b e a m p a t t e r n is a l l o w e d i t s o w n r o l l e s t i m a t e , t h e r e is a c t u a l l y o n l y required to  independent •  determine  the  satellite roll angle.  T h e r e are two  reasons  one  for  the  as  the  estimates:  T h e centre of e a c h b e a m p a t t e r n m a y v a r y slowly w i t h respect p a t t e r n s themselves m a y slowly change over  •  a  one.  proceeds f r o m the inner b e a m s to the outer  parameter  a  to each other,  time.  U n c e r t a i n t y i n one b e a m p a t t e r n does not necessarily translate to  another.  A s G o u l d i n g mentioned, given enough d a t a these relative centers c a n be calculated b e t t e r e s t i m a t e s of the b e a m p a t t e r n edges c a n b e m a d e .  E a c h independent  and  measurement  c a n t h e n b e u s e d to f u r t h e r refine t h e roll error. Goulding marginal.  performed the  During  this  algorithm on  procedure,  four test  images  some implementation  and  the  results  issues arose,  such  were as  deemed  how  often  t h e R D G C s w e r e u p d a t e d , a n d w h i c h p r o c e s s o r is c a p a b l e o f i m p l e m e n t i n g t h i s a l g o r i t h m . F i g u r e s 2.1,  2.2 a n d 2.3  provide an example of Goulding's ratio algorithm.  was a s i m u l a t i o n w i t h a — 0 . 0 3 ° roll error a n d the correct R D G C ,  This  o n the S C N B  example  and  S C W B  ( W 2 - S 5 ) S c a n S A R b e a m . F i g u r e 2.1 is t h e o v e r a l l s w a t h w i t h t h e r e s u l t a n t d a t a a n d c o r r e c t RDGCs.  A l t h o u g h i t s h o w s t h e t r a n s i t i o n p o i n t i n t h e f i g u r e , i t is n o t u s e d d u r i n g G o u l d i n g ' s  a l g o r i t h m . F i g u r e 2.2 f o c u s e s o n t h e o v e r l a p r e g i o n o n l y ; h o w e v e r , i t s t i l l d i s p l a y s t h e  beam  d a t a as w e l l as t h e c o r r e c t R D G C s i n t h e t o p p o r t i o n , w h i l e d i s p l a y i n g t h e c o r r e c t e d  beams  in the  bottom portion.  Note,  t h e r e is a 10 d B offset b e t w e e n b e a m s  only.  30  for d i s p l a y  purposes  Goulding's algorithm operates by taking the mean of the log ratio calculated in step 4) and attempts to find the estimated roll angle, via its R D G C , which produces a mean nearest to 1. Figure 2.3 shows the log ratio mean for R D G C s with roll errors ranging from —0.2° to +0.2°. Figures 2.1 and 2.2 both show the correct R D G C for this simulation. However, Goulding's algorithm found that the R D G C for —0.055° produces a mean log ratio closest to one. However, the data set is created with a —0.03° roll, so this represents an algorithm estimation error of 0.025°.  Figure 2.1: The range swath consisting of beams W2 and S5 with corresponding RDGCs. Steep slopes in the beam patterns increase the sensitivity to roll errors. In this case, the far beam pattern is more sensitive to roll errors (notably from 30° to 31.5°) than the near beam pattern (from 34° to 35.5°) in the overlap area.  31  Goulding Algorithm Implementation  i-H (8  a  70  40 I  1  1  1  1  '  30  31  32  33  34  E l e v a t i o n Angle  <-  35  (Degrees)  Figure 2.2: Overlap area beam data with respective RDGCs and the corrected beams. Even without the 10 dB separation (included here to show separate corrected range lines), visual determination of a fraction of a dB gain error for a single range line in this format is difficult.  32  Figure 2.3: The mean of the log ratio for several different roll angle estimates  Overall, Goulding's algorithm suffered from the following: • Uncertainties in the actual beam patterns (beam gain uncertainty), • Uncertainties in the relative beam centre angles, • Although the ratio operation should remove scene content from the equation, the algorithm showed variations in accuracy based on the type of area that was imaged. This suggests there may still be indirect dependence on scene content, perhaps as a function of the noise level to scene content. The first obstacle listed above, beam gain uncertainty, is perhaps the most significant. During his investigation, Goulding noticed that the patterns exhibited significant deviations from the averaged range lines, even in fairly uniform scenes such as an Amazon data set, normally considered to be a very uniform scene.  33  2.3  Jin's Algorithm  This  a l g o r i t h m is b a s e d  patterns.  on a correlation with  a kernel derived from  T h e r a n g e - D o p p l e r i n t e n s i t y i m a g e is f i r s t e x p r e s s e d  the  known  antenna  thus:  I (x, y) = W(x - x , y - y ) a(x, y) 7(2:, y) s  where  W(x  — x, Q  y — y) Q  0  is t h e  (2.5)  0  a n t e n n a p a t t e r n , o~{x, y)  speckle noise w i t h a n exponential distribution.  is t h e b a c k s c a t t e r ,  a n d ^(x,  y)  J i n t h e n takes the l o g a r i t h m i c ratio of  i n t e n s i t y for t w o scenes i n o r d e r t o c a n c e l t h e b a c k s c a t t e r t e r m a n d c h a n g e t h e s p e c k l e f r o m m u l t i p l i c a t i v e to additive.  T h i s produces the  R(x)  2  A(x - x )  +  c  w h e r e B(x)  +  [W (x-x ) 2  this noise  following:  Wi(s-si)  =  is  B(x)  0»0 .72 0 *0 7i  (2.6) (2.7)  is a w e l l b e h a v e d r a n d o m p r o c e s s w i t h m e a n z e r o a n d v a r i a n c e o f 3 . 2 9 .  In general,  t h e a l g o r i t h m o p e r a t e s o n two m a i n s t e p s for e i t h e r t h e a z i m u t h or r a n g e c e n t r o i d :  1. F i n d  the  1st  o r d e r d e r i v a t i v e o f A(x  c o n v o l v e it w i t h  2. D e t e c t  — x)  A(x  c  — x ),  f r o m t h e p a y l o a d file,  c  and  R(x).  t h e z e r o - c r o s s i n g p o i n t i n t h e i n t e r v a l (x  2  — y , x i — y)  where X  is t h e  image  size.  In order to do this, J i n assumes that the range patterns are well k n o w n , w h i c h t h a t their differences, i m p l i e s t h a t A(x  — x\)  W\(x  — x\)  a n d W (x 2  is c o n s t a n t .  — x ),  are also well k n o w n .  2  F u r t h e r m o r e , this  A s m e n t i o n e d i n S e c t i o n 1.3.2, a l t h o u g h t h i s  was p r e v i o u s l y a s s u m e d true, recent o b s e r v a t i o n has s h o w n t h a t this c a n n o t be accurate i n the b e a m edge area.  implies  assumption considered  However, m a i n t a i n i n g this a s s u m p t i o n allows the  variance  of Jin's s o l u t i o n to be calculated:  f  v  r  var[X \ c  1  ^  61.64(A  g i  Ag ) 5x n 2  +  2  2  s  >  (2.8) Mi  where  Agi  is t h e  absolute  g a i n difference  of range lines i n v o l v e d i n the estimate.  for e a c h e n d o f t h e  T h e term n  s  b e t w e e n t h e i n t e r v a l r e p r e s e n t i n g t h e o v e r l a p r e g i o n Af  34  represents  overlap, the  Af/ is t h e  number  relationship n  a n d the sample spacing  s  8f.  =  ^j-  J i n f o u n d this a l g o r i t h m p r o d u c e s a n elevation e s t i m a t e w i t h a s t a n d a r d d e v i a t i o n of 0.003 degrees.  However,  as s t a t e d b y M i t t e r m a y e r a n d G o u l d i n g ,  produces  less d e s i r a b l e r e s u l t s  its use  in actual  t h a n a d i r e c t l i n e a r fit o r r a t i o f u n c t i o n .  applications  Essentially,  his  a l g o r i t h m s u f f e r s f r o m t h e s a m e f a c t o r s as G o u l d i n g ' s . H o w e v e r , b o t h G o u l d i n g ' s r a t i o a n d B a m l e r ' s l i n e a r fit m e t h o d gain regions.  T h e l i n e a r fit w o r k s o n t h e  can be considered accurate A(x  — x ), c  a r e less s u s c e p t i b l e  a n d the  to u n k n o w n b e a m - p a t t e r n gains i n the  ratio of the  other m a y not  be.  two  beam  patterns,  Jin's m e t h o d  one  of  low  which  is c o n v o l u t i o n  with  t h e d e r i v a t i v e o f t h e t w o b e a m - p a t t e r n r a t i o s , w h i c h is m o r e s e n s i t i v e t o u n k n o w n  b e a m - p a t t e r n errors. In all cases, i m p r o v e d k n o w l e d g e of the b e a m p a t t e r n s c a n b e u s e d a p p l y weights to the roll estimates i n order to m i n i m i z e influences  f r o m less r e l i a b l e  to  beam  combinations.  2.4  Dragosevic's Algorithm  D r a g o s e v i c p r o p o s e d a s i m i l a r a l g o r i t h m [18] t o J i n ' s . H o w e v e r , i t d i f f e r s i n t h a t i t a c h i e v e s a simultaneous to outside.  s o l u t i o n for a l l t h e b e a m p a t t e r n s at o n c e , r a t h e r t h a n w o r k i n g f r o m i n s i d e  T h e e s t i m a t e s for t h i s a l g o r i t h m are a n L M S s o l u t i o n t o  systems of equations.  an  over-determined  It is i t e r a t i v e b u t d o e s t a k e i n t o a c c o u n t a l l t h e r a n g e s w a t h s a t  T h i s a l g o r i t h m m o d e l a c c o u n t s for a n t e n n a gains, t a r g e t b a c k - s c a t t e r i n g a n d speckle  once. noise.  A s w i t h the other two algorithms, this a l g o r i t h m works directly o n the d a t a values u s e s a c o n s t a n t g a i n offset i n o r d e r t o c o m p e n s a t e swaths a n d A D C s a t u r a t i o n , if either occur.  for different r e p l i c a e n e r g y levels b e t w e e n  A c c o r d i n g l y , t h i s a l g o r i t h m is m o r e s e n s i t i v e  t h a n G o u l d i n g ' s to errors in the R D G C , due to either squint angle a n d / o r a z i m u t h angle changes.  and  elevation  H e n c e , the presence of s c a l l o p i n g errors i m p l i e s errors i n the range c a l i b r a t i o n .  S t r o n g n a d i r r e t u r n s c a n a l s o affect o f p r e - f i l t e r i n g , s u c h as a m e d i a n  the constant filter,  g a i n offset.  Dragosevic suggested the  to remove any n a d i r error.  use  T h e a p p r o a c h used  is  m a t r i x b a s e d a n d t h e t e r m s i n v o l v e d a r e m o r e e a s i l y e x p l a i n e d w i t h t h e a i d o f F i g u r e 2.4. T h e s i g n a l i n t e n s i t y is d e f i n e d as I  s  = Gi(r)  + cr — i r + ji  w h e r e Gi(r)  is t h e s e n s o r g a i n ,  is t h e t a r g e t b a c k - s c a t t e r a n d 7$ is a s p e c k l e n o i s e t e r m . T h e a n t e n n a p a t t e r n s a r e by  Wf(<f>) + W?(<p)  for t h e far a n d n e a r  fields,  35  respectively.  a  denoted  A l s o s h o w n are the b e a m  gain  Beam Offsets  Near Overlap  Range  Far Overlap  Figure 2.4: Matrix notation for Dragosevic algorithm offsets,  Hi.  U s i n g this n o t a t i o n , D r a g o s e v i c defines  m) w h i c h is e s s e n t i a l l y  Di(<p)  =  as t h e f o l l o w i n g :  (2.9)  ^wi{ >)-^-wr M) (t  +  the difference of the b e a m p a t t e r n variations.  C o n t i n u i n g further into  her a l g o r i t h m , she derives a s y s t e m of e q u a t i o n s b a s e d o n the following:  5 =  W(4>)  w h e r e M is a m a t r i x o f z e r o s a n d o n e s .  + MH  + 7  (2.10)  S h e linearizes this i n the r e g i o n of interest to  the  following:  s-  w{4> ) {k)  = \D{^\  M  (2.H)  H w h i c h produces two algorithms d e p e n d i n g o n whether just the roll angle requires estimation o r w h e t h e r b o t h i t a n d offsets r e q u i r e e s t i m a t i o n .  If j u s t r o l l a n g l e e s t i m a t i o n is r e q u i r e d ,  h e r s o l u t i o n is E q u a t i o n ( 2 . 1 2 ) , a n d w h e n b o t h a r e r e q u i r e d t h e s o l u t i o n is E q u a t i o n ( 2 . 1 3 ) .  A<f>  =  *+i  EtiAA^ ) (A/ -A^(0W)) AA(^) AA(^ 0  k+1  EtiA(^) A#*>) T  (fc)  =  r  s  r  36  (2-12)  fc  (2-13)  w h e r e for s o m e p a r a m e t e r X ,  AXi(<p) = X^cj)) — Xi{4>).  T h e means are s u b t r a c t e d f r o m  the  vectors by:  AD0V  0V)-D0 ) k)  =  AW0  = W0 )  k)  - W0 )  k)  AI {^  =  S  (2.14)  D  k)  (2.15)  I (4> ) - SS ) {k)  s  ik)  (2-16)  A s D r a g o s e v i c p o i n t s out, if the b e a m p a t t e r n differences are a linear f u n c t i o n o f roll angle then  D(<p)  =  D(<j>) =>• AD^ifi)  for R A D A R S A T - 1  =  0 a n d t h e s o l u t i o n is u n d e t e r m i n e d , as s e e m s t o b e t h e c a s e  mode S C W A and  SCNA.  O v e r a l l , t h i s a p p r o a c h p r o d u c e s a d e q u a t e r e s u l t s o n t h e t h r e e t e s t s c e n e s , b u t is d e p e n d e n t on  the  particular S c a n S A R  b e a m used for the scene.  It is a l s o s e n s i t i v e t o o t h e r e r r o r s ,  i n c l u d i n g the same b e a m - p a t t e r n variations, a n d u n c e r t a i n b e a m centre angles,  that  affect  Goulding's method.  2.5  Current Algorithm Summary  T h e s e a l g o r i t h m s are a l l s e n s i t i v e t o a few s i g n i f i c a n t f a c t o r s . in the overlap regions.  First, all three m e t h o d s  operate  T h e s e regions are at the edge of the range s w a t h a n d have low a n t e n n a  g a i n , w h i c h lowers S N R . H e n c e , noise m a y b e significant o n s o m e scenes. S e c o n d , b e a m g a i n u n c e r t a i n t y i m p l i e s t h a t there are uncertainties i n the b e a m - p a t t e r n gains near the  beam  edges.  data.  The RDGCs  Unknown  are t a k e n d i r e c t l y f r o m the  variations between the  R D G C  beam patterns  a n d a p p l i e d to the  a n d actual pattern gains  w i l l affect  T h i r d , a n y u n c e r t a i n t i e s i n t h e r e l a t i v e b e a m c e n t e r s w i l l affect r e s u l t s . as s i g n i f i c a n t as t h e p r e v i o u s t w o f a c t o r s .  the  results.  H o w e v e r , t h i s is n o t  A n y successful a l g o r i t h m s h o u l d , to some extent,  l e s s e n t h e effect o f s o m e o r a l l o f t h e s e f a c t o r s i n o r d e r t o i m p r o v e p e r f o r m a n c e . The  n e x t c h a p t e r lays t h e g r o u n d w o r k for a l g o r i t h m d e v e l o p m e n t  quired roll angle  estimation  accuracy.  T h i s a c c u r a c y is r e l a t e d t o  b y d i s c u s s i n g t h e reall the  S c a n S A R b e a m s a n d explains the sensitivity of these b e a m s to roll errors.  37  RADARSAT-1  Chapter 3  Required Roll Angle Accuracy 3.1  Introduction  R A D A R S A T - l ' s r o l l a n g l e is m a i n t a i n e d u s i n g o n - b o a r d i n s t r u m e n t s a n d t h e a t t i t u d e c o n t r o l system.  It  is t y p i c a l l y a c c u r a t e  to  ±0.3°  of its  programmed parameters.  However,  the  a c c u r a c y o f t h e a t t i t u d e e r r o r d a t a is l i t t l e b e t t e r t h a n t h e a c c u r a c y o f t h e a c t u a l a t t i t u d e The  [19].  a p p e a r a n c e of stripes i n the resulting image d a t a , w h i c h c a n be a t t r i b u t e d to roll errors,  i m p l i e s t h a t t h e r e is a s t r o n g r e q u i r e m e n t for e s t i m a t i n g t h e r o l l a n g l e f r o m t h e d a t a itself.  3.2  Required Roll Angle Accuracy  D e f i n i n g a r e q u i r e d a c c u r a c y for t h e satellite r o l l a n g l e s i m p l e d e f i n i t i o n o f t h e p r o b l e m g i v e n i n S e c t i o n 1.3.1 all  the variables inherent in The  is n o t  a trivial requirement.  The  n o l o n g e r suffices w h e n d e a l i n g w i t h  RADARSAT-1.  b e a m - p a t t e r n differences v a r y significantly f r o m one o v e r l a p r e g i o n to a n o t h e r .  Since  the m a i n defects c a u s e d b y roll angle e s t i m a t i o n errors i n S c a n S A R i m a g e r y are g a i n variat i o n s , i t is u s e f u l t o l o o k a t t h e v a r y i n g p a t t e r n s h a p e s a n d a n a l y z e h o w t h o s e v a r i a t i o n s a r e created.  3.2.1  D e t e r m i n i n g the R o l l Angle E r r o r L i m i t  T h e r e are s e v e r a l m e t h o d s for s t i t c h i n g t o g e t h e r S c a n S A R d a t a . s i m p l e , a b r u p t t r a n s i t i o n f r o m B e a m 1 t o B e a m 2; h o w e v e r , also a v a l i d m e t h o d .  B o t h methods  C h a p t e r one illustrates  a l i n e a r m e r g e r o f t h e d a t a is  are e x a m i n e d next a l o n g w i t h their respective  38  the  results.  O t h e r m e t h o d s d o exist a n d i n c o r p o r a t e other variables into the s t i t c h i n g process;  however,  t h e a b r u p t t r a n s i t i o n m e t h o d r e q u i r e s t h e g r e a t e s t r o l l a c c u r a c y w h i l e t h e l i n e a r m e r g e is n o t as d e m a n d i n g . lie s o m e w h e r e  It is a s s u m e d t h a t t h e r e q u i r e d a c c u r a c y f o r o t h e r s t i t c h i n g m e t h o d s in  would  between.  A b r u p t Transition T h e five S c a n S A R b e a m i n t e r f a c e s w e r e s i m u l a t e d a n d i n e a c h c a s e , a 0.2 d B d i s c o n t i n u i t y a t t h e i n t e r f a c e p o i n t w a s set as t h e r o l l a n g l e l i m i t .  T h e initial roll error b e g a n at  a n d increased i n 0 . 0 0 5 ° increments until + 0 . 2 0 ° was reached.  T h e size of the  —0.20°  discontinuity,  w h i c h resulted f r o m the roll error, was stored in a vector. T h e smallest positive/negative  roll  a n g l e f r o m t h i s v e c t o r , w h i c h p r o d u c e d t h e 0.2 d B d i s c o n t i n u i t y , w a s c h o s e n a s t h e m a x i m u m tolerable roll angle.  T h e i n t e r f a c e i t s e l f is t h e r a n g e c e l l , a t w h i c h p o i n t d a t a is  switched  f r o m B e a m 1 t o B e a m 2. T h e r e s u l t s w e r e d e t e r m i n e d i n a s i m i l a r m a n n e r t o t h e d i s c o n t i n u i t i e s s h o w n i n F i g u r e s 1.9 and  1.8,  except  that  only the  backscatter was simulated.  actual beam  gains  In e a c h case, the R D G C  were  used;  no  noise,  speckle  or  radar  was c a l c u l a t e d a s s u m i n g there was 0 °  roll error a n d t h e n applied to the b e a m patterns rolled by the previous increments.  F i g u r e 3.1  illustrates the creation of a single discontinuity o n the W 1 W 2 interface w i t h a — 0 . 2 0 °  roll  error. F i g u r e 3.2 f u r t h e r i l l u s t r a t e s t h e d i s c o n t i n u i t i e s t h a t r e s u l t i f r o l l e r r o r s f r o m — 0 . 2 0 ° +0.20°,  i n i n c r e m e n t s of 0 . 0 5 ° , o c c u r a n d are n o t c o r r e c t e d .  F i g u r e 3.1 b u t w i t h e i g h t d i f f e r e n t r o l l e r r o r s .  This  A l s o , the R D G C s  figure  is a n e x t e n s i o n  a r e n o t s h o w n , n o r is  c o m p l e t e s w a t h f r o m e a c h b e a m ; a l l t h a t is p r e s e n t is t h e c o r r e c t e d b e a m d a t a t h a t t h e o v e r l a p p o r t i o n of t h e r a n g e line (large t h a n s h o w n i n F i g u r e 3.1).  e a c h b e a m p a t t e r n has its o w n slope i n t h e o v e r l a p r e g i o n .  a p p r o a c h e s i t s s t e e p d r o p - o f f r e g i o n w h i l e t h e o t h e r is a p p r o a c h i n g i t s  N o t i c e t h a t at  T y p i c a l l y , one flatter  of the  completes  t r a n s i t i o n p o i n t , t h e v a l u e o f t h e g a i n e r r o r is g r e a t e r f o r o n e b e a m t h a n t h e o t h e r . is b e c a u s e  to  the This  beam  m a i n region,  d e p e n d i n g o n w h e t h e r t h e r o l l e r r o r is p o s i t i v e o r n e g a t i v e . A s p r e v i o u s l y m e n t i o n e d , a 0.2 d B l i m i t w a s set as t h e r e q u i r e d c a l i b r a t i o n g o a l . F i g u r e 3 . 3 i l l u s t r a t e s t h a t e a c h i n t e r f a c e h a s a d i f f e r e n t r o l l e r r o r t o l e r a n c e i n r e a c h i n g t h i s 0.2 d B l i m i t .  39  Resultant  Discontinuity  from  Roll  Estimation  Error  o f -0.2  Degrees  1i  — i  1  1  1  Elevation  1  —  Angle  r  (degs)  Figure 3.1: W1-W2 interface discontinuity for a —0.20° roll error  This figure simply measures the discontinuity present at the transition point for each interface over the range of roll errors from —0.2° to 0.2° in 0.005° increments, which is smaller than the 0.05° increments in Figures 3.2. These slopes can be considered the sensitivity slope for each interface line in Figure 3.3, and can be considered linear in the region of interest from ±0.2 d B . More specifically, the sensitivity slopes in Figure 3.3 are related to the beam-pattern slopes at the interface. Interfaces which have a low beam-pattern slope from both patterns can tolerate more error and vice versa. Adding to the complexity is the fact that the beampattern slopes may change with roll error so that interfaces with an initially high error tolerance may become sensitive to roll angle errors of greater magnitude. However, this does not appear to be the case for R A D A R S A T - 1 ,  at least in the region of interest.  The beam patterns themselves can be modelled as a 4th or 5th order polynomial with sufficient accuracy. This implies that their difference can be modelled thusly: Beami(x)  — 75eam (a;) = a i + a x + a x  2  2  2  40  3  + a^x + a x ... 3  4  5  (3-1)  Resultant 1  D i s c o n t i n u i t i e s from R o l l E r r o r s from + 0 . 2 0 t o - 0 . 