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An investigation of single channel, global positioning system receivers for forestry applications Shannon, Tim 1992

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AN INVESTIGATION OF SINGLE CHANNEL, GLOBAL POSITIONING SYSTEM RECEIVERS FOR FORESTRY APPLICATIONS  by Tim Shannon B.SF. University of British Columbia, 1982  A THESIS SUBMITIED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY  in THE FACULTY OF GRADUATE STUDIES Department of Harvesting and Wood Science  We accept this thesis as conforming to the required standarcj  THE UNIVERSITY OF BRITISH COLUMBIA July 1992 © Timothy George Shannon, 1992  In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l make i t freely  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  I f u r t h e r agree  that permission f o r extensive copying or p u b l i c a t i o n of t h i s thesis for financial written  g a i n s h a l l n o t be a l l o w e d w i t h o u t my  permission.  Department o f H a r v e s t i n g and Wood S c i e n c e The U n i v e r s i t y o f B r i t i s h Columbia 2357 Main M a l l Vancouver, Canada V6T 1Z4  Abstract  The  forest industry  of i t s s p a t i a l  i n B r i t i s h Columbia i s c o n v e r t i n g  d a t a t o d i g i t a l format f o r i n p u t  G e o g r a p h i c I n f o r m a t i o n Systems. databases s t i l l  involves  much  into  The u p d a t i n g o f t h e s e  d i g i t i z i n g of analog data.  large  This  t h e s i s examines t h e s u i t a b i l i t y o f a s i n g l e c h a n n e l hand held Global  P o s i t i o n i n g System (GPS) r e c e i v e r  of B r i t i s h Columbia. capturing  i n the forests  GPS p r o v i d e s a means o f d i r e c t l y  digital spatial  attributes i n the f i e l d .  Field  t r i a l s t o e v a l u a t e t h e e f f e c t s o f f o r e s t canopy on t h e reception  o f s a t e l l i t e s i g n a l s were conducted a t t h e Malcolm  Knapp R e s e a r c h F o r e s t i n Maple R i d g e .  I s s u e s t h a t need t o be c o n s i d e r e d when i m p l e m e n t i n g GPS i n capturing  spatial  information  are:  1) t h e frame o f r e f e r e n c e  from w h i c h p o s i t i o n s a r e c a l c u l a t e d ,  (datums) 2) methods  used t o c a l c u l a t e t h e a c c u r a c y o f p o s i t i o n , 3) t h e a c c u r a c y o f s i n g l e p o i n t p o s i t i o n s , 4) t h e a c c u r a c y o f d i f f e r e n t i a l p o s i t i o n i n g , and 5) t h e e f f e c t s o f t h e f o r e s t canopy on t h e reception  o f s i g n a l s from t h e s a t e l l i t e s .  The e f f e c t o f  c h o o s i n g a d i f f e r e n t datum t h a n t h a t used t o produce t h e base map c a n l e a d t o p o s i t i o n i n g e r r o r s o f s e v e r a l metres.  hundred  W h i l e commonly t h e l a r g e s t source o f e r r o r , i t i s  preventable.  S i n g l e p o i n t p o s i t i o n s can be e x p e c t e d t o be  w i t h i n 25-metres, i n two d i m e n s i o n s , when S e l e c t i v e Availability  i s not enabled.  When S e l e c t i v e A v a i l a b i l i t y i s  e n a b l e d the a c c u r a c y w i l l be degraded t o 100 r e g a i n the a c c u r a c y l o s t due differential  GPS  to S e l e c t i v e  w i l l need t o be used.  metres.  To  Availability, Differentially  c o r r e c t e d p o s i t i o n s can be e x p e c t e d t o be w i t h i n 10-metres i n two  dimensions.  The  the s i g n a l s emitted  e f f e c t of the canopy on  attenuating  from the s a t e l l i t e s i s of c o n c e r n .  At  b e s t , the u s e r can o n l y expect i n t e r m i t t e n t s i g n a l s under a c l o s e d canopy w i t h the equipment t e s t e d .  Evolving technologies sensitivity  are i n c r e a s i n g the a c c u r a c y , speed  of r e c e i v e r s , w h i l e d e c r e a s i n g  consumption, and c o s t .  The  the s i z e ,  i n t e g r a t i o n o f GPS  with  and  power other  p o s i t i o n i n g and n a v i g a t i o n a l a i d s shows the most promise f o r i m p l e m e n t i n g GPS  i n t o f o r e s t management i n B r i t i s h Columbia.  TABLE OF CONTENTS page ABSTRACT LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENT INTRODUCTION: CHAPTER 1 - DATUMS Introduction: C o o r d i n a t e r e f e r e n c e systems: Datums i n GPS: The Problem: Method: Results: Discussion: Conclusion: CHAPTER 2 ACCURACY - INTRODUCTION Introduction: PDOP and UERE Terms used i n d e s c r i b i n g a c c u r a c y Assumptions: CHAPTER 3 ACCURACY - SINGLE POINT POSITIONING Purpose: Method: Results: Averaging: Discussion: Averaging:  i i v i i viii x 1 4 4 4 5 6 8 9 10 12 13 13 15 17 19 20 20 20 20 26 30 3.1  C o n c l u s i o n and Recommendations: 32 CHAPTER 4 - RECEIVER NOISE AND DIFFERENTIAL POSITIONING . 33 Introduction:  33  Objective: Scope: Method:  35 35 35  CHAPTER 5 ACCURACY - RELATIVE POSITIONING  43  Introduction: Objective: Scope: Method: Results: Discussion: Conclusions: CHAPTER 6 UNDER CANOPY TRIALS Introduction Scope o f Study Objectives  43 43 43 44 45 47 49 50 50 52 52  Methods and P r o c e d u r e s Introduction Data C o l l e c t i o n Site Selection  53 53 53 53  Procedures  55  Static tests Discussion of Results  56 59  Static tests  59  Results  61  Dynamic t e s t s : Discussion of Results  61 63  Dynamic t e s t s : Conclusions  63 64  Recommendations CHAPTER 7 - D i s c u s s i o n and CONCLUSIONS Discussion Conclusions  65 67 67 73  Literature Cited  75'  APPENDIX A - VINCENTY INVERSE  78  Introduction:  78  Objective  78  Convergence:  78  Geodesies: Purpose:  81 81  Method:  82 V  Results: Discussion: Conclusion: Bibliography APPENDIX B - ORBITSET Introduction Objective: Method: Results: Discussion: F u t u r e Developments: Conclusion: Bibliography  82 84 85 85 87 87 87 88 88 90 94 95 97  Appendix B- I P r a t t S o l u t i o n Appendix B - I I O r b i t s e t Users g u i d e APPENDIX C - GPSDXF Description: Introduction: Purpose:  99 101 109 109 109 110  Method: Results: Discussion:  I l l 112 117  F u t u r e Developments:  118  Conclusions:  119  Bibliography  120  Appendix C-I  User's Guide  121  Getting started: Menus Changing t h e c o n f i g u r a t i o n :  121 122 122  Editing:  122  Fields:  123  U s i n g GPSDXF:  125  U s i n g SEEPLOT:  125  Appendix C - I I Database s t r u c t u r e s Appendix D  G l o s s a r y of Terms  127 129  LIST OF TABLES Table 1-1 3-1 3-2 3-3 3- 4 4- 1 4- 2 5- 1 5-2 5- 3 6- 1 6-2 6-3 6-4  A-2 B-1 C-1  page  Comparison o f c o o r d i n a t e s o f one l o c a t i o n u s i n g d i f f e r e n t datums Ranges i n measurements w i t h d i f f e r i n g PDOP S t a n d a r d error(m) o f t h e mean i n p o s i t i o n w i t h d i f f e r i n g PDOP E r r o r i n mean p o s i t i o n s from l o n g term average position Means o f d a t a s e s s i o n s a t 2849 Cambridge St Comparison o f a c c u r a c y between s y n c h r o n i z e d v s . u n s y n c h r o n i z e d averaged p o s i t i o n s Comparison o f ranges i n f i x e s between h i g h PDOP v s . low PDOP s e s s i o n s R e l a t i v e a c c u r a c y between Monument 1123 and base s t a t i o n Pearson c o r r e l a t i o n c o e f f i c i e n t : E r r o r v s . PDOP A c c u r a c y o f r e l a t i v e v e r s u s autonomous positioning D e s c r i p t i o n o f p l o t s used a t Malcolm Knapp Research F o r e s t Under canopy s i n g l e p o i n t a c q u i s i t i o n s w i t h v a r y i n g antenna h e i g h t Percentage of successful/attempted f i x e s i n d r y v e r s u s wet canopy Ratio of successful/attempted f i x e s i n dry v e r s u s wet canopy. Two r e c e i v e r s a t 1 and 3metres e l e v a t i o n used s i m u l t a n e o u s l y Comparison o f d i s t a n c e s from GSrugpc and Geodist Comparison o f ORBITSET t o P r a t t N u m e r i c a l example Comparison o f r e s u l t s from GPSDXF and CS87 i n a n a l y z i n g GPS d a t a  9 25 26 27 30 37 38 45 45 47 54 57 57  63 84 89 116  LIST OF FIGURES Figure  page  2-1 P r e c i s i o n and A c c u r a c y 2-lA a p r e c i s e sample mean t o e s t i m a t e t h e t r u e mean w i t h a l a r g e b i a s 2- l B an i m p r e c i s e sample mean t h a t e s t i m a t e s t h e t r u e mean more a c c u r a t e l y 3- 1 P o s i t i o n i n g o f GPS antenna 3-2 An example o f PDOP v s . Time. 16 s a t e l l i t e constellation 3-3 RMS e r r o r and o b s e r v a t i o n s a v a i l a b l e v s . PDOP 3-4 P o s i t i o n f i x e s o f S e s s i o n C0426t-1. Low PDOP (average 3.4) 3-5 P o s i t i o n f i x e s o f S e s s i o n C0426t-2. H i g h PDOP (average 26) 3-6 P o s i t i o n s o f s e s s i o n means w i t h PDOP <10 3- 7 P o s i t i o n s o f s e s s i o n means w i t h PDOP <6 4- 1 E r r o r i n d i f f e r e n t i a l l y c o r r e c t e d p o s i t i o n v s . PDOP 4- 2 S c a t t e r o f N o r t h i n g  13 13 13 22 23 24 28 28 29 29 40  Vs. E a s t i n g . A l l  observations 5- 1 E r r o r from t r u e p o s i t i o n v s . PDOP i n 3D space.. R e l a t i v e P o s i t i o n i n g 5- 2 E r r o r from t r u e p o s i t i o n Vs S e s s i o n . R e l a t i v e Positioning  41  6- 1 S i g n a l q u a l i t y i n d e x v s . S a t e l l i t e e l e v a t i o n  58  48 48  6-2 M a l c o l m Knapp G o l f c o u r s e t r a v e r s e . A l l 2D 3D p o s i t i o n s w i t h PDOP < 10 6-3 M a l c o l m Knapp G o l f course t r a v e r s e . A l l 3D  62  p o s i t i o n s w U h PDOP < 10 2D e x c l u d e d  62  A-1 B-1  Convergence S a t e l l i t e e l e v a t i o n above t h e h o r i z o n v s . Time. December 197 8  80 92  B-2 S a t e l l i t e e l e v a t i o n above t h e h o r i z o n v s . Time. December 1988  93  c-1 A n a l y s i s o f GPS s e s s i o n C0403-3 by CS87 s o f t w a r e . ALSKA datum used. H e i g h t above e l l i p s o i d only C-2 A n a l y s i s o f GPS s e s s i o n C0403-3 by GPSDXF s o f t w a r e . ALSKA datum used. E l e v a t i o n g i v e n as h e i g h t above g e o i d C-3A A n a l y s i s o f GPS s o f t w a r e . ALSKA as h e i g h t above C-3B Same f i l e as i n ellipsoid  s e s s i o n C0403-3 by GPSDXF datum used. E l e v a t i o n g i v e n ellipsoid C-3A but w i t h WGS84  113  114  115 115  ACKNOWLEDGMENT I w i s h t o e x p r e s s my a p p r e c i a t i o n t o my s u p e r v i s o r Dr. J.D. N e l s o n f o r h i s s u p p o r t , s u g g e s t i o n s and p a t i e n c e throughout t h e s t u d y . I a l s o w i s h t o g i v e thanks t o t h e o t h e r members o f my academic committee. Dr. H. S c h r e i e r , and Dr. J . McNeel f o r r e v i e w i n g t h e m a n u s c r i p t and f o r t h e i r h e l p f u l suggestions. I am g r a t e f u l t o Dr. B. K l i n k e n b e r g f o r h i s a s s i s t a n c e i n t e c h n i c a l m a t t e r s r e g a r d i n g p o s i t i o n i n g . I am a l s o i n d e b t e d t o Mr. C h r i s Cryderman o f U n d e r h i l l G e o g r a p h i c a l S e r v i c e s L t d . f o r t h e l o a n o f a second r e c e i v e r , which e n a b l e d t h e study o f d i f f e r e n t i a l p o s i t i o n i n g . My g r a t i t u d e i s a l s o extended t o t h e S c i e n c e C o u n c i l o f B r i t i s h Columbia f o r f i n a n c i a l support d u r i n g t h i s s t u d y .  AN INVESTIGATION OF SINGLE CHANNEL, GLOBAL POSITIONING SYSTEM RECEIVERS FOR FORESTRY APPLICATIONS  IWTRODDCTION: The f o r e s t i n d u s t r y i n B r i t i s h Columbia i s t h e most i m p o r t a n t c o n t r i b u t o r t o t h e economic w e l l - b e i n g o f t h e province. I t i s a l s o t h e most e x t e n s i v e i n d u s t r y , h a v i n g a p r e s e n c e i n v i r t u a l l y every community i n t h e p r o v i n c e . N e a r l y e v e r y a c t i v i t y i n f o r e s t management can be r e l a t e d t o a s p e c i f i c l o c a t i o n on a map. These c h a r a c t e r i s t i c s o f t h e i n d u s t r y r e q u i r e t h a t a l a r g e s t o c k o f updated a c c u r a t e maps of the l a n d base be m a i n t a i n e d . Great s t r i d e s i n G e o g r a p h i c I n f o r m a t i o n System (GIS) t e c h n o l o g i e s have been made i n r e c e n t y e a r s i n p r o v i d i n g f o r e s t managers w i t h t h e s e maps. The b o t t l e n e c k i s i n s u p p l y i n g t h e GIS database w i t h a c c u r a t e , r e l e v a n t d a t a and p r o v i d i n g a means o f s u p p l y i n g updates between i n v e n t o r y programs. There i s a l s o a problem o f i m p l e m e n t i n g t h e p l a n n e r ' s p r e s c r i p t i o n on t h e ground. The problem o f f i e l d crews t y i n g t h e m s e l v e s t o a spot on t h e ground w i t h an a i r photo and t h e n onto an i n a c c u r a t e map i s w e l l known t o t h e man who i s two k i l o m e t e r s i n the bush and even t o t h e crew p a r k e d a t a road i n t e r s e c t i o n . The a u t h o r i s f a m i l i a r w i t h f r u i t l e s s searches f o r stands t a k i n g whole days. The f o r e s t i n d u s t r y i s p r o b a b l y t h e l a r g e s t employer o f n a v i g a t o r s . P e r s o n n e l h i r e d as f o r e s t t e c h n i c i a n s spend a m a j o r i t y o f t h e i r t i m e n a v i g a t i n g t o and w i t h i n t h e bush. Other i n d u s t r i e s , such as a i r t r a v e l , have d i s p e n s e d w i t h f u l l t i m e n a v i g a t o r s and r e p l a c e d them w i t h t h e a p p r o p r i a t e technology. The n a v i g a t i o n f o r a f o r e s t r y f i e l d crew s t a r t s e a r l y i n t h e morning w i t h t h e assembly o f a i r photographs and maps. One p e r s o n i n t h e t r u c k i s u s u a l l y a s s i g n e d t o  k e e p i n g an eye on the maps, photographs and the s u r r o u n d i n g terrain. Once they have reached t h e i r work s i t e , t h e r e i s the ceremony of u n r a v e l l i n g the c h a i n and c a l i b r a t i n g the equipment. The f i e l d equipment, w h i c h i s u s u a l l y a n y l o n c h a i n , S i l v a compass and Suunto c l i n o m e t e r , i s l i g h t and rugged. U n f o r t u n a t e l y , the hand instriaments r e l y on a l i n e of s i g h t t o t h e o t h e r crew member t o o b t a i n a r e a d i n g . The l i n e of s i g h t i n a f o r e s t s t a n d i s u s u a l l y i m p a i r e d by t r e e s and b r u s h , making f o r s h o r t d i s t a n c e s between s t a t i o n s . These c o n d i t i o n s r e s u l t i n expensive n a v i g a t i o n and surveying. The same equipment i s a l s o used f o r s u r v e y i n g l a r g e c u t - b l o c k s a f t e r h a r v e s t . The l i n e of s i g h t i s u s u a l l y u n i m p a i r e d , however, the l e n g t h of c h a i n , u s u a l l y f i f t y m e t e r s , l i m i t s the d i s t a n c e between s t a t i o n s . Other a c t i v i t i e s i n f o r e s t r y r e l y on the p o s i t i o n of v e h i c l e s and crews f o r s a f e and e f f i c i e n t w o r k i n g c o n d i t i o n s . The p o s i t i o n i n g of f i r e f i g h t e r s and l o g g i n g t r u c k s i s u s u a l l y done by v e r b a l means over the r a d i o . This i s u s u a l l y adequate u n t i l the o p e r a t i o n becomes l a r g e . Too much c h a t t e r on the r a d i o degrades the s a f e t y of t r a f f i c on l o g g i n g roads and i m p a i r s the a b i l i t y of a f i r e boss t o manage r e s o u r c e s a l l o c a t e d t o the f i r e , e f f e c t i v e l y . The p o s i t i o n i n g of crews and v e h i c l e s , the l o c a t i o n of roads and c u t b l o c k s and the p r o d u c t i o n of a c c u r a t e maps r e q u i r e s b o t h s k i l l and e x p e r i e n c e i n a f i e l d f o r e s t e r . W i t h more complex r o a d networks and polygons b e i n g added each y e a r , the t a s k of l o c a t i n g o n e s e l f w i l l become more demanding. The l i n e of s i g h t w i l l degrade i n the brushy second growth forests. For f o r e s t e r s t o be e f f e c t i v e i n the f i e l d , b e t t e r t o o l s w i l l be r e q u i r e d t o l e s s e n the n a v i g a t i o n a l burden, thus a l l o w i n g f o r e s t r y crews t o a t t e n d t o o t h e r t a s k s w h i l e i n the bush.  The g l o b a l p o s i t i o n i n g system (GPS) may a i d t h e f o r e s t e r i n many p o s i t i o n a l and n a v i g a t i o n a l t a s k s . T h i s paper i n v e s t i g a t e s s e v e r a l i s s u e s o f u s i n g GPS i n f o r e s t r y . C h a p t e r 1 d e s c r i b e s how a r e c e i v e r r e l a t e s a p o s i t i o n o f a u s e r on t h e e a r t h ' s s u r f a c e . I t a l s o i n v e s t i g a t e s how t h e r e c e i v e r used i n t h e s t u d y h a n d l e s t h e datums used t o f i x a c o o r d i n a t e system. Chapter 2 e x p l a i n s t h e terms u s e d and some i s s u e s i n v o l v e d i n e x p r e s s i n g p o s i t i o n a l a c c u r a c y . Chapter 3 i n v e s t i g a t e s the accuracy of the r e c e i v e r i n s i n g l e p o i n t p o s i t i o n i n g . Chapter 4 i n v e s t i g a t e s t h e magnitude o f d i f f e r e n t i a l e r r o r due t o n o i s e i n t r o d u c e d by the r e c e i v e r s t h e m s e l v e s . I t a l s o i n v e s t i g a t e s t h e advantage o f u s i n g s y n c h r o n i z e d v e r s u s u n s y n c h r o n i z e d d i f f e r e n t i a l p o s i t i o n i n g . Chapter 5 i n v e s t i g a t e s t h e accuracy of d i f f e r e n t i a l p o s i t i o n i n g . Chapter 6 i n v e s t i g a t e s t h e s u c c e s s o f t h e GPS s i g n a l i n p e n e t r a t i n g a f o r e s t canopy. C h a p t e r 7 summarizes t h e c o n c l u s i o n s found i n t h e s t u d i e s performed, p r o v i d e s recommendations f o r t h e use o f GPS, and suggest t o p i c s f o r f u r t h e r s t u d y . Appendix A d e s c r i b e s and t e s t s a computer program t h a t c a l c u l a t e s d i s t a n c e s based on g e o d e t i c c o o r d i n a t e s . Appendix B d e s c r i b e s and t e s t s a computer program t h a t was used t o p r e d i c t s a t e l l i t e a v a i l a b i l i t y . Appendix C d e s c r i b e s a computer program t h a t was w r i t t e n t o a n a l y z e t h e d a t a i n t h i s s t u d y . Appendix D p r o v i d e s a g l o s s a r y o f terms used t h r o u g h o u t t h e t h e s i s .  CHAPTER 1 - DATTJMg Introduction:  Coordinate reference systems: A GPS r e c e i v e r c a l c u l a t e s a p o s i t i o n i n t h r e e d i m e n s i o n a l space. The p o s i t i o n i s d e s c r i b e d i n a t h r e e d i m e n s i o n a l C a r t e s i a n (X-Y-Z) c o o r d i n a t e system, w h i c h has i t s o r i g i n a t the c e n t r e o f t h e e a r t h . The e r r o r i n t h e d e t e r m i n a t i o n o f a range t o a s a t e l l i t e i s 6-metres e r r o r i n t h i s r e f e r e n c e frame (Feess, si. ^ 1987) . The c o o r d i n a t e s d e s c r i b i n g a p o s i t i o n i n t h i s system a r e not u s e f u l f o r p o s i t i o n i n g o n e s e l f on t h e e a r t h ' s s u r f a c e . In o r d e r f o r t h e p o s i t i o n i n g data t o be u s e f u l , t h e r e c e i v e r must t r a n s f o r m t h e C a r t e s i a n c o o r d i n a t e s i n t o c o o r d i n a t e s based on a model o f t h e e a r t h . The b e s t model o f t h e e a r t h ' s s u r f a c e i s t h e g e o i d . The g e o i d i s e s s e n t i a l l y mean sea l e v e l . The mean s e a - l e v e l i s based on where t h e w a t e r l e v e l w o u l d be i f s m a l l channels were c u t t h r o u g h t h e l a n d masses on t h e p l a n e t and f r i c t i o n and t i d e s were i g n o r e d . S i n c e i t i s g r a v i t y t h a t would determine t h e w a t e r s u r f a c e l e v e l , and g r a v i t y i s n o t c o n s t a n t t h r o u g h o u t t h e w o r l d , t h e g e o i d i s v e r y i r r e g u l a r . Maps a r e n o t m a n u f a c t u r e d on p r o j e c t i o n s o f t h e g e o i d , because o f t h e i r r e g u l a r i t y o f t h e s u r f a c e . There i s no convenient m a t h e m a t i c a l f u n c t i o n t o d e s c r i b e t h e g e o i d (Ewing 1970). The model used f o r p o s i t i o n i n g on t h e h o r i z o n t a l i s an ellipsoid. There a r e many e l l i p s o i d models o f t h e e a r t h , w i t h each c o n t i n e n t u s u a l l y h a v i n g a d i f f e r e n t e l l i p s o i d model t o d e s c r i b e i t . The C l a r k e e l l i p s o i d o f 1866 i s t h e base f o r most on t h e maps o f N o r t h America. T h i s i s t h e  model used by t h e N o r t h American Datvim o f 1927 (NAD27). The C l a r k e e l l i p s o i d , when a s s i g n e d a s p e c i f i c o r i g i n (such as Meades Ranch i n Kansas, f o r NAD27), d e f i n e s a datum. The o r i g i n o f t h e e l l i p s o i d f o r NAD27-CONUS, does n o t i n t e r s e c t the c e n t r e o f t h e e a r t h . The NAD27-Alaska uses t h e same C l a r k e e l l i p s o i d , t h a t has t h e same semi-major and semiminor a x i s , but uses a d i f f e r e n t o r i g i n . P o s i t i o n s d e t e r m i n e d on t h e s u r f a c e o f t h e e a r t h a r e reduced, t h r o u g h a plumb l i n e , t o t h e r e f e r e n c e e l l i p s o i d . The l a t i t u d e and l o n g i t u d e a r e t h e 2-D c o o r d i n a t e s o f t h e position. The w o r l d a c c o r d i n g t o s u r v e y o r s i s n o t t h r e e d i m e n s i o n a l b u t two d i m e n s i o n a l , p l u s one d i m e n s i o n (Lachappele 1991). The e l e v a t i o n i s d e s c r i b e d as t h e h e i g h t above t h e g e o i d . S i n c e t h e g e o i d i s based on t h e i r r e g u l a r g r a v i t y f i e l d o f t h e e a r t h , t h e g r a v i t y f i e l d i s sampled and a model o f t h e g e o i d i s developed. T h i s has r e s u l t e d i n t h e development o f many models o f t h e g e o i d . When i n mountainous a r e a s , t h e g e o i d may u n d u l a t e d r a m a t i c a l l y . On the ocean t h e g e o i d i s easy t o model because t h e u n d u l a t i o n s have a l o n g , smooth wavelength.  Datums i n GPS: The n a t i v e datum f o r GPS i s t h e World G e o d e t i c System (WGS84), w h i c h uses t h e G e o d e t i c R e f e r e n c e System (GRS80) ellipsoid. T h i s i s e s s e n t i a l l y t h e e l l i p s o i d model used f o r NAD83. The o r i g i n i s t h e c e n t r e o f t h e e a r t h . T h i s i s convenient f o r s a t e l l i t e p o s i t i o n i n g , since the s a t e l l i t e s o r b i t around t h e c e n t r e o f mass o f t h e e a r t h . GPS was used t o d e t e r m i n e t h e new c o o r d i n a t e s f o r many o f t h e c o n t r o l p o i n t s used i n d e t e r m i n i n g t h e NAD83 network. The t a s k f o r a r e c e i v e r , i s t o c a l c u l a t e a p o s i t i o n i n a t h r e e d i m e n s i o n a l c o o r d i n a t e system, t r a n s l a t e i t t o a  l a t i t u d e and l o n g i t u d e on a r e f e r e n c e e l l i p s o i d , and c o n v e r t i t t o a s e t of map c o o r d i n a t e s based on a p r o j e c t i o n . F o r e s t r y maps a r e based on the U n i v e r s a l T r a n s v e r s e M e r c a t o r (UTM) p r o j e c t i o n w i t h e l e v a t i o n g i v e n as h e i g h t above mean s e a - l e v e l . The c a l c u l a t i o n f o r the e l e v a t i o n , i n a r e c e i v e r , i s g i v e n as the h e i g h t above the r e f e r e n c e ellipsoid. The h e i g h t above s e a - l e v e l must be c a l c u l a t e d from the h e i g h t above e l l i p s o i d . The f i n a l p o s i t i o n must a l s o be i n t e r p r e t e d as one t h a t must r e l a t e t o c o o r d i n a t e s a s s i g n e d t o a c o n t r o l p o i n t based on a l e a s t s q u a r e s a d j u s t m e n t . T h i s i s d e s c r i b e d i n the next s e c t i o n . The M a g e l l a n r e c e i v e r used i n t h i s s t u d y , can d i s p l a y p o s i t i o n s i n r e f e r e n c e t o a v a r i e t y of datums. There a r e e i g h t datums b u i l t i n t o the r e c e i v e r as w e l l as the c a p a b i l i t y o f s t o r i n g f i v e u s e r d e f i n e d datiams. The t r a n s f o r m a t i o n between d i f f e r i n g e l l i p s o i d a l models i s m a t h e m a t i c a l l y r i g o r o u s . For example, t o change from a c o o r d i n a t e i n WGS84 t o NAD83 the f l a t t e n i n g f a c t o r i s reduced by 0.3726 x 10"'^. The t r a n s f o r m a t i o n can t a k e p l a c e w i t h t h e one new parameter. The  Problem:  A datum can be d e s c r i b e d by an e l l i p s o i d w i t h an o r i g i n . To implement t h e datum on the ground, a c o o r d i n a t e r e f e r e n c e system must be b u i l t on a network of c o n t r o l p o i n t s . The u s e r s cannot d e s c r i b e t h e i r p o s i t i o n i n r e f e r e n c e t o t h e axes of the e l l i p s o i d , but t o a s e t of c o o r d i n a t e s based on the datum t h a t i s used t o d e s c r i b e p o s i t i o n s o f monuments an the ground. The p a r a m e t e r s d e s c r i b i n g the a r e p r e c i s e . The c o o r d i n a t e s f o r NAD27 however, were based l e v e l i n g s t a r t i n g i n Kansas.  e l l i p s o i d and o r i g i n of NAD27 d e s c r i b i n g the c o n t r o l p o i n t s on t r i a n g u l a t i o n and s p i r i t The d i s t o r t i o n s from the  t r i a n g u l a t i o n p r o c e s s accumulate as one i n c r e a s e s t h e d i s t a n c e from t h e o r i g i n . The t r i a n g u l a t i o n was completed and a d j u s t e d u s i n g l e a s t squares i n t h e c o n t i n e n t a l U n i t e d S t a t e s . When Canada c o n t i n u e d w i t h t h e t r i a n g u l a t i o n i t used p o i n t s t h a t were a l r e a d y a d j u s t e d i n t h e A m e r i c a n network. Thus t h e c o n t r o l p o i n t s used t o a d j u s t t h e network i n Canada were a l r e a d y t h e product o f an a d j u s t m e n t (Lachappele 1991) . T h i s c o n t r i b u t e d t o even g r e a t e r d i s t o r t i o n s i n B r i t i s h Columbia. Separate a d j u s t m e n t s such as t h e A l a s k a datum were made as an i n t e r i m s o l u t i o n t o reduce some d i s t o r t i o n s i n t h e northwest s e c t i o n o f N o r t h A m e r i c a . T h e r e f o r e NAD27-ALASKA was used f o r t h e d a t a collection i n this project. The t r a n s f o r m a t i o n o f c o o r d i n a t e s f o r a s e t o f c o n t r o l p o i n t s between d i f f e r i n g datums i s not an easy p r o c e s s . The NAD27 datum can be d e s c r i b e d a c c u r a t e l y w i t h o n l y f i v e p a r a m e t e r s (Magellan 1990). The c o o r d i n a t e s used t o d e s c r i b e a s u r v e y monument however, a r e t h e r e s u l t o f a l e a s t s q u a r e s adjustment. I n d i v i d u a l c o n t r o l p o i n t s a l s o s u f f e r t h e problems of b l u n d e r s o r l o c a l d i s t o r t i o n s . The t r a n s f o r m a t i o n s o f t w a r e s u p p l i e d by B.C. M i n i s t r y o f Crown Lands a p p l i e s a seven parameter t r a n s f o r m a t i o n . A n o t h e r program t h e n computes a p o l y n o m i a l d i s t o r t i o n model t o remove most o f t h e r e m a i n i n g d i s t o r t i o n . ( F a r l e y and J u n k i n s 1990). I t i s recommended t h a t t h e i n v e r s e t r a n s f o r m a t i o n , from NAD83 t o NAD2 7, not be attempted. The M a g e l l a n r e c e i v e r w i l l d i s p l a y c o o r d i n a t e s and e l e v a t i o n s based on t h e datums. The t r a n s f o r m a t i o n w i t h i n ' the u n i t however, i s p r o b a b l y a s i m p l e t r a n s f o r m a t i o n between t h e e l l i p s o i d models used i n each datum. The e l e v a t i o n , when expressed i n metres above mean s e a - l e v e l , i s a l s o based on a model. The e l e v a t i o n as d i s p l a y e d , i s based on g e o i d s e p a r a t i o n s from t h e e l l i p s o i d based on a crude model. T h i s can be i n e r r o r o f up t o 5-metres (Magellan  1990). M a g e l l a n recommends t h a t the o p e r a t o r use the e l l i p s o i d h e i g h t and a p p l y the l o c a l g e o i d s e p a r a t i o n h e i g h t above e l l i p s o i d .  