2 0 Degrees 1  1  1  1  +0.20  I 24  i 26  i  25  i 28  I  27 Elevation  Angle  Ranging  1  Roll  Error  i 29  I  1  30  31  (degs)  Figure 3.2: W1-W2 interface with —0.2° to +0.2° roll error. Gain variations outside the overlap region can also be severe and cause radiometric problems in the overall range swath. These errors can be used to provide roll estimates for single beam operation on uniform scenes. where x  represents  l o w e r t h a n 5 o r 6.  t h e r a n g e c e l l a t t h e i n t e r f a c e a n d a is t h e  coefficient  vector of  F i g u r e 3.3 c a n b e u s e d t o s h o w t h a t i f t h e r o l l e r r o r is m a i n t a i n e d w i t h i n  a s m a l l region of interest,  approximately 0 ° ±  0.05°,  then  all the  higher order terms  i n s i g n i f i c a n t as t h e f u n c t i o n is n e a r l y l i n e a r . T h e d i f f e r e n c e o f t h e b e a m - p a t t e r n is as  are  derivatives  follows:  d(B ) a  d(B )  -dW-^w and  length  can then be considered a constant.  face used.  2  =  s l o m  -  -  slope2  (3  2)  T h i s c o n s t a n t is d e p e n d e n t o n t h e a c t u a l b e a m i n t e r -  T h i s i n f o r m a t i o n is u s e f u l b e c a u s e e a c h i n t e r f a c e m a y h a v e a u n i q u e d i s c o n t i n u i t y  w h i c h is r e l a t e d t o o t h e r s b y t h e f u n c t i o n c h a r t e d i n F i g u r e 3 . 3 .  It s h o u l d a l s o b e  pointed  out that a l t h o u g h the discontinuities m a y be the most visually obvious, they m a y not be  the  largest g a i n errors i n the scene.  the  F i g u r e 3.2 s h o w s t h a t t h e r e a r e g a i n v a r i a t i o n s b e s i d e s  41  discontinuity, and depending on the roll error, these gain differences may be larger than the discontinuity. The slopes for each beam combination illustrate a very important point: the sensitivity of each beam pattern. The beam pattern slopes indicate the shape of gain errors that result from improper R D G C application. The shape of these sensitivity slopes remain fairly constant as the roll error changes; however, their mean error increases with roll error as given by Eqn. 3.2. This allows both a calculation of the required accuracy, as is done next, and a calculation of a potential accuracy weighting for each beam combination. Combinations likely to produce more accurate estimates can be weighted heavier than those likely to produce poor estimates.  42  R o l l Angle E s t i m a t i o n 0.5  ,  dB G a i n  E r r o r Vs D i s c o n t i n u i t y  ,  ^ r j ^  1  . S5S6 W1 W2 W2W3 W2S5 W3S7  0.4 0.3 0.2 d B U p p e r  Limit  0.2 0.1 0  S 5 S 6 = 0 . 028  •  W1W2 = 0.034  -0.1  W2S5=0.035 W3S7 = 0.043  -0.2 0.2 d B L o w e r  Limit  -0.3 -0.4 -0.5 - 0 06  -W2W3=-0.041  -0.04  -0.02  0  R o l l Angle Estimation  0.02 Error  0.04  (Degrees)  Figure 3.3: Sensitivity to roll errors for each ScanSAR interface 43  0.06  Linear Merging  The overlap regions of some interfaces are quite large, up to 40% of the standard beam width. Whereas the abrupt transition method essentially disregards half of the overlap SAR data, the linear merging method is designed to use more of the overlap data by averaging data based on a linear weighting. Based on slant range, data that are closer to the centre of their respective beam, are given a higher weighting than the corresponding data from the other beam. The weighting is complementary; therefore, there is no increase in the signal gain. A more accurate linear merge could be achieved by accounting for beam sensitivity and uncertainty in the weighting.  Figure 3.4: Linear merging method for beam stitching  Figure 3.4 illustrates this method. The figure also shows that the percentage, and starting point, of the merge area with respect to the overall overlap area are major considerations. The interaction between beam patterns and weighting factors produces different results for every beam combination. For this reason, the accuracy results in this simulation simply utilized the 50% of the overlap area nearest the centre of the overlap. This was constant for all overlaps; hence, some combinations averaged much fewer range cells than others as not all overlap areas are of the same size. Utilizing this method, discontinuities are not be sudden gain jumps, rather, large variations in the overall signal strength may be present. These occur as dips and peaks in the radiometric strength. Depending on their relative strength these effects may be signifi44  cant. T y p i c a l l y , any g a i n variations t h a t result from a r o l l angle error are s m o o t h and have a relatively constant slope t h a t changes only over several h u n d r e d range lines. U s i n g the merger technique, it is possible for these intensity variations t o have large peak t o peak g a i n changes. F i g u r e s 3.5 a n d 3.6 shows this effect for a single r o l l error of 0.2° a n d several r o l l errors r a n g i n g from 0.2° to —0.2°, respectively.  Figure 3.5: Linear merging method with roll error of —0.1° Since the differences i n b e a m p a t t e r n gain have linear gain variations (3.2), a n d the w e i g h t i n g factors are linear, the effects of r o l l errors o n any relative g a i n variations are also linear. T h e b o t t o m p o r t i o n of F i g u r e 3.3 illustrates this fact. I n this figure, the peak to peak g a i n v a r i a t i o n per roll angle error is given for each b e a m c o m b i n a t i o n . A g a i n , these beams are fixed at h a l f of the available overlap length. U s e of a different size overlap region affects the required accuracies. 45  D i s c o n t i n u i t i e s Produced U s i n g L i n e a r Merqe w i t h V a r i o u s r o l l E r r o r s 1  -1 I 24  i 25  -  !  — i  !  i 26  i  r  1  i 27  1  1  1  1  29  30  31  1-  28  E l e v a t i o n Angle  r  (degs)  Figure 3.6: Linear merging method with roll errors of —0.2° to 0.2°  It should be noted that Figure 3.5 shows the creation of two new discontinuities at the seam edge. These discontinuities are abrupt changes in slope and not gain jumps. It was determined that the resulting peak to peak variation from the linear merge was more noticeable, and hence restrictive, than these two discontinuities. Therefore, they were not used in determining accuracy requirements. It should also be noted that seaming may change the radiometric resolution, which could be critical for some applications.  3.2.2  Accuracy Results  A l l the previous figures were created with the following assumptions: • The beam patterns are as specified in payload file 25.  46  • The beam pattern centers remain at the same position relative to one another, and their swath widths are constant. • The outer beam edges ( W l near and W2 far) are ignored due the extremely large variations that can occur in areas that already have low signal gain. • Either there is no averaging in the overlap area (abrupt transition method), and the interface is the point where one corrected beam stops and the next begins, or • There is linear data averaging in a designated portion of the overlap region (linear merge method), however there is no increase in gain due to merging. • There is an range factor, R~ , partially designed into the beam patterns. This range 3  factor was removed for the simulation. • The roll limits were set at 0.2 dB for the abrupt transition method and 0.4 dB for the linear merge method. The determination of the discontinuity size that created the roll limits is based on a subjective approach. As mentioned in Chapter 1, there are several ideas as to what the required radiometric calibration can be so that the human eye does not notice artifacts. This section clarifies what errors the eye can notice and how they are incorporated into the given beam patterns. The abrupt transition method is based on the jump size in the grayscale background of 8look gaussian noise that can be noticed by a human observer. Figure 3.7 a) illustrates changes in the background from 0.1 to 1.0 dB in 0.1 dB increments. The gain jumps are applied to a noiseless background and then 8-look Gaussian noise for comparison. Observations on computer screens indicate that humans can notice a discontinuity of 0.2 dB or greater. Hence, 0.2 dB is used as the abrupt transition limit. The linear merge method, however, is not based on a gain jump but rather peak to peak gain variations. Figure 3.7 b) illustrates the effects of these gain variations. The initial peak to peak gain change is 0.2 dB and each consecutive peak to peak gain is increased by 0.2 dB up to 2.0 dB. The resultant gain variations are displayed on a noiseless grayscale background and also applied to 8-look gaussian noise. The limit was determined to be the peak to peak gain which caused a vertical line to be discerned. Any slope would eventually cause a perceptible grayscale change given enough pixels. The aim of this figure is to determine 47  which peak to peak gain causes the eye to notice the vertical line where the gain variation occurs in a typical amount of image space assigned to the overlap region. It was determined that 0.4 d B was a suitable limit. Figure 3.8 a) illustrates the effects of discontinuities generated using the abrupt transition method on the W 1 W 2 interface (Figure 3.2) when applied to simulated 8-look data, with a typical Gaussian distribution. In the figure, the discontinuity sizes are considered to linearly increase from top to bottom. The left hand side is the roll angle scale which reflects the roll error applied to the beam patterns, from 0.10° to —0.10°. O n a good computer screen the discontinuities can be discerned as low as 0.2 d B , approximately —0.034°. The overall maximum discontinuity in this figure is approximately 0.7 d B and occurs at —0.10°. The gain variations and discontinuities generated from the gains shown in Figure 1.6 are given without (a) and with (b) simulated data. The 0.2 d B limit is shown on each portion as a white arrow. There is both a positive and negative roll error, each of which has its own 0.2 d B limit; however, the first 0.2 dB limit is the only one displayed and in this case occurs with approximately —0.034° roll error. In the Figure 3.8 b), the effects of changes in the corrected actual beam-pattern slopes for the W 1 W 2 interface (see Figure 3.6) are shown for the linear merge method. These gain variations vary in strength with roll error; however, positive and negative roll errors do not produce the same d B gains. The limit was set based on the absolute value of the roll angle error that first reached the 0.4 dB limit. Again, the effects are given both without (c) and with (d) simulated data being applied to the patterns. The same range of roll errors from 0.10° to —0.10° was applied to the beam patterns. The gain variations range across the image vertically but do not exceed the 0.4 dB limit inside of the ±0.073° range given from Figure 3.3. Hence, there are no noticeable gain variations in the middle of the image, while there is a noticeable gain change near the top and bottom.  48  Determination of D i s c e r n i b l e Change i n Grayscale Images  Noiseless Grayscale  dB Change  i n Grayscale  Value  8-Look Gaussian Noise  dB Change  i n Grayscale  Value  b)  Noiseless Grayscale  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.8  Peak t o Peak dB Change i n G r a y s c a l e  Value  Peak t o Peak dB Change  Value  2.0  8-Look Gaussian Noise  i n Grayscale  Figure 3.7: Visual determination of noticeable changes in grayscale background  49  Figure 3.8: W1-W2 interface applied to 8 look Gaussian noise  50  Based on this simulation, and the analysis of the sensitivity of each interface from Figure 3.3, it was determined that the following Table 3.2.2 would be used as the algorithm accuracy requirements. W1W2  W2W3  W2S5  W3S7  S5S6  Discontinuity Limit  0.034°  0.041°  0.035°  0.043°  0.028°  Absolute Gain Variation  0.073°  0.077°  0.10°  0.135°  0.045°  Table 3.1: Roll estimation accuracy requirements based on beam pattern and stitching method  These values come directly from the nearest 0.2 dB crossing to 0° for each interface and the 0.4 dB limit crossings. All the crossings are indicated in Figure 3.3 as vertical dotted lines. The S5S6 combination requires the highest accuracy for either case. It is necessary to clarify that whatever technique is used to merge ScanSAR data together, only the roll accuracy requirement is affected. ScanSAR roll angle determination is a separate problem from determining the best beam-stitching technique. This means that if the linear merging technique is used, then the roll accuracy requirement is always less demanding than that for the abrupt transition method. If another beam-stitching method is developed and used, then its accuracy requirements will vary from either of the methods used in this thesis. It should also be noted that these roll requirements are based on noticeable artifacts that appear as banding in the overlap area. Gain variations also appear elsewhere in the scene and may be more noticeable in ScanSAR mode as compared to single beam mode.  3.3  Required Accuracy Summary  In this chapter, the mechanisms whereby roll errors create radiometric errors are discussed. The relationship between any roll angle errors and the resulting discontinuities are presented for RADARSAT-1 ScanSAR. These are used to determine, via simulation, the required roll accuracy for each interface. Calibration errors of varying strength are shown as well as the sensitivities of each interface. This information is used in later chapters to discuss the usefulness of the proposed algorithms.  51  Chapter 4  Proposed Algorithms for R o l l Angle Estimation 4.1  Conception of Algorithm Idea  Initial investigation  of the S c a n S A R b e a m edge detection  sition of real R A D A R S A T - 1  p r o b l e m necessitated the  S c a n S A R R A W , o r l e v e l 0, d a t a .  L e v e l 0 d a t a is  d a t a w h i c h is s a m p l e d d i r e c t l y f r o m t h e s a t e l l i t e a n t e n n a r e c e i v e d s i g n a l . acquired  is a R A D A R S A T - 1  image  of P r i n c e A l b e r t ,  Saskatchewan.  acqui-  unprocessed  O n e of the scenes  It is a t h r e e  swath  S C N B s c e n e , c o m p r i s e d o f b e a m s W 2 , S 5 , a n d S 6 . T h e s e b e a m s a r e i l l u s t r a t e d i n F i g u r e 1.6 along w i t h the remaining R A D A R S A T - 1 S c a n S A R modes.  M A T L A B ™  is u s e d f o r r e a d i n g  the d a t a format a n d b e g i n n i n g the initial processing of the data, u p to the stage at r a n g e c a l i b r a t i o n is r e q u i r e d .  D u r i n g this initial phase,  a significant  amount  which  of time  was  s p e n t a d j u s t i n g t h e r e a d a l g o r i t h m so t h a t t h e n e c e s s a r y h e a d e r i n f o r m a t i o n [19] is s t r i p p e d f r o m t h e d a t a itself.  T h i s h e a d e r i n f o r m a t i o n is r e q u i r e d t o e n s u r e a c c u r a c y i n f o r m a t t i n g  the  Upon  S A R raw data.  successful  completion  of this task,  the  r a w d a t a is t h e n  c o m p r e s s e d u s i n g the c h i r p pulse s u p p l i e d i n the level 0 d a t a , or r a w d a t a .  Satellite  e t e r s , a p p e n d e d t o t h e d a t a i n a s p e c i f i c f o r m a t [2] f o r d o w n - l i n k p u r p o s e s , a r e  range param-  subsequently  removed. The  i m a g i n g p a r a m e t e r s for this scene d i c t a t e t h a t e a c h b u r s t b e c o m p r i s e d of 95  85 o f w h i c h are c o n s i d e r e d v a l i d pulses. it w a s e x p e c t e d  pulses,  B a s e d o n previous knowledge of the i m a g i n g process,  t h a t all the i n v a l i d pulses w o u l d a p p e a r at the start of the burst;  t h i s is n o t t h e c a s e a n d t h e r e a r e i n v a l i d p u l s e s a t t h e s t a r t a n d e n d o f e a c h  52  pulse.  however,  Range C o m p r e s s e d Data Format for One Swath Burst  1000  2000  3000  4000  5000  6000  7000  8000  Range Line Cell  5  5.5 d  B  x  1 C  Figure 4.1: Data format for one range sub-swath burst F i g u r e 4.1 s h o w s t h e r e s u l t a n t d a t a f r o m t h e s c e n e .  In a t t e m p t i n g to discover what  c a u s e o f t h i s i n v a l i d d a t a a c t u a l l y is, a n d if t h e r e is a n y u s e f u l s i g n a l p r e s e n t quickly realized that change, one  if  the satellite always t r a n s m i t s pulses,  t h e n there m a y be useful signal present.  b e a m pattern a n d received b y another.  there, it  the was  e v e n as t h e a n t e n n a  patterns  T h i s s i g n a l d a t a is t r a n s m i t t e d  through  Obviously, the entire b e a m - p a t t e r n pulse  not i n - d i s t i n g u i s h a b l e f r o m noise, b u t there are s o m e useful d a t a . proposed algorithms.  53  T h i s is t h e b a s i s f o r  is the  4.2  Algorithm Mechanisms  Figure 4.2 illustrates how a pulse can be transmitted and received by two different beam patterns. The example used is the W1-W2 beam interface, which is used in three of the four R A D A R S A T - 1 ScanSAR modes. There is an overlap between these beams of approximately 2°. Allowing the pulse to be transmitted in W l and received in W 2 creates a signal return, from a uniform scene, that has the resultant new pattern called W 1 W 2 . The signal data obtained through this new pattern is termed "hybrid data", while signal data transmitted and received by one beam pattern is called normal data. The shape of the W 1 W 2 beam, or any hybrid combination, is dependent on the shape of both the near and far beams in the overlap area. Thus, errors from roll angle uncertainty or beam gain uncertainty affect the hybrid pattern based on the mean of their effect on each individual beam. New Beam-Pattern Created From W1-W2  Overlap  E l e v a t i o n Angle (Degrees)  Figure 4.2:  Creation of W1W2 beam from W l and W2 patterns. Receiving hybrid data in this manner  should not pose any hardware problems [20]  54  Wt  PRF  Rgd  W2  1331.56 Hz  60.34 us.  659.1  fis  S5  1291.65 Hz  166.63 ps  576.1  us  S6  1333.20 Hz  67.76 lis  548.9 /is  Beam  Table 4.1: ScanSAR timing parameters for SCNB from the Prince Albert scene T i m i n g is a c r i t i c a l f a c t o r i n d e t e r m i n i n g w h e t h e r o r n o t t h i s h y b r i d d a t a w i l l a c t u a l l y b e r e c o r d e d . T h e r e are three m a i n t i m i n g parameters: the range gate delay, the range w i n d o w r e c e i v e t i m e (W ), t  a n d the pulse repetition frequency. R i gc  triggered until the receive w i n d o w opens.  is t h e t i m e d e l a y a f t e r t h e p u l s e is  T h e r e c e i v e w i n d o w is s i m p l y t h a t t i m e p e r i o d i n  w h i c h t h e s a t e l l i t e r e c o r d s t h e s i g n a l d a t a f r o m t h e r e c e i v i n g a n t e n n a . T h e P R F is t h e r a t e at w h i c h the satellite t r a n s m i t s each i n d i v i d u a l c h i r p pulse. F i g u r e 4.3 illustrates the t i m i n g for t h e S5 B e a m f r o m T a b l e 4.2.  T h e P R F is s i m p l y  Rg + W + Dt d  where D  is t h e d e l a y t i m e  t  t  for t h e e n d o f t h e r e c e p t i o n w i n d o w u n t i l t h e n e x t p u l s e t r i g g e r .  Timing Diagram f o r S i n g l e S5 P u l s e  40  1  '  30  1  1  , Pulse T r i g g e r at  1  —i  1—  Next Pulse  /  /  t=o  1  /  20 -  -  Echo Data  10 0 0  i  r  i  i  i  i  I  "H  1=  Transmit Pulse 42 us  11  X  10"  4  Seconds Rx Window = 576.16 us  RGD = 166.6 us  Figure 4.3: Timing for one range data line  55  Current Last  Near  2-Beam R e c e p t i o n S5  Beam  Standard  Timing with  a  PRF  Increase •S t a r t  Beam  of  Overlap  Region  Pulse \*  RGD1  |l/PRFl  •"'  First F a r , Beam  Range  Line  Consecutive  2-Beam  Timing  Data  -Waiks—due—to—PRF~ differences  Far  Beam  Transmit 1/PRF2  Pulses (Red  First  Box)  F a r Beam  Standard  Pulse-  Received  S6  Beam  RGD2 A=Start  Time  o f 2-beam d a t a  i n r e f e r e n c e t o Beam  1  B=Start  Time  o f 2-beam d a t a  i n r e f e r e n c e t o Beam  2 Rx w i n d o w  C=Difference  Same Far  of A  As Above  and B due t o d i f f e r e n c e  but with  Pulses  arranged  Beam 2-Beam  Transmit  i n R G D 1 and RGD2  Side  by Far  Data  Rx w i n d o w  Side Beam  Rx  Window  Pulse  Last  T  Standard Beam  Near  First  Pulse  Standard Far  Beam  Pulse  Figure 4.4: Possible hybrid data reception if transmit pulses are always O N for the S5-S6 overlap area and the P R F increases from the near to far beam  56  T i m i n g p a r a m e t e r s d e t e r m i n e where a n y useful h y b r i d d a t a will be r e c o r d e d i n the line.  C o n s i d e r F i g u r e 4.4  satellite continuously  a) w h i c h h a s h y b r i d d a t a r e s u l t i n g f r o m t h e S 5 - S 6 o v e r l a p i f t h e  transmits  pulses.  f r o m a r e a l S A R s c e n e (see T a b l e 4 . 2 ) . the S5 burst.  range  T h i s f i g u r e is b a s e d o n a c t u a l t i m i n g  parameters  T h e first o f t h e e l e v e n r a n g e l i n e s is t h e l a s t p u l s e o f  T h e n e x t 9 r a n g e l i n e s a r e a v a i l a b l e f o r h y b r i d d a t a r e c e p t i o n as t h e  o f p u l s e s i n t h e a i r h a s i n c r e a s e d f r o m 8 t o 9.  T h e f i n a l r a n g e l i n e is t h e  first  number  normal data  for t h e S6 b u r s t . T h e h y b r i d d a t a i n i t i a l l y shifts r i g h t as t h e S 5 R d  is g r e a t e r t h a n t h e S 6 R [.  g  d a t a then consecutively S6.  that  the n o r m a l receive  and timing parameters,  window  the  a n d q u i c k l y s h i f t s so f a r t o t h e  f u r t h e r i l l u s t r a t e s t h i s effect b y p l a c i n g t h e s a m e p u l s e s s i d e s b y s i d e . h y b r i d d a t a is b a s e d o n t h e d i f f e r e n c e s i n P R F s a n d R d g  a) the  a n d b)  except  that  hybrid  d a t a walks  illustrates  P R F decreases, left,  instead  p e r i o d for t h e far b e a m is n o w I n b o t h F i g u r e s 4.4 a n d 4 . 5 ,  r a t h e r t h a n increases, o f r i g h t , for e a c h  patterns  f r o m the  consecutive  b)  evident.  near  to  parameters  far b e a m .  line,  since  The  the  pulse  t h e h y b r i d d a t a is n o t w e l l s u i t e d f o r r e c e p t i o n as i t  either  greater.  c o n f l i c t s w i t h t h e t r a n s m i t p u l s e o r is r e c e i v e d o u t s i d e t h e a v a i l a b l e r e c e i v e  window.  F o r all b e a m c o m b i n a t i o n s , a n increase i n the P R F , f r o m n e a r t o far b e a m , a l w a y s i n a w a l k t o t h e r i g h t , w h i l e a P R F d e c r e a s e a l w a y s r e s u l t s i n a left w a l k .  results  S i n c e t h e P R F is  a f u n c t i o n of the required a z i m u t h s a m p l i n g rate, the o n l y situation that causes a n in the  right  F i g u r e 4.4  and timing  range  is  T h e movement of the  a n d is c l e a r l y  the exact same b e a m  than  hybrid data  it w r a p s a r o u n d a n d a p p e a r s at t h e b e g i n n i n g of t h e n e x t r a n g e line.  F i g u r e 4.5  T h e hybrid  s h i f t s f u r t h e r r i g h t as t h e p u l s e p e r i o d f o r S 5 is a l s o g r e a t e r  F o r this p a r t i c u l a r c o m b i n a t i o n of b e a m s  initially received outside  gC  increase  P R F f r o m n e a r t o f a r b e a m is w h e n t h e r e q u i r e d n u m b e r o f p u l s e s i n t h e a i r  increase to m a i n t a i n p r o p e r a z i m u t h s a m p l i n g .  57  must  Current  a) Last  2-Beam R e c e p t i o n  Timing  with  a PRF D e c r e a s e Start  Near  Standard  S5  Beam  Beam  ^  of Overlap Region^ 1/PRF1  Pulse"  First F a r , Beam  Range  2-Beam Data • ecmsectrti-ve Walks  due  Timing-;;;; t o PRF  di f f s r m m s  1/PRF2  First  F a r Beam  Standard  Pulse  Received  S6  Beam  RGD2 T i m e o f 2-beam d a t a i n r e f e r e n c e t o Beam 1 Rx w i n d o w B = S t a r t T i m e o f 2-beam d a t a i n r e f e r e n c e t o Beam 2 Rx w i n d o w C = D i f f e r e n c e o f A a n d B d u e t o d i f f e r e n c e i n RGD1 a n d RGD2  A=Start  Same A s A b o v e  but with  Pulses  arranged  Side  by Side Far  b)  Last  Beam Rx  Window  Standard Beam  First  Near  Standard F a r  Beam  Pulse  Pulse  Figure 4.5: Possible hybrid data reception if transmit pulses are always ON for the S5-S6 overlap area and the PRF decreases from the near to far beam 58  S i n c e t h e t i m i n g p a r a m e t e r s for R A D A R S A T - 1 are v e r y a c c u r a t e l y k n o w n for a p a r t i c u l a r scene, the h y b r i d d a t a c a n b e e x t r a c t e d f r o m the r e m a i n i n g noise.  T h i s is d o n e b y s i m p l y  d e t e r m i n i n g the shift t h a t o c c u r s u s i n g the following:  T  shlft  where m 1,2...8.  =  the n u m b e r of pulses  + (m-  l)(l/PRFi  - \/PRF )  (4.1)  2  received after the b e a m p a t t e r n s c h a n g e ,  typically m  S  data from  patterns, shifts  gd  T h i s t i m e s h i f t , T hi/t, is c o n v e r t e d t o r a n g e c e l l s b a s e d o n k n o w l e d g e  s a m p l i n g i n t e r v a l (Si). signal  = AR  W l  B a r r i n g a n y l i m i t i n g p a r a m e t e r s , s u c h as n a d i r r e t u r n , t h e  W 1 W 2 should adequately  and W 2 .  U t i l i z i n g this  represent  timing method,  a c o m b i n a t i o n of the a n y useful  of the h y b r i d d a t a i n the receive window.  F i g u r e 4.4  new  hybrid  actual  hybrid data  o u t o f t h e r e c e i v e w i n d o w f o r t h e u p c o m i n g b e a m a n d is l o s t .  the movement  of the  =  beam  eventually illustrates  S i n c e t h e P R F is a f u n c t i o n of  satellite p a r a m e t e r s , it c a n n o t b e a d j u s t e d to e n a b l e a d e q u a t e r e c e p t i o n o f t h e h y b r i d d a t a . H o w e v e r , i t is p o s s i b l e t o a d j u s t e i t h e r t h e R d g  for t h e u p c o m i n g b u r s t (for m p u l s e s ) , o r t h e  t i m e p e r i o d b e t w e e n b u r s t s w i t c h - o v e r s i n o r d e r t o a c c o u n t f o r t h e T^ft the next.  from one pulse  T h i s results i n a m a x i m u m a m o u n t of useful h y b r i d d a t a b e i n g received.  Overlap  areas m a y not a l w a y s h a v e s i m i l a r t i m i n g p a r a m e t e r s a n d m o s t of the d a t a m a y be lost, i n F i g u r e 4.4.  E i t h e r of these m e t h o d s help ensure m a x i m u m d a t a reception.  59  to  as  4.2.1  Pulse Trigger Delay  T h e simplest of the two adjustments u p c o m i n g b u r s t so t h a t  is t o s u f f i c i e n t l y d e l a y t h e  first  p u l s e trigger for  the receive w i n d o w o p e n s either at the start of the h y b r i d  the  pulse  r e t u r n o r closes at its e n d , d e p e n d i n g o n w h i c h d i r e c t i o n t h e h y b r i d d a t a m o v e s i n m e m o r y . F i g u r e 4.6  i l l u s t r a t e s t h i s m e t h o d for the  same  o v e r l a p as F i g u r e 4.4.  c h a n g e is p o s i t i v e f r o m t h e n e a r t o t h e f a r b e a m , t h e w a l k is t o t h e r i g h t .  Since the P R F Hence, the  p u l s e o f t h e f a r b e a m is d e l a y e d , so t h a t t h e first h y b r i d p u l s e is r e c e i v e d j u s t a s t h e window opens.  first  receive  T h e r e m a i n i n g r a n g e lines are n o t d e l a y e d . T h e h y b r i d d a t a still w a l k s to the  r i g h t ; h o w e v e r , t h e r e is n o w s u f f i c i e n t r o o m i n t h e r e c e i v e w i n d o w t o r e c e i v e a l l t h e  pulses.  F i g u r e 4.6 a) d i s p l a y s t h e r e s u l t s f r o m t h i s d e l a y i n t e r m s o f t h e p l a c e m e n t o f h y b r i d d a t a i n m e m o r y . T h e t i m e d e l a y is n o t s h o w n i n a ) s i n c e i t o n l y a f f e c t s w h e n t h e r a n g e l i n e s a r e r e c o r d e d a n d h a s n o v i s i b l e effect o n t h e n o r m a l d a t a . F i g u r e 4.6 b ) d i s p l a y s t h e p u l s e s s i d e b y s i d e .  T h i s arrangement clearly shows the  d e l a y j u s t p r i o r t o t h e first f a r b e a m p u l s e t r i g g e r . R e c e p t i o n o f n o r m a l d a t a is n o t  time  affected  b u t t h e h y b r i d d a t a is n o w p l a c e d e n t i r e l y w i t h i n t h e a v a i l a b l e r e c e i v e w i n d o w . The  a i m of d e l a y i n g the  receive w i n d o w .  first  p u l s e is t o s h i f t r e c e p t i o n o f t h e d a t a t o fit t h e  available  If t h i s f a i l s t o a d e q u a t e l y r e c e i v e a l l t h e a v a i l a b l e h y b r i d d a t a , t h e n  r e c e i v e w i n d o w c a n a l s o b e s h i f t e d t o b e s t fit t h e h y b r i d d a t a . next.  60  T h i s m e t h o d is  the  discussed  2-Beam Data R e c e p t i o n w i t h Delay on 1 s t F a r Beam P u l s e T r i g g e r Last  Near  Standard  S5  Beam  Start  Beam  of  Overlap  Region  Pulse  1/PRF1 First Far. Beam  Range  Line  1/PRF2  First  F a r Beam  Standard  Pulse"  Received  A=Start  Same  Time  As Above  b)  Far Time  Delay  A-RGD2  Last  Beam  data  but with  Pulses  2-Beam  Pulse  \  i n reference  arranged  Beam  Transmit  =  Standard  o f 2-beam  Near  Data  t o Beam  1 Rx  Side  Side  by Far  Beam  Rx  Window  First  Pulse  window  1/  Standard  Beam  Pulse  Figure 4.6: Hybrid data reception with delay of first pulse in upcoming burst  61  Far  4.2.2  Range Gate Delay Adjustment  A d j u s t m e n t of R  is m o r e c o m p l e x t h a n a s i m p l e t i m e d e l a y , as e a c h r a n g e l i n e m  g d  a r e a m a y r e q u i r e a d i f f e r e n t R d-  Rd  g  g  i n this  a d j u s t m e n t is b a s e d o n a m o d i f i c a t i o n o f ( 4 . 1 )  as  the  following:  R™d =  gd  R  B  + Tshift  (4.2)  a n d m u s t o b e y this:  r  < R™ <  P  where r  v  - W  d  (4.3)  2beam  is t h e c h i r p p u l s e l e n g t h a n d W2beam is t h e r e c e p t i o n w i n d o w o f t h e h y b r i d d a t a .  T h e superscript  C  B  i m p l i e s t h e c u r r e n t b e a m . A t m o s t , t h i s w i n d o w is a b o u t 1 0 % — 4 0 % o f  n o r m a l receive w i n d o w length.  T h e m a i n o b j e c t i v e o f (4.3)  for t h e r e t u r n t i m e of t h e h y b r i d d a t a . t h i s p u l s e is l o s t .  If (4.3)  is t o a d j u s t t h e r e c e i v e  window  is n o t m e t , s o m e o r a l l t h e h y b r i d d a t a f o r  T y p i c a l l y , t h e p u l s e d e l a y m e t h o d a l l o w s t h i s l i m i t t o b e m e t as t h e r e c e i v e  w i n d o w is m u c h l a r g e r t h a n t h e d i f f e r e n c e s i n P R F s f r o m m o s t n e a r t o f a r b e a m s w i t c h - o v e r s . H o w e v e r , t h e r e m a y b e s o m e c a s e s w h e r e t h e P R F d i f f e r e n c e is l a r g e e n o u g h t h a t e v e n w i t h a p r o p e r pulse delay the range walk m a y still move h y b r i d d a t a out of the receive In this case,  it m a y b e u s e f u l t o a d j u s t t h e receive w i n d o w t o a t t e m p t  window.  m a x i m u m hybrid  reception. F i g u r e 4 . 7 i l l u s t r a t e s t h i s r e q u i r e m e n t for t h e s a m e b e a m p a t t e r n s a s F i g u r e 4.4, b u t w i t h t h e P R F d e c r e a s e d / i n c r e a s e d f o r t h e n e a r / f a r b e a m b y 40 H z e a c h . F i g u r e 4 . 7 a) Rgd  illustrates  a d j u s t m e n t as t h e b l a c k r e c e i v e w i n d o w , w h i l e t h e n o r m a l r e c e i v e w i n d o w is r e d .  a d j u s t m e n t of R  g d  The  s h o w n here was used i n c o n j u n c t i o n w i t h the pulse delay m e t h o d .  T h e h y b r i d d a t a w a l k is n o t a f f e c t e d b y s h i f t i n g t h e r e c e i v e w i n d o w ; h o w e v e r , i t i s e v i d e n t that  a l l t h e h y b r i d d a t a falls w i t h i n t h e s h i f t e d receive w i n d o w  (black) while the  normal  receive w i n d o w (red) c a n n o t receive the last pulse. It is i m p o r t a n t t o n o t e t h a t a n y R d g  adjustment m u s t be r e t u r n e d to the s t a n d a r d setting  i n o r d e r t o r e c e i v e n o r m a l d a t a . T h i s is b e c a u s e t h e s a t e l l i t e s t i l l t r a n s m i t s p u l s e s a t a r e g u l a r rate. A f t e r r e c e p t i o n of the last h y b r i d pulse, the n o r m a l pulses b e g i n a r r i v i n g a n d t h e y are operating w i t h their s t a n d a r d t i m i n g parameters. n o r m a l d a t a is s e v e r e l y  impaired.  62  If R  g d  is n o t r e s e t t h e n t h e r e c e p t i o n o f  E i t h e r t i m i n g a d j u s t m e n t s h o w s h o w s i g n a l d a t a , t h a t is o t h e r w i s e l o s t , c a n b e r e c o v e r e d . T h i s is p a r t i c u l a r l y u s e f u l f o r t h e p r o p o s e d a l g o r i t h m as h y b r i d d a t a is p r o d u c e d a t a r a t e of a b o u t  1 r a n g e l i n e f o r e v e r y 10 o r 12 n o r m a l r a n g e l i n e s .  T h e a b i l i t y t o m a x i m i z e use of  t h e s i g n a l is a c l e a r a d v a n t a g e o v e r n o t m a k i n g a n y t i m i n g a d j u s t m e n t s .  C u r r e n t l y , as  the  satellite switches f r o m b u r s t to b u r s t , all the t i m i n g p a r a m e t e r s s w i t c h at the b e g i n n i n g of t h e n e w b u r s t [20].  T h e r e f o r e , if R A D A R S A T - 1 does t r a n s m i t continuously, all the  s i g n a l d a t a is a l l o c a t e d t o t h e d a t a b u r s t o f t h e u p c o m i n g b e a m , n o t t h e p r e v i o u s  63  hybrid  beam.  2-Beam Data Reception with Delay on 1st Far Beam Pulse T r i g g e r and RGD Adjustment  a) Last  Near  S5  Beam  Standard  First Far,  1/PRF1 2-Beam  •  Data  Line  RGD  Adjustment  Consecutive  =  PRF  1  r  Differences Remaining  Timing  ..,>-""--Walks c u e - t o  PRF  differences  r  RGD  Adjustment available after  Overlap  RGD1  <  Range  First  of  Region  Pulse \*  Beam  •Start  Beam  =  time  1/PRF2  Rx  Window  First  F a r Beam  Standard  Pulse  Received  S6  Beam  RGD 2 Red Black  Same  As Above  = standard = RGD  but with  Rx w i n d o w  adjusted  Pulses  Rx w i n d o w  arranged  Side  by Side  Adjusted Far  b)  Last  Standard Beam  Near  First  Pulse  Standard  Beam  Figure 4.7: Hybrid data reception with delay of first pulse in upcoming burst and R  gd  64  Far  Pulse  adjustment  Current  Proposed System  System  Pulse  Pulse Receiver  Transmitter  Number (X  Transmitter  pulses/  Receiver  Number (X  pulse Burst)  Burst)  Beam 1 In  X-8  X-8  X-6  X-6  Both  Systems, Pulses are Received approximately 8  Pulses after  Transmission  Old  System  X-3  Proposed  Satellite Stops  Satellite  Transmitting  X-2  Pulses Pulses  Continues Transmitting  approximately 8  X-3  System  Pulses X-l  until  Switchover  Before Switchover x  Beam Switchover Point  Beam 2  Figure 4.8: Current vs. proposed data acquisition for burst switching  65  X-2  A l t h o u g h t h e r e q u i r e d h y b r i d d a t a is n o t c u r r e n t l y a c q u i r e d b y R A D A R S A T - 1 , t h e r e b e n o s i g n i f i c a n t h a r d w a r e s y s t e m c h a n g e s r e q u i r e d i n o r d e r t o d o so. software  changes to the b e a m switching process  A l l t h a t is r e q u i r e d a r e  so t h a t t h e t r a n s m i t t e r a l w a y s  r a t h e r t h a n s h u t t i n g off a t t h e e n d o f e a c h b u r s t .  may  transmits,  F i g u r e 4.8 c o m p a r e s t h e c u r r e n t t i m i n g  s y s t e m i n place o n R A D A R S A T - 1 to the p r o p o s e d acquisition m e t h o d , w h i c h receives h y b r i d data. I n t h i s f i g u r e , t h e c u r r e n t s y s t e m d o e s n o t r e c e i v e a n y s i g n a l d a t a f o r t h e f i r s t 8-10 as i t t a k e s t h a t  l o n g for the s i g n a l to t r a v e l to a n d f r o m the t a r g e t .  lines  Since the radar  only  s t a r t s t r a n s m i t t i n g a t i t s r e s p e c t i v e s t a r t t i m e , t h i s g a p i n s i g n a l d a t a is a l w a y s p r e s e n t  and  t h i s a r e a is c o n s i d e r e d i n v a l i d d a t a . The beam The  p r o p o s e d s y s t e m utilizes this i n v a l i d d a t a a r e a b y m a i n t a i n i n g t r a n s m i s s i o n of 1 pulse,  t h r o u g h the  beam  1-pattern,  right up until the  point of burst  the  switch-over.  satellite then begins t r a n s m i t t i n g the b e a m 2 pulse t h r o u g h the b e a m 2-pattern.  This  r e s u l t s i n t h e n e x t 8 o r so p u l s e s b e i n g t r a n s m i t t e d t h r o u g h b e a m 1 a n d r e c e i v e d i n b e a m 2. T h e n u m b e r o f p u l s e s i n t h e a i r , m, calculates m  as t h e  is a f u n c t i o n o f t h e P R F a n d s l a n t r a n g e . E q u a t i o n 4.4  following:  c The  g o a l o f c h o o s i n g p r o p e r t i m i n g p a r a m e t e r s is t o e n s u r e a d e q u a t e r a n g e c o v e r a g e  while  still m a i n t a i n i n g p r o p e r a z i m u t h s a m p l i n g . T h u s , i n order to refrain f r o m lowering the P R F as s l a n t r a n g e i n c r e a s e s , t h e n u m b e r o f p u l s e s i n t h e a i r m u s t i n c r e a s e . of  Slant range changes  approximately  w i l l g e n e r a l l y n e c e s s i t a t e t h e n e e d for a c h a n g e i n As  an example,  the t i m i n g d a t a f r o m the  m.  previously mentioned  P r i n c e A l b e r t s c e n e is  g i v e n i n T a b l e 4 . 2 . 2 . T h e P R F is m a i n t a i n e d a t a r o u n d 1 3 0 0 H z as t h e s l a n t r a n g e s t a r t i n g w i t h the W 2 b e a m , then S5 a n d e n d i n g w i t h S6.  increases  B e a m s W 2 a n d S5 each have  pulses i n t h e air w i t h t h e i r m e a n slant r a n g e differing b y 37 k m (  9 1 Q  +  1 0 0 9  _  9 5 4  +  1 0 4 0  =  8  37).  T h e m e a n s l a n t r a n g e f o r b e a m S 6 is 1 0 6 3 . 5 k m , a d i f f e r e n c e o f 103.5 k m f r o m t h e m e a n s l a n t range of b e a m W 2 .  H e n c e , i n o r d e r to m a i n t a i n a p p r o x i m a t e l y 1300  o f p u l s e s i n t h e a i r m u s t i n c r e a s e t o 9.  66  H z P R F , the  number  Beam  W2  S5  S6  PRF  1331.56  1291.65  1333.2  Hz  Rgd  60.3395  166.63  67.766  [IS  659.093  576.165  548.93  lis  Pulse Period  751  774.2  750.08  [IS  Pulses in Air  8  8  9  Min Payload 9  25.63°  29.46°  34.59°  Max Payload 9  35.97°  38.67°  41.82°  Min Actual 9  26.95°  31.07°  36.08°  Max Actual 9  35.19°  37.17°  40.62°  Min Slant Range  910  954  1022  km  Max Slant Range  1009  1040  1105  km  Rx Wt "  Units  n/a  Table 4.2: Actual RADARSAT-1 ScanSAR timing parameters from Prince Albert scene Note  that  there  receive w i n d o w .  are some significant  changes between the  individual beam's  Rd  and  g  T h e a c t u a l r a n g e w i d t h u s e d f o r e a c h b e a m is a l s o s i g n i f i c a n t l y less t h a n  w h a t is p o s s i b l e u s i n g t h e m i n i m u m a n d m a x i m u m s w a t h a n g l e s f r o m t h e p a y l o a d  file.  t h i s p a r t i c u l a r s c e n e , t h e r a n g e c o v e r a g e o f e a c h b e a m is i n t e n t i o n a l l y r e d u c e d . T h i s is  For most  likely d u e to the large overlap between beams, the desire to m a i n t a i n a d e q u a t e d a t a rates i n t e r m s of d a t a s a m p l i n g a n d flow rates, a n d t h e fact t h a t t h e a n g l e s u s e d m o r e c l o s e l y  match  t h e k n o w n -3 d B w i d t h s (see T a b l e 4 . 3 ) . A l t h o u g h a change in the n u m b e r of pulses i n the air represents a significant t i m i n g change for t h e s y s t e m , t h e effects o n t i m i n g f o r h y b r i d d a t a r e c e p t i o n a r e n o t c r i t i c a l . T o b e g i n w i t h , the n u m b e r of pulses o n l y increases pulses i n the air t h a n farther beams.  as r a n g e i n c r e a s e s ;  beams  do not  require more  T h i s i m p l i e s t h a t h y b r i d d a t a , w h i c h is a l w a y s  t o the b e g i n n i n g o n t h e u p c o m i n g b u r s t , has sufficient The  closer  r a n g e lines a v a i l a b l e for  allocated reception.  o n l y e x c e p t i o n is t h e S C N A b e a m as t h e W 2 (far) b e a m s w i t c h e s t o t h e W l ( n e a r ) ,  t h i s is o n l y t r u e i f t h e n u m b e r o f p u l s e s is  different b e t w e e n  the beams.  If t h e p u l s e  and  numbers  a r e d i f f e r e n t , t h e n t h e l a s t l i n e o f h y b r i d d a t a is l o s t . As  g i v e n i n T a b i e 4.2.2, a n y c h a n g e i n p u l s e r e p e t i t i o n p e r i o d , receive w i n d o w , o r  Ri gt  is  m u c h s h o r t e r t h a n t h e p u l s e r e p e t i t i o n p e r i o d itself. T h e r e f o r e , a t l e a s t o n e o f t h e p r e v i o u s l y  67  mentioned timing adjustment methods should be able to cope with any timing difference. This is true whether the time change is caused by a increase in the number of pulses or any other system parameter.  4.3  Algorithm Implementation  The use of hybrid data presents two different methods of implementation. Each method is utilized and all their results are compared side-by-side in Chapter 6. In order of complexity, here are these algorithms: 1. Hybrid Peak Detection, 2. Three Beam Overlap Ratio. Implementation of these algorithms have a varying number of steps, all of which occur after range compression (range compression is not required for all roll estimation algorithms). However, the first two steps are intended to compensate for any R  gd  variations and are  common to all: 1. Extract all relevant signal data from the W 1 W 2 hybrid pattern. 