to  the  The o b j e c t i v e of t h i s s e c t i o n i s t o show how the s e l e c t i o n of d i f f e r i n g datums can a f f e c t the c o o r d i n a t e s of a p o s i t i o n  Method: The r e c e i v e r was s e t up on a s i n g l e l o c a t i o n t o r e c o r d 200 fixes. The p o s i t i o n was l o c a t e d a t 2849 Cambridge S t r e e t i n Vancouver B.C. The d a t a c o l l e c t i o n took p l a c e on March 12, 1991 from 22:57-23:33 UTC. The average p o s i t i o n a l d i l u t i o n of p r e c i s i o n (PDOP) f o r the s e s s i o n was 3.3. PDOP i s a measure of the s t r e n g t h of the geometry of the s a t e l l i t e constellation. The UTM zone was 10. The a v e r a g i n g f e a t u r e of the r e c e i v e r was used t o c a l c u l a t e an average p o s i t i o n from the 200 f i x e s . The data b u f f e r was then u p l o a d e d t o a p e r s o n a l computer f o r c o n v e r s i o n . C o o r d i n a t e s e t 1 was produced by f i r s t p a s s i n g the raw b u f f e r f i l e t o the program RE4MAT87 s u p p l i e d by the m a n u f a c t u r e r . The datum s e l e c t e d was NAD27-Alaska and h e i g h t above the g e o i d . The c o n v e r t e d f i l e was t h e n p a s s e d onto the program GPSDXF, w r i t t e n by the a u t h o r , t o c a l c u l a t e averaged p o s i t i o n s . C o o r d i n a t e s e t 2 was receiver.  copied  from the d i s p l a y of  I t i s the average of the 200  fixes.  the The  receiver  o n l y d i s p l a y s e l e v a t i o n above mean s e a - l e v e l . C o o r d i n a t e s e t 3 was c a l c u l a t e d w i t h GPSDXF from the d a t a f i l e based on NAD27-Alaska based w i t h h e i g h t above the e l l i p s o i d f o r the e l e v a t i o n .  C o o r d i n a t e s e t 4 was c o p i e d from t h e d i s p l a y o f t h e r e c e i v e r i n NAD27. C o o r d i n a t e s e t 5 was c a l c u l a t e d i n t h e same manner as c o o r d i n a t e s e t 3, b u t u s i n g WGS84 as t h e datum. C o o r d i n a t e s e t 6 was c a l c u l a t e d i n t h e same manner as s e t 1 but u s i n g WGS84. C o o r d i n a t e s e t 7 was c a l c u l a t e d i n t h e same manner as s e t 2 but u s i n g NAD83. C o o r d i n a t e s e t 8 was c o p i e d from t h e d i s p l a y o f t h e r e c e i v e r u s i n g NAD83. Results : Table 1-1 Comparison of coordinates of one location using d i f f e r e n t datums Magellan NAV 1000 PRO Set  Easting  Northing  Elev  1  NAD27-ALSKA g e o i d / c a l c  496778  5459156  66  2  NAD27-ALSKA g e o i d / d i s p l a y  496778  5459156  66  3  NAD27-ALSKA  496778  5459156  48  4  NAD27/geoid/display  496782  5459156  48  5  WGS84-ellip/calc  496688  5459353  66  6  WGS84-geoid/calc  496688  5459353  66  7  NAD83-qeoid/calc  496690  5459350  66  8  NAD83-geoid/display  496691  5459350  66  197  18  ellip/calc  Range i n p o s i t i o n ( m e t r e s ) A l l measurements a r e i n metres.  90  The e l e v a t i o n of the p o i n t , as s u r v e y e d monument was 43.33m  from a NAD27  Discussion: A comparison between the f i r s t two s e t s o f c o o r d i n a t e s , suggests t h a t the c a l c u l a t i o n and d i s p l a y w i t h i n the r e c e i v e r agree w i t h the r e s u l t s from GPSDXF as p e r f o r m e d on a p e r s o n a l computer. The p o s i t i o n , as determined i n NAD27 i n s e t 4 v e r s u s t h a t d e t e r m i n e d by NAD27-Alaska, shows a s h i f t i n c o o r d i n a t e s d e s c r i b i n g the p o s i t i o n . The s h i f t from 2 t o 4 i s 4-metres i n the E a s t i n g but no s h i f t i n the N o r t h i n g . The comparison between s e t 1 and s e t 6 show a l a r g e s h i f t between the g e o c e n t r i c WGS84 and the c o n v e n t i o n a l NAD27. T h i s amounts t o a n e g a t i v e 90-m s h i f t i n the E a s t i n g and p o s i t i v e s h i f t of 197-m i n the N o r t h i n g . The comparison of s e t 1 and 7 i l l u s t r a t e s a l a r g e d i s c r e p a n c y i n c o o r d i n a t e s . The s h i f t i s -88-m i n t h e E a s t i n g and 194-m i n the N o r t h i n g . An example of how a u s e r might e x p e r i e n c e t h i s s h i f t i s by comparing t h e c o o r d i n a t e s of a p o i n t i n Vancouver on a NAD27 M i n i s t r y of F o r e s t s , f o r e s t i n v e n t o r y map, and a M i n i s t r y of Crown Lands TRIM map based on NAD83. T h i s s h i f t v a r i e s as one moves around t h e province. I t appears t h a t the g e o i d a l h e i g h t i s i n s e n s i t i v e t o t h e datum s e l e c t e d on the r e c e i v e r . I f e l l i p s o i d h e i g h t i s s e l e c t e d i n RE4MAT87, the h e i g h t above the e l l i p s o i d i s 18metres g r e a t e r than the g e o i d a l h e i g h t . T h e r e f o r e the model i n t h e M a g e l l a n r e c e i v e r e s t i m a t e s the e l l i p s o i d - g e o i d s e p a r a t i o n i n Vancouver t o be 18m based on NAD27. The  method t h e M a g e l l a n r e c e i v e r uses t o c a l c u l a t e t h e h e i g h t above s e a - l e v e l based on t h e e l l i p s o i d , i s c o n s i s t e n t among the datums chosen. The e l l i p s o i d - g e o i d s e p a r a t i o n (1989) can be e x p r e s s e d a s :  according  to  Hein,  ^  N = h - H where: N i s t h e s e p a r a t i o n i n metres h i s t h e e l e v a t i o n from t h e e l l i p s o i d H i s the orthometric  height  (above  sea-level)  The s e p a r a t i o n , based on t h e Rapp 78 g e o i d model a t 49.375°N and 236.625° (123.375° W) would be: N = 3.40m NAD27 N = -15.73m NAD83 The e l l i p s o i d - g e o i d model w i t h i n t h e r e c e i v e r i s i n e r r o r by 21.4m as compared t o t h e f i g u r e s i n NAD27. The r e c e i v e r model i s i n e r r o r by o n l y 2.27m when NAD83 i s used. If the height  above e l l i p s o i d was used w i t h t h e l o c a l  e l l i p s o i d - g e o i d separation,  t h e r e s u l t would be:  h - N = H 48 - 3.4 = 44.6m w h i c h compares f a v o r a b l y w i t h t h e s u r v e y e d e l e v a t i o n o f 43.33m.  Conclusion: The datum i n w h i c h t h e c o o r d i n a t e s a r e d i s p l a y e d has a s i g n i f i c a n t e f f e c t on t h e p o s i t i o n i n d i c a t e d on t h e e a r t h ' s s u r f a c e . To a c h i e v e t h e a c c u r a c y i n h e r e n t i n a GPS f i x , t h e datums and method o f e x p r e s s i n g t h e e l e v a t i o n , between t h e map and r e c e i v e r d i s p l a y must be i d e n t i c a l . To a c h i e v e a c c u r a t e o r t h o m e t r i c h e i g h t s , t h e e l e v a t i o n s as d i s p l a y e d by the r e c e i v e r , and c a l c u l a t e d by t h e program RE4MAT87, s h o u l d be compared o n l y w i t h e l e v a t i o n s on maps based on NAD83. I t would be p r e f e r a b l e t o do a l l h e i g h t c a l c u l a t i o n s based on the e l l i p s o i d and s u p p l y a l o c a l e l l i p s o i d - g e o i d s e p a r a t i o n .  CHAPTER 2 AÇÇyRAÇY - INTRQPgÇTIQN  mus  Introduction: To a d d r e s s t h e q u e s t i o n o f t h e a c c u r a c y i n GPS, some s t u d y of s t a t i s t i c s and geodesy i s r e q u i r e d . Geodesy i s " t h a t b r a n c h o f a p p l i e d mathematics which d e t e r m i n e s , by o b s e r v a t i o n and measurement, t h e s i z e and shape o f t h e e a r t h , t h e c o o r d i n a t e s o f p o i n t s , t h e l e n g t h and d i r e c t i o n of l i n e s on t h e e a r t h ' s s u r f a c e . . . . " (Ewing and M i t c h e l l 1970).  X - t r u e mean 0 sample mean F i g u r e 2-1 P r e c i s i o n and A c c u r a c y F i g u r e 2 - l A a p r e c i s e sample mean t o e s t i m a t e  t h e t r u e mean  with a large bias. F i g u r e 2 - l B an i m p r e c i s e sample mean t h a t e s t i m a t e s  the true  mean more a c c u r a t e l y The t r a d i t i o n a l method of e x p l a i n i n g a c c u r a c y i n s t a t i s t i c s , i s t o e x p l a i n t h e p r e c i s i o n of t h e o b s e r v a t i o n s ,  and t h e  b i a s o f t h e sample mean from t h e t r u e mean. i l l u s t r a t e s t h e s e concepts.  F i g u r e 2-1  A l t h o u g h knowing t h e magnitude and d i r e c t i o n o f t h e b i a s i n the c a l c u l a t e d p o s i t i o n i s i m p o r t a n t , i t i s beyond t h e scope of t h i s s t u d y . The reasons a r e i n d i c a t e d i n C h a p t e r 1. That i s , GPS c a l c u l a t e s p o s i t i o n s based on t h e WGS84-NAD83 ellipsoid. C o o r d i n a t e s f o r a c o n t r o l p o i n t need t o be based on NAD83. U n f o r t u n a t e l y , because o f u n a c c e p t a b l e d i s t o r t i o n s i n t r i a l s f o r B.C., t h e l e a s t squares adjustment f o r NAD83 c o o r d i n a t e s have not been r e l e a s e d f o r B r i t i s h Columbia. T h e r e f o r e , t h e c o o r d i n a t e s t h a t would bê g i v e n f o r a c o n t r o l monument would be i n NAD27 o r a p r e l i m i n a r y adjustment o f NAD83. A p p r o x i m a t i o n s o f t h e datum s h i f t c o u l d be made, b u t these would be i n v a l i d when t h e o f f i c i a l c o o r d i n a t e s a r e made p u b l i c . I t was f e l t t h a t e s t i m a t i n g the p r e c i s i o n over a p e r i o d , by d i f f e r e n t r e c e i v e r s , u s i n g d i f f e r e n t s a t e l l i t e s would p r o v i d e a s a t i s f a c t o r y d e s c r i p t i o n o f t h e system's a c c u r a c y . In r e l a t i v e , o r d i f f e r e n t i a l p o s i t i o n i n g , t h e a b s o l u t e a c c u r a c y i s not u s u a l l y a f a c t o r . The c o o r d i n a t e o f t h e c o n t r o l monument i s g i v e n by t h e u s e r . I t may be based on any datum. The c o r r e c t e d p o s i t i o n o f t h e remote r e c e i v e r i s based on t h e c o o r d i n a t e s g i v e n t o t h e base s t a t i o n . The accuracy of d i f f e r e n t i a l p o s i t i o n i n g p e r t a i n s t o the vector between t h e two s t a t i o n s . RMS error: I n a l l cases, t h e t r u e u s e r p o s i t i o n i s assumed t o be t h e average o f t h e p o s i t i o n f i x e s . The e r r o r v e c t o r i s c a l c u l a t e d f o r each p o s i t i o n from t h e t r u e u s e r p o s i t i o n . The RMS i s t h e square r o o t of t h e average o f t h e s q u a r e s o f the l e n g t h s o f t h e e r r o r v e c t o r s .  (2-2)  where x i s t h e E a s t i n g component o f t h e e r r o r v e c t o r , y i s t h e N o r t h i n g component o f t h e e r r o r v e c t o r . A n o t h e r d e f i n i t i o n by Lachappele (1991) i s t h a t 2D RMS i s square r o o t o f t h e sums o f t h e v a r i a n c e s i n t h e E a s t i n g and Northing. PDOP and UERE The use o f a r e c e i v e r f o r f i e l d n a v i g a t i o n , o r r e c o r d i n g t h e p o s i t i o n of a feature, u s u a l l y requires the estimated a c c u r a c y o f t h e c o o r d i n a t e s g i v e n by t h e r e c e i v e r . The c o n f i d e n c e a u s e r can put i n t o t h e p o s i t i o n f i x i s i n d i c a t e d by t h e PDOP. The PDOP i s a s c a l a r t h a t i s used t o m u l t i p l y the " i i s e r ^.quivalent £ange ^ r r o r " (UERE) t o a r r i v e a t t h e r o o t mean square (rms) e r r o r of t h e p o s i t i o n . The UERE i s t h e sum of t h e e r r o r s t h a t a r e c e i v e r e n c o u n t e r s when c a l c u l a t i n g a pseudo-range. The pseudo-range i s t h e d i s t a n c e c a l c u l a t e d between t h e r e c e i v e r and a s a t e l l i t e . The range o f t h e u s e r from t h e s a t e l l i t e , p l a c e s t h e u s e r on a sphere encompassing t h e s a t e l l i t e , ( w i t h r a d i u s e q u a l t o the pseudo-range). The r e c e i v e r needs t o o b t a i n pseudoranges from f o u r s a t e l l i t e s t o c a l c u l a t e a p o s i t i o n f i x . The range i s p r e f a c e d w i t h -pseudo" because t h e range c a l c u l a t e d i s not t h e a c t u a l range from t h e u s e r t o t h e satellite. The range must be c o r r e c t e d by t i m e (the t i m e d i f f e r e n c e between t h e GPS time and t h e c l o c k i n s i d e t h e r e c e i v e r ) w h i c h i s a f u n c t i o n o f t h e e x t r a s a t e l l i t e (e.g. 4 s a t e l l i t e s f o r 3 D ) . I f t h e e x t r a s a t e l l i t e i s n o t used, the t i m e b i a s can cause e r r o r s o f hundreds o f k i l o m e t r e s ( W e l l s , ^ ^ 1986).  The PDOP i s e s s e n t i a l l y an i n d e x o f t h e s t r e n g t h o f t h e geometry o f t h e s a t e l l i t e s . Since the o r b i t s of the s a t e l l i t e s a r e s t a b l e , t h e PDOP can be c a l c u l a t e d b e f o r e venturing i n t o the f i e l d . The most d e s i r a b l e geometry would be t h r e e s a t e l l i t e s e q u a l l y spaced 10° above t h e h o r i z o n , and one s a t e l l i t e d i r e c t l y overhead ( U n f o r t u n a t e l y t h i s geometry i s t h e worst f o r s i g n a l p e n e t r a t i o n o f t h e atmosphere, landscape and v e g e t a t i o n ) . The PDOP o f a p o s i t i o n i s u s u a l l y saved as an a t t r i b u t e o f t h e p o s i t i o n f i x i n a GPS r e c e i v e r . According t o Leick(1990) the equation f o r e r r o r i n p o s i t i o n i s given as: s = DOP x So  (2-1)  where S Q i s t h e s t a n d a r d d e v i a t i o n o f t h e o b s e r v e d pseudo ranges, s i s t h e s t a n d a r d d e v i a t i o n o f t h e component i n q u e s t i o n (e.g. 2 D p o s i t i o n ) . The s t a n d a r d d e v i a t i o n s o f the pseudo-ranges a r e determined by t h e system e r r o r s , a t m o s p h e r i c d e l a y s and r e c e i v e r n o i s e . The d i l u t i o n o f p r e c i s i o n (DOP) can be c a l c u l a t e d from t h e p o s i t i o n o f t h e s a t e l l i t e s i n r e l a t i o n t o t h e u s e r . The DOP can be c a l c u l a t e d f o r v e r t i c a l DOP, g e o m e t r i c DOP, time DOP and p o s i t i o n DOP. The S Q i s d i f f i c u l t t o determine when w i t h t h e r e c e i v e r used i n t h i s s t u d y . I n t h e M a g e l l a n r e c e i v e r o n l y t h e r e s u l t a n t p o s i t i o n i s g i v e n : t h e pseudo-range d a t a cannot be a n a l y z e d . S e l e c t i v e a v a i l a b i l i t y (SA) i s t h e method i n w h i c h t h e U.S. m i l i t a r y w i l l deny a c c u r a t e p o s i t i o n i n g t o u n a u t h o r i z e d u s e r s (see Appendix D ) . P a r k i n s o n and F i t z g i b b o n (1987), e s t i m a t e t h e UERE t o be 6.7-metres w i t h o u t SA t u r n e d on. T h i s i n c r e a s e s t o 20.8-metres w i t h SA e n a b l e d . The r a n g i n g e r r o r s t y p i c a l l y v a r y by a f a c t o r of two t o t h r e e . E r r o r s  c o n t r i b u t i n g t o t h e UERE can v a r y w i d e l y , b u t u s u a l l y have a compensating e f f e c t . W e l l s , ^ 1 (1986) e s t i m a t e s t h a t t h e i o n o s p h e r i c d e l a y b i a s i s 150-metres a t t h e h o r i z o n and d e c r e a s e s t o 50-metres when t h e s a t e l l i t e i s a t t h e z e n i t h . The Troposphere i n t r o d u c e s a b i a s o f 20-metres a t 10^ above t h e h o r i z o n , w h i l e d e c r e a s i n g t o 2-metres a t t h e z e n i t h . The DOP e f f e c t may v a r y by a f a c t o r o f t e n o r more. To achieve a p r e c i s e p o s i t i o n i t i s best t o c o l l e c t data d u r i n g a t i m e o f low PDOP. F o r example u s i n g e q u a t i o n 2-2: PDOP= 2, UERE = 6 m 3D P o s i t i o n a l e r r o r = 2 x 6 3D P o s i t i o n a l e r r o r = 12-m 3D rms The e r r o r o f a p o s i t i o n i n t h e example i s 12 metres rms i n 3 d i m e n s i o n s . T h i s can be i n t e r p r e t e d as t h e s t a n d a r d d e v i a t i o n i n the p o s i t i o n . S i x t y - e i g h t percent of the o b s e r v a t i o n s used t o determine t h e mean p o s i t i o n can be found w i t h i n 12-metres of t h e average p o s i t i o n . I n o t h e r words a sphere w i t h a r a d i u s of 12-metres would c o n t a i n 68 p e r c e n t o f t h e o b s e r v a t i o n s . Some e r r o r s can be modeled o r d i f f e r e n c e d out, however, t h e PDOP i s a s e p a r a t e e f f e c t .  Terms used i n describing accuracy The  statistics  c a l c u l a t e d by GPSDXF a r e based on an i n t e r n a l  memo o f M a g e l l a n  Systems C o r p o r a t i o n  (Magellan 1990) .  These  include : C i r c u l a r Error Probable (CEP): i s t h e r a d i u s o f t h e c i r c l e c e n t r e d on t h e mean p o s i t i o n . The c i r c l e c o n t a i n s one h a l f t h e p o s i t i o n f i x e s t h a t a r e used t o c a l c u l a t e t h e mean position. I n o t h e r words a c i r c l e w i t h 50% p r o b a b i l i t y .  Spherical Error Probable (SEP): i s t h e r a d i u s o f t h e s p h e r e c e n t r e d on t h e mean p o s i t i o n . The sphere c o n t a i n s one h a l f the p o s i t i o n f i x e s t h a t a r e used t o c a l c u l a t e t h e mean position. Mean Radial Deviation: i s t h e average l e n g t h o f t h e e r r o r vectors  where  from t h e mean p o s i t i o n .  x i s t h e E a s t i n g component o f t h e e r r o r v e c t o r , y i s t h e N o r t h i n g component o f t h e e r r o r v e c t o r .  T h i s term i s p r o b a b l y t h e e a s i e s t t o v i s u a l i z e . I t answers the q u e s t i o n o f : "on average, how f a r a r e t h e f i x e s from t h e mean p o s i t i o n ? " ppm: p a r t s p e r m i l l i o n . The use v a r i e s 1) When a b s o l u t e a c c u r a c y i s g i v e n , ppm i s t h e r a t i o o f t h e e r r o r i n p o s i t i o n to the r a d i u s of the earth. I t i s used i n GPS t o d e s c r i b e the e r r o r o f a s i n g l e p o s i t i o n on t h e r e f e r e n c e e l l i p s o i d . 2) ppm: i s a l s o used when d e s c r i b i n g t h e d i f f e r e n c e between positions. The number then r e f e r s t o t h e r a t i o o f e r r o r i n measurement o f t h e d i s t a n c e between p o i n t s , and t h e d i s t a n c e between t h e p o i n t s . I t i s used i n d i f f e r e n t i a l GPS t o d e s c r i b e t h e e r r o r between p o i n t s . The measure o f a c c u r a c y t o be used, i s d e t e r m i n e d by t h e end use o f t h e a c c u r a c y e s t i m a t e . I f t h e u s e r was u s i n g GPS t o t a r g e t f i r e r e t a r d a n t drops, CEP might be a u s e f u l description. I f t h e u s e r i s g o i n g t o p l o t an e r r o r e l l i p s e , the s t a n d a r d d e v i a t i o n f o r each component would be u s e f u l . The most common form o f s t a t i n g t h e a c c u r a c y i n t h e  l i t e r a t u r e i s 2D and 3D RMS, e s p e c i a l l y i n d i f f e r e n t i a l positioning. "How f a r i s t h e c a l c u l a t e d p o s i t i o n from t h e ' t r u e ' p o s i t i o n ? " i s u s u a l l y asked. Due t o t h e u n c e r t a i n t y o f t h e " t r u e " p o s i t i o n as d i s c u s s e d e a r l i e r , t h e means t o t e s t t h e b i a s o f a mean p o s i t i o n a r e beyond t h e scope o f t h i s s t u d y . Assxunptions: The a s s u m p t i o n i s made t h a t t h e p r e c i s i o n o f a measurement d e t e r m i n e s i t s a c c u r a c y . That i s , t h e t r u e s e t o f c o o r d i n a t e s i s assumed t o be t h e averaged p o s i t i o n . The d e s c r i p t i o n o f t h e v a r i a t i o n o f a s e t o f p o s i t i o n means w i l l i n d i c a t e t h e a c c u r a c y of t h e system. T h i s would be t h e equivalent t o repeatable accuracy. The s p r e a d o f f i x e s about t h e mean i s assumed t o be c i r c u l a r n o r m a l l y d i s t r i b u t e d . A c c o r d i n g t o Lachappele(1991) t h e p r o b a b i l i t y o f a c i r c l e w i t h a r a d i u s o f RMS v a r i e s from to  STD(Northing) = STD(Easting) STD(Northing) = 10 x STD(Easting)  where STD i s t h e s t a n d a r d d e v i a t i o n . appreciable difference  p= 0.63 p= 0.68 T h i s i s n o t an  and t h i s assumption w i l l  c a l c u l a t i o n of t h e d e s c r i p t i o n  of e r r o r .  s i m p l i f y the  Purpose : The p u r p o s e of t h i s s e c t i o n of the study was t o d e t e r m i n e the a c c u r a c y of the M a g e l l a n r e c e i v e r over a p e r i o d of t i m e , w i t h d i f f e r i n g s a t e l l i t e c o n f i g u r a t i o n s . An attempt i s a l s o made t o d e t e r m i n e the number of f i x e s needed t o o b t a i n a r e q u i r e d c o n f i d e n c e i n one's p o s i t i o n . T h i s s t u d y was r e s t r i c t e d t o s i n g l e p o i n t or autonomous p o s i t i o n i n g , and autonomous p o s i t i o n i n g w i t h a v e r a g i n g . Method: The M a g e l l a n 1000 NAV PRO was used f o r d a t a c o l l e c t i o n . The M a g e l l a n r e c e i v e r was a t t a c h e d t o an e x t e r n a l antenna. The e x t e r n a l antenna was a t t a c h e d t o a p o l e 5-metres h i g h , t o 2849 Cambridge S t r e e t , Vancouver, B.C.. The s i t e i s shown i n F i g u r e 3-1. I t was f e l t the antenna extended h i g h enough t o be f r e e from m u l t i p a t h e f f e c t s . Data were c o l l e c t e d from O c t o b e r 19 t o October 30, 1990. SA was not a c t i v a t e d during t h i s period. A l l the f i l e s f o r the l o c a t i o n 2849 Cambridge S t . were c o p i e d i n t o one f i l e . T h i s r e s u l t e d i n 1676 u s a b l e positions. P o s i t i o n s were then e l i m i n a t e d a c c o r d i n g t o the PDOP, i n decrements of one. For i n s t a n c e , a l l o b s e r v a t i o n s when the PDOP was g r e a t e r than 5 were e l i m i n a t e d f o r the c l a s s PD0P=5. Results : When the GPS system i s f u l l y o p e r a t i o n a l , i t i s r e a s o n a b l e t o expect t h a t most o b s e r v a t i o n s w i l l be t a k e n when the PDOP  i s l e s s t h a n s i x (Lachappele 1991). When t h e c o n s t e l l a t i o n of s a t e l l i t e s i s complete, t h e r e w i l l be a t l e a s t 4, and u s u a l l y 6 s a t e l l i t e s above t h e h o r i z o n . I f one r e f e r s t o F i g u r e 3-2, i t can be deduced t h a t when t h e r e a r e a t l e a s t 4 s a t e l l i t e s a v a i l a b l e , t h e PDOP w i l l g e n e r a l l y be l e s s t h a n five. T h e r e f o r e , a c c o r d i n g t o F i g u r e 3-3, i f t h e PDOP i s l e s s than f i v e t h e 2D RMS would be 24-metres, based on 1033 o b s e r v a t i o n s . The 3D RMS would be 49.5-metres. That i s , one c o u l d expect t h a t when t h e PDOP i s l e s s t h a n 5 and u s i n g a s i n g l e p o s i t i o n f i x , one c o u l d l o c a t e o n e s e l f w i t h i n 24metres on t h e e a r t h ' s s u r f a c e 68% o f t h e t i m e . T h i s would be i n r e l a t i o n t o t h e mean p o s i t i o n of many f i x e s f o r t h a t particular receiver. T h i s assumes t h a t t h e p o s i t i o n s t h a t comprise t h e mean a r e d i s t r i b u t e d i n a c i r c u l a r normal pattern. An a p p l i c a t i o n o f t h i s s t a t i s t i c would be t o d e s c r i b e repeatability. That i s , i f a u s e r were t o t r y t o r e t u r n t o a l o c a t i o n p r e v i o u s l y determined by t h e r e c e i v e r , how c l o s e c o u l d one r e t u r n t o t h e p o s i t i o n . I f u s e r s r e l i e d on a s i n g l e f i x , and t r i e d t o r e t u r n t o t h e p o i n t 100 t i m e s , t h e y would be w i t h i n 24-metres of t h e averaged l o c a t i o n 68 t i m e s .  F i g u r e 3-1 P o s i t i o n i n g o f GPS antenna a t 2849 Cambridge S t .  Sta 1  Eu!.''lr'tQ  Norttihg  Monument 1123  496 87&126  5 459 139^14  35^  Monunenf 3689  496 7 0 6 ^  6 459 137^1  42^1  Base at 2849  496 791^13  5 459 167^11  43^  Bevotlon  Surveyed a n d d r o w n b y Tim Shannon Sept 24, 1990  F i g u r e 3-2 An example o f PDOP v s . Time. 16 s a t e l l i t e  constellation  10 8  6 4  r i  1  _-  E  3  u  12  18  24  Time (lirs)  10 8  \-  6 4  •._  2 0 12  18  Time (hrs)  (adopted from Lochappelie, 1991)  24  F i g u r e 3-3 RMS e r r o r and number o f o b s e r v a t i o n s a v a i l a b l e v s . PDOP Autonomous s i n g l e p o i n t p o s i t i o n i n g at 2849 Cambridge S t .  I f a u s e r were t o r e l y s o l e l y on a s i n g l e p o s i t i o n , t h e range o f p o s i t i o n s o l u t i o n s t h a t can be encountered i s i l l u s t r a t e d i n T a b l e 3-1. Table 3-1 Ranges i n measurements with d i f f e r i n g PDOP PDOP  Ob s  Range E  Range N  11 10 9 8 7 6 5 4 3  1676 1574 1503 1401 1346 1206 1003 787 297  283 191 191 191 191 191 131 113 69  482 195 191 191 191 191 149 136 78  Range Elev. 1521 535 535 478 478 451 451 449 155  A l l measurements a r e i n metres. When t h e PDOP e x c l u s i o n l i m i t was s e t a t 11, t h e range o f p o s s i b l e p o s i t i o n f i x e s was as h i g h as 283-metres i n t h e E a s t i n g , 482-metres i n t h e N o r t h i n g , and 1521-metres i n t h e elevation. T a b l e 3-2 shows t h e s t a n d a r d e r r o r when t h e assumption i s made t h a t each s e s s i o n i s a randomly s e l e c t e d event, and t h a t t h e u s e r would encounter t h e same p r o p o r t i o n o f ranges of PDOP as encountered i n t h i s study The s t a n d a r d e r r o r o f t h e mean i s t h e s t a n d a r d d e v i a t i o n o f a s e t o f sample means. The s t a n d a r d e r r o r o f t h e mean i s e s s e n t i a l l y c o n s t a n t i n t h i s data s e t . The c o n f i d e n c e t h e u s e r would have i n a mean p o s i t i o n , would t h e r e f o r e remain constant.  Table 3-2 Standard error(m) of the mean i n position with d i f f e r i n g PDOP PDOP 11 10 9 8 7 6 5 4 3  Easting 0.5 0.4 0.4 0.5 0.5 0.5 0.5 0. 5 0.6  Northing 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0. 8  Elevation 1.7 1.4 1.4 1.4 1.3 1.3 1.3 1.5 1.6  a l l measurements a r e i n metres. Averaging: A v e r a g i n g s e v e r a l f i x e s w i l l g i v e a u s e r a mean p o s i t i o n and a s t a t i s t i c on how v a r i a b l e t h e o b s e r v a t i o n s were i n c a l c u l a t i n g the p o s i t i o n . I n Chapter 2, an a s s u m p t i o n was made t h a t t h e o b s e r v a t i o n s would f o l l o w a c i r c u l a r normal d i s t r i b u t i o n . F i g u r e 3-4 i l l u s t r a t e s how t h i s a s s u m p t i o n h o l d s d u r i n g a p e r i o d o f low PDOP. F i g u r e 3-5 i l l u s t r a t e s how t h i s assumption can be v i o l a t e d when t h e d a t a c o l l e c t i o n t a k e s p l a c e d u r i n g a p e r i o d o f h i g h PDOP. The c o r r e l a t i o n c o e f f i c i e n t between t h e E a s t i n g and N o r t h i n g c o o r d i n a t e s i n F i g u r e 3-5 i s 0.95. T h i s i l l u s t r a t e s t h e t r u e meaning o f PDOP. PDOP i s d e s c r i b e d i n Chapter 2 as an i n d e x o f t h e expected v a r i a b i l i t y o f t h e d a t a f o r simplicity. I t i s a c t u a l l y t h e sum o f t h e d i a g o n a l elements o f t h e t r a n s f o r m e d c o v a r i a n c e m a t r i x . I t i s based on t h e ' p o s i t i o n of the s a t e l l i t e s i n r e l a t i o n t o the user. The d a t a p l o t t e d i n F i g u r e s 3-5 and 3-6 a r e from t h e same d a t a c o l l e c t i o n s e s s i o n . F i g u r e 3-5 c o n t a i n s a l l 199 r e c o r d s from t h e s e s s i o n . The average PDOP i s 26. F i g u r e 3-6 c o n t a i n s t h e f i x e s t h a t were r e c o r d e d when t h e PDOP was  l e s s than 10. The average PDOP i s 5. The d i f f e r e n c e s i n the means o f p o s i t i o n s i s t a b u l a t e d i n T a b l e 3-3. A l t h o u g h the s c a t t e r o f each f i l e l o o k s d i f f e r e n t , and t h e p r e c i s i o n of t h e d a t a v a r i e s by a f a c t o r of s i x (2D RMS), t h e mean p o s i t i o n s c a l c u l a t e d do not d i f f e r a g r e a t d e a l . The mean E a s t i n g s d i f f e r by o n l y 16-metres, t h e N o r t h i n g s by 19metres and t h e e l e v a t i o n s by 51- metres. The d i f f e r e n c e i n p o s i t i o n i n 3D space i s 556 metres. Table 3-3 Error i n mean positions from long term average p o s i t i o n Trial  Fixes  Avg. PDOP  Error in Easting (m)  Error i n Northing (m)  Error i n E l e v . (m)  Error i n 3D position (m)  1  199  26  23  4  18  29  1-  41  5  7  23  34  42  edited LT  2355  LT i s t h e l o n g term averaged p o s i t i o n . The l o n g - t e r m average i s assumed t o be c o r r e c t . The h i g h PDOP s e s s i o n d i f f e r s from a l o n g term average o f l e s s than the low PDOP e d i t e d f i l e . This suggests t h a t i s would n o t be prudent t o d e l e t e h i g h PDOP f i x e s from a f i l e , t o i n c r e a s e a c c u r a c y . The p r e c i s i o n o f t h e e d i t e d f i l e i s a t l e a s t f i v e t i m e s g r e a t e r than t h e u n e d i t e d f i l e , but i t i s no more a c c u r a t e . F i g u r e 3-5 i l l u s t r a t e s how an autonomous p o s i t i o n can d i f f e r i n a s i n g l e d a t a s e s s i o n when the Average PDOP i s 26. The p r o b a b i l i t y i s s m a l l , but two autonomous p o s i t i o n s from t h e same r e c e i v e r w i t h i n an hour c o u l d d i f f e r by 1167-metres E a s t i n g , 398-metres N o r t h i n g and 1813-metres i n e l e v a t i o n .  F i g u r e 3-4 P o s i t i o n f i x e s o f S e s s i o n C0426t-1. Low PDOP (average 3.4)  5459250  "T  I  I  I  I  I  r  ^  ^  ^  5459200 -  5459150 -  .1!.,;::.. • ; • ":'"i  •  .".'