2. Average hybrid data to form one range line.  4.3.1  Data Extraction  Each range line that has a possibility of W1W2 signal data being present should be considered for use in the algorithms. The useful hybrid data should only be as wide as the overlap region, and correspond to the known overlap elevation angles of the beam patterns. It is possible for signal data to be received in areas outside the overlap region since these areas are still within one of the beam's known gain regions. The S N R of this data can be quite low, but bright targets may appear. Data from regions outside the known beam patterns should not be used, since the pattern in this region has to be extrapolated. This process is not recommended as it recovers little useful information while introducing the possibility of significant error. Using a timing delay between bursts allows hybrid data to then be extracted according to this:  T  ahift  = AR  gd  + (m - l)A(l/PRF) 68  + Delay  (4.6)  4.3.2  Data Averaging  A f t e r d e t e r m i n i n g w h i c h d a t a will be used i n the averaging process, the m e a n of the d a t a is f o u n d .  Proper alignment  m e a n r a n g e c e l l is a s s i g n e d  then,  o f t h e d a t a b a s e d o n s l a n t r a n g e t i m i n g is c r i t i c a l .  a specific range t i m e slot (similar to a n o r m a l r a n g e  If c u r r e n t R A D A R S A T - 1 as s e e n i n F i g u r e 4.9,  intensity  t i m i n g is m a i n t a i n e d each  range line has  {R d g  and time  a different  delay  amount  Each  line).  are not  adjusted)  of useable d a t a .  This  f i g u r e is s i m u l a t e d d a t a f r o m t h e o n l y t w o b e a m R A D A R S A T - 1 S c a n S A R , w h i c h is t h e W l W2  (SCNA)  beam.  T h e d a t a is d i s p l a y e d as ( L o g - I n t e n s i t y )  2  d a t a for b e t t e r c o n t r a s t .  The  d a t a is s i m u l a t e d w i t h o n l y 7 l i n e s o f v a l i d d a t a for e v e r y 8 l i n e s o f i n v a l i d d a t a , f o r d i s p l a y purposes only.  T h e i n v a l i d d a t a a r e a for e a c h b e a m a p p e a r s p r i o r to t h e v a l i d d a t a i n t e r m s  of a z i m u t h line n u m b e r . F i g u r e 4.9 p r o v i d e s a n e x a m p l e v a r i a b l e T hift S  as d e f i n e d b y ( 4 . 1 ) . T h e 1st, 2 n d , 3 r d , a n d 4 t h l i n e s t h a t o c c u r a f t e r  to b e a m 2 are indicated. beam  1.  o f t h e h y b r i d d a t a w a l k t h a t o c c u r s as c o n t r o l l e d b y  the  switching  T h e s e lines o c c u p y t h e i n v a l i d a r e a a n d follow t h a t v a l i d a r e a for  E a c h line has shifted f r o m the previous b y a fixed a m o u n t .  In fact, there are still  f o u r m o r e r e m a i n i n g i n v a l i d l i n e s b u t t h e T h%ft h a s m o v e d t h e u s e a b l e s i g n a l r e t u r n o u t s i d e s  of the b e a m receive w i n d o w . switching  to B e a m  1.  T h i s p r o c e d u r e is r e p e a t e d f o r d a t a i m m e d i a t e l y p r e s e n t  However,  t h e T \if st  t  acts in the opposite  direction.  h y b r i d d a t a stored in the n o r m a l l y invalid d a t a area, the exact T ^ j f the useable h y b r i d d a t a must be re-aligned according to  69  range.  t  In order to  after use  must be calculated a n d  Simulated  2-Beam  ScanSAR  Acquisition  M e m o r y Range Cell Number  Figure 4.9: Hybrid data acquired from current RADARSAT-1 timing. Hybrid data is now received between normal data reception in the previously invalid data area. The hybrid data moves in memory according to changes in the timing parameters.  70  RADARSAT  1 ScanSAR C o m b i n a t i o n s w i t h New H y b r i d 1  1  " ~T  -  S6  S5  .  \\  • // / /  New S5S6  -  Patterns New S5S6 -3 dB Beamwidth 2°  1 30  25  20  40  35  0  W2  Wl  -5  -1 0  / / \>  -/  W^New  _  \  W1W2 \  New W1W2 -3 dB Beamwidth 1.75°  i  40  35  30  25  20  E l e v a t i o n Angle  (Degrees)  0 -5  _  -10  -  -1 5  20  [fx  1  New W2W3  -20  W3  W2  \ 40  35  30  25  0  S7  W3  -5 -  ^  -  New W3S7 1  25  l  ll Ij  / L  30  L  \\  -1 5  a) • 20  v  -  New W2S5 —f—  1  S5  ^^ff^  -1 o  -  New W3S7 -3 dB Beamwidth 2.18°  (Degrees) t  -  \ "  35  E l e v a t i o n Angle W2  New W2W3 -3 dB Beamwidth 2 . 54°  New W2S5 -3 dB Beamwidth 4.25°  \  / / 30  E l e v a t i o n Angle  (Degrees)  -3  dB Beamwidth i s  from  Max p o i n t o f  hybrid  pattern  Figure 4.10: All beam interfaces and their resultant new beam patterns for R A D A R S A T - 1  71  4.4  The Proposed Algorithms  4.4.1 The  H y b r i d Peak Detection s h a p e o f t h e g a i n p e a k s i n t h e a v e r a g e d h y b r i d d a t a is m u c h n a r r o w e r t h a n t h a t o f t h e  normal b e a m patterns  (with the exception  of the W 2 - S 5 b e a m ) .  F i g u r e 4.10  illustrates  fact q u i t e c l e a r l y for a l l the b e a m s , e x c e p t for W 2 S 5 . B a s e d o n this, a h y b r i d p e a k a l g o r i t h m is g e n e r a l l y a c c u r a t e a n d q u i t e s i m p l e .  detection  It is b a s e d s o l e l y o n p e a k m a t c h i n g b e t w e e n  a s e c o n d , t h i r d , a n d f o u r t h o r d e r p o l y n o m i a l fit o n t h e a c q u i r e d h y b r i d s i g n a l d a t a a n d known hybrid gain A l t h o u g h the  this  the  patterns.  hybrid patterns  are fairly s y m m e t r i c ,  scene r a d i o m e t r y m a y v a r y  signifi-  c a n t l y a n d shift the lower o r d e r p e a k s to either edge. T h i s p r o d u c e s p o o r e s t i m a t e s f r o m the l o w e r o r d e r p e a k s o n s o m e scenes. C o n v e r s e l y , t h e h i g h e r o r d e r fits a r e m o r e l i k e l y t o p r o d u c e p o o r e s t i m a t e s w h e n t h e r e c e i v e d d a t a is f a i r l y s y m m e t r i c a l b u t s t i l l h a s s o m e r a d i o m e t r i c variations near the peak.  F o r t h i s r e a s o n , a w e i g h t i n g is u s e d t o d e t e r m i n e w h i c h e s t i m a t e s  are m o r e likely to be correct. best for this The  T h e c o m b i n a t i o n o f a 2 n d , 3 r d a n d 4 t h o r d e r fit w o r k s  the  method.  peak location does not necessarily  to the k n o w n peak locations  m a t c h t h e i n t e r f a c e p o i n t , r a t h e r it is c o m p a r e d  c a l c u l a t e d f r o m t h e p a y l o a d files.  as a p r i m a r y e s t i m a t e , w i t h m a r g i n a l t o m o d e r a t e  success, or to greatly reduce the  space a n d p r o v i d e a secondary estimate to other algorithms.  1. F i t a s e c o n d , t h i r d a n d f o u r t h o r d e r p o l y n o m i a l t o t h e 2. D e t e r m i n e a w e i g h t e d  T h i s algorithm can be  average p e a k for all t h r e e  3. C o m p a r e t h i s p e a k t o t h e k n o w n h y b r i d R D G C  used  search  It h a s t h r e e s t e p s :  data.  fits. peaks.  These peaks can be  calculated  o n c e f o r e v e r y u p d a t e d p a y l o a d file a n d t h e n s i m p l y u s e d as a l o o k - u p t a b l e .  The  a l g o r i t h m operates based o n the  #e = w h e r e QRDGC, average  peak  QRDGC,  following:  3 ORDGC,  is t h e p e a k o f t h e R D G C of the  p o l y n o m i a l fit t o t h e  = min (\9 Ci RDG  - d k\)  for k n o w n roll a n g l e data.  72  i  T h r e e different  to e s t i m a t e the d a t a p e a k since s o m e scenes c a n have  (4.7)  pea  and  9 k pea  is t h e  polynomial  fits  weighted are  used  a dramatically varying R C S , which  m a y shift  the  peak more significantly  u s i n g a w e i g h t e d average of the three not  removed.  for a s e c o n d fits,  D u e to the scene content  o r d e r fit t h a n a t h i r d ,  a n d so o n .  By  t h e effects o f s c e n e c o n t e n t a r e r e d u c e d , a l t h o u g h dependence  of this m e t h o d ,  i t is n o t  accurate  on  diverse scenes b u t still provides a n adequate b o u n d a r y w i t h i n w h i c h the other a l g o r i t h m s c a n operate.  A l s o , the W 2 S 5 overlap region does not provide a well-defined peak a n d this m e t h o d  is n o t u s e f u l w i t h t h i s o v e r l a p .  T h e w e i g h t i n g is d e t e r m i n e d b y c o r r e c t i n g t h e h y b r i d  data  w i t h e a c h p o l y n o m i a l a n d t h e n c a l c u l a t i n g the- f l a t n e s s o f e a c h c o r r e c t i o n . T h e p o l y n o m i a l w h i c h c r e a t e s t h e o v e r a l l f l a t t e s t d a t a is g i v e n t h e h i g h e s t w e i g h t i n g , a n d so F i g u r e 4.11 overlap region.  forth.  s h o w s t h e p o l y n o m i a l fit t o t h e d a t a f o r t h e M e l f o r t s c e n e w i t h t h e T h e a c t u a l h y b r i d p a t t e r n u s e d is a l s o s h o w n as t h e g r e e n l i n e .  W1W2  Although  s c e n e c o n t e n t is c l e a r l y v i s i b l e i n t h e s i g n a l s t r e n g t h , t h e a l g o r i t h m p r o d u c e s m a r g i n a l r e s u l t s o f ± 0 . 0 7 ° t h a t r e s u l t s i n a p p r o x i m a t e l y 0.45 d B c a l i b r a t i o n a c r o s s t h e  73  swath.  Peak D e t e c t i o n 1  1  on W1-W2  O v e r l a p on M e l f o r t  1  1  1  Actual Hybrid  26  26.5  27  27.5  E l e v a t i o n Angle  28  Scene 1  Pattern  28.5  (Degrees)  Figure 4.11: Polynomial fit to hybrid data for hybrid peak detection on Melfort scene. The actual hybrid pattern is given at the top of the data while the 2nd, 3rd, and 4th order polynomials are embedded in the data.  74  4.4.2  Three B e a m Overlap Ratio  F r o m C h a p t e r 2, r e c a l l t h a t G o u l d i n g ' s a l g o r i t h m u s e s t h e r a t i o o f t h e n e a r a n d f a r b e a m p a t t e r n overlap area to derive a n estimate. idea to  incorporate hybrid data,  This proposed method  w h i c h covers  the  is a n e x t e n s i o n o f  exact s a m e receive  provides a t h i r d range line, w i t h w h i c h a ratio c a n be m a d e .  window.  that  This  now  T h e r e a r e five s t e p s t o  this  method:  1.  C o m p u t e the l o g r a t i o of t h e c o r r e c t e d h y b r i d d a t a w i t h t h e c o r r e c t e d far b e a m edge.  2. C o m p u t e t h e l o g r a t i o o f t h e c o r r e c t e d h y b r i d d a t a w i t h t h e c o r r e c t e d n e a r b e a m e d g e . 3. C o m p u t e t h e l o g r a t i o o f t h e c o r r e c t e d f a r b e a m e d g e w i t h t h e c o r r e c t e d n e a r  beam  edge ( G o u l d i n g ' s M e t h o d ) . 4.  C a l c u l a t e a 4 t h o r d e r p o l y n o m i a l for e a c h o f t h e  5.  D r i v e the  absolute  s u m of the differences  possible by v a r y i n g the roll angle of the  G o u l d i n g ' s a l g o r i t h m u s e s (2.1)  a n d (2.4)  o f t h e t h r e e p o l y n o m i a l s as c l o s e t o z e r o  to d e t e r m i n e the e s t i m a t e .  2  +  |ALr  2  3  e  J  +  =  Ok*  |ALr ieJ  =  min(  |ALr  =  Lr  -  3  where A L r ^  where L r ; a n d Lr,- represent  i d i  hybrid/near data, and 3 =  and  i ^  1  2  e  Lr^  x  J  far/near d a t a respectively),  +  |ALr  2 3  0 | +  pages.  75  x  |ALr  3  W  J)  (4.9) (4-10)  x  =  (1 =  hybrid/far data,  each respective  T h e l o g r a t i o s a r e c a l c u l a t e d as p e r G o u l d i n g ' s m e t h o d .  d o w n m o r e s u c c i n c t l y i n t h e n e x t few  following:  (4.8)  the log ratio of the b e a m s a c t u a l l y u s e d  2 =  j.  x  I n c o r p o r a t i o n of the  T h e e s t i m a t e is n o w t h e  9  e  as  RDGCs.  h y b r i d d a t a results i n three log ratios, i n s t e a d of one.  |ALri eJ  ratios.  roll  angle,  T h e a l g o r i t h m is b r o k e n  Detailed Operation F i g u r e 4.12 a) s h o w s t h e n o r m a l d a t a a n d t h e h y b r i d d a t a s i m u l a t e d f o r t h e W 1 - W 2 i n t e r f a c e . The  d a t a was g e n e r a t e d w i t h a roll of + 0 . 1 0 ° .  T h i s f i g u r e s h o w s t h e W l d a t a as b l u e , t h e W 2  d a t a as r e d , a n d t h e h y b r i d W 1 W 2 d a t a as g r e e n .  S c e n e c o n t e n t is v i s i b l e i n t h e r a d i o m e t r i c  s t r e n g t h as d i p s a n d p e a k s . F i g u r e 4.12  b)  illustrates  the  RDGCs  l o o k - u p t a b l e f o r a r o l l e s t i m a t e of - 0 . 0 6 ° . red  a n d the W 1 W 2 R D G C  generated  from the  p a y l o a d file a n d s t o r e d  A g a i n , the W l R D G C  is b l u e , t h e W 2 R D G C  a is  is g r e e n .  F i g u r e 4.12 c) is t h e r e s u l t o f a p p l y i n g t h e R D G C s  i n b) to the d a t a i n a).  is s t i l l v i s i b l e a n d t h e b e a m s d i s p l a y a v a r y i n g g a i n a c r o s s t h e s w a t h . t h e o v e r l a p r e g i o n for finer d e t a i l . b y -10 a n d + 1 0  in  d B for d i s p l a y  Scene  F i g u r e 4.12 d)  content enlarges  T h e c o r r e c t e d d a t a f o r t h e W l a n d W 2 b e a m s a r e offset  purposes.  76  Implementation  of Proposed  3-Beam A l g o r i t h m  -5 -10 Wl  RDGC  -15 -20  W1W2  RDGC  -25 I 20  25  30  Elevation  Angle  (Degrees)  Corrected  W2  data  Corrected  70  W1W2  Data  ^  20  —  -75  Zoom  ~~3G-. _ ^  i n on O v e r l a p  Region  Only  11 0 i W2  Data  offset for  26  by  +10  dB  Display  26.5 Elevation  27  27.5  Angle  (Degrees)  Figure 4.12: Implementation of proposed algorithm Part 1  77  35  F i g u r e 4.13  e) is a n e x a c t c o p y o f d ) a n d is s h o w n a g a i n f o r c l a r i t y .  r a t i o s h a v e b e e n t a k e n f o r t h e a l l t h e b e a m s a n d a r e as  In p a r t f), the  log  follows:  W1W2 • J. W2 wo is m a g e n t a ,  •  W1W2 is y e l l o w ,  wi  •  l^ 2  Note  is b l a c k .  that  using the  an estimate.  Goulding method,  Scene content  only the  black log ratio ( W 2 / W 1 )  Lr, = x^  and  are the  for  is n o l o n g e r v i s i b l e as t h e r a t i o o p e r a t i o n r e m o v e s t h e d i p s a n d  p e a k s f r o m t h e r a n g e l i n e . T h e l o g r a t i o s t e p i t s e l f is b a s e d o n t h e  where  is a v a i l a b l e  slant  range  following:  ]2j2l  (4.11)  cells w h i c h cover the  overlap area f r o m cell  1 to  G o u l d i n g ' s m e t h o d t o o k t h e m e a n o f t h e l o g r a t i o , M , as \ Yl L r » . S i n c e t h e r e a r e n o w  i.  three  different l o g ratios, a different a p p r o a c h c a n be used. F i g u r e 4.13  g) is a 4 t h o r d e r p o l y n o m i a l fit t o t h e l o g r a t i o s i n f ) .  A p o l y n o m i a l fit  is  p e r f o r m e d so t h a t s l i g h t v a r i a t i o n s i n t h e l o g r a t i o s t r e n g t h are n o t c a n c e l l e d o u t b y r a n d o m noise terms. calculated.  T h e absolute  sum  of the  F o r this p a r t i c u l a r case, the  difference —0.06°  between the  RDGCs  three  polynomials  p r o d u c e a s u m of  is  then  approximately  140. F i g u r e 4 . 1 3 h ) is t h e s u m for a l l t h e R D G C s The  from - 0 . 2 0 ° to + 0 . 2 0 ° in 0 . 0 0 5 °  l o w e s t s u m is t h e b e s t fit a n d o c c u r s a t + 0 . 0 9 ° .  A s mentioned,  t h e d a t a is  w i t h a + 0 . 1 0 ° r o l l , so t h i s m e a n s t h e a l g o r i t h m h a s a n e r r o r o f 0 . 0 1 ° , w h i c h is D u r i n g a c t u a l i m p l e m e n t a t i o n i t is n o t n e c e s s a r y F i g u r e 4.13  increments. generated  acceptable.  to c a l c u l a t e t h e s u m for e v e r y  h) s h o w s t h a t t h e s u m s are q u i t e l i n e a r , a n d hence,  RDGC.  depending on whether  s u m increases or decreases, a n iterative a p p r o a c h w i t h v a r y i n g steps works quite well. l i n e a r i t y of t h e s u m s for all the R D G C s fact,  the w i d t h of a n y curve that  the The  a l s o i m p l i e s t h a t t h e e s t i m a t e is f a i r l y r o b u s t .  In  m a y a p p e a r a t t h e l o w e r e n d is a g o o d e s t i m a t e o f  the  s u i t a b i l i t y of this a l g o r i t h m to a p a r t i c u l a r scene. T h i s e s t i m a t e c a n b e i m p r o v e d t h r o u g h t h e s a m e i t e r a t i v e a p p r o a c h as t a k e n i n G o u l d i n g ' s m e t h o d , starting w i t h the inner b e a m a n d w o r k i n g out.  78  Implementation  of Proposed  3-Beam A l g o r i t h m  Cont'd  Take Log Ratios  e) PQ  cc! CD  f)  O •H 4-1  rd Pi  01 O  26  26.5  27  Elevation  g)  Polynomial  27.5 Angle  28  28.5  (Degrees)  ( 4 t hOrder)  f i t t o Log Ratios  . 2-beam/W2 2-beam/Wl W2/W1  rd  Pi  D) O  The  sum o f  the  absolute  three  log  ratios  a l l  25.5 300  _,  i  26  26.5  a  u  28.5  28 1  roll  sum.  1  angle  i n g)  error  unique  thel o g  are f o ra  o f -0.6  29  1  has a  Example,  ratios  <u  in in -H Q  a ,  1  Each '  for  27.5  1—  200 -  between  errox  27  CD  u  calculated  specific, r o l l  1  1  difference  is  roll  degrees  1 00 The  lowest  the  best  sum i s  estimate  -  -0.2  -0.15 In  this  however, that <  -0.1  the r o l l  the actual  algorithm  0  -0.05  case, was  i  i  i  roll  meets  0.1  e s t i m a t e i s 0.0 9 was  0.10  degrees.  accurate to within  i  t  0.05  0.01  0.15 degrees; This  degrees  means which  the requirement.  Figure 4.13: Implementation of proposed algorithm Part 2  79  0.2  The  m a i n i m p r o v e m e n t i n t h e three b e a m m e t h o d over G o u l d i n g ' s m e t h o d comes  from  c o m p a r i n g the steep slopes f r o m either of the n o r m a l patterns to the slopes i n the h y b r i d patterns. for  U s i n g G o u l d i n g ' s a l g o r i t h m , only one of the b e a m patterns has significant  e i t h e r s i d e o f t h e o v e r l a p a r e a , t h a t is a f f e c t e d  b y a roll angle.  slope,  W i t h t h e i n c l u s i o n of  h y b r i d d a t a , t w o o f t h e t h r e e l o g r a t i o s u s e d i n t h e t h r e e b e a m m e t h o d is a l w a y s b a s e d o n d a t a c o r r e c t e d b y R D G C s w i t h steep slopes.  Hence, a n y errors c a n b e m o r e easily noticed.  F i g u r e 4 . 1 4 i l l u s t r a t e s t h e s l o p e s o f a l l s i x n o r m a l b e a m p a t t e r n s a n d t h e five h y b r i d p a t t e r n s used i n R A D A R S A T - 1  S c a n S A R mode.  N o t e that the slopes of the h y b r i d patterns are the  m e a n of t h e n o r m a l patterns i n t h e overlap regions.  S l o p e s o f a l l S i x S t a n d a r d and F i v e H y b r i d ScanSAR Beams 1  t  1  1  : —  1  1  'I  0.02  i ';?  6  \  l\  1  W1W2  2  W2W3  3  W2S5  4  W3S7  5  S5S6  6  W1  7  W2  8  W3  9  S7  10  S6  11  S5  15  \  8  •,10  \ll  5\\  <r ^C' — X  \  \>  \  :  \\  '.  i 't  •  1  1  20  25  30  E l e v a t i o n Angle  \\ s :  i  35  40  (Degrees)  Figure 4.14: A l l ScanSAR normal pattern slopes and hybrid slopes. These slopes indicate the sensitivity of each beam to roll errors. The hybrid slopes are an average of their respective two normal beams. In this figure, the actual normal beam derivatives are shown while a quadratic representation of the hybrid beam is given in order to highlight differences between hybrid beams.  U s i n g the h y b r i d patterns allows a further c o m p a r i s o n to another b e a m p a t t e r n w h i c h also h a s significant slope.  U p o n a p p l i c a t i o n of t h e R D G C s , a n y difference between t h e slope  80  present i n the d a t a a n d the R D G C large slopes i n the R D G C  slope causes a larger s u m i n the  final  are b e n e f i c i a l to t h e a l g o r i t h m . F i g u r e 4.15  calculation. illustrates the  of each of the new h y b r i d patterns w i t h o u t the presence of the n o r m a l patterns. figure,  the  expected  W 1 W 2 is s e e n t o  that  the  have  the  largest  slope a n d the  best slope c o m b i n a t i o n will have  a large average  sufficient b e a m - w i d t h to allow for m o r e s a m p l e s to b e The  W2S5  Hence,  has  the  slopes  From  lowest.  this It  slope c o m b i n e d  with  summed.  t o t a l a v a i l a b l e h y b r i d p a t t e r n w i d t h is b a s e d o n t h e k n o w n b e a m p a t t e r n s f r o m  p a y l o a d file a n d d o e s n o t c h a n g e .  versus  a v a i l a b l e b e a m - w i d t h is c o n s t a n t  for a l l b e a m s ,  percentage  the W 2 S 5 pattern  should  p r o d u c e t h e p o o r e s t e s t i m a t e , as a l t h o u g h i t is q u i t e w i d e ( a p p r o x i m a t e l y 4 . 2 5 ° ) , i t h a s lowest slope.  T h e W 1 W 2 p a t t e r n has the largest slope b u t also has the narrowest  The  W 2 W 3 p a t t e r n is t h e s e c o n d w i d e s t b u t a l s o d o e s n o t h a v e s i g n i f i c a n t s l o p e .  and  W 3 S 7 patterns  W1W2,  are b o t h  the  H o w e v e r , t h e a c t u a l b e a m - w i d t h f o r e a c h h y b r i d p a t t e r n is  b a s e d o n t h e t i m i n g p a r a m e t e r s s e l e c t e d for e a c h i n d i v i d u a l scene. A s s u m i n g the of a c t u a l  is  over  2° wide  a n d have  a n d W 3 S 7 should p r o d u c e the best estimates.  81  larger slopes.  the  pattern.  T h e S5S6  Therefore, the  S5S6,  Average 0.015  i  Slope  1  1  Comparisons 1  1  of  Hybrid  1  Patterns 1  1  1  0.01  0.005 <D U 01 0) P PQ -0.005  -0.01  -0.015 24  1 2 3 4 5  W1W2 W2W3 W2S5 W3S7 S5S6 26  0.0089 db/Degree 0.0064 db/Degree 28  30  32 Elevation  _J  L_  34  36  38  40  42  Angle  Figure 4.15: Average Slopes of the hybrid patterns shown in Figure 4.14. Hybrid beams with steeper slopi and sufficient width are expected to provide the best results.  