••'l'îii  5459100 -  5459050  5459000 I  1  1  ^  ^  EASTING  F i g u r e 3-5 P o s i t i o n f i x e s o f S e s s i o n C0426t-2. High PDOP (average 261 5459400  5459300 -  5459200 -  5459100 -  5459000 -  5458900 496000  496500  497000  EASTING  497500  F i g u r e 3-6 P o s i t i o n s o f s e s s i o n means w i t h PDOP <10  5459190  5459180 -  5459170 -  5459160 -  5459150 -  5459140 496770  496780  496790  496800  EASTING  F i g u r e 3-7 P o s i t i o n s o f s e s s i o n means w i t h PDOP <6 5459185  5459180 -  5459175 -  5459170 -  5459165 -  5459160 496770  496775  496780 EASTING  496785  496790  F i g u r e 3-7 i s a s c a t t e r o f 16 s e s s i o n means t a k e n when t h e PDOP was l e s s than 6. The s c a t t e r appears randomlydistributed. The p r o p e r t i e s o f t h e means o f d a t a s e s s i o n s a r e d i s p l a y e d i n T a b l e 3-4. Table 3-4 Means of data sessions at 2849 Cambridge St. E  N  Elev.  StdE  StdN  StdElev  Min  496772  5459162  19.8  9.1  10  24.7  Max  496787  5459184  90  34.8  30.1  56.4  Range  16  21.2  70.2  25.7  20.1  31.7  Std  4.7  5.3  17.5  15.7  15.8  37.8  Mean  496780  5459174  53.1  6.7  6.3  8.4  The s t a n d a r d d e v i a t i o n o f t h e means i s 4.7-metres i n t h e E a s t i n g 5.3-metres i n t h e N o r t h i n g and 17.5-metres i n t h e elevation. The v a r i a b i l i t y of t h e e l e v a t i o n means i s t h r e e times t h a t o f t h e v a r i a b i l i t y o f t h e E a s t i n g and N o r t h i n g . The a p p l i c a t i o n o f these d e s c r i p t o r s i s i n r e t u r n i n g t o a g i v e n l o c a t i o n . I f u s e r s were u s i n g t h e same r e c e i v e r t o r e t u r n t o a l o c a t i o n 100 times, and averaged s e v e r a l f i x e s , t h e y c o u l d expect t o r e t u r n t o w i t h i n a p p r o x i m a t e l y 5-metres of t h e t r u e p o s i t i o n 68 t i m e s . Discussion: The q u e s t i o n i s f r e q u e n t l y asked o f t h e u l t i m a t e a c c u r a c y o f the system. What would be t h e a c c u r a c y i f t h e u s e r was t o occupy a s i t e c o n t i n u o u s l y w i t h a r e c e i v e r ? T a b l e 3-2 shows t h a t one would d e r i v e l i t t l e b e n e f i t by i n c r e a s i n g t h e number o f o b s e r v a t i o n s w i t h no r e g a r d t o PDOP windows. I f the u s e r c o l l e c t e d p o s i t i o n s when t h e PDOP was l e s s than 4, o n l y 1003 f i x e s need be c o l l e c t e d t o d e r i v e t h e same c o n f i d e n c e i n p o s i t i o n , as i f 1676 f i x e s were c o l l e c t e d w i t h o u t r e g a r d t o PDOP.  C o n v e r s e l y , one c o u l d argue t h a t i t i s n o t w o r t h t h e t r o u b l e to e d i t f i x e s w i t h a h i g h PDOP. As suggested i n F i g u r e 3-3, the RMS seems t o i n c r e a s e more d r a m a t i c a l l y a t a PDOP g r e a t e r t h a n 10. Below a PDOP o f 10 t h e curve has o n l y a s l i g h t downward s l o p e . Only i f one c o u l d a c h i e v e a l o n g p e r i o d o f PDOP below 3 would t h e r e be a l a r g e drop i n t h e RMS. Johannessen (1987) s t a t e s t h a t even w i t h t h e f u l l 21 s a t e l l i t e c o n s t e l l a t i o n , t h e r e i s o n l y a 70 p e r c e n t p r o b a b i l i t y t h a t a l l s a t e l l i t e s w i l l be o p e r a t i n g p r o p e r l y . T h i s w i l l produce times when t h e PDOP w i l l go i n f i n i t e , though o n l y f o r a s h o r t time. These outages a l o n g w i t h sunspot a c t i v i t y and b a t t e r y l i f e i n a r e c e i v e r , would make i t d i f f i c u l t t o c o l l e c t a continuous stream o f q u a l i t y f i x e s to f i n d one's "exact " p o s i t i o n . Averaging : The use o f an average of s e v e r a l f i x e s t o d e r i v e a c o o r d i n a t e o f a p o s i t i o n g r e a t l y enhances t h e a c c u r a c y o f the s t a t e d c o o r d i n a t e s . This i s e s p e c i a l l y true i n periods of h i g h PDOP. The v a r i a b i l i t y i n e l e v a t i o n means i s t h r e e times t h e mean i n t h e E a s t i n g and N o r t h i n g d i r e c t i o n . This i s i n h e r e n t i n t h e GPS system. The r e a s o n f o r t h e poor p r e c i s i o n i n e l e v a t i o n i s t h e r e q u i r e d geometry o f t h e s a t e l l i t e s t o o b t a i n a f i x . The e l e v a t i o n would have s i m i l a r v a r i a b i l i t y i f the receiver could receive s i g n a l s from a s a t e l l i t e a t z e n i t h , and one d i r e c t l y b e h i n d t h e r e c e i v e r on t h e o t h e r s i d e o f t h e e a r t h . U n f o r t u n a t e l y , t h e s i g n a l s do n o t p e n e t r a t e t h e e a r t h .  Conclusion and Recommendations : The p o s i t i o n f i x g i v e n by a r e c e i v e r i s v a r i a b l e . W i t h 9 hours o f c o l l e c t i o n time over t w e l v e days and PDOP l e s s t h a n 5, t h e i n d i c a t e d a c c u r a c y i s a p p r o x i m a t e l y 14-metres s t a n d a r d d e v i a t i o n i n t h e E a s t i n g , 15-metres i n t h e N o r t h i n g and 42-metres i n e l e v a t i o n . T h i s i s w i t h i n t h e s p e c i f i c a t i o n s as s t a t e d i n t h e m a n u f a c t u r e r ' s b r o c h u r e s . The a b s o l u t e a c c u r a c y as compared t o t h e t r u e mean i s unknown. The u s e r can expect v a r i a t i o n s o f hundreds o f metres i n r e t u r n i n g t o a spot i f o n l y a s i n g l e p o s i t i o n f i x i s used t o l o c a t e a p o s i t i o n on t h e ground. I t would be b e t t e r t o use an average o f a t l e a s t 30 f i x e s t o o b t a i n a c o o r d i n a t e f o r a location. I f a u s e r c o l l e c t e d s e s s i o n means of a t l e a s t 30 o b s e r v a t i o n s , t h e e x p e c t a t i o n would be t o r e p e a t t h e c o o r d i n a t e s more p r e c i s e l y . The s e s s i o n means o f 16 d a t a s e s s i o n s shows a s t a n d a r d d e v i a t i o n o f 4.7-metres i n t h e E a s t i n g , 5.3-metres i n t h e N o r t h i n g , and 17.5- metres i n t h e elevation.  CHAPTER 4 - RSCEIVER NOISE MP DIFFERENTIAL PgSITIQNINg Introduction: A code based GPS r e c e i v e r , l i k e t h e one used i n t h i s s t u d y , u t i l i z e s pseudorandom n o i s e codes t o c a l c u l a t e a range from a GPS s a t e l l i t e t o t h e r e c e i v e r antenna. The r e c e i v e r then i n t e r s e c t s t h e ranges from a m u l t i p l e o f s a t e l l i t e s t o calculate a position f i x . The e r r o r s i n f i n d i n g a range t o a s a t e l l i t e stem from many s o u r c e s . They can be broken down i n t o two t y p e s ; 1) e r r o r s c o r r e c t a b l e by d i f f e r e n t i a l p o s i t i o n i n g and 2) e r r o r s not c o r r e c t a b l e by d i f f e r e n t i a l p o s i t i o n i n g . The e r r o r s i n range, d e s c r i b e d as RMS e r r o r , w i t h s e l e c t i v e a v a i l a b i l i t y activated are: Correctable Clock Ephemeris Ionosphere Troposphere Selective A v a i l a b i l i t y TOTAL  3.0 m 2.7 m 8.2 m 1.8m 27.4m 28.9 m  Not Correctable Receiver noise Multipath TOTAL  9.1 m 3.0 m 9.6m  The numbers do not add up because t h e t o t a l s a r e based on rms c a l c u l a t i o n s .  These numbers a r e s u p p l i e d by t h e  m a n u f a c t u r e r f o r t h e NAV 1000 PRO r e c e i v e r , and do not a p p l y to a l l receivers  and d a t a s e s s i o n s  (Magellan 1990).  The e r r o r s i n the f i r s t group are determined t o be c o r r e c t a b l e by d i f f e r e n t i a l p o s i t i o n i n g because t h e y a r e e r r o r s t h a t a r e e x p e r i e n c e d by r e c e i v e r s i n the same r e g i o n . T h i s r e g i o n can be up t o 300 km wide. M u l t i p a t h e f f e c t s a r e the r e s u l t of s i g n a l s bouncing o f f s u r f a c e s and a r r i v i n g a t the antenna l a t e r than i f they a r r i v e d d i r e c t l y from t h e satellite. R e c e i v e r n o i s e i s the l a r g e s t e r r o r s o u r c e when d i f f e r e n t i a l p o s i t i o n i n g i s used. The method of d i f f e r e n t i a l p o s i t i o n i n g i n the r e c e i v e r s used i n t h i s s t u d y i s based on e r r o r s i n c a l c u l a t e d p o s i t i o n s , d i f f e r e n c e d a g a i n s t a known p o s i t i o n . An e r r o r v e c t o r from the r e c e i v e r l e f t on a known p o s i t i o n i s a p p l i e d t o the c a l c u l a t e d p o s i t i o n of the remote r e c e i v e r . To p e r f o r m the d i f f e r e n c i n g , t h e two r e c e i v e r s must be u s i n g the same s a t e l l i t e s t o c a l c u l a t e p o s i t i o n s . They a l s o must o b t a i n the p o s i t i o n f i x e s at the same i n s t a n t . t o ensure t h a t the r e c e i v e r s a r e s y n c h r o n i z e d , the u s e r must s e l e c t t h e s y n c h r o n i z e d mode on each r e c e i v e r . T h i s r e s t r i c t s the r e c e i v e r t o c a l c u l a t e a f i x every 20 seconds. If left in u n s y n c h r o n i z e d mode, each r e c e i v e r would r e c o r d a f i x e v e r y 11 seconds. The main r e a s o n time s y n c h r o n i z a t i o n was used by t h e m a n u f a c t u r e r , was t o d e f e a t SA (Magellan 1990). SA implements a q u i c k changing a l g o r i t h m t o d i t h e r i n f o r m a t i o n coming from the s a t e l l i t e s . T h i s d e n i e s the u s e r t h e a c c u r a c y i n h e r e n t t o the system. Thus, i f s i g n a l s between a f i x e d and remote r e c e i v e r are t o be d i f f e r e n c e d , t h a t i s they a r e t o share the same e r r o r s , they need t o be t a k e n a t p r e c i s e l y the same t i m e . D u r i n g d a t a c o l l e c t i o n s e s s i o n s , SA was not e n a b l e d by the U.S. m i l i t a r y . Since the other e r r o r f a c t o r s v a r y s l o w l y throughout the day, s t r i c t time s y n c h r o n i z a t i o n i s not needed t o a c h i e v e r e a s o n a b l e a c c u r a c y . However, s o f t w a r e p r o v i d e d by the m a n u f a c t u r e r can o n l y d e a l w i t h s t r i c t time s y n c h r o n i z a t i o n .  Objective: To d e t e r m i n e r e c e i v e r n o i s e between t h e two r e c e i v e r s used i n t h i s study. An a d d i t i o n a l study was made t o d e t e r m i n e i f t h e r e was an advantage i n u s i n g u n s y n c h r o n i z e d f i x e s from each r e c e i v e r t o p e r f o r m d i f f e r e n t i a l c o r r e c t i o n s , when SA is inactive. Scope: The g e o m e t r i c d i l u t i o n of p r e c i s i o n (GDOP) i s a composite i n d e x o f t h e s t r e n g t h of t h e s a t e l l i t e geometry on t h e p o s i t i o n and time e s t i m a t e ( L e i c k 1990). The p o s i t i o n a l d i l u t i o n o f p r e c i s i o n (PDOP) i s a composite o f t h e e x p e c t e d v a r i a n c e i n t h e N o r t h i n g , E a s t i n g and e l e v a t i o n . A l t h o u g h the v a r i a n c e f o r each component of t h e PDOP can be a n a l y z e d , i t i s d o u b t f u l t h a t t h e i n f o r m a t i o n would be used i n p o s i t i o n i n g i n f o r e s t r y . The g o a l o f a data c o l l e c t i o n s e s s i o n i s t o d e r i v e a p r e c i s e p o s i t i o n i n a l l dimensions. The lower t h e PDOP, t h e more p r e c i s e t h e p o s i t i o n . T h e r e f o r e t h e PDOP, which i s t h e i n d e x u s u a l l y p r o v i d e d by r e c e i v e r s , w i l l be used f o r t h i s study. There i s no d i f f e r e n t i a l p o s i t i o n i n g t a k i n g p l a c e i n t h i s study. Both r e c e i v e r s a r e measuring t h e same p o s i t i o n simultaneously. The d i f f e r e n t i a l a c c u r a c y i s i n d i c a t e d by the d i f f e r e n c e i n p o s i t i o n c a l c u l a t e d by t h e two r e c e i v e r s a t t h e same s p o t . Method: The two r e c e i v e r s were p l a c e d on t h e r o o f o f 2849 Cambridge S t r e e t . Data were c o l l e c t e d i n 3D mode, u s i n g t h e same f o u r s a t e l l i t e s f o r b o t h r e c e i v e r s . The l o n g e s t d a t a c o l l e c t i o n  time was attempted f o r each s e s s i o n (200 p o i n t s ) . Data were c o l l e c t e d from A p r i l 22, 1991 t o May 3, 1991. SA was b e l i e v e d t o be i n a c t i v e . The antennae o f t h e r e c e i v e r s were a p p r o x i m a t e l y 3 0-cm a p a r t and were above t h e peak o f t h e r o o f . I t was assumed t h a t b o t h r e c e i v e r s would s h a r e t h e same, i f any, m u l t i p a t h e f f e c t . S e s s i o n s were c a r r i e d out by s e t t i n g t h e r e c e i v e r s i n s y n c h r o n i z e d mode. A f i x i s determined every twenty seconds when t h e s y n c h r o n i z e o p t i o n i s s e l e c t e d . The f i x e s a r e t h e n matched t o t h e n e a r e s t second. The s e s s i o n s were then r e p e a t e d w i t h t h e r e c e i v e r s s e t t o u n s y n c h r o n i z e d mode. The r e c e i v e r s c a l c u l a t e d f i x e s a p p r o x i m a t e l y every e l e v e n seconds. The u n s y n c h r o n i z e d s e s s i o n s were s t a r t e d s i m u l t a n e o u s l y , and used t h e same satellites. The f i l e s were then e d i t e d t o c o n t a i n o n l y f i x e s t a k e n w i t h i n t h e same minute. The f i x e s s h o u l d be w i t h i n t h e same minute because t h e r e c e i v e r s were a t t h e same l o c a t i o n and were t u r n e d on a t t h e same time. The d a t a were a n a l y z e d u s i n g GPSDXF (see appendix C ) . F i l e s were e d i t e d t o ensure t h a t t h e f i x e s between t h e two r e c e i v e r s were s y n c h r o n i z e d i n time. F i l e s t h a t c o n t a i n e d p o s i t i o n s where t h e PDOP was g r e a t e r than t e n , were e d i t e d and a n a l y z e d a g a i n . Results and Discussion: The r e s u l t s o f t h e a n a l y s i s a r e d i s p l a y e d i n T a b l e 4-1. The f i r s t two columns c o n t a i n t h e average d i f f e r e n c e s i n t h r e e dimensions between t h e s e s s i o n means of b o t h r e c e i v e r s . There were e l e v e n s e s s i o n s . There was no e d i t i n g f o r PDOP. The l a s t two columns c o n t a i n t h e same d a t a t h a t has been e d i t e d t o remove f i x e s o b t a i n e d when t h e PDOP was g r e a t e r  than ten. There are fewer s e s s i o n averages, because some s e s s i o n s c o n t a i n e d no f i x e s when the PDOP was l e s s t h a n t e n . Table 4-1 Comparison of accuracy between synchronized unsynchronized averaged positions  n  vs. <10  Synched <10  Unsynched All  Synched All  Unsynched  11  11  8  9  11.3  7.5  6.1  4.8  Avg  PDOP  Avg  Diff  E  3.1  2.1  -1  1.5  Avg  Diff  N  1.5  3.2  -1.2  -3.2  Avg  Diff  Elev  6.1  1.7  -1.4  -0.1  Avg  ABS  E  5.6  3.9  2.2  2.8  Avg  ABS  N  4.5  3.5  2.8  4.1  Avg  ABS  Elev  11.5  8.7  6.0  7.3  Std E  11.9  4.3  2.9  3.5  Std  N  5.8  4.8  3.7  4.7  Std  Elev  19.4  12  7.6  9.3  2D  RMS  13 .2  6.5  4.7  5.9  3D  RMS  23 . 