82  4.5  Algorithm Pros and Cons  4.5.1  Pros  F r o m F i g u r e 4.2, it c a n b e s e e n t h a t t h e n e w h y b r i d p a t t e r n , W 1 W 2 , h a s a u n i q u e s h a p e . fact, c o m p a r i n g all the b e a m interfaces present i n R A D A R S A T - 1 t h a t each n e w h y b r i d p a t t e r n has the  •  A  new  b e a m pattern that  has  A n overall range dependent  illustrates  following:  a higher g a i n t h a n the  b e a m s , w h i c h e n h a n c e s e s t i m a t i o n o n l o w e r a°  •  i n F i g u r e 4.10,  In  low  g a i n edges of the  normal  scenes,  g a i n t h a t is t h e a v e r a g e o f t h e t w o b e a m s ,  which  reduces  t h e effects o f b e a m g a i n u n c e r t a i n t y ,  •  A n e w b e a m p a t t e r n t h a t h a s a w e l l - d e f i n e d p e a k ( e x c e p t f o r W 2 S 5 ) , w h i c h is e a s i e r locate t h a n the edge of a single  •  beam,  T h e log ratio of d a t a a c q u i r e d t h r o u g h the differently  to  roll errors.  differences  produces  to  T h e ability to  a final scene that  near,  far, a n d h y b r i d  m a t c h these log ratios  has  patterns  and  m i n i m a l gain variations,  responds  minimize  their  even if the  roll  for t h e n e w h y b r i d p a t t e r n s .  All  t h e n e w h y b r i d p a t t e r n s a r e s i g n i f i c a n t l y s m a l l e r i n r a n g e t h a n t h e -3 d B b e a m - w i d t h s  (see  T a b l e 4.3)  the  estimate does not n o r m a l l y meet the accuracy requirement.  A l s o s h o w n i n F i g u r e 4.10  a r e t h e -3 d B b e a m - w i d t h s  for t h e w i d e b e a m p a t t e r n s  standard b e a m patterns  ( W 1 , W 2 , a n d W 3 ) , a n d a b o u t half the w i d t h of  (S5, S6, a n d S7).  Beam -3 dB Width  S5  S6  S7  Wl  W2  W3  4.83°  3.82°  3.72°  10.39°  7.57°  5.65°  Table 4.3: RADARSAT-1 -3 dB beam-widths for standard and wide beams used in ScanSAR mode  83  Overall Gain In  G o u l d i n g ' s a l g o r i t h m , the gain estimates are always m a d e  f r o m the averaging of signal  d a t a . S i g n a l d a t a is a c q u i r e d w i t h a l o w s i g n a l g a i n for o n e b e a m a n d w i t h a h i g h s i g n a l g a i n for t h e o t h e r b e a m , u n t i l t h e b e a m s c r o s s o v e r a n d t h i s is t h e n r e v e r s e d . T h e e s t i m a t e e r r o r s are t h e n b a s e d o n the a d d i t i o n of the signal errors present, these errors c a n be significant i n the low gain regions. S i n c e t h e o v e r l a p r e g i o n is t y p i c a l l y a l o w S N R r e g i o n t o b e g i n w i t h , t h e r e is a n  advantage  t o w o r k i n g w i t h d a t a t h a t is, o n a v e r a g e , a f e w d B a b o v e t h e l o w e s t g a i n o f t h e t w o o r i g i n a l b e a m patterns.  S i n c e t h e n o i s e e q u i v a l e n t o~° is f a i r l y c o n s t a n t , t h i s h i g h e r g a i n t h e n  i m p r o v e d p e r f o r m a n c e o n scenes t h a t m a y have a n overall lower  implies  a°.  B e a m G a i n Uncertainty i n L o w G a i n Regions The  l o w - g a i n r e g i o n s o f e a c h b e a m a r e n o t as w e l l k n o w n as t h e m a i n , h i g h e r g a i n  and  c o u l d suffer f r o m m o r e g a i n u n c e r t a i n t y . T h e h y b r i d p a t t e r n s a r e a c o m b i n a t i o n o f  normal beams.  Since the  lesser k n o w n p a t t e r n .  normal beams  overlap, one  two  well k n o w n p a t t e r n c o m p l e m e n t s  U t i l i z i n g h y b r i d d a t a , a n y g a i n u n c e r t a i n t y is t h e r e f o r e  reduced  c o m b i n i n g a well k n o w n p a t t e r n w i t h a lesser k n o w n p a t t e r n , r a t h e r t h a n solely t h e lesser k n o w n p a t t e r n s .  regions  a by  utilizing  T h i s is p o t e n t i a l l y m o r e b e n e f i c i a l t h a n t h e S N R i s s u e m e n t i o n e d  a b o v e , a n d is t a k e n a d v a n t a g e o f t h r o u g h u s e o f t h e p r o p o s e d a l g o r i t h m s .  Well-Defined With and  the  Peak  exception  of the  W 2 - S 5 overlap, the  new  beam  pattern peaks  are well  defined  c a n b e l o c a t e d w i t h m o d e r a t e s u c c e s s o n scenes t h a t h a v e a t least a m e d i u m d e g r e e of  uniformity.  T h i s process  provides a good  t h e s e a r c h s p a c e for o t h e r m e t h o d s . payload  files.  s e c o n d a r y e s t i m a t e , o r a t least, a b o u n d a r y for  T h e s e p e a k locations d e p e n d o n scene p a r a m e t e r s  H o w e v e r , since the n o r m a l b e a m s generally act i n a n opposite  o v e r l a p a r e a , d e f i n i n g a p r o m i n e n t p e a k is n o t u s u a l l y a p r o b l e m .  84  and  m a n n e r in the  L o g R a t i o Differences W i t h G o u l d i n g ' s m e t h o d , t h e r e is o n l y o n e l o g r a t i o a v a i l a b l e f o r u s e i n t h e a l g o r i t h m . t h o u g h its m e a n m a y a p p r o a c h one, t h e r e s u l t a n t e s t i m a t i o n error c a n still be large.  Even Using  h y b r i d d a t a a d d s a n o t h e r d i m e n s i o n to the l o g ratio estimates b y a l l o w i n g the differences  of  three log ratios to be calculated.  4.5.2  Cons  It m u s t b e r e m e m b e r e d t h a t t h e h y b r i d d a t a r e q u i r e d f o r t h e s e a l g o r i t h m s is n o t c u r r e n t l y a c q u i r e d w i t h a n y satellite system.  T h e hybrid data must be simulated, which m a y introduce  errors i n t o the e v a l u a t i o n of these a l g o r i t h m s .  •  A l s o , i t is u s e f u l t o r e a l i z e t h e  following:  D u e t o t h e m a n n e r i n w h i c h t h e u s e f u l h y b r i d s i g n a l d a t a is a c q u i r e d , t h e r e is a p p r o x i m a t e l y 10 t o 12 t i m e s less d a t a a v a i l a b l e f o r t h e e s t i m a t e s as c o m p a r e d t o n o r m a l d a t a . In the s i m u l a t i o n s t h a t follow, h y b r i d line t o ease p r o c e s s i n g  •  a p p r o x i m a t e l y six n o r m a l lines are p r o d u c e d for  every  times.  Since the  h y b r i d d a t a is p r o d u c e d a t a s l o w e r r a t e t h a n t h e n o r m a l d a t a , i t m a y  be  necessary  to a c q u i r e several b u r s t s of d a t a i n o r d e r to p r o d u c e sufficient  of  useable h y b r i d data.  T h e viewing angles involved m a y then encompass  imuth beam pattern.  Speckle m a y become  amounts  the entire  az-  a factor for these a l g o r i t h m s ; however,  the  i n c o h e r e n t a d d i t i o n o f s e v e r a l r a n g e lines r e d u c e s t h i s affect.  T h i s is p a r t i a l l y o f f s e t b y  t h e f a c t t h a t t h e h y b r i d d a t a is a c q u i r e d a t n e a r l y t h e s a m e v i e w i n g a n g l e as n o r m a l data.  Speckle statistics s h o u l d , therefore, be quite similar b e t w e e n n o r m a l a n d  data.  D e p e n d i n g o n the  final  a m o u n t of h y b r i d d a t a r e q u i r e d for a c c u r a t e  hybrid  estimates,  t h e effects o f s p e c k l e m a y b e r e d u c e d .  •  T h e h y b r i d p e a k d e t e c t i o n m e t h o d m a y be significantly affected b y scene content. is b e c a u s e t h e h y b r i d d a t a h a s o n l y o n e b e a m - p a t t e r n s h a p e .  I n t h i s m e t h o d , t h e r e is n o  c o m p a r i s o n ( l o g r a t i o ) t o o t h e r d a t a a n d h e n c e s c e n e c o n t e n t is n o t r e m o v e d . t h e i n c o h e r e n t a d d i t i o n o f r a n g e l i n e s m a y a g a i n r e d u c e t h i s effect as w e l l .  85  This  However,  4.6  Conclusion  T h e c o n c e p t i o n a n d i m p l e m e n t a t i o n of the p r o p o s e d a l g o r i t h m s are o u t l i n e d i n this c h a p t e r . The the  m a i n benefits of these algorithms end of Chapter  2.  are listed  a n d address  T h e pros a n d cons o f these a l g o r i t h m s  the  data.  86  mentioned  are also given.  c h a p t e r e x p l a i n s t h e r e a l i s t i c d a t a s i m u l a t i o n r e q u i r e d for t e s t i n g i n a m a n n e r w h i c h reflects r e a l S c a n S A R  concerns  the proposed  The  at  next  algorithms  Chapter 5  D a t a Simulation 5.1  Introduction  C u r r e n t l y , n o S A R s y s t e m a c q u i r e s h y b r i d d a t a as d e s c r i b e d i n C h a p t e r 4. necessary  T h e r e f o r e , i t is  to s i m u l a t e h y b r i d d a t a i n o r d e r to prove the v a l i d i t y of the p r o p o s e d a l g o r i t h m .  T h i s c h a p t e r defines the s i m u l a t i o n p a r a m e t e r s a n d software  mechanisms  used to create  a  realistic d a t a simulation.  5.2 As  Data Simulation previously  mentioned,  all the  proposed algorithms, operate  current roll  o n the energy present  is n o t i m p o r t a n t t o t h e s e a l g o r i t h m s ; t h u s , r a d i o m e t r i c r a n d o m n e s s due to speckle  5.2.1  angle  phase  detection  algorithms,  in the radar data.  as  Phase  well  as  information  i n f o r m a t i o n is n o t s i m u l a t e d e x c e p t  ( w h i c h is a p h a s e  the  for  phenomenon).  D a t a Requirements  Comparison to Real D a t a T h e d a t a s i m u l a t i o n is b a s e d o n a n a d e q u a t e r e p r e s e n t a t i o n o f r e a l R A D A R S A T - 1 d a t a i n terms of the  following:  •  V a r i a n c e in log intensity  •  System  •  B e a m - p a t t e r n energy,  data;  noise,  87  ScanSAR  •  S u b - s w a t h p a r a m e t e r s s u c h as w i d t h , s a m p l i n g i n t e r v a l , a n d s o f o r t h ,  •  S y s t e m s p a r a m e t e r s s u c h as s w a t h o v e r l a p a n d t i m i n g  differences.  F a c t o r s used t o S i m u l a t e R e a l i s t i c D a t a T h e e n t i r e s i m u l a t i o n is b a s e d o n t h e c o h e r e n t s u m o f r e t u r n s f r o m i n d i v i d u a l p o i n t t a r g e t s p l a c e d so t h a t e a c h p o i n t t a r g e t r e p r e s e n t s simulation has the  one g r o u n d resolution cell.  the  following:  •  A D o p p l e r history,  •  A specific gain, based u p o n range a n d elevation  •  A specific, a z i m u t h frequency based, a z i m u t h b e a m - p a t t e r n g a i n ,  •  A u n i q u e range to  •  A speckle  •  A unique radar brightness  5.3  E v e r y target i n  angle,  target,  term, term.  Variance  A r e a l i s t i c v a r i a n c e w a s c r e a t e d a n d c o m p a r e d t o a r e a l S c a n S A R scene for s t a t i s t i c a l  refer-  ence. T h e v a r i a n c e present i n a single real r a n g e - l i n e r a n g e d f r o m 31-35 d B . T h e scene u s e d w a s a P r i n c e A l b e r t s c e n e a n d is f r o m a m o d e r a t e l y d i v e r s e b a c k g r o u n d : s o m e  fields,  trees,  a n d s o f o r t h . It w a s n o t p o s s i b l e t o u s e t h e P r i n c e A l b e r t s c e n e f o r t h e R C S b a c k g r o u n d o f t h e s i m u l a t e d d a t a as o n l y t h e r a w d a t a w a s a v a i l a b l e a n d n o t t h e f u l l y p r o c e s s e d  scene.  A similar variance was created in the simulated d a t a based o n the a p p l i c a t i o n of speckle  to  t h e s c e n e . O l i v e r a n d Q u e g a n [21] d e s c r i b e a s i m p l e s p e c k l e m o d e l i n t e r m s o f d i s t r i b u t i o n s , p h y s i c a l m e c h a n i s m s c a u s i n g scattering, a n d the a c t u a l o c c u r r e n c e s of speckle i n r e a l d a t a . For the in-phase independent, function  (I) a n d q u a d r a t u r e ( Q ) c o m p o n e n t s  of r a w s i g n a l d a t a , t h e y are g i v e n  identically distributed G a u s s i a n r a n d o m variables with a probability  as  density  (PDF):  (5.1)  Zi = Acos(0) -> I  (5.2)  Z  (5.3)  2  =• Asm((j)) -* 88  Q  w h e r e a° /2 2  is t h e v a r i a n c e , c r °  represents the average intensity of a r e s o l u t i o n cell o n  2  the  ground. The  a l g o r i t h m operates o n the intensity, I  d a t a , a n d their distributions are described The  = I  2  t  + Q, 2  or log intensity, D = m ( /  >  +  Q ), 2  next.  i n t e n s i t y d a t a is a n e g a t i v e e x p o n e n t i a l d i s t r i b u t i o n g i v e n  It  2  thus:  0  (5.5)  w h e r e t h e m e a n a n d s t a n d a r d d e v i a t i o n a r e b o t h a° . 2  T h e log intensity d a t a has a Fischer-  T i p p e t t [22] d i s t r i b u t i o n g i v e n t h u s :  e ( e = — e [-— ) D  P (D) D  w h e r e t h e m e a n is l n < x °  2  — 7^  D  2  W  \  (5.6)  2  RS 0 . 5 7 7 2 2 is E u l e r ' s c o n s t a n t )  (7^  N o t i c e t h a t t h e v a r i a n c e is i n d e p e n d e n t o f t h e m e a n .  D  n  P  DN  where K  =  10 l o g  /  =  ^PD(DJK)  =  10 l o g  1 0  1 0  t  =  a n d t h e v a r i a n c e is 7 r / 6 . 2  C o n v e r t i n g to a d B scale gives this:  (10 l o g i e ) D  (5.7)  0  (5.8)  e  (5.9)  T h e s e t h r e e d i s t r i b u t i o n s a r e i l l u s t r a t e d i n F i g u r e 5.1, f o r t h e G a u s s i a n , n e g a t i v e and  exponential,  Fischer-Tippet distributions. The  theoretical distributions agree closely w i t h observed real d a t a f r o m the P r i n c e A l b e r t  s c e n e , i n t h e t o p o f F i g u r e 5.2, a constant  a n d s i m u l a t e d d a t a i n t h e b o t t o m o f F i g u r e 5.2.  g a i n offset b e t w e e n t h e o r e t i c a l , a c t u a l , a n d s i m u l a t e d d a t a .  T h e r e is  T h i s is d u e t o  the  f a c t t h a t t h e a u s e d i n t h e t h e o r e t i c a l is for a s i n g l e t a r g e t , w h i l e i n t h e r e a l a n d s i m u l a t e d there were t h o u s a n d s o f targets, c o h e r e n t l y s u m m e d i n a z i m u t h , range c o m p r e s s e d , a n d e a c h t a r g e t h a d a d i f f e r e n t a n d u n k n o w n i n i t i a l a.  T h i s d o e s n o t affect  the simulation data,  as  t h e v a r i a n c e is i n d e p e n d e n t o f t h e m e a n , w h i c h m e a n s t h e l o g - i n t e n s i t y b e a m - p a t t e r n s h a p e s t h e m s e l v e s are n o t  affected.  8 9  D i s t r i b u t i o n f o r Gaussian, Negative Exponential and Fischer-Tippett x10' 2  4  i  1  1  1  1  1  1  0  100  -i  1  1  300  400  Gaussian D i s t r i b u t i o n for e i t h e r I or Q  -500 . 400 x 10 4  -300  -200  -100  200  Negative Exponential For Intensity Data  0  0.5  1  1.5  0.4  0.2  Fischer-Tippet For Log Intensity-  Figure 5.1: Theoretical distributions of SAR. data as given by Quegan [21]  90  500  Data D i s t r i b u t i o n f o r Real Data  SAR  Figure 5.2: Actual and simulated distributions of SAR data  91  Real Range Compressed Data from P r i n c e A l b e r t Scene  V a r i a n c e i n Uniform area = 1.1 dB a f t e r RDGC a p p l i c a t i o n (Not Shown Here)  80 TO 0.94  0.98  0.96  1  S l a n t Range  (m)  1.02  1.04  1.06  1.04  1  Simulated Range Compressed Data from TopView Scene  0.94  110 h  m  a  1  0.98  1  1  1.02 I  i  1  x  06  10! -  100  •H 4J  0.96  I  PIT  90  I  Wr  1  80 70  i 0.94  0.96  dB V a r i a n c e i n Uniform a r e a = 1.0 a f t e r RDGC a p p l i c a t i o n (Not Shown Here) i  1  1  i  0 . 9 8 ^  1  ,  .  S l a n t Range (m) n  u  1.02  1.04  1  06  Figure 5.3: Actual data for Prince Albert scene and simulated data for Melfort scene each with range cross section of 108 averaged lines. Dashed RDGC shown real data is a manual fit and does not take incidence angle or other effects into account, it is included to illustrate difficulty in matching the correct RDGC to data.  92  A l t h o u g h Q u e g a n [21] d e s c r i b e s d i f f e r e n t s p e c k l e m o d e l s f o r d i f f e r e n t t e r r a i n t y p e s , r e q u i r e m e n t f o r a s p e c k l e m o d e l i n s i m u l a t e d d a t a is n o t so c o m p l e x . Ron  the  After discussion with  C a v e s ( S A R engineer at M D A ) , it was d e t e r m i n e d t h a t a s i m p l e G a u s s i a n m o d e l for  s p e c k l e d i s t r i b u t i o n is a d e q u a t e .  T h i s c o n c l u s i o n w a s r e a c h e d b e c a u s e t h e d a t a is n o t  c e s s e d b e y o n d t h e r a n g e c o m p r e s s i o n s t a g e , a n d is o n l y v i e w e d i n t e r m s o f a v e r a g e T h e r e is n o a n a l y s i s o f t h e s t a t i s t i c a l d i s t r i b u t i o n s t h e m s e l v e s  pro-  energy.  during any roll-angle estima-  t i o n a l g o r i t h m . F i g u r e 5.3 s h o w s a p o r t i o n o f t h e P r i n c e A l b e r t s c e n e i n a r a n g e - c o m p r e s s e d f o r m a t a l o n g w i t h a n a v e r a g e o f 108 r a n g e l i n e s .  F i g u r e 5.3 a l s o h a s a s i m u l a t e d i m a g e ,  in  t h e b o t t o m p o r t i o n , w h i c h s h o w s a n a v e r a g e o f 108 r a n g e l i n e s . N o t i c e t h a t t h e v a r i a n c e f o r e a c h o f t h e a v e r a g e d r a n g e l i n e s a r e r e a s o n a b l y c l o s e (1 d B v e r s u s 1.1 d B ) . A l s o s h o w n i n t h e P r i n c e A l b e r t a scene d a t a ( T o p of F i g u r e 5.3), are t h e e x p e c t e d line) a n d t h e best f i t t i n g ( d a s h e d line) R D G C .  In this case the d a s h e d R D G C  m a y provide  t h e b e s t fit b u t d o e s n o t a c c o u n t f o r i n c i d e n c e a n g l e o r p o s s i b l e d e p e n d e n c e o n a.  Since the  d a t a is a c t u a l S A R d a t a , t h e e x a c t r o l l a n g l e is n o t k n o w n ( t h e m a i n p o i n t o f t h i s T h i s fact c o m b i n e d w i t h several a s s u m p t i o n s r e g a r d i n g the e a r t h m o d e l a n d satellite p r o b a b l y a c c o u n t f o r t h e d i f f e r e n c e b e t w e e n t h e p a y l o a d file e x p e c t e d fitting R D G C .  T h e fit is d o n e m a n u a l l y f o r d i s p l a y o n l y .  d a t a ( b o t t o m o f F i g u r e 5.3)  93  thesis). height  a n d the  T h e r o l l a n g l e for t h e  is k n o w n e x a c t l y a n d i t s c o r r e c t R D G C  line.  R D G C  (solid  best  simulated  is a l s o g i v e n as a s o l i d  5.4  Speckle  S p e c k l e is a p p l i e d t o t h e d a t a o n e p o i n t a t a t i m e u s i n g M A T L A B ' s b u i l t i n G a u s s i a n r a n d o m n u m b e r g e n e r a t o r . E a c h I a n d Q c o m p o n e n t was assigned its o w n s p e c k l e t e r m a n d s u m m e d according to the following:  R a n g e C e l l ( 0 , (j)) = a(0,  < £ ) G ( 0 , 4>) x (l  0  x randn + Q  e  x randn)  (5.10)  w h e r e r a n d n is t h e c o d e d e x p r e s s i o n f o r t h e G a u s s i a n r a n d o m n u m b e r g e n e r a t o r ( m e a n a n d variance are equal to one). (f> a r e t h e  elevation  G is t h e a n t e n n a p a t t e r n s , a is t h e a v e r a g e t a r g e t R C S , 9 a n d  a n d a z i m u t h angles  respectively,  and I  and Q  q u a d r a t u r e c o m p o n e n t s of a s i m u l a t e d range c o m p r e s s e d c h i r p . t e r m b a s e d o n a b a c k g r o u n d scene.  are the  in-phase  and  E a c h t a r g e t is a s s i g n e d a a  T h a t is, e a c h p i x e l ' s g r a y - s c a l e v a l u e ( 0 - 2 5 5 ) is u s e d as  t h e a f o r a s i n g l e r e s o l u t i o n c e l l . T h e i n t e n t i o n is t o u s e v a r i o u s t y p e s o f s c e n e s t o s i m u l a t e v a r y i n g levels of a for e v e r y r e s o l u t i o n cell i n t h e s i m u l a t e d d a t a . Six different b a c k g r o u n d scenes are used, some were a g r i c u l t u r a l w i t h a n d w i t h o u t speckle a l r e a d y p r e s e n t . A n o t h e r is a f o r e s t r y s c e n e , a n d t h e r e is a l s o a n e n t i r e l y u r b a n s c e n e . of  the  six scenes are S A R scenes.  One non-SAR  Four  s c e n e is a n i n t e g r a t e d o p t i c a l / t h e m a t i c  i m a g e a n d h a s l a r g e v a r i a t i o n s i n t h e s i m u l a t e d a as t h e r e a r e t r a n s i t i o n s f r o m o c e a n t o c i t y land.  T h i s o p t i c a l s c e n e is s p e c i f i c a l l y u s e d i n o r d e r t o g e n e r a t e  difficult b y the a l g o r i t h m . a g r i c u l t u r a l scene.  d a t a t h a t is r e g a r d e d as  T h e l a s t s c e n e is f r o m a n u n k n o w n s e n s o r t y p e t h a t i m a g e s  an  It is u s e d d u e t o t h e s t r a i g h t v e r t i c a l a n d h o r i z o n t a l l i n e s i n t h e s i m u l a t e d  a values t h a t m a y present a challenge to the a l g o r i t h m s . E a c h of the scenes s h o w n next F i g u r e s 5.4 t o 5.9 is u s e d a t l e a s t o n c e o n e a c h i n t e r f a c e .  