5  13.6  8.9  11  where : - a l l measurements are i n metres, n - i s the number of data s e s s i o n s . Avg D i f f N - i s the average d i f f e r e n c e i n the N o r t h i n g between the two r e c e i v e r s . Avg D i f f E - i s the average d i f f e r e n c e i n the E a s t i n g between the two r e c e i v e r s . Avg D i f f E l e v - the average d i f f e r e n c e i n E l e v a t i o n between the two r e c e i v e r s . Avg ABS - i s the average of the a b s o l u t e v a l u e s of d i f f e r e n c e s between the two r e c e i v e r s . S t d - i s the s t a n d a r d d e v i a t i o n . 2D RMS - i s the r o o t mean squared e r r o r i n two d i m e n s i o n s . The f i l e s t h a t c o n t a i n e d p o s i t i o n s w i t h h i g h PDOPs a l s o c o n t a i n e d the most v a r i a t i o n between the two r e c e i v e r s . The d a t a c o n t a i n s the confounding f a c t o r of d i f f e r i n g PDOPs between s e s s i o n s . The l a s t two columns i n T a b l e 4-1 show  t h a t u n s y n c h r o n i z e d f i x e s , may determine more p r e c i s e d i f f e r e n t i a l p o s i t i o n s . This i s e v i d e n c e d by t h e l o w e r RMS v a l u e s f o r u n s y n c h r o n i z e d s e s s i o n s , a l t h o u g h t h e average PDOP v a l u e s a r e h i g h e r . T a b l e 4-2 c o n t a i n s two d i f f e r e n t i a l s e s s i o n s w i t h d i f f e r i n g PDOPs i n s y n c h r o n i z e d mode. The d i f f e r e n c e i n t h e ranges o f the f i x e s between t h e s e s s i o n s i s l a r g e . The d a t a show t h a t d i f f e r e n t i a l p o s i t i o n i n g i s a f f e c t e d by a h i g h PDOP. However, t h e e r r o r o f t h e averaged d i f f e r e n c e d p o s i t i o n when the PDOP i s h i g h i s not n e a r l y as extreme as t h e range i n the autonomous p o s i t i o n s . The t a b l e c o n t a i n s o n l y one comparison between s e s s i o n s . The e r r o r s between t h e two r e c e i v e r s a r e p r o b a b l y due t o t h e d i f f e r e n c e s i n t h e r e c e i v e r c l o c k s . The method o f d i f f e r e n t i a l used i n t h i s study does n o t remove r e c e i v e r clock biases. Double-differenced s o l u t i o n s u s i n g pseudoranges w i l l reduce t h e r e c e i v e r n o i s e , by removing t h e receiver clock biases. Table 4-2 Comparison of ranges i n fixes between synchronized high PDOP vs. low PDOP sessions Session  Obs.  Avg.  Rge. N  Rge. Elev  Dif f E  Dif f  Diff  PDOP  Rge E  N  Elev  56  112  185  0.2  3  5.8  C0423t-1  198  3 .45  C0426t-2  199  26.5  1167  398  1813  40  13  62 .7  7.7  20.8  3.5  9.8  200  4.3  10.8  Ratio  A l l measurements i n metres except PDOP. Rge denotes range i n t h e component d i r e c t i o n . F i g u r e 4-1 i l l u s t r a t e s t h a t t h e d i f f e r e n c e d a c c u r a c y i n t h e N o r t h i n g , E a s t i n g and E l e v a t i o n dimensions, i s n o t s t r o n g l y c o r r e l a t e d t o PDOP. The N o r t h i n g i s somewhat c o r r e l a t e d t o  PDOP (0.23). The c o r r e l a t i o n o f t h e N o r t h i n g t o PDOP i s p r o b a b l y a p e c u l i a r i t y of t h e data s e t c o l l e c t e d . This i s i n d i c a t e d i n F i g u r e 4-2 which i s p l o t o f a l l s e s s i o n s . The s p r e a d i n t h e f i x e s i n t h e E a s t i n g i s about 3.5 times as l a r g e as t h a t i n t h e N o r t h i n g . T h i s spread may change d i r e c t i o n s , depending on t h e s a t e l l i t e geometry. The PDOP between two s e s s i o n s may be o f t h e same magnitude, but t h e v a r i a b i l i t y i n one d i r e c t i o n may be much g r e a t e r than a n o t h e r . The l i n e a r e f f e c t s i n F i g u r e 4-2 a r e from i n d i v i d u a l d a t a s e s s i o n s where t h e PDOP was h i g h . I f a l l the h i g h PDOP f i x e s a r e removed, t h e s c a t t e r appears more n o r m a l l y d i s t r i b u t e d . Only two dimensions a r e p l o t t e d t o i l l u s t r a t e t h e spread i n f i x e s because a t h r e e d i m e n s i o n a l p l o t i s hard t o analyze. There may be some advantage t o a n a l y z i n g t h e components o f the p r e d i c t e d PDOP. F o r example: i f one d e t e r m i n e d an average p o s i t i o n when t h e E a s t i n g was h i g h l y v a r i a b l e , b u t the N o r t h i n g was f a i r l y s t a b l e , t h e r e may be some advantage to r e t u r n i n g t o t h e l o c a t i o n when t h e p r e d i c t e d E a s t i n g component was t o e x p e r i e n c e a low v a r i a t i o n . The p l o t t e d d a t a may resemble F i g u r e 4-2, but t h e average p o s i t i o n may be q u i t a c c u r a t e . T h i s may a l l o w t h e user t o c o l l e c t v a l u a b l e d a t a when t h e PDOP was h i g h , but t h e E a s t i n g component low, and use lower PDOP windows f o r c o l l e c t i n g fresh data.  F i g u r e 4-1 E r r o r i n d i f f e r e n t i a l l y c o r r e c t e d p o s i t i o n v s . PDOP  ELEV EASTING NORTHING  20 r  PDOP  F i g u r e 4-2 S c a t t e r o f N o r t h i n g Vs. E a s t i n g . A l l o b s e r v a t i o n s a t 28 Cambridge S t .  5459500 6459400 5459300 g  5459200  I-  Q  5459100 5459000 6458900  -  6458800 495500 496000 496500 497000 497500 498000 EASTING  Conclusions The v a r i a t i o n i n t r o d u c e d by t h e r e c e i v e r i s u n c o r r e l a t e d w i t h o t h e r r e c e i v e r s t h a t may be p a i r e d f o r d i f f e r e n t i a l p o s i t i o n i n g . The magnitude o f t h e v a r i a t i o n i n t h i s s t u d y i n unsynchronized d i f f e r e n t i a l p o s i t i o n i n g i n three d i m e n s i o n s , was e s t i m a t e d t o be 8.9-metres RMS, when t h e PDOP i s l e s s than 10. T h i s i n c r e a s e d t o 11-metres when t h e f i x e s were s y n c h r o n i z e d between t h e two r e c e i v e r s . S y n c h r o n i z e d f i x e s t a k e 180% more time than u n s y n c h r o n i z e d f i x e s i n t h e r e c e i v e r used. T h e r e f o r e , when SA i s i n a c t i v e , t h e r e i s no advantage t o s y n c h r o n i z i n g t h e f i x e s between r e c e i v e r s . However, t h e r e c e i v e r s must c o l l e c t t h e d a t a t o be d i f f e r e n c e d a t t h e same t i m e . F u r t h e r study i n t o t h e components o f PDOP may r e v e a l means of improving the e f f i c i e n c y of data c o l l e c t i o n .  Introduction: C h a p t e r 4 i n d i c a t e s the expected a c c u r a c y i n r e l a t i v e positioning. However, the a c c u r a c y of a p o s i t i o n d e t e r m i n e d by a base r e c e i v e r r e l a t i v e t o a remote r e c e i v e r , i s not a d d r e s s e d . The e f f e c t of m u l t i p a t h from r e c e i v e r s a t d i f f e r e n t s i t e s i s a f a c t o r i n the e r r o r i n d i s t a n c e between t h e two r e c e i v e r s . I n Chapter 4, the r e c e i v e r s were a t the same l o c a t i o n and i t was assumed they would e x p e r i e n c e the same m u l t i p a t h e f f e c t s . There i s s t i l l a r e q u i r e m e n t t o t e s t t h e a c c u r a c y of r e l a t i v e p o s i t i o n i n g between two p o i n t s at d i f f e r e n t p o i n t s at d i f f e r e n t s i t e s .  Objective: To t e s t the a c c u r a c y of the M a g e l l a n NAV 1000 Pro GPS r e c e i v e r i n d i f f e r e n t i a l mode and t o compare the a c c u r a c i e s of d i f f e r e n t i a l and autonomous modes. Scope: T h i s t e s t i s l i m i t e d t o a s i n g l e channel r e c e i v e r u s i n g code based p o s i t i o n i n g . Code based s o l u t i o n s r e l y on c o r r e l a t i n g t h e pseudorandom n o i s e code t h a t modulates the GPS s i g n a l . By c o r r e l a t i n g the s i g n a l s generated w i t h i n the r e c e i v e r , w i t h those r e c e i v e d by a s a t e l l i t e , the r e c e i v e r may c a l c u l a t e the time o f f s e t and thus the range of t h e s a t e l l i t e t o the antenna. Much more a c c u r a t e ranges can be c a l c u l a t e d by d i f f e r i n g the phases of the c a r r i e r s i g n a l between two r e c e i v e r s . However, phase based measurements r e l y on c o n t i n u o u s phase l o c k f o r the d u r a t i o n of t h e d a t a  c o l l e c t i o n session. This i s v i r t u a l l y impossible t o achieve i n a f o r e s t e d environment. SA was not a c t i v a t e d d u r i n g data c o l l e c t i o n . The t e s t i n v o l v e s r e p e a t e d sampling w i t h r e s p e c t t o t h e same two points. Method: A base r e c e i v e r was e s t a b l i s h e d a t 2849 Cambridge S t r e e t i n Vancouver, B.C. An e x t e r n a l antenna was used t o c o l l e c t t h e p o s i t i o n a l d a t a . The c o o r d i n a t e s o f t h e antenna were e s t a b l i s h e d w i t h a t h e o d o l i t e and e l e c t r o n i c d i s t a n c e measuring equipment. Survey monuments from t h e C i t y o f Vancouver were used as a c o n t r o l . F i g u r e 3-1 i l l u s t r a t e s the r e l a t i o n s h i p of t h e p o s i t i o n s s t u d i e d . The remote l o c a t i o n was e s t a b l i s h e d over monument 1123. S i n c e a l l p o s i t i o n a l a c c u r a c i e s a r e expressed i n r e l a t i v e terms, no attempt was made t o convert between datums. NAD 27 was used throughout t h e study. Data c o l l e c t i o n took p l a c e from October 19 t o O c t o b e r 30, 1990. Data s e s s i o n s were based on c o l l e c t i n g a t l e a s t 30 o b s e r v a t i o n s a t t h e remote s t a t i o n . A l l s e s s i o n s where t h e average PDOP was g r e a t e r than 6 were e x c l u d e d . Observations p e r s e s s i o n v a r i e d because t h e number o f u s a b l e o b s e r v a t i o n s c o u l d n o t be r e l i a b l y p r e d i c t e d . The d a t a were p r o c e s s e d u s i n g GPSDXF. The d a t a s e s s i o n summaries were imported i n t o Q u a t t r o PRO where t h e e r r o r s i n d i s t a n c e s were c a l c u l a t e d . The s u r v e y e d d i s t a n c e between t h e base s t a t i o n and monument 1123 was taken t o be t r u e . The d i s t a n c e between averaged p o s i t i o n s i n a d i f f e r e n t i a l s e s s i o n were d i f f e r e n c e d t o  c a l c u l a t e t h e GPS d i s t a n c e s o l u t i o n . The base s t a t i o n p o s i t i o n was assumed t o be t r u e . The e r r o r term r e p o r t e d i s the v e c t o r d i s t a n c e from t h e d i f f e r e n t i a l l y c o r r e c t e d GPS remote p o s i t i o n t o t h e t r u e p o s i t i o n o f t h e monument. Results: T a b l e 5-1 c o n t a i n s e r r o r s e x p e r i e n c e d i n two and t h r e e d i m e n s i o n s . The PDOP averaged 3.6 f o r a l l s e s s i o n s , and h i g h e s t s e s s i o n average r e c o r d e d was 6.  Relative  Table 5-1 accuracy between Monument 1123 and base s t a t i o n R e l a t i v e 2D (m)  R e l a t i v e 3D (m)  sessions  10  10  Minimum  2.2  2.9  Maximum  14.8  17  Mean  6.0  10.1  Std  4.17  4.96  The mean d i f f e r e n c e between a d i f f e r e n t i a l l y c o r r e c t e d p o s i t i o n and t h e t r u e p o s i t i o n i s 6-metres i n two dimensions and 10.1-metres i n t h r e e dimensions. F i g u r e 5-1 c o n t a i n s a s c a t t e r o f t h e e r r o r i n t h r e e dimensions v e r s u s PDOP. The sampling s p r e a d o f PDOP i s l i m i t e d , however, i t i s apparent t h a t t h e e r r o r i n a d i f f e r e n t i a l l y c o r r e c t e d p o s i t i o n i s not c o r r e l a t e d t o PDOP, p r o v i d e d t h e PDOP i s l e s s than 6. The c o r r e l a t i o n o f PDOP to e r r o r i s c o n t a i n e d i n Table 5-2. Table 5-2 Pearson correlation c o e f f i c i e n t : Error vs. PDOP  PDOP  2D  3D  Easting  Northing  Elev.  0.22  -0 . 05  -0.07  -0.17  0.23  The Pearson c o r r e l a t i o n c o e f f i c i e n t i s 1.0 when t h e y v a r i a b l e i s c o m p l e t e l y dependent on t h e x v a r i a b l e . T a b l e 5-2 i l l u s t r a t e s t h e weak c o r r e l a t i o n o f e r r o r w i t h PDOP. The s t r o n g e s t c o r r e l a t i o n i s i n t h e e l e v a t i o n t o PDOP, w h i c h i s t h e component most s e n s i t i v e t o s a t e l l i t e geometry. The c o e f f i c i e n t of determination describes the r a t i o of the v a r i a t i o n i n t h e dependent v a r i a b l e , over t h e dependent v a r i a b l e . I t i s t h e square o f t h e c o r r e l a t i o n c o e f f i c i e n t . F i v e p e r c e n t o f t h e v a r i a t i o n i n t h e e l e v a t i o n c o u l d be e x p l a i n e d by t h e v a r i a t i o n i n t h e PDOP. F i g u r e 5-2 c o n t a i n s a s c a t t e r p l o t o f t h e e r r o r o f t h e component o f a p o s i t i o n f o r each s e s s i o n . The e r r o r component i s from t h e t r u e p o s i t i o n and not t h e o v e r a l l mean. The s c a t t e r seems e v e n l y d i s t r i b u t e d about z e r o . I f the mean o f t h e s e s s i o n means i s unbiased, t h e e x p e c t e d sum of t h e e r r o r terms i s zero. However, t h e sums o f t h e e r r o r terms a r e -13.6 m E a s t i n g , -22.7 m N o r t h i n g , and 23.8m i n elevation. A l t h o u g h t h e e r r o r s appear t o be c y c l i c a l between s e s s i o n s , i t i s p r o b a b l y c o i n c i d e n t a l . The magnitude of t h e e r r o r i s u n e x p l a i n e d by t h e datum problem. R e l a t i v e d i s t a n c e s s h o u l d be s i m i l a r between datums, e s p e c i a l l y f o r s h o r t v e c t o r s (as compared t o t h e r a d i u s o f t h e e a r t h ) . The e x p l a n a t i o n o f t h e b i a s p r o b a b l y l i e s i n t h e s a m p l i n g times. The windows o f s a t e l l i t e a v a i l a b i l i t y e n s u r e d t h a t sampling would t a k e p l a c e w i t h s i m i l a r c o n f i g u r a t i o n s o f satellites. A b i a s f o r one s e s s i o n would not be compensated f o r by a b i a s i n t h e o p p o s i t e d i r e c t i o n f o r a d i f f e r e n t s a m p l i n g time.  The mean of t h e t e n s e s s i o n averages y i e l d s a d i f f e r e n c e from t h e s u r v e y e d p o s i t i o n o f 1.4-metres i n E a s t i n g , 2.5metres i n N o r t h i n g and 2.4-metres i n e l e v a t i o n . These component e r r o r s y i e l d e d an e r r o r i n p o s i t i o n o f 2.9-metres i n two d i m e n s i o n s and 3.7-metres i n t h r e e d i m e n s i o n s . The use o f r e l a t i v e p o s i t i o n i n g v e r s u s autonomous p o s i t i o n i n g i s compared i n Table 5-3. Both methods used a v e r a g i n g o f a t l e a s t 30 o b s e r v a t i o n s . Table 5-3 Accuracy of r e l a t i v e versus autonomous positioning. Method  2D RMS (m)  3D RMS (m)  Autonomous  7 .1  17.5  Relative  6.7  10. 6  The 95% c o n f i d e n c e r e g i o n f o r a d i f f e r e n t i a l s e s s i o n o f a t l e a s t 30 o b s e r v a t i o n s has a r a d i u s o f 13.4-metres. The 95% c o n f i d e n c e r e g i o n f o r an autonomous averaged p o s i t i o n i s 14.2-metres. Discussion: The use o f r e l a t i v e p o s i t i o n i n g y i e l d s a p o s i t i o n t h a t i s s l i g h t l y l e s s v a r i a b l e than u s i n g autonomous p o s i t i o n i n g w i t h a v e r a g i n g . The comparison i s r e s t r i c t e d t o t h e v a r i a b i l i t y o f t h e d e r i v e d averaged p o s i t i o n s . W i t h SA n o t a c t i v a t e d , t h e d i f f e r e n c e between t h e v a r i a b i l i t y between the two methods i s expected t o be s m a l l . When SA i s a c t i v a t e d , t h e use o f r e l a t i v e p o s i t i o n i n g w i l l become mandatory i n o r d e r t o remove t h e e f f e c t s o f t h e i n c r e a s e d e r r o r s added by t h e o p e r a t o r s o f GPS, and a c h i e v e a c c u r a c i e s of l e s s t h a n 100-metres.  F i g u r e 5-1 E r r o r from t r u e p o s i t i o n v s . PDOP i n 3D space. Positioning  Relative  2 0  Q  CO  O cc cc  UJ  F i g u r e 5-2 E r r o r from t r u e p o s i t i o n v s . S e s s i o n . R e l a t i v e  Positioning  2 0  1 0  i  E L E V A T I O N E A S T I N G  °  LU - 1 0  - 2 0  N O R T H I N G  ^  0  ^  1  '  2  '  3  '  4  '  5  '  6  S E S S I O N  1  7  I  8  I  9  I  10  s i n c e t h e base s t a t i o n s h o u l d be p l a c e d a t a known p o i n t i n r e l a t i v e p o s i t i o n i n g , t h e c o r r e c t e d remote s t a t i o n w i l l have any system b i a s e s removed. The autonomous averaged p o s i t i o n may be p r e c i s e but i t may c o n t a i n a l a r g e b i a s . Without u s i n g a d j u s t e d NAD83 maps, i t would be d i f f i c u l t t o t e s t this bias. However, t h e a n a l y s i s o f many averaged autonomous p o s i t i o n s taken over a p e r i o d o f a few weeks, i n d i c a t e t h a t an averaged p o s i t i o n does not become s i g n i f i c a n t l y more v a r i a b l e than one d i f f e r e n t i a l l y corrected. The use o f r e l a t i v e p o s i t i o n i n g , depends on a r e l i a b l e base station. R e l a t i v e p o s i t i o n i n g demands t h e e x t r a l o g i s t i c s of s t a r t i n g d a t a c o l l e c t i o n s e s s i o n s s i m u l t a n e o u s l y , and communication between t h e remote and base s t a t i o n s . I f care i s not t a k e n t o view t h e same s a t e l l i t e s s i m u l t a n e o u s l y , t h e r e may be no matched f i x e s t o p e r f o r m t h e c o r r e c t i o n s . F o r t u n a t e l y , i f no matches can be found between t h e base and the remote s t a t i o n s , an autonomous averaged p o s i t i o n can be used. Conclusions : The use o f d i f f e r e n t i a l p o s i t i o n i n g w i t h t h e equipment t e s t e d does n o t m e r i t the e x t r a l o g i s t i c a l e f f o r t . The enhancement o f a c c u r a c y i s s l i g h t . The m a r g i n a l i n c r e a s e i n a c c u r a c y does not e l e v a t e the survey t o a h i g h e r o r d e r . When SA i s a c t i v a t e d , f u r t h e r t e s t i n g s h o u l d be c a r r i e d o u t .  CHAPTER 6 UNDER CANOPY TRIALS Introduction The u t i l i t y o f GPS w i l l be c o n s t r a i n e d by the b l o c k a g e o f the s i g n a l s by topography and the a t t e n u a t i o n o f s i g n a l s due to t h e f o r e s t canopy. I n t h i s c h a p t e r , the s u c c e s s o f o b t a i n i n g p o s i t i o n f i x e s under a f o r e s t canopy i s investigated. The i s s u e o f whether the GPS s i g n a l p e n e t r a t e s a f o r e s t canopy has been addressed by G e r l a c h and Jasumbach (1989). U n f o r t u n a t e l y , the f o r e s t s they have s t u d i e d a r e l o c a t e d i n w e s t e r n Montana. These f o r e s t s are c h a r a c t e r i z e d by i n t e r i o r Douglas f i r (Pseudotsuga m e n z i e s i i (Mirb.) Franco) l o d g e p o l e p i n e (Pinus c o n t o r t a Dougl.) and ponderosa p i n e (Pinus ponderosae Laws.). The amount o f biomass o c c u p y i n g the s i t e s i s not r e p o r t e d , however, an e s t i m a t e would be 200 to 300 m3/ha i n the densest s t a n d s . Other a u t h o r s r e p o r t on the problems o f s i g n a l p e n e t r a t i o n of a f o r e s t canopy. However, they r a r e l y p r o v i d e any a n a l y s i s o f the problem. Newcomer (1990), r e p o r t s t h a t s a t e l l i t e v i s i b i l i t y i s a problem i n f o r e s t e d a r e a s . He s t a t e s t h a t the antenna cannot be taken i n t o a f o r e s t . This would b l o c k the s i g n a l and a l o s s o f s i g n a l l o c k would o c c u r , thus p r e v e n t i n g k i n e m a t i c s u r v e y s . In Z a i r e , W i l k i e (1990), found t h a t s i g n a l s were r e a d i l y a v a i l a b l e where openings were g r e a t e r than 0.125 ha and the a n g l e t o h o r i z o n r a r e l y exceeded 3 0°. A l t h o u g h g r e a t e r o c c u p a t i o n times were r e q u i r e d , p o s i t i o n s were o b t a i n e d when t h e a n g l e t o h o r i z o n exceeded 40° and canopy c l o s u r e reached 3 0 percent. F o r e s t gaps where canopy c l o s u r e exceeded 3 0 p e r c e n t and a n g l e t o h o r i z o n averaged more than 50°  g e n e r a l l y p r e c l u d e d a c q u i s i t i o n of a t h r e e o r f o u r - s a t e l l i t e , constellation. He c o n c l u d e s t h a t w a i t i n g f o r s a t e l l i t e s t o be more v i s i b l e when they a r e g r e a t e r than 70° above t h e horizon i s counterproductive. The g e o m e t r i c d i l u t i o n o f p r e c i s i o n d e t e r i o r a t e s when t h e s a t e l l i t e s c l u s t e r d i r e c t l y overhead. T h i s l e a d s t o i m p r e c i s e p o s i t i o n a l d a t a . The p r o b l e m o f f o l i a g e has been mentioned but r a r e l y has i t been s t u d i e d . Stratton the s u i t a b i l i t y o f GPS on r u r a l roads b u t b l o c k a g e i n an urban environment. M i n k e l  i n the l i t e r a t u r e , (1987) mentions encountered s i g n a l (1989) r e p o r t s t h e  l o s s o f phase l o c k due t o i n t e r m i t t e n t b l o c k a g e from nearby trees i n his t r i a l s . This l e d t o t h e e l i m i n a t i o n o f t h e a f f e c t e d s t a t i o n from t h e survey. Johannessen (1987) e x p r e s s e d c o n c e r n f o r s i g n a l b l o c k a g e and f o l i a g e a t t e n u a t i o n o f t h e s i g n a l . He c o n c l u d e s t h a t GPS f o r v e h i c l e m o n i t o r i n g would r e q u i r e t h e i n t e g r a t i o n o f a n o t h e r system such as a d i f f e r e n t i a l odometer. N o l a n and C a r p e n t e r (1988) r e p o r t on t h e problem of shadowing of GPS s i g n a l s i n an urban environment. They a t t r i b u t e some problems o f o b t a i n i n g a f i x t o a t t e n u a t i o n of t h e s i g n a l from f o l i a g e . Mooney (1985) r e p o r t s on urban t r i a l s w i t h t r e e l i n e d s t r e e t s o f oak p i n e and maple. S i g n a l a t t e n u a t i o n , under the t r e e s , was apparent w i t h t h e s i g n a l t o n o i s e r a t i o d r o p p i n g from 10 t o 7 dB when s a t e l l i t e e l e v a t i o n was l e s s than 40 degrees. French (1987) a l s o f i n d s t h a t GPS s h o u l d be i n t e g r a t e d w i t h another n a v i g a t i o n a l system due t o s i g n a l a b e r r a t i o n s due t o shadowing by b u i l d i n g s , b r i d g e s and f o l i a g e . K n o e r n s c h i l d , (1986) c l a i m s t h a t t h e GPS s i g n a l i s not a f f e c t e d by f o l i a g e but g i v e s no i n d i c a t i o n t h a t he has tested that claim. The q u e s t i o n o f t h e s u i t a b i l i t y o f u s i n g a s i n g l e c h a n n e l r e c e i v e r on t h e coast of B r i t i s h Columbia remains unanswered.  Scope of Study The s t u d y was l i m i t e d t o a s i n g l e channel GPS r e c e i v e r , u s i n g t h e pseudorandom n o i s e codes f o r o b t a i n i n g p o s i t i o n fixes. The o b j e c t i v e of the study was t o d e c i d e i f t h e r e c e i v e r was s u i t a b l e f o r p o s i t i o n i n g under a f o r e s t canopy i n the c o a s t a l r e g i o n of B r i t i s h Columbia. The p o s s i b i l i t y e x i s t s t o do an a n a l y s i s of the d a t a w i t h r e g a r d s t o the s a t e l l i t e geometry. However, no attempt a t s e p a r a t i n g the attempted d a t a s e s s i o n s based on s a t e l l i t e geometry was made. T h i s was o m i t t e d due t o the l o g i s t i c s of c o l l e c t i n g d a t a at s p e c i f i c times when t h e r e were o t h e r c o n s t r a i n t s on d a t a c o l l e c t i o n such as s h o r t v i e w i n g windows. I t i s u n l i k e l y t h a t a f o r e s t e r would c o n s u l t more than one o r two i n d i c e s t o d e c i d e whether t o attempt t o use GPS f o r a g i v e n p r o j e c t . An example of d a t a o r i n d i c e s t h a t may be c o n s i d e r e d a r e ; the p o s i t i o n a l d i l u t i o n of p r e c i s i o n , e l e v a t i o n of a s a t e l l i t e above the h o r i z o n and i n t e r v a l of an e f f e c t i v e window. No economic c r i t e r i a were examined i n t h i s study. Objectives 1) The f i r s t o b j e c t i v e of the study was t o f i n d the s u i t a b i l i t y of u s i n g a s i n g l e channel r e c e i v e r under v a r i o u s f o r e s t c a n o p i e s . The p r o b a b i l i t y of o b t a i n i n g a f i x under a canopy was t o be determined. 2) The second of o b j e c t i v e t h i s study was t o d e c i d e what a p p l i c a t i o n s i n f o r e s t r y s h o u l d be attempted w i t h a s i n g l e chann e l r e c e i v e r .  Methods and Procedures Introduction T r i a l s were conducted f o r k i n e m a t i c and f i x e d p o s i t i o n s . F i v e p l o t s were e s t a b l i s h e d t o t e s t t h e s i g n a l p e n e t r a t i o n under v a r i o u s f o r e s t canopies and c o n d i t i o n s . The s t u d y i n c l u d e d t r i a l s t o determine t h e p e n e t r a t i o n o f s i g n a l s under v a r i o u s crown c l o s u r e s , wet v e r s u s d r y c a n o p i e s , d i f f e r i n g s a t e l l i t e e l e v a t i o n s and antenna h e i g h t s . Data C o l l e c t i o n The d a t a c o l l e c t i o n took p l a c e from August t o November i n 1990. Data were c o l l e c t e d u s i n g t h e M a g e l l a n NAV 1000 PRO s i n g l e c h a n n e l sequencing r e c e i v e r . The r e c e i v e r b u f f e r was downloaded onto an IBM c o m p a t i b l e computer. Site Selection The U.B.C. M a l c o l m Knapp Research F o r e s t was used f o r canopy e f f e c t s t h e s t u d y . The f o r e s t i s l o c a t e d 40 k i l o m e t r e s east of t h e U n i v e r s i t y of B r i t i s h Columbia campus, i n Maple Ridge. A d e s c r i p t i o n of t h e p l o t s f o l l o w s and i s summarized i n T a b l e 6-1. P l o t 1 was i n t h e m i d d l e o f t h e road. I t was c o n s i d e r e d t h e control. I t d i d not have a c l e a r view t o t h e sky. The road r i g h t - o f - w a y was narrow (10m) w i t h t r e e s 14m - 27m i n h e i g h t on each s i d e . P l o t 2 was i n a p l a n t a t i o n of almost pure D o u g l a s - f i r . The t r e e s were pruned t o a h e i g h t of about 2-metres. T h i s a r e a  i s o f t e n c a l l e d t h e "Golf c o u r s e . " The canopy was c l o s e d w i t h crown c l o s u r e o f 100%. P l o t 3 was i n a n a t u r a l l y e s t a b l i s h e d second growth s t a n d o f D o u g l a s - f i r and Western hemlock. I t i s a dense s t a n d w i t h a low l i v e crown r a t i o and f u l l crown c l o s u r e . P l o t 4 was s i t u a t e d on a bench above p l o t 3. I t had been t h i n n e d i n 1983. The canopy was much more open t h a n p l o t 3. P l o t 5 was w i t h i n t h e same s t a n d as p l o t 4, however t h e p l o t was more open than p l o t 4. Table 6-1 Description of plots used at Malcolm Knapp Research Forest Plot  Description  Avg. DBH  Avg Ht.  Density  Volume  cm  m  stems/ha  m3 / ha  1  Road  _  _  _  2  G o l f Course  18 . 6  14  650  -  3  2nd gwth. natural  33 .4  26  365  278  4  2nd gwth.  37.2  26  276  267  33.1  26.8  279  214  spaced 5  2nd gwth. spaced  The " G o l f c o u r s e " was a l s o used t o t e s t t h e r e c e i v e r i n a k i n e m a t i c mode. T r a v e r s e s o f t h e area were p e r f o r m e d over a p e r i o d o f a week. Antenna h e i g h t was v a r i e d from h a n d h e l d (1.3-metres), t o 3-metres.  