94  as  M e l f o r t , Saskatchewan Heavily Speckled Mean dB = -2.5 dB S t a n d a r d D e v i a t i o n = 2.3 dB CV 580 A i r b o r n e SAR C-W J u l y 1983  Figure 5.4: Melfort Scene © C C R S / C C T  95  1983  Vancouver, BC No Speckle ( o p t i c a l ) Mean dB = -5 dB Standard D e v i a t i o n = 5 dB I n t e g r a t e d Spot (PLA) and LandSat (TM) J u l y 1992  Figure 5.5: Vancouver Scene (Optical Scene) © C C R S / C C T 1993  96  Unknown L o c a t i o n - named Topview Low S p e c k l e ? Mean dB = -3 dB S t a n d a r d D e v i a t i o n = 2.3 dB Unknown CNES S e n s o r Unknown Data  Figure 5.6: Topview Scene © u n k n o w n  97  L a b r a d o r ( C o a s t ) , Canada Indeterminate Speckle Mean dB = -3.5 dB S t a n d a r d D e v i a t i o n = 1.4 dB RADARSAT SCW March 1997  Figure 5.7: Labrador Scene © C S A 1997  98  Toronto, O n t a r i o Low S p e c k l e Mean dB = -4 dB S t a n d a r d D e v i a t i o n = 2.7 dB RADARSAT F4 Beam May 1996  Figure 5.8: Toronto Scene © C S A 1996  99  V i r d e n , Manitoba Low S p e c k l e Mean dB = -3.6 dB S t a n d a r d D e v i a t i o n = 3.3 dB CRS A i r b o r n e SAR C-HH A p r i l 1995  Figure 5.9: Virden Scene © C C R S / C C T 1995  100  5.5  Beam-Pattern Energy  A s p r e v i o u s l y m e n t i o n e d , R A D A R S A T - 1 p a y l o a d file 25 is u s e d t o g e n e r a t e  the b e a m  pat-  t e r n s i n t h e s i m u l a t i o n . T h e g a i n a n d r e s p e c t i v e e l e v a t i o n a n g l e s a r e k e p t as c l o s e a s p o s s i b l e t o t h e r e a l p a r a m e t e r s . E a c h b e a m p a t t e r n is c o r r e c t e d f o r r a n g e a n d c o n v e r t e d t o s l a n t r a n g e for a p p l i c a t i o n t o t h e d a t a , w h i c h a t t h i s p o i n t is s t i l l i n a s l a n t r a n g e f o r m a t .  5.5.1  Range Gain Removal  O f a l l t h e f a c t o r s m e n t i o n e d i n S e c t i o n 3.2.2, t h e r e m o v a l o r c o r r e c t i o n of t h e r a n g e f a c t o r , R~ , 3  m o s t needs further clarification. T h e original design of R A D A R S A T - 1  1 incorporates  p a r t i a l g a i n c o m p e n s a t i o n for the e x p e c t e d  r a n g e f a l l off.  T h i s r a n g e f a c t o r is r e m o v e d i n  F i g u r e 1.6 b u t i t is i n c l u d e d i n F i g u r e 5.11  where the o r i g i n a l two-way p a t t e r n s are  shown  w i t h the range gain. The  s i m u l a t i o n d o e s n o t i n c o r p o r a t e a r a n g e p o w e r loss factor i n t o t h e s i g n a l  strength,  as t h e r a n g e is e x a c t l y k n o w n , a n d h e n c e , e x a c t l y r e m o v e d . T h e b e a m p a t t e r n s h a v e t o m o d i f i e d so t h a t  the resulting image d a t a best represents  t h e s i g n a l d a t a t h a t is  be  present.  T h i s is d o n e f o r e a s e o f s i m u l a t i o n o n l y so t h a t r e s u l t s c a n b e c o m p a r e d t o a flat l i n e , i n s t e a d o f t h e R~  3  p o w e r loss line.  T h i s r e m o v a l is i n c l u d e d h e r e s o t h a t r e a d e r s f a m i l i a r w i t h  the  t y p i c a l b e a m p a t t e r n s r e c o g n i z e t h a t t h e p a t t e r n s are m o d i f i e d for a specific r e a s o n . F i g u r e 5.12  is a n i l l u s t r a t i o n o f t h e d e p e n d e n c e  of elevation  angle o n g r o u n d  coverage.  T h i s r e s u l t s i n t h e n e e d t o c o n v e r t t h e p a y l o a d file d a t a f r o m e l e v a t i o n a n g l e t o s l a n t r a n g e . S i n c e t h i s is a s i m u l a t i o n , a n d m a i n t a i n i n g a p r o p e r e n e r g y b a l a n c e is c r i t i c a l ,  therefore  the f o l l o w i n g c o n s t r a i n t s are a p p l i e d :  •  E a c h s l a n t r a n g e c e l l is a s s i g n e d a u n i q u e b e a m g a i n b a s e d o n s l a n t r a n g e .  •  E a c h s l a n t r a n g e c e l l is a s s i g n e d a u n i q u e , i n c i d e n c e a n g l e i n d e p e n d e n t , t a r g e t . s p a c i n g i n r a n g e v a r i e s as t h e i n c i d e n c e a n g l e v a r i e s .  T h e R C S is i n d e p e n d e n t o f i n c i -  d e n t angle, since a n y c o r r e c t i o n for i n c i d e n c e angle v a r i a t i o n s are e x a c t , knowledge  Target  due to  exact  of the e a r t h m o d e l , a n d therefore c o m p u t a t i o n a l l y r e d u n d a n t i n the  same  m a n n e r as t h e r a n g e g a i n r e m o v a l . If h e i g h t v a r i a t i o n s ( s l o p e s , h i l l s , m o u n t a i n , e t c )  101  are  to be used in the simulation, then dependence  o n the incidence angle s h o u l d also  be  included.  Comparison of S7 Beam with/without Range Correction 10 r  1  1  1  1  <~  1  1  Slant R a n g e in M e t e r s  x10  6  Figure 5.10: Example of elevation angle to slant range conversion for the S7 beam  R e f e r t o F i g u r e 5.10 beam. of R  0  t o see  t h e e l e v a t i o n a n g l e t o s l a n t r a n g e c o n v e r s i o n effect f o r  T h e S7 b e a m has a n average slant range m u c h greater t h a n the n o m i n a l slant = 951 k m u s e d for t h e t y p i c a l  )  -  3  r a n g e f a c t o r g a i n c o n v e r s i o n [11].  one  range  Therefore, the  e n t i r e S 7 b e a m h a s a c o r r e c t e d g a i n t h a t is l o w e r t h a n t h e p a y l o a d file g a i n . A l s o p r e s e n t i n t h e b o t t o m h a l f o f F i g u r e 5.10  is t h e r a n g e c o r r e c t e d b e a m p a t t e r n ,  but  displayed relative to slant range. T h i s p a t t e r n illustrates that the near elevation angle  data  appears  same  "compressed"  effect is s e e n i n t h e to a decrease  as t h e p i x e l s p a c i n g is l a r g e r t h a n t h e f a r e l e v a t i o n d a t a .  bottom  p o r t i o n for a l l t h e  b e a m patterns  i n g r o u n d r a n g e p e r r e s o l u t i o n r a n g e c e l l as  the  in Figure elevation  F i g u r e s 5.12 a n d 5.13 i l l u s t r a t e t h e g e o m e t r y t h a t c a u s e s t h i s effect.  102  5.11 angle  The a n d is  due  increases.  Beam-Pattern  0  7 &?  (0  —  i  •20  CN  1  35 (Degrees)  i  i  S7  W2  Wl  o — m•10 nJ  w i t h / w i t h o u t Range L o s s Term  25 30 E l e v a t i o n Angle  1  I  3  Comparison  0.9  0.85  ^  ^  1  0.95  Slant  Range  ^  ^ 1.1  1.05  1.15  (m)  x 10  Figure 5.11: Comparison of payload file a) original 2-Way gains, b) as in (a) but with R  6  gain correction,  3  and c) same as (b) but converted to slant range  In  the  coverage.  final Both  scene,  i t is d e s i r e d t h a t  each pixel represent  the  same  amount  pixel a n d g r o u n d cell coverage v a r y w i t h incidence angle.  It is  of g r o u n d therefore  necessary to re-sample the d a t a w h e n processing the final scene, otherwise the "compression" s e e n i n 5.10 w i l l b e v i s i b l e . I n t h i s t h e s i s , t h e d a t a is not on  r e - s a m p l e d as t h e a l g o r i t h m s o p e r a t e  d a t a j u s t after t h e r a n g e c o m p r e s s i o n a n d r a n g e cell m i g r a t i o n c o r r e c t i o n stages. R e - s a m p l i n g is n e c e s s a r y f o r t h e b e a m p a t t e r n s t h e m s e l v e s ,  angle, not slant range. initial and  phase  of the  as t h e y a r e b a s e d o n e l e v a t i o n  R e - s a m p l i n g i n t h e s i m u l a t o r is p e r f o r m e d n u m e r i c a l l y d u r i n g  s i m u l a t i o n as  all the  parameters  a r e set.  This  ensures  a c c u r a t e range, g a i n , a n d o t h e r i n f o r m a t i o n are assigned for e a c h target.  illustrates the geometric m o d e l used a n d the terms involved.  103  that  the  unique  Figure  5.13  Figure 5.12: Geometry affecting slant range  The initial parameters were calculated knowing the earth radius, R , satellite altitude, e  A, and the min and max elevation angles (from the payload files), 6 , nf  tively.  aT  and 6j , respecar  The range gate delay, R d, window receive time, W , sampling interval, Si, and g  t  pulse repetition frequency, P R F , are all taken from the header information found in the real R A D A R S A T - 1 ScanSAR scene of Prince Albert, Saskatchewan. These timing parameters are used to determine the slant range resolution in meters. The targets are then placed so that one target is present in the middle of each slant range cell according to [23]: h(i) = R  s i n a = \/R {i) - {A + x(i)f 2  e  e  (5.11)  where i represents the i t h target along the range swath, a is the angle at the earth centre e  between the target and the satellite, R is the slant range and h is the cross distance between the target and the satellite nadir.  104  Figure 5.13: Geometric model used in simulation  105  5.5.2 The  B e a m Gain Uncertainty Simulation  uncertainty  RADARSAT-1. describes  the  in the  lower  However,  beam  g a i n areas,  H a w k i n s [7] h a s  or skirts,  has  not  yet  performed some analysis  been  modelled  on this p r o b l e m a n d  2-way b e a m s t a b i l i t y as ± 0 . 2 d B i n t h e m a i n l o b e a r e a a n d ± 0 . 4 d B i n  i n t e r b e a m regions.  Variations in the one-way  for  p a t t e r n o f 0.8 d B a r e n o t u n c o m m o n .  t h e t i m i n g f o r e v e r y S c a n S A R b e a m is v a r i a b l e a n d t h e g a i n u n c e r t a i n t y d o e s n o t  the  Since have  s p e c i f i c m o d e l , i t w a s d e c i d e d t o s i m u l a t e t h i s u n c e r t a i n t y as a l i n e a r g a i n u n c e r t a i n t y .  a  That  is, t h e u n c e r t a i n t y is l i m i t e d t o a l i n e a r effect o n t h e b e a m s h a p e s i n t h e o v e r l a p r e g i o n o n l y ( s i n c e t h i s is w h e r e t h e a l g o r i t h m s o p e r a t e a n y w a y s ) . t h e s a m e l i n e a r m o d e l . F i g u r e 5.14  E v e r y b e a m is a d j u s t e d a c c o r d i n g t o  i l l u s t r a t e s t h e effects f o r t h e S 5 b e a m w i t h n o r o l l e r r o r .  R e s u l t s o f S i m u l a t i n g Beam G a i n U n c e r t a i n t y on S5 Beam  E l e v a t i o n Angle  (Degrees)  Figure 5.14: Beam uncertainty model used in simulation on S5 beam. Negative and positive uncertainty is applied to the outer edges of the payload beam pattern. I n F i g u r e 5.14, change to  the  amount  of gain uncertainty  varies b y  the outer edge of the beam pattern.  m a x i m u m percentage,  at the outside  incorporating a ± 3 0 % gain  T h i s g a i n c h a n g e is l i n e a r l y r e d u c e d f r o m  e d g e , t o 0% m o v i n g i n t o w a r d s  106  a point that  is  20%  of the overall beam width. This introduces an error to the algorithms by modifying the beam patterns with an unknown gain variation, while the algorithms attempt to produce an estimate using the payload file beam pattern data. Figure 5.15 illustrates the far half of the S5 beam with a +30, -30, and zero percent gain change to the outer edge. The same effects, with varying percentage levels, are applied to all the beams prior to R D G C correction for all algorithms used in this thesis.  0 |  Far Side of S5 Beam Only 1  1  1  1  1  1  1  1  r  E l e v a t i o n Angle (Degs)  Figure 5.15: Gain uncertainty applied to S5 beam. The percentage uncertainty is greatest at the outer edge and linearly decreases towards the start of the overlap region. The uncertainty applied to the outer edge ranges from +30% to -30% in 3% increments. Thus, although 30% uncertainty quite large, it is only applied to the outer edge and only for one simulation.  At the outer beam edges, a ± 3 0 % error in the beam pattern gain can be considered extreme, approximately 5 dB for the S5 beam. This large range is used for the purpose of testing the limits of the algorithms and seeing how they are affected by uncertainties, even large uncertainties. Introducing a linear percentage to the gain uncertainty allows for the simplest modelling of the error while still allowing: • Maintenance of an overall beam pattern shape that is reasonably close to the original, • Introduction of gain errors that match typical errors described by Hawkins of up to 0.8 107  dB in the overlap regions most likely recorded in ScanSAR mode, • Gain errors to effect each pattern in a similar manner, thus allowing the gain uncertainty of one beam to be compared to another,  • Effective implementation in the data simulator.  5.6  General System Parameters  The Canadian Data Processing Facility (CDPF) bases its earth model solely on a locally spherical earth; however, the earth's radius is allowed to change depending on latitude. For computational simplicity in this thesis, a cylindrical earth model with a locally dependent radius is used. This model combined with a narrower azimuth beam-width and zero squint angle reduces the effects of range cell migration (RCM) to less than one cell at the outermost azimuth beam edge. The simpler geometrical calculations and absence of R C M significantly improve processing performance. Since processing time is a factor in simulating ScanSAR scenes, the individual scenes are limited to 250 range lines using the cylindrical model. Initially, the time required to create a single range line was approximately one minute; however, further improvements reduced this time to around 8-10 seconds. Over the course of this research, several hundred different simulations were performed and analyzed for accuracy. The final results are based on approximately 120 of the latest and most accurate simulations. Based on the differences between the cylindrical and spherical earth model, the timing parameters are quite close to RADARSAT-1 parameters, but not exact. This does not affect the accuracy of the simulation though, as it is the beam-pattern energy, or shape and elevation angle that are of interest. Small variations between simulated and real data, such as differences in the number of range cells per line, or constant and known timing differences do not significantly affect the outcome of this simulation.  108  5.7  Conclusion  This chapter explored the issue of data simulation. The parameters used to generate realistic data were explained. Scene statistics for real, theoretical, and simulated data were compared and found to have similar probability density functions. A constant gain offset between statistical models is acceptable as this does not affect the mean or variance of the data, nor does it impair the estimation algorithms. Comparison of real and simulated data indicates that the simulated data should adequately represent real ScanSAR data from a radiometric point of view.  109  Chapter 6  Results from Proposed Algorithms and Goulding Algorithm 6.1  Introduction  T h e two proposed algorithms are compared to the existing G o u l d i n g a l g o r i t h m . Since the final form of the three b e a m a l g o r i t h m is so close to G o u l d i n g ' s a l g o r i t h m , we use G o u l d i n g ' s as a c o m p a r i s o n . T h i s also allows for lower processing requirements, a significant factor i n this research, since the n o r m a l d a t a lines do not need to change forms between algorithms. A brief s u m m a r y of each a l g o r i t h m follows.  6.1.1  Goulding Summary  G o u l d i n g ' s a l g o r i t h m is three basic steps: 1. A p p l y R D G C to range compressed data. 2. C a l c u l a t e l o g ratio of d a t a i n overlap region. 3. D r i v e m e a n of log ratio to a value of one using various R D G C s .  6.1.2  H y b r i d Peak Detection Summary  T h e peak detection a l g o r i t h m operates using these steps: 1. C r e a t e a look up table of various peak l o c a t i o n from p a y l o a d files. 2. F i t a 2nd, 3rd, a n d 4 t h order p o l y n o m i a l to h y b r i d d a t a a n d weight their peak estimates according to the m i n i m u m derivative of each. 110  3. Compare estimated and known peak locations to produce estimate. 6.1.3  Three B e a m Summary  The three beam method is similar to Goulding's detection: 1. Apply RDGC to range compressed data, including hybrid data. 2. Calculate log ratio of data in overlap region for each possible combination of the three available data lines. 3. Fit a polynomial to each log ratio. 4. Drive differences between polynomials to zero using various RDGCs.  6.2  Illustration and Explanation of Results  Six different scenes are used to simulate the RCS content of the simulated data. Each scene is used to simulate 250 range lines of data for each interface. The algorithms are then tested on each of these simulated scenes in an effort to determine accuracy based on the following: 1. Beam gain uncertainty, 2. Noise, 3. Beam combination, 4. Scene content. Refer to Figure 4.10 for an illustration of all possible beam combinations. Each scene was simulated for each combination at least once. The scenes were all previously presented as Figures 5.4 to 5.9. 6.2.1  R e s u l t Subsets  The first set of results shown are those from beam gain uncertainty; the second set has varying cr° levels. Each set has three subsets: • Overall results from the average of all beam combinations and scene content for each algorithm, 111  • Results based on beam combination, • Results based on scene content. The roll error presented in this chapter is in terms of the absolute roll error.  Both  negative and positive roll error estimates were produced. Also, speckle and noise were always present in the data and added to the uncertainty that all the algorithms faced. Hence, none of the algorithms minimize the roll estimate to zero error consistently  for any simulation  combination; however, some particular combinations did produce an exact estimate. The roll requirement table is brought forward from Chapter 3 and presented here as Table 6.1 for easier comparison with the results. Although each combination varies in its required roll accuracy, assuming a general roll error of 0.05° can provide an quick overview of a particular algorithms results. W1W2  W2W3  W2S5  W3S7  S5S6  Discontinuity Limit (1)  0.034°  0.041°  0.035°  0.043°  0.028°  Slope Change Limit (2)  0.081°  0.067°  0.099°  0.081°  0.033°  Table 6.1: Beam accuracy requirements  112  6.3  B e a m Gain Uncertainty Results  Beam gain uncertainty is described in Chapter 5 as the application of a gain uncertainty to the outer beam edges that has the effect of broadening/narrowing the beam pattern in range; that is, the swath coverage increased or decreased. The variable used to accomplish this is a linear percentage that ranges from + 3 0 % to —30%. All the gain uncertainty results are in terms of this gain change percentage. The results from this section are presented as two dimensional graphs with the roll error (in degrees) on the vertical axis and the percentage gain uncertainty (in percent) on the horizontal axis. Figure 6.1 a) illustrates the overall results from beam gain uncertainty on all three algorithms. The hybrid peak detection method shows slight dependence on gain uncertainty. A  +30%  change produces an average accuracy of 0 . 1 2 5 ° that linearly increases to  0.17°  at  — 3 0 % gain change. It will be shown further on that most of this dependence is due to one particular beam combination. The average hybrid accuracy is approximately  0.147°.  As  previously mentioned, and will be seen throughout all the results, this method on its own is a good general indicator, but typically does not produce sufficiently accurate results. In general, the polynomial fits used to estimate peak are not significantly affected by beam uncertainty. Both Goulding and the three beam method have a well defined dependence on gain uncertainty as seen by the "V" pattern that each algorithm exhibits. This dependence is expected as both algorithms incorporate the entire overlap region into the estimate. A gain change to the edge of the beam pattern misleads both algorithms when the log ratio step is applied. For Goulding's method, the log ratio approaches a value of one further from the actual roll angle. The three beam method produces a higher minimum sum of differences, as compared to no gain changes, and this sum is again be located further from the actual roll angle.  113  All  Beams, A l l M e t h o d s O v e r a l l  Results  0.3, a)  0.25  -30  Goulding Three Beam - — Peak Detection  -20  Individual  On  a l l figures, the  standard that  'x'  represents  deviationf o r color  -10 0 10 Percentage Uncertainty Beam R e s u l t s  F o r T h r e e Beam  20  30  Ratio  0.3 W1W2 W3S7 W2W3 W2S5 S5S6  -30  -20  -10  0  Percentage  10  Uncertainty  Figure 6.1: Overall results from beam gain uncertainty and individual beam combinations with three beam method  114  As  expected,  average  t h e b e s t a c c u r a c y is p r o d u c e d f o r z e r o u n c e r t a i n t y w i t h a 0 . 0 3 ° a n d  e r r o r for t h e  three  beam and Goulding method,  respectively.  A s the  0.038°  beam  become uncertain, the three b e a m method's accuracy deteriorates m o r e slowly t h a n  gains Gould-  i n g ' s a n d p r o d u c e s a n a v e r a g e a c c u r a c y t h a t is a b o u t 0 . 0 3 ° b e t t e r w i t h t h e m a x i m u m g a i n change.  T h e a v e r a g e s t a n d a r d d e v i a t i o n f o r t h e t h r e e b e a m m e t h o d is a b o u t 0 . 0 1 ° g r e a t e r  t h a n the G o u l d i n g method.  A s w i l l be discussed n e x t , the h i g h e r s t a n d a r d d e v i a t i o n for the  t h r e e b e a m m e t h o d is d u e m a i n l y t o p o o r r e s u l t s f r o m t h e W 2 S 5 b e a m c o m b i n a t i o n . F i g u r e 6.1 method.  b) s h o w s t h e results b r o k e n d o w n b y b e a m c o m b i n a t i o n for t h e t h r e e  T h e i n c r e a s e d s t a n d a r d d e v i a t i o n for t h e  three b e a m  method  is a r e s u l t  beam of  the  W 2 S 5 b e a m c o m b i n a t i o n . T h e W 2 S 5 c o m b i n a t i o n p r o d u c e s the poorest estimates a n d has a s t a n d a r d d e v i a t i o n significantly higher t h a n all other b e a m c o m b i n a t i o n s . Goulding's method can  T h i s h o l d s t r u e for  ( F i g u r e 6.2 a)) b u t affects i t less. T h e r e a s o n f o r t h e W 2 S 5  b e s e e n f r o m t h e o v e r l a p r e g i o n i t s e l f (see  F i g u r e s 4.15 a n d  4.10).  uncertainty  The W2S5  overlap  is q u i t e b r o a d ; n e i t h e r b e a m d r o p s off s i g n i f i c a n t l y a n d t h e r e is a l a r g e p o r t i o n w h e r e n o r m a l b e a m s are fairly close i n strength.  the  S i n c e the three b e a m m e t h o d relies s i g n i f i c a n t l y o n  a steep slope i n the b e a m p a t t e r n s to p r o d u c e a c c u r a t e estimates, the flatness i n the  W2S5  p a t t e r n a c t s t o r e d u c e t h e t h r e e b e a m m e t h o d a c c u r a c y . G o u l d i n g ' s m e t h o d is a f f e c t e d by the flatness f r o m the far edge of the W 2  less  beam.  C o m p a r i n g F i g u r e s 6.1 b ) a n d 6.2 a) i l l u s t r a t e s a s i g n i f i c a n t i m p r o v e m e n t i n t h e  tolerance  of a l l b e a m s , e x c e p t W 1 W 2 , u s i n g t h e t h r e e b e a m m e t h o d over G o u l d i n g ' s m e t h o d . the W 1 W 2 p a t t e r n being the narrowest, gain uncertainties in the edges significantly  Due  to  influence  the a l g o r i t h m . Interestingly, a positive gain change i n the three b e a m m e t h o d does not  exert  m u c h effect o n t h e s a m e f o u r b e a m s t h a t s h o w e d i m p r o v e m e n t o v e r G o u l d i n g ' s m e t h o d . The  h y b r i d peak detection m e t h o d performs better o n the W 3 S 7 c o m b i n a t i o n  other four.  A g a i n , F i g u r e s 4.15  the h y b r i d patterns. has a wider range. The  a n d 4.10  T h e W 3 S 7 beam's  versus  illustrate the differing slopes a n d b e a m - w i d t h s s l o p e is a p p r o x i m a t e l y h a l f t h a t  of W 1 W 2 b u t  the of it  T h e S 5 S 6 b e a m is s i m i l a r t o W 3 S 7 b u t s l i g h t l y s t e e p e r a n d n a r r o w e r .  fact t h a t the W 3 S 7 b e a m performs better t h a n either the W l W 2 or S 5 S 6 b e a m s c a n be  p a r t l y e x p l a i n e d b y scene dependence;  the R C S content  also be due to the wider range a n d increased elevation  115  m a y have favoured W 3 S 7 . angle,  It  may  b o t h of w h i c h contribute  to  p r o d u c i n g m o r e r a n g e cells for W 3 S 7 t h a n e i t h e r W 1 W 2 or S 5 S 6 , w h i l e still m a i n t a i n i n g a large average gain Due  slope.  to the large b e a m w i d t h a n d shallow slope, the W 2 S 5 c o m b i n a t i o n frequently  duces very p o o r results,  and when extreme  g a r d e d for h y b r i d p e a k detection. d i r e c t l y f r o m the results.  errors are observed,  t h i s c o m b i n a t i o n is d i s r e -  O n a l l t h e r e s u l t s s h o w n , t h e s t a n d a r d d e v i a t i o n is d r a w n  If t h e e s t i m a t i o n e r r o r r e a c h e s t h e s i m u l a t i o n m a x i m u m i t is c a p p e d  at that m a x i m u m a n d hence, the s t a n d a r d d e v i a t i o n drops significantly. F i g u r e 6.1  pro-  T h i s c a n be seen in  b) for t h e t h r e e b e a m W 2 S 5 s t a n d a r d d e v i a t i o n f r o m a b o u t -10 to -30  percent.  If t h i s e f f e c t is s i g n i f i c a n t a n d t h e s t a n d a r d d e v i a t i o n is l o w e r e d b y t h e s i m u l a t i o n c a p t h e s t a n d a r d d e v i a t i o n is o m i t t e d a n d o n l y d a t a w h i c h is n o t c a p p e d is g i v e n i n t h e T h i s o n l y o c c u r r e d for the W 2 S 5 b e a m .  then  figures.  T h e c a p s are set at ± 0 . 2 0 ° for b o t h G o u l d i n g ' s a n d  t h e t h r e e b e a m m e t h o d a n d ± 0 . 5 0 ° for h y b r i d p e a k d e t e c t i o n .  Since the m a x i m u m roll error  i n t r o d u c e d t o t h e d a t a is ± 0 . 1 0 ° , G o u l d i n g a n d t h e t h r e e b e a m m e t h o d p r o d u c e a m a x i m u m error of 0 . 3 0 °  a n d h y b r i d peak detection produces a 0 . 6 0 ° error.  A l l the graphs are l i m i t e d  to 0 . 3 0 ° , w i t h the exception of the two graphs d e p i c t i n g the h y b r i d p e a k detection  method  only; thus, some large estimates f r o m the W 2 S 5 p a t t e r n using h y b r i d p e a k detection are not c a p p e d b u t d o not a p p e a r o n the graphs.  116  I n d i v i d u a l Beam R e s u l t s F o r G o u l d i n g 0.3 W1W2 W3S7 W2W3 W2S5 S5S6  -30  -20  -10  0  10  Percentage UncertaintyI n d i v i d u a l Beam R e s u l t s F o r Peak  Detection  0.5  b) 0.45 0.4  W1W2 W3S7 W2W3 W2S5 S5S6  0.35  u o u  w  <u u  01  Pi  (U Q  Ul  -30  -20  -10  0  Percentage  10  Uncertainty  Figure 6.2: Individual beam combinations with Goulding and hybrid peak detection methods  117  In Figure 6.2 a), the best estimates for the S5S6, W3S7, and W 2 W 3 beams occur at — 10%, —6%, and +10%, respectively. The W 1 W 2 beam is centered on zero while the W2S5 shows less dependence on gain uncertainty. This is most likely due to the large errors the W2S5 beam incurs from having such a flat, wide interface. These results are due to the position of the beam interface point in terms of the overall overlap region. As previously described for the abrupt transition method, the beam interface is the point where the far beam and near beam have equal gain. Here it is represented as a percentage of the overall length of the overlap region. Hence, those beams where the interface occurred  prior  to half of the overlap length show an increase in accuracy as the gain is lowered, up  to a limit. Beams with an interface after half of the overlap length increase in accuracy as the beam gain increases, up to a limit. The W 1 W 2 beam interface is slightly over half the overlap length and is centered on zero gain uncertainty. Figure 4.10 is again useful i n showing that the beam interface for each combination occurs at 38%, 52%, 72%, and 34% of the overlap region length for the S5S6, W 1 W 2 , W 2 W 3 , and W3S7 beams, respectively. The same effects can be seen in the three beam method (Figure 6.1 b)) but not to the same extent. This positioning of the best accuracy results per beam is due to the log ratio operation on the corrected data. The goal of Goulding's algorithm is to drive the mean of the log ratio as close as possible to one. A n error which significantly affects the  rate  at which the  ratio approaches one, due to changes in an already steep slope, may improve the estimate due to the application of a large gain uncertainty to a steep slope. It is only the steeper slopes which display this effect. If the roll angle increment between R D G C s is small, the R D G C s do not significantly change from one roll angle to the next. Thus, with small or no gain uncertainty, the mean ratio from the correct estimate and the mean ratio from the nearest incorrect estimate are quite close, and this results in a less accurate estimate. A gain uncertainty in one beam, if that beam dominates the overlap, changes the slope of the data and produce larger differences in the mean ratio. This leads to a better estimate provided that the gain uncertainty itself does not dominate the overlap region. This analysis seems to explain these results; however, due to the simplicity of the gain uncertainty model this effect was not further researched.  118  The previously mentioned slight dependence of the hybrid peak detection method on beam gain uncertainty can be more clearly seen in Figure 6.2 b). The W 2 W 3 beam is clearly dependent on the gain change, as it linearly decreases from approximately 0.025° to 0.01°, left to right. This is due to the W 2 W 3 beam having a small range of slopes (see Figure 4.15) as well as having its interface situated well to the far side of the overlap region. Hence, any gain uncertainty effects are more easily noticed with this particular beam.  119  -30  -20  -10 Percentage  0 10 Uncertainty  20  30  Figure 6.3: Results from Vancouver and Labrador scenes with all three methods  120  Figure 6.4: Results from Melfort and Topview scenes with all three methods  121  Figure 6.5: Results from Virden and Toronto scenes with all three methods  122  For results based on scene content, five of the six scenes produce fairly similar results for Goulding's and the three beam method. The three beam method typically produces better results and could tolerate more gain uncertainty than Goulding's method. Hybrid peak detection shows strong dependence on scene content. The Virden scene produces the best hybrid peak detection estimates with an average error of 0.06°, while the Vancouver scene produces the worst with an average error of 0.25°. A l l algorithms suffer reduced performance on the Vancouver scene due to its sharp ocean to land transitions and overall lower mean o~°. This problem is worsened by inclusion of the results from W2S5 combination. This combination continuously produces poor results and Figure 6.6 a) shows the results when it is not included on the Vancouver scene. A l l algorithms are significantly improved, with Goulding's improving by 0.0175°, the three beam by 0.025°, and.hybrid peak detection by 0.02°, all at zero gain uncertainty. The shapes of the result patterns are not significantly changed. The removal of the W2S5 combination for all scenes and beam combinations is shown in Figure 6.6 b). Again, the overall accuracy for each method improves, especially near zero uncertainty for the three beam and Goulding method.  Considering that the W2S5  combination does not form a ScanSAR beam on its own, and considering the detrimental effect it has on roll angle estimate accuracy, it is therefore suggested that the W2S5 beam combination not be involved in the estimation process.  123  Results From Vancouver with/without W2S5 Combination a)  0.3  0.25  -30  G with W2S5 G without W2S5 3-beam with W2S5 3-beam without W2S5 Peak with W2S5 Peak without W2S5  -20  Vancouver Scene  -10  0  10  20  30  Percentage U n c e r t a i n t y O v e r a l l Results with/without W2S5 Combination 0.3  b) 0.25  -30  G with W2S5 G without W2S5 3-beam with W2S5 3-beam without W2S5 Peak with W2S5 Peak without W2S5  -20  -10  0  10  20  30  Percentage Uncertainty  Figure 6.6: Gain uncertainty results with and without W2S5 combination for Vancouver scene and overall results  124  6.4  Noise Results  V a r y i n g l e v e l s o f n o i s e a r e u s e d t o s i m u l a t e t e r r a i n a° l e v e l s f r o m - 2 0 t o 0 d B . T h e s e l e v e l s a r e a l l d i r e c t l y t r a n s l a t e d t o a n a v e r a g e s c e n e a° a n d a r e i n d i c a t e d o n t h e b o t t o m o f e a c h g r a p h . Noise c a n be a t t r i b u t e d to m a n y sources,  s u c h as i n t e r n a l r e c e i v e r n o i s e ,  noise received  by  t h e a n t e n n a , a n d so o n . R a t h e r t h a n isolate e a c h s o u r c e a n d a t t e m p t t o s i m u l a t e its effects, a l l n o i s e is s i m p l y a s s u m e d t o b e u n i f o r m i n d i s t r i b u t i o n a n d v a r y i n g i n i n t e n s i t y .  a°(neq),  e a c h s c e n e is p r o c e s s e d w i t h a v a r y i n g n o i s e e q u i v a l e n t s i g m a n o u g h t , a v a r i a t i o n o f t h e m e a n s c e n e s i g m a n o u g h t , a°,  Therefore,  that  simulates  f r o m -20 to 0 d B .  T h i s l e v e l is b a s e d o n a r a t i o w i t h t h e m a x i m u m p o s s i b l e s i m u l a t e d s i g n a l s t r e n g t h . t h e s c e n e s a r e i n c o r p o r a t e d i n t o t h e s i m u l a t i o n as 8 b i t g r a y - s c a l e i m a g e s to  255,  a v a l u e o f 255  strength that  represents  it receives,  or a  0  =  a resolution cell 0 d B . A target  (or t a r g e t )  that  Since  ranging from  reflects  all the  0  signal  w i t h a g r a y - s c a l e v a l u e of 0 reflects  no  t a r g e t e n e r g y , w h i c h g i v e s t h e s i m u l a t i o n a d y n a m i c r a n g e o f a p p r o x i m a t e l y 25 d B f o r t a r g e t strength.  RADARSAT-1  has a t y p i c a l noise  equivalent  a°  of -23  d B , w h i c h is  calculated  u s i n g E q n . 1.1 a n d c o n f i r m e d i n [2]. A t y p i c a l A m a z o n s c e n e m a y h a v e a n a v e r a g e a  0  o f -6  or -7 d B . F r o m F i g u r e 6.7 a ) , t h e h y b r i d p e a k d e t e c t i o n m e t h o d is s e e n t o b e i n d e p e n d e n t o f n o i s e a n d has a n average error of a r o u n d 0 . 1 9 ° . of noise  d u e to the p o l y n o m i a l  fitting  H y b r i d p e a k d e t e c t i o n is f o u n d t o b e  used o n the h y b r i d data.  independent  N o i s e affects d a t a at  p e a k , o r h i g h e s t g a i n l e v e l , i n t h e s a m e m a n n e r as t h e l o w e r g a i n l e v e l s .  However, the  noise  a p p l i c a t i o n is u n i f o r m l y d i s t r i b u t e d a n d d o e s n o t s i g n i f i c a n t l y affect t h e p e a k l o c a t i o n , t h o u g h the o v e r a l l s i g n a l s t r e n g t h i n the lower levels m a y b e affected.  In fact,  the  even  unless  the  s i g n a l s t r e n g t h is s o l o w t h a t t h e p e a k is b u r i e d i n n o i s e , t h e h y b r i d p e a k d e t e c t i o n p e r f o r m s s i m i l a r l y to the results given here. G o u l d i n g ' s a n d the three b e a m m e t h o d have results w h i c h are similar to each other until cr° =  —6 d B a t w h i c h p o i n t t h e t h r e e b e a m m e t h o d h a s a 3 t o 4 d B a d v a n t a g e o v e r G o u l d i n g ' s  a l g o r i t h m all the way to a  0  =  — 20 d B . B o t h t h e t h r e e b e a m a n d t h e G o u l d i n g m e t h o d  c l e a r d e p e n d e n c e o n t h e m e a n v a l u e of  show  a. 0  F i g u r e 6.7 b ) p r o v i d e s t h e r e s u l t s f r o m t h e t h r e e b e a m m e t h o d b a s e d o n i n d i v i d u a l b e a m s .  125  It s h o w s t h a t t h e W 2 S 5 c o m b i n a t i o n p r o d u c e s p o o r r e s u l t s , f o l l o w e d c l o s e l y b y t h e combination.  W2W3  T h e W 3 S 7 a n d W 1 W 2 combinations p r o d u c e g o o d results a n d the S 5 S 6  d u c e s a d e q u a t e r e s u l t s u n t i l - 1 2 d B is r e a c h e d . A s m e n t i o n e d i n t h e g a i n u n c e r t a i n t y  pro-  results,  t h e W 2 S 5 a n d W 2 W 3 p a t t e r n s are t h e flattest a n d h a v e t h e least r a n g e i n s l o p e v a r i a t i o n s of all the h y b r i d combinations.  T h e W 3 S 7 , W 1 W 2 a n d S5S6 all produce good estimates until  a° r e a c h e s a p p r o x i m a t e l y — 1 2 d B . W 3 S 7 s h o w s a d e c r e a s e a f t e r t h i s p o i n t w h i c h is p r o b a b l y d u e t o s c e n e c o n t e n t effects.  M o r e simulation would p r o b a b l y show the W 3 S 7 pattern in-  creases i n error a l o n g w i t h the other patterns. should not maximums.  be considered  valid beyond  —10  T h e s t a n d a r d d e v i a t i o n for the W 2 S 5 d B as t h i s b e a m  T h e s a m e effect is s e e n f o r W 2 S 5 i n F i g u r e 6.8  126  a).  was  approaching  pattern  simulation  All  Beams, A l l M e t h o d s  Overall  Results  0.3  0.25  -20  Goulding Three Beam Peak Detection  -18  -16  -14  Noise Equivalent Sigma Nought=-2 3 dB  -12  -10  Sigma Individual  - 8 - 6 - 4  -2  Nought  Beam R e s u l t s  F o r T h r e e Beam  Ratio  0.3  b) 0.25  W1W2 W3S7 W2W3 W2S5 S5S6  Noise Equivalent Sigma Nought=-23 dB  0.2  u o u  <D (D 0.15  U  en O CD  <& p w  XX  <  0.1  0.05  -12  -10  Sigma  -8  Nought  Figure 6.7: Overall results from noise and individual beam combinations with three beam method 127  Individual  Beam R e s u l t s  For Goulding  0.3  a)  0.25  -20  W1W2 W3S7 W2W3 W2S5 S5S6  -18  Noise Equivalent Sigma Nought=-23 dB  -16  Individual  -14  •2  -12 -10 -8 Sigma Nought  Beam R e s u l t s  F o r Peak  0  Detection  0.5 b) 0.45 0.4  W1 W2 W3S7 W2W3 W2S5 S5S6  Noise Equivalent Sigma Nought=-23 dB  0.35  u o u u  H  0.3 <u 0.25  u  Oi (U Q  0.2  0.1 0.05  -20  -16  -14  -12 -10 -8 Sigma Nought  -2  Figure 6.8: Individual beam combinations with Goulding and hybrid peak detection methods 128  Figure 6.8 a) illustrates beam combination results for Goulding's method. Again, the W2S5 combination produces the worst results, followed by W 2 W 3 . The remaining combinations produce better results but are inferior to those from the three beam method as the dependence on noise is stronger for the noise levels indicated. Figure 6.8 b) gives the results from the hybrid peak detection method. The W3S7 and W 1 W 2 combinations give the best results with an average error of 0.09° and 0.14°, respectively. The varying results based on beam combinations indicate that the algorithm is dependent on beam combination.  129  All  Methods  Overall  Results  For Individual  Scenes  0.3 a)  0.25  Goulding Three Beam Peak Detection Vancouver  Scene  0.2  0.05  0 L_ -20  -18  -16  -14  -12  -10  Sigma  -8  -6  -4  -2  Nought  0.3 b) 0.25  Goulding Three Beam Peak Detection Labrador  Scene  0.2  -20  -18  -16  -14  -12  -10  Sigma  -8  -6  Nought  Figure 6.9: Results from Vancouver and Labrador scenes with all three methods  130  All  Methods O v e r a l l  Results  For Individual  Scenes  0.3  0.25 W  Goulding Three Beam Peak Detection  Melfort  Scene  0.2  0.15  0.1 f  0.05  •12  -10  Sigma  0.3  0.25  -8  - 4 - 2  0  Nought  ~1  1  Goulding Three Beam Peak Detection  Topview  Scene  0.2  0.15  0.05  -12  -10  Sigma  -8  Nought  Figure 6.10: Results from Melfort and Topview scenes with all three methods  131  Figure 6.11: Results from Virden and Toronto scenes with all three methods  132  R e s u l t s From Vancouver w i t h / w i t h o u t W2S5 Combination 0.3  a)  0.25  u o u u  w  o Pi to  <  G with W 2 S 5 G without W 2 S 5 3-beam with W 2 S 5 3-beam without W 2 S 5 Peak with W 2 S 5 Peak without W 2 S 5  Vancouver Scene  0.2  w  a) 0.15 u P 0.1  0.05  -20  -18  -16  -14  -12  -10  Sigma  b)  0.3  0.25  -20  -8  Nought  O v e r a l l R e s u l t s w i t h / w i t h o u t W2S5 Combination G with W2S5 G without W2S5 3-beam with W2S5 3-beam without W2S5 Peak with W2S5 Peak without W2S5  -18  -16  -14  -12  -10  Sigma  -8  -6  -4  Nought  Figure 6.12: Noise results with/without W2S5 combination for Vancouver scene and overall results 133  F i g u r e s 6.9, 6.10,  6.11  illustrate t h e results f r o m the six different scenes.  A l l the  suggest t h a t h y b r i d p e a k detection has little dependence o n noise b u t s t r o n g o n scene content. scene content,  results  dependence  T h e G o u l d i n g a n d three b e a m m e t h o d s b o t h show slight dependence  except  for the V a n c o u v e r scene.  T h e V a n c o u v e r scene a g a i n p r o d u c e s  on the  w o r s t r e s u l t s for b o t h these a l g o r i t h m s . S i n c e o v e r a l l noise results a r e s i g n i f i c a n t l y affected b y the W 2 S 5 c o m b i n a t i o n , it was r e m o v e d f r o m the V a n c o u v e r scene a n d the n e w results are i l l u s t r a t e d i n F i g u r e 6.12 a ) . R e m o v a l o f t h e W 2 S 5 b e a m f r o m a l l t h e n o i s e d a t a is s h o w n i n F i g u r e 6.12  b).  For both  figures,  t h e results for e a c h o f t h e t h r e e m e t h o d s a r e s i g n i f i c a n t l y  improved.  134  6.5  Tabular Results  The requirement table from Chapter 3 is again presented for comparison to the overall results.  W1W2  W2W3  W2S5  W3S7  S5S6  Discontinuity Limit (1)  0.034°  0.041°  0.035°  0.043°  0.028°  Slope Change Limit (2)  0.081°  0.067°  0.099°  0.081°  0.033°  Table 6.2: Beam accuracy requirements  Based on these requirements, the overall results were calculated for noise tolerance (in terms of lowest possible a°) and tolerance to gain uncertainty, and presented as Table 6.3. Tolerance to uncertainty is given in terms of the percent gain uncertainty used to change the beam gain as in the previous figures. The maximum gain uncertainty used in the simulation was 60% from —30% to +30%; therefore the maximum tolerance is limited to 60%. Also, the two limits from the above table are called limit 1 and 2 for the discontinuity and slope change limit, respectively. The numbers on the left represent the  minimum o~°  required to meet the requirements  in Table 6.2. The right side is the maximum, absolute-valued, beam uncertainty which still allows Table 6.2 requirements to be achieved.  135  Goulding  Peak  3-Beam  S5S6 (1)  8  0  16  -10  S5S6 (2)  11  0  21  0  -15  W1W2 (1)  12  0  12  -16  0  -20  W1W2 (2)  31  0  30  W2W3 (1)  -7  0  -7  W2W3 (1)  20  0  27  W2W3 (2)  -9  0  -9  W2W3 (2)  27  0  37  W3S7 (1)  -12  0  -20  W3S7 (1)  21  0  45  W3S7 (2)  -15  0  -20  W3S7 (2)  44  0  57  W2S5 (1)  0  0  0  W2S5 (1)  0  0  0  W2S5 (2)  -6  0  -6  W2S5 (2)  0  0  0  Overall (1)  -6  0  -10  W2S5 (1)  16  0  20  Overall (2)  -10  0  -13  W2S5 (2)  23  0  29  (7° (dB)  Goulding  Peak  3-Beam  S5S6 (1)  -5  0  -7  S5S6 (2)  -6  0  W1W2 (1)  -8  W1W2 (2)  Gain uncertainty (%)  Table 6.3: Tabular results for all beams (including W2S5), all methods. Results are presented in terms of noise, gain uncertainty, beam combination and estimation algorithm used. The noise results represent the lowest a° for which that beam combination and algorithm still met the requirements in Table 6.2. The gain uncertainty results represent the maximum amount of gain uncertainty for which that beam combination and algorithm still met the same requirements. See Figure 6.13 for a conversion to dB uncertainty.  R e s u l t s f r o m t h e W 2 S 5 b e a m m e e t t h e r e q u i r e d l i m i t for g a i n u n c e r t a i n t y ; however, t h e y are o n l y m e t at the e x t r e m e valid.  edges a n d not near zero p e r c e n t t h e y are not  since  considered  A l s o , t h e h y b r i d p e a k d e t e c t i o n m e t h o d d o e s n o t fall w i t h i n r e q u i r e m e n t s a l t h o u g h it  clearly displays significant independence  of noise a n d g a i n u n c e r t a i n t y .  T h e overall results c o n f i r m that the three b e a m m e t h o d tolerates 3 to 4 d B m o r e noise a n d 4 t o 7 p e r c e n t (0.2 t o 0.4 d B ) m o r e g a i n u n c e r t a i n t y .  S i n c e t h e h y b r i d d a t a is a p r o d u c t  of the h y b r i d p a t t e r n s , w h i c h have g a i n levels t h a t are 3 t o 4 d B h i g h e r t h a n t h e low areas of the  normal beam,  t h e r e s u l t is e x p e c t e d .  Also,  the same h y b r i d patterns  average of the two n o r m a l patterns f o r m i n g the interface; hence,they u n c e r t a i n t y is p r e s e n t i n o n e o f t h e n o r m a l p a t t e r n s .  136  gain  are  are m o r e stable  an  when  Gain Uncertainty  0  5  Conversion  10  from  15  Beam G a i n U n c e r t a i n t y  Percentage  20  as  t o dB  25  30  Percentage  Figure 6.13: Conversion of gain uncertainty from a percentage to dB  As for the simulation itself, each scene is simulated with 250 range lines. This resulted in Goulding's algorithm operating on an average of approximately 72 range lines for each of the near and far beams. The three beam and hybrid peak detection methods have approximately 96 range lines of hybrid data. However, this hybrid data is simulated as if R A D A R S A T - 1 simply did not turn off the transmitter; the timing parameters are not adjusted to receive maximum signal returns. This reduces the number of valid hybrid range lines to approximately 30. Incorporation of either timing adjustment method given in Chapter 4 would double this number. Further exploration of the number of data lines used versus roll accuracy is performed using the W3S7 beam. Approximately 5000 ranges lines were simulated. There are 95 ranges lines per burst with 8 of these lines being hybrid data. This produces a standard ratio of 11:1 normal to hybrid line production. The algorithms process the data in various sized data chunks. The results are illustrated in Figure 6.14. This figure indicates that Goulding's method is more accurate until about 90 hybrid lines are used with about 1000 normal lines in the three beam method. This figure also indicates that Goulding's algorithm does not improve significantly with an increase in data averaging. However, this number was only researched on one beam combination and one scene. Processing requirements limited this 137  investigation and further research is required. The results from the other simulations suggest that a ratio of about 30 hybrid with 72 normal lines produces better results with the three beam algorithm. The variance of the averaged hybrid data was higher than the normal data. Although an actual system produces a 10:1 rate of normal versus hybrid data, the differences in variances are eventually reduced below any noticeable dB errors by averaging thousands of range lines. Figure 6.14 suggests further improvement in algorithm accuracy using more hybrid data. Estimation Algorithm  A c c u r a c y Vs # o f Data L i n e s  Used  i CO CU  cuu cn  —  0.1  —  g 0.08  Goulding Peak Detection Three Beam  u 0.061 o £  o  0.041 0.02  OS  J  1  1.5  i  i  2  2.5  i  i  3  LoglO Number o f A v e r a g e d Normal Data Lines  Figure 6.14: Roll accuracy vs number of average range lines. In this simulation there were 11 normal data lines produced for every hybrid line. Since the three beam algorithm depends heavily on hybrid data, it does not equal Goulding's accuracy until about 1000 normal data lines are used. This means about 90 hybrid data lines were available for the three beam method. As the number of hybrid lines used increases past 90 the three beam method provides better results than Goulding.  6.6  Results Summary  This chapter presented the results for the three algorithms that were tested using simulated data. A current algorithm (Goulding) is tested alongside two proposed algorithms (Hybrid Peak Detection and Three Beam Ratio). The hybrid peak detection method displays little dependence on noise, some dependence on gain uncertainty (from the W 2 W 3 beam), and significant dependence on scene and beam  138  combination.  It is e x p e c t e d  that  this  method  could be  affected  b y some scene types  as  s i g n i f i c a n t R C S c h a n g e s c a n affect t h e p o l y n o m i a l fit u s e d t o e s t i m a t e t h e p e a k o f t h e d a t a . T h e s l o p e s a n d w i d t h o f t h e h y b r i d p a t t e r n s p r o v e t o s i g n i f i c a n t l y affect  results.  B o t h G o u l d i n g ' s a n d the three b e a m m e t h o d are d e p e n d e n t o n noise a n d g a i n uncertainty. Scene content in the  is o n l y s i g n i f i c a n t w h e n t h e r e a r e s t r o n g R C S v a r i a t i o n s a c r o s s t h e s c e n e ,  V a n c o u v e r scene.  B e a m c o m b i n a t i o n also plays  c o m b i n a t i o n p r o d u c i n g very p o o r results.  Overall,  the  a significant three  b e s t r e s u l t s for a l l c o m b i n a t i o n s p r o d u c e d i n t h e s i m u l a t i o n .  139  beam  role w i t h method  the  as  W2S5  produces  the  Chapter 7  Conclusions 7.1  Review  For R A D A R S A T - 1 ,  the shapes a n d sensitivities of range b e a m patterns i n the overlap  c o m b i n e d w i t h u n k n o w n roll errors of u p to 0 . 3 ° necessitate tolerances a l g o r i t h m s o n the order of 0 . 0 3 ° .  on roll  areas  estimation  L a r g e r e s t i m a t e errors m a y l e a d to artifacts i n the final  scene. T h e s e artifacts c a n o c c u r at the s t i t c h i n g p o i n t b e t w e e n a n t e n n a b e a m s , or t h r o u g h o u t the range swath, a n d c a n severely degrade the overall scene r a d i o m e t r i c accuracy. T h i s t h e s i s h a s p r e s e n t e d t h e t h e o r e t i c a l b a c k g r o u n d as w e l l as b o t h c u r r e n t a n d p r o p o s e d a l g o r i t h m s for S c a n S A R  range calibration.  T h e objectives  of the p r o p o s e d algorithms  are  t o a c h i e v e a r e q u i r e d r o l l a n g l e a c c u r a c y for e a c h interface, s u c h t h a t a specific r a d i o m e t r i c c r i t e r i a is m e t .  T h i s r a d i o m e t r i c c r i t e r i a is b a s e d o n s e v e r a l f a c t o r s s u c h as t h e  •  T h e b e a m stitching method  •  T h e b e a m c o m b i n a t i o n used,  •  T h e s p e c i f i c b e a m w i d t h c h o s e n for e a c h c o m b i n a t i o n .  C h a p t e r 3 discussed  following:  used,  this c r i t e r i a a n d c a m e u p w i t h a u n i q u e roll a c c u r a c y r e q u i r e m e n t for  each b e a m combination.  T h i s r e q u i r e m e n t was  used to d e t e r m i n e  the effectiveness of  the  proposed and current algorithms. The  proposed algorithms operate  advantage received  on data that  is a c q u i r e d i n a n e w  of p r e v i o u s l y unused d a t a space to record a c h i r p pulse that  by two  different  acquired, was discussed  antenna beams.  The method  i n d e t a i l i n C h a p t e r 4.  140  manner by  taking  is t r a n s m i t t e d  by w h i c h this new  and  hybrid data  is  T h i s h y b r i d d a t a is r e c e i v e d i n p r e v i o u s l y  i n v a l i d d a t a areas i n the signal s t r e a m .  T h e h y b r i d d a t a tolerates a n overall lower scene  a°  a n d greater b e a m gain uncertainty. S i m u l a t i o n was p e r f o r m e d using real R A D A R S A T - 1 parameters i n order to p r o d u c e radiom e t r i c a l l y c o r r e c t n o r m a l as w e l l as h y b r i d S c a n S A R d a t a . T h i s h y b r i d d a t a w a s u s i n g two different a l g o r i t h m s , each of w h i c h y i e l d e d u n i q u e results.  processed  T h e s e results were c o m -  pared side-by-side with a n existing algorithm that operates on n o r m a l data.  O t h e r existing  current algorithms c a n be modified to incorporate h y b r i d data; however, since the p r o p o s e d a l g o r i t h m w a s q u i t e s i m i l a r t o t h e G o u l d i n g a l g o r i t h m , it was d e c i d e d t o use t h e  Goulding  a l g o r i t h m s for c o m p a r i s o n . E a c h of the two p r o p o s e d a l g o r i t h m s h a d u n i q u e results, presented  7.2  next.  Hybrid Peak Detection Conclusions  T h e h y b r i d p e a k d e t e c t i o n m e t h o d is u s e f u l f o r a c o u r s e r o l l a n g l e e s t i m a t i o n w h i l e r e m a i n i n g independent 0.165°;  of noise a n d b e a m g a i n u n c e r t a i n t y .  however,  scene content changes,  the  hybrid  peak  detection  and beam combination.  T h e o v e r a l l a c c u r a c y is  algorithm shows considerable  approximately dependence  T h e V a n c o u v e r scene, w i t h s t r o n g r a d i o m e t r i c scene  produces a n average roll estimate error of 0 . 3 0 ° a n d the V i r d e n scene p r o d u c e s  average roll estimate error of 0 . 0 9 5 ° .  on  T h e W 2 S 5 b e a m p r o d u c e s the worst results,  an  averaging  0 . 3 2 5 ° , while the W 3 S 7 b e a m p r o d u c e s the best, averaging 0 . 0 9 ° . While  the  requirements,  hybrid  peak  detection  i t is a n a d e q u a t e  method  general  d i d not  typically meet  i n d i c a t o r for t h r e e  of the  any  of the  accuracy  five i n t e r f a c e s .  Further  refinement of the a l g o r i t h m w i t h real h y b r i d d a t a c a n p r o b a b l y i m p r o v e results.  7.3  Three Beam Ratio Conclusions  T h e t h r e e b e a m r a t i o p r o d u c e s m o r e a c c u r a t e r e s u l t s , b u t is m o r e s u s c e p t i b l e g a i n u n c e r t a i n t y effects t h a n h y b r i d p e a k d e t e c t i o n .  In c o m p a r i s o n to the current G o u l d i n g  a l g o r i t h m , the three b e a m m e t h o d outperforms G o u l d i n g i n terms of the  •  Noise,  •  B e a m gain uncertainty,  •  Scene  content.  141  to noise a n d  following:  T h e t h r e e b e a m m e t h o d d o e s n o t h a v e a s p e c i f i c a v e r a g e r o l l e s t i m a t e e r r o r , as i t is a f f e c t e d s i g n i f i c a n t l y b y n o i s e a n d g a i n u n c e r t a i n t y . It is s h o w n , h o w e v e r , t h a t t h e t h r e e b e a m m e t h o d c a n t o l e r a t e a a° The  l e v e l as l o w as —11.4  three b e a m m e t h o d  d B , o n a v e r a g e , as c o m p a r e d t o G o u l d i n g ' s —8.3  c a n also tolerate  4 t o 7%  (0.2  t o 0.4  d B ) more gain  dB.  uncertainty  t h a n G o u l d i n g algorithms.  7.4  Conclusion Summary  Overall,  the  proposed new  v i o u s l y i n v a l i d d a t a areas  data acquisition method of the  offers  the  possibility of u t i l i z i n g pre-  d o w n l o a d for c a l i b r a t i o n p u r p o s e s .  T w o algorithms  are  p r o p o s e d w h i c h take advantage of this data. O n e a l g o r i t h m , the three b e a m ratio a l g o r i t h m , p r o d u c e s superior results to the current G o u l d i n g a l g o r i t h m . T h i s a l g o r i t h m tolerates m o r e g a i n u n c e r t a i n t y a n d lower scene r a d i o m e t r i c s t r e n g t h while still m e e t i n g quirements.  7.5  T h e a c q u i s i t i o n o f a c t u a l h y b r i d d a t a w o u l d offer c o n f i r m a t i o n o f i t s u s e f u l n e s s .  Immediate Improvements  B o t h proposed algorithms, hybrid peak detection the  roll a c c u r a c y re-  current G o u l d i n g  method  a n d the three b e a m m e t h o d ,  p r o d u c e d p o o r results  using the  W 3 S 7 c o m b i n a t i o n was s h o w n to generally p r o v i d e the m o s t  W2S5  as w e l l  combination.  accurate results.  The  T h e varying  levels of a c c u r a c y t h a t result f r o m e a c h b e a m s h o u l d , therefore, b e t a k e n into a c c o u n t d e t e r m i n i n g a n o v e r a l l r o l l e s t i m a t e for t h e scene.  as  C o n s i d e r i n g the large errors that  when  usually  r e s u l t e d f r o m t h e W 2 S 5 b e a m , i t is s u g g e s t e d t h a t t h i s b e a m p a t t e r n n o t b e i n c l u d e d i n t h e estimate. It is s u g g e s t e d t h a t a w e i g h t i n g b e u s e d t o d e t e r m i n e a n o v e r a l l r o l l e s t i m a t e . b i n a t i o n s showed clear p e r f o r m a n c e i m p r o v e m e n t s over others.  T h e sensitivity a n d relative  b e a m w i d t h of each p a t t e r n s h o u l d be i n c o r p o r a t e d into any weighting The  b e a m gain uncertainty used  a simple  linear m o d e l .  A  Some com-  technique.  more accurate  uncertainty  m o d e l s h o u l d b e d e v e l o p e d i n o r d e r t o b e t t e r e s t i m a t e a c t u a l u n c e r t a i n t y effects. C u r r e n t l y , t h e b e s t r o l l e s t i m a t e f o r a l l a l g o r i t h m s is b a s e d o n r e s u l t s w h i c h a p p r o a c h a minimum. F i g u r e 3.3,  A better estimate could be made by  fitting  the k n o w n gain errors, e x a m i n e d  directly to the d a t a p r o d u c e d b y a p p l y i n g various R D G C s  142  to the signal  in  data.  T h i s w o u l d be  similar to  a p p l y i n g a p o l y n o m i a l fit t o t h e  data and estimating  the  zero-  c r o s s i n g r a t h e r t h a n the l o c a l m i n i m a . H o w e v e r , i n this case, the d a t a w o u l d b e fitted to  the  r e s u l t s i n F i g u r e 3.3.  7.6  Future W o r k  T h e r e s u l t s s u g g e s t t h a t a c q u i s i t i o n o f h y b r i d d a t a is a w o r t h w h i l e e n d e a v o u r .  T h i s acquisi-  t i o n allows the o p e r a t i o n of a l g o r i t h m s t h a t i m p r o v e the overall roll angle e s t i m a t i o n  process.  T h e inclusion of a t i m i n g m e c h a n i s m i n order to m a x i m i z e signal reception w i n d o w s  would  further improve three b e a m algorithm performance. T h i s research was  entirely simulation based.  d a t a from a S A R system, sources  B a r r i n g the  actual p r o d u c t i o n of  further work p r o d u c i n g simulations that  of error i n a S A R s y s t e m are w o r t h w h i l e i n the a t t e m p t  m i m i c all the  hybrid possible  to c o n f i r m the benefit  of  this approach. A n o t h e r i m p o r t a n t i s s u e is t h e c a l i b r a t i o n p r o c e s s o f t h e p a y l o a d files t h e m s e l v e s . H a w k i n s [24] m e n t i o n s t h a t t h e i s s u e is c o m p l e x , a n d s o m e o f t h e f a c t o r s t h a t m u s t b e t a k e n i n t o are the  following:  antenna  pattern,  replica power,  a n d g a i n offset  account  between beams.  The  acquisition of h y b r i d d a t a m a y a i d i n the d e t e r m i n a t i o n of these factors. T h e a n t e n n a p a t t e r n s are u n c e r t a i n i n the low gain area b e c a u s e of the low S N R .  New  h y b r i d d a t a h a s b e e n s h o w n t o h a v e a 3-4 d B i n c r e a s e o v e r t h e l o w e r b e a m . A n y n e w e s t i m a t e w o u l d b e m a d e w i t h a w e l l k n o w n p a t t e r n a n d a less " u n c e r t a i n " p a t t e r n . A s f o r r e p l i c a p o w e r , t h e p u l s e is t r a n s m i t t e d a n d r e c e i v e d b y t w o b e a m s , w i t h t h e a n t e n n a a n d satellite i n different b e a m m o d e s ,  a n d is b e p r o c e s s e d i n d i f f e r e n t b u r s t s .  overall signal strength f r o m one burst to the next, i n the  final  A n a l y s i s of  scene, m a y p r o v i d e  insight  i n t o a n y r e p l i c a differences. F i n a l l y , a g a i n offset m a y b e f o u n d u s i n g a m o d i f i e d t h r e e b e a m m e t h o d . r o l l a n g l e is f o u n d , t h e b e a m s  A f t e r the  best  are t h e n i n d i v i d u a l l y raised or lowered o n their overall g a i n .  T h i s w o u l d affect t w o o u t o f t h e t h r e e l o g r a t i o s a n d s h o u l d p r o d u c e a g a i n offset e s t i m a t e . O b v i o u s l y , a l l of these issues r e q u i r e f u r t h e r research.  143  Bibliography [1] Canadian Ice Service, http://ice-glaces.ec.gc.ca/, Government of Canada, Jan 2002. [2] R A D A R S A T International,  " R A D A R S A T - 1 Data Products Specification:  RSI-GS-026 3.0", 8 May, 2000. [3] Curlander,  J.C.  and  McDonough,  Synthetic Aperture Radar: Systems and Signal Processing,  R.N., John  Wiley  and Sons,Inc: New York, 1991. [4] Ryerson, R . A . , and Rencz A . , Manual of Remote Sensing, John Wiley and Sons,Inc: New York, 1999. [5] Ulaby,  F.T.,  R.K.  Moore,  and  A.K.  Fung  (1982).  Microwave Remote Sensing, Vol. 2, Addison-Wesley, Reading, M A . [6] Raney, R . K . , Runge, H . , Bamler, R., Cumming, I., A n d Wong, F . , "Precision S A R Processing without Interpolation for Range Cell Migration Correction". IEEE  Trans, on GeoSci.  and Remote Sensing, Vol. 32, No.4, July 1994  [7] Hawkins R. K . , Wolfe J . , Murnaghan K . , and Jefferies W . C . "Exploring the Elevation Beam Overlap Region in R A D A R S A T - 1 ScanSAR", Proceedings of the CEOS  Calibration  Workshop,  Tokyo, A p r i l , 2001.  [8] Luscombe, A . P . , "Using the Overlap Regions to Improve ScanSAR Calibration", CEOS  SAR  Calibration  Workshop,  The Netherlands: E S A p. 341-346.  144  1993. E S A / E S T E C , Noordwijk,  [9] Jin, M . "Optimal Range and Doppler Centroid Estimation for a ScanSAR System", IEEE  Trans.  On Geoscience  and Remote  Sensing,  vol.34, p.  479-  488, March 1996. [10] Franceschetti,  G . , and Lanari, R., Synthetic Aperture Radar Processing,  Boca Rotan: C R C Press, 1999. [11] Hawkins, R . K . , " R A D A R S A T Payload Parameter File and C A L I B R A T I O N " , Canada Centre for Remote Sensing, 1999. [12] Mittermayer,  J.  Moreira,  A.,  and  Davidson,  G,  and  Bamler,  R.,  SIR-C ScanSAR Processing, Deutsche Forschungsanstalt fur Luft-und Raumfahrt e.V., Forshungsbericht, 96-25. [13] Martin, P., Williams, J., Nicoll, R., Guritz, T., and Bicknell, T., "Calibration of the R A D A R S A T S W B Processor at the Alaska S A R Facility",  2000, 24-28 July 2000,  IGARSS  Honululu, Hawaii.  [14] Lancashire, D . C . , "ScanSAR Calibration", CEOS  SAR  Calibration  Work-  shop, 1998. E S A / E S T E C , Noordwijk, The Netherlans:ESA p.241-245. [15] Alaska  S A R Facility,  http://www.asf.alaska.edu/RADARSAT/agc.html,  " R A D A R S A T ' s Automatic Gain Control", University of Alaska, 01 Jan 2001. [16] Goulding, M . , "Roll Angle Estimation for ScanSAR Processing in the C D P F " , MacDonald Dettwiler internal document, April 8, 1997. [17] Bamler, R., "Roll Angle Estimation in SIR-C ScanSAR Processing", J P L Interoffice Memo, 16 March, 1994. [18] Dragosevic, M . V . , "Roll Angle Measurement and Compensation Strategy for R A D A R S A T ScanSAR", CEOS  SAR  Workshop, E S C - C N E S , Toulose, 26-29  Oct, 1999. [19] Canadian Space Agency, " R A D A R S A T Spacecraft to Data Acquisition Network (X-Band) I C D : RSCSA-IC0009", 25 Jul, 1997.  145  [20] Several Emails between Cathy Vigneron, Martie Goulding, myself and Tony Luscombe, subject "ScanSAR". [21] Oliver, C. and Quegan, S, Understanding Synthetic Aperture Radar Images, Boston: Artech House, 1998. [22] Arsenault, H . H . , and April, G . , "Properties of Speckle Integrated with a Finite Aperture and Logarithmically Transformed," J . opt. Soc. Amer., Vol. 66 1976, pp. 1160-1163 [23] Goulding, M . M . , "Performance of Dynamic Roll Estimator for R A D A R S A T ScanSAR", MacDonald Dettwiler internal document, August 12, 1998. [24] Hawkins, R . K . , and Srivastava, S.K. "The Radiometric Calibration Budget of R A D A R S A T - 1 " Proceedings  of CEOS  26-29 , 1999  146  Workshop, Toulouse, France, October  

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