Procedures The almanac on t h e r e c e i v e r , which c o n t a i n s d a t a t o determine t h e p o s i t i o n o f t h e s a t e l l i t e s , (see appendix D) was used t o f i n d when a window o c c u r r e d f o r p o s i t i o n i n g i n t h r e e d i m e n s i o n s . An attempt was made t e n minutes a f t e r t h e b e g i n n i n g o f t h e window t o o b t a i n a p o s i t i o n f i x . For t h e f i x e d p l o t measurements, t h e r e c e i v e r was t u r n e d on at t h e p l o t and g i v e n 10 minutes t o s e a r c h f o r t h e satellites. I f l e s s than f o u r s a t e l l i t e s were found, t h e attempt was deemed t o have f a i l e d . Four s a t e l l i t e s a r e r e q u i r e d t o o b t a i n a 3-dimensional f i x . For t h e t r a v e r s e , t h e r e c e i v e r was a l l o w e d t o s e a r c h u n t i l a f i x was o b t a i n e d . T h i s was done i n an open g r a s s y a r e a near the f o r e s t e n t r a n c e . I f t h e r e c e i v e r l o s t l o c k on t h e s a t e l l i t e s w h i l e on t h e t r a v e r s e , t h e t r a v e r s e was s t o p p e d u n t i l a p o s i t i o n f i x was o b t a i n e d . A s e r i e s of traverses was r u n on t h e same course. Two r e c e i v e r s were used s i m u l t a n e o u s l y w i t h t h e antennas a t d i f f e r e n t h e i g h t s . A range p o l e was used t o e l e v a t e an e x t e r n a l antenna t o 3metres. The antenna a f f i x e d t o t h e s i d e o f t h e r e c e i v e r was used f o r t h e handheld h e i g h t of a p p r o x i m a t e l y 1.3-metres. The mode was s e l e c t e d on t h e r e c e i v e r , t o r e c o r d p o s i t i o n s i n 2D (3 s a t e l l i t e s - 2 d i m e n s i o n a l p o s i t i o n i n g ) o r 3D (4 s a t e l l i t e s 3 - d i m e n s i o n a l p o s i t i o n i n g ) . I n 2D t h e e l e v a t i o n was s u p p l i e d . The e l e v a t i o n used, v a r i e d from 80 t o 206- . metres. The  r e c e i v e r a l s o r e c o r d e d t h e time, and t h e s i g n a l q u a l i t y  of each s a t e l l i t e used f o r a f i x . T h i s was used t o f i n d t h e e l e v a t i o n o f t h e s a t e l l i t e s u s i n g t h e program O r b i t s e t . A  c o r r e l a t i o n was made between t h e e l e v a t i o n and t h e s i g n a l q u a l i t y . Results  of the s a t e l l i t e ,  S t a t i c tests The s i n g l e p o i n t t r i a l s suggest t h a t t h e canopy i s an e f f e c t i v e b a r r i e r t o GPS s i g n a l s . Table 6-2 summarizes t h e s u c c e s s r a t e o f o b t a i n i n g f i x e s under a canopy. T a b l e 6-3 compares t h e s u c c e s s of o b t a i n i n g f i x e s under d r y v e r s u s wet f o r e s t c a n o p i e s . The e f f e c t of t h e e l e v a t i o n o f t h e s a t e l l i t e on r e c e i v e d s i g n a l q u a l i t y i s a l s o e x p l o r e d . Column 1 d e s c r i b e s t h e p l o t number and t h e antenna h e i g h t used t o attempt t o c o l l e c t d a t a . Column 2 i s t h e t o t a l number o f f i x e s a c q u i r e d . Column 3 i s t h e p e r c e n t a g e o f t h e p o t e n t i a l number o f f i x e s t h a t c o u l d have been a c q u i r e d d u r i n g a s u c c e s s f u l data c o l l e c t i o n s e s s i o n . The p o t e n t i a l number o f f i x e s i s t h e number o f f i x e s t h a t would have been a c q u i r e d i f f i x e s were o b t a i n e d w i t h o u t i n t e r r u p t i o n d u r i n g a s u c c e s s f u l s e s s i o n . Column 4 i s t h e number o f s e s s i o n a t t e m p t s made a t t h e p a r t i c u l a r p l o t antenna h e i g h t c o m b i n a t i o n . Column 5 i s t h e number o f s u c c e s s f u l a t t e m p t s of a t l e a s t one f i x d u r i n g a data c o l l e c t i o n s e s s i o n . Column 6 i s t h e p e r c e n t a g e of s u c c e s s f u l s e s s i o n a t t e m p t s . Wet and d r y c a n o p i e s were compared f o r d a t a c o l l e c t e d a t p l o t 2 w i t h a 2-metre antenna h e i g h t . The mean p e r c e n t a c q u i r e d r e p r e s e n t s t h e average of t h e p e r c e n t o f s u c c e s s f u l f i x e s o f p o t e n t i a l f i x e s . The average of t h e p r o p o r t i o n s c o n t a i n mixed sample s i z e s .  Table 6-2 Under canopy single point acquisitions with varying antenna height Plot antenna h t .  # fixes  acquired  Attemp ts  Succès s  Success  P l o t 1 - 5m  122  70  8  8  100  P l o t 1 - 2m  38  95  1  1  100  P l o t 2 - 5m  358  57  9  6  67  P l o t 2 - 2m  172  40  9  6  67  P l o t 3 - 5m  0  0  7  0  0  P l o t 3 - 2m  0  0  1  0  0  P l o t 4 - 5m  0  0  7  0  0  P l o t 4 - 2m  18  17  2  1  50  P l o t 5 - 5m  0  0  7  0  0  P l o t 5 - 2m  0  0  2  0  0  1  2  3  4  5  6  %  %  Table 6-3 Percentage of successful/attempted fixes i n dry versus wet canopy Dry  Wet  56  62  Standard d e v i a t i o n  38  16  number o f s e s s i o n s  4  2  Mean p e r c e n t  Wilkie(1990)  acquired  reports that the higher a s a t e l l i t e  i s above  the h o r i z o n , the greater the l i k e l i h o o d of o b t a i n i n g a f i x . The assumption was made t h a t s i g n a l s t r e n g t h  (signal  q u a l i t y ) i s c o r r e l a t e d t o the p r o b a b i l i t y of being able t o o b t a i n a f i x . T h i s assumption was used t o study t h e e f f e c t o f t h e canopy on t h e a b i l i t y o f o b t a i n i n g a p o s i t i o n f i x . F i g u r e 6-1 i l l u s t r a t e s t h e c o r r e l a t i o n between t h e s i g n a l q u a l i t y and t h e s a t e l l i t e e l e v a t i o n .  The s i g n a l  quality  d i s p l a y e d by t h e r e c e i v e r as an index o f 0 t o 9, where 9 has the highest s i g n a l s t r e n g t h .  A l i n e a r r e g r e s s i o n was  p e r f o r m e d on the d a t a u s i n g S y s t a t u s i n g d i s t a n c e weighted l e a s t squares and a c o n f i d e n c e i n t e r v a l of 0.95. The c o r r e l a t i o n i s not s t r o n g . The Pearson c o r r e l a t i o n c o e f f i c i e n t i s 0.32, s u g g e s t i n g a weak c o r r e l a t i o n between t h e s i g n a l q u a l i t y and the e l e v a t i o n of the s a t e l l i t e above the h o r i z o n . The c o e f f i c i e n t of d e t e r m i n a t i o n i s 0.10. That i s 10% o f t h e v a r i a t i o n i n the s i g n a l q u a l i t y can be e x p l a i n e d by the v a r i a t i o n i n the e l e v a t i o n of the satellite.  F i g u r e 6-1 S i g n a l q u a l i t y index v s . S a t e l l i t e  elevation  Discussion of Results Static  tests  The s i n g l e p o i n t p o s i t i o n i n g t r i a l s i n d i c a t e t h a t the GPS s i g n a l p e n e t r a t e s the f o r e s t canopy t o a l i m i t e d degree. However, the p r o b a b i l i t y of a s u c c e s s f u l p o s i t i o n f i x drops d r a m a t i c a l l y as the s i z e of the s t a n d i n c r e a s e s beyond 14metres i n h e i g h t . When s i t u a t e d at p l o t s 3 through 5, t h e r e were many i n s t a n c e s of s a t e l l i t e a c q u i s i t i o n and d a t a c o l l e c t i o n , w i t h o n l y two and t h r e e s a t e l l i t e s . However, i n t w e n t y - s i x a t t e m p t s , t h e r e was o n l y one i n s t a n c e of a s u c c e s s f u l d a t a s e s s i o n i n those p l o t s . T h i s r e p r e s e n t s a 0.038 p r o b a b i l i t y of o b t a i n i n g a p o s i t i o n f i x . A l l attempts were made i n 3D mode. I f 2D mode were used t h e r e would have l i k e l y been more s u c c e s s f u l a t t e m p t s . In p l o t 1, (on the road) t h e r e was a p r o b a b i l i t y of 1.0 of o b t a i n i n g a f i x . I n the G o l f course ( p l o t 2) the s u c c e s s r a t e of o b t a i n i n g a f i x was the same whether a 2-metre o r 5metre antenna h e i g h t was used. However, the antenna a t 5metres c o l l e c t e d over t w i c e the number of f i x e s as were c o l l e c t e d w i t h the antenna at 2-metres i n h e i g h t , d u r i n g the same p e r i o d . There was no advantage i n u s i n g a h i g h e r antenna i n p l o t s one and f o u r . P l o t one was on the road surrounded by t r e e s . There i s too s m a l l a sample s i z e to say t h a t i t may a p p l y t o o t h e r s i t u a t i o n s . However i t seems t h a t i f t h e r e i s a c l e a r view t o the sky t h e r e would be no advantage t o r a i s i n g the antenna. I n p l o t f o u r , the base of the l i v e crown was about 15 t o 20-metres above the ground and t h e r e was v e r y l i t t l e  undergrowth. There was no advantage i n u s i n g a l o n g e r p o l e (5-in) because t h e antenna would s t i l l be f a r below t h e crowns. I n t a b l e 6-2 t h e r e was a s u c c e s s f u l attempt i n a c h i e v i n g a f i x w i t h 2-metre p o l e . T h i s was p r o b a b l y a chance o c c u r r e n c e I n p l o t 2 however, t h e i n c r e a s e d antenna h e i g h t r e s u l t e d i n a 208% i n c r e a s e i n t h e number o f f i x e s f o r a g i v e n p e r i o d . T h i s may be because t h e antenna p o s i t i o n i s b e t t e r e d by raising i t . The i n c r e a s e i n h e i g h t t o 5-metres p u t s t h e antenna above most o f t h e crown, whereas a t 2-metres t h e crown i s above t h e antenna. However, t h e r e was no i n c r e a s e i n t h e number o f s u c c e s s f u l data c o l l e c t i o n s e s s i o n s w i t h i n c r e a s e d antenna h e i g h t . The l a c k of i n c r e a s e i n s u c c e s s f u l a t t e m p t s w i t h t h e i n c r e a s e d antenna h e i g h t i s p r o b a b l y because a 10-minute s e s s i o n i s s u f f i c i e n t t o o b t a i n a p o s i t i o n f i x w i t h a lower antenna h e i g h t . The e l e v a t i o n o f t h e antenna poses a r i s k o f damaging t h e unit. The antenna used i n t h e study i s s u s c e p t i b l e t o shocks. When t h e antenna i s s i t u a t e d 5-metres above t h e ground, g r e a t c a r e i s needed t o keep i t from swaying and h i t t i n g t h e t r e e s . An antenna was damaged and r e n d e r e d i n o p e r a b l e d u r i n g t h e study. The c h o i c e t o e l e v a t e t h e antenna i n c r e a s e s t h e c o m p l e x i t y o f t h e f i e l d o p e r a t i o n s . There i s a l s o an i n c r e a s e d r i s k o f component f a i l u r e . A h a n d h e l d u n i t i s s i m p l e t o t r a n s p o r t , power and p r o t e c t . The h a n d h e l d r e c e i v e r weighs 0.85-kg., b u t when an e x t e r n a l antenna i s used, t h e r e i s exposed c a b l i n g , an a d d i t i o n a l b a t t e r y and antenna, i n c r e a s i n g t h e weight t o 3.7-kg. Some problems o f o b t a i n i n g a f i x stem from t h e l a c k o f satellites.  D u r i n g a t e n minute attempt, t h e r e were u s u a l l y  i n s u f f i c i e n t s a t e l l i t e s a v a i l a b l e f o r the receiver t o attempt a n o t h e r s a t e l l i t e c o n f i g u r a t i o n .  The s u c c e s s r a t e  s h o u l d i n c r e a s e as t h e number o f s a t e l l i t e s  increase.  A n o t h e r f a c t o r t h a t would a i d i n t h e a n a l y s i s o f t h e r e s u l t s would be t o m o n i t o r t h e s a t e l l i t e s t a t u s b u l l e t i n s . I t was o n l y on c o m p l e t i o n o f t h e study t h a t i n f o r m a t i o n s o u r c e s f o r the c o n s t e l l a t i o n s t a t u s were d i s c o v e r e d . Some u n s u c c e s s f u l a t t e m p t s a t a c q u i r i n g a f i x may have stemmed from t h e s a t e l l i t e b e i n g t u r n e d o f f by t h e U n i t e d S t a t e s m i l i t a r y , r a t h e r t h a n where t h e antenna was s i t u a t e d . The d a t a s u g g e s t s a potential fixes for s i z e s , w i t h unequal suggests that there a c q u i s i t i o n under a  s l i g h t l y higher p r o p o r t i o n of f i x e s t o a wet canopy. However, t h e s m a l l sample sample s i z e s and l a r g e v a r i a n c e s i s no s i g n i f i c a n t d i f f e r e n c e s i g n a l wet o r d r y canopy.  Results Dynamic t e s t s : The t r a v e r s e c o u r s e was i n t h e s o u t h e r n end o f t h e M a l c o l m Knapp f o r e s t . The o v e r l a i d data a r e d i s p l a y e d i n F i g u r e 6-2 which c o n t a i n s a l l p o s i t i o n s determined when PDOP was l e s s than t e n . I t i s composed of 1365 p o i n t s . Some p o s i t i o n s were d e t e r m i n e d i n 2D mode. F i g u r e 6-3 c o n t a i n s o n l y t h e f i x e s t h a t were determined i n 3D mode. I t c o n t a i n s 175 points. T a b l e 6-4 c o n t a i n s t h e r e s u l t s o f s i x t r a v e r s e s w i t h two receivers t r a c k i n g p o s i t i o n s simultaneously. The mode o f each r e c e i v e r was s e t a t e i t h e r 3D o r 2D. The r a t i o i s the. number o f f i x e s of one r e c e i v e r over t h e o t h e r on t h e same traverse.  Figure Malcolm  Knapp  Golf  course with  traverse.  A i l  2D  -  3D  positions  PDOP < 10  \  5458000 I  6-2  1  1  1  1  5456500 ' 1 ' ' ' ' 530600 530800 531000 531200 531400 531600 EASTING Figure Malcolm  Knapp  Golf  course  6-3  traverse.  PDOP < 10 2D 5457600  1  A i l  3D  positions  excluded.  1  1  1  , ^'  5457500 5457400 5457300 z 1-  cr  -  5457200  § 5457100 - •  -  .v"  5457000  ' ".-  '. •  5456900 -  1 1 1 1 5456800 530900 531000 531100 531200 531300 531400  EASTING  with  Table 6-4 Ratio of successful/attempted fixes i n dry versus wet canopyTwo receivers at 1 and 3-metres elevation used simultaneously Ratio of number of fixes Traverse  Antenna  Mode D # f i x e s  Ratio 0.76  Ht. 1  3in  3  98  dry  handheld  2  129  2  3m  2  200  dry  handheld  2  200  3  3m  3  41  wet  handheld  2  118  4  3m  2  194  wet  handheld  2  139  5  3m  3  36  wet  handheld  2  135  6  3m  2  160  wet  handheld  2  24  1 0.35 1.4 0.27 6.67  Discussion of Results Dynamic t e s t s : The dynamic t e s t of p e r f o r m i n g a t r a v e r s e i n d i c a t e s t h a t o p e r a t i n g t h e r e c e i v e r i n 2D mode enhances t h e r e c e p t i o n o f GPS s i g n a l s . The r a t i o o f 3D/2D f i x e s i s 0.45. T h i s i s p a r t i a l l y due t o t h e f a s t e r d a t a c a p t u r e r a t e i n 2D mode i n h e r e n t i n t h e r e c e i v e r . The r e c e i v e r c a l c u l a t e s a p o s i t i o n f i x every 11 seconds i n 2D i f u n o b s t r u c t e d . T h i s i n c r e a s e s t o 15 seconds when 3D mode i s chosen. This alone would account f o r a r a t i o of 3D/2D f i x e s o f 0.73. I f t h e e f f e c t o f t h e s l o w e r a c q u i s i t i o n r a t e i n 3D mode i s c o n s i d e r e d , and t h e e f f e c t o f a h i g h e r antenna i s i g n o r e d ,  the 3D/2D r a t i o would s t i l l be 0.62. T h i s s u g g e s t s t h a t t h e p r o b a b i l i t y t h a t t h e r e c e i v e r o b t a i n s a p o s i t i o n f i x when u s i n g 2D i s g r e a t l y enhanced. The antenna h e i g h t a l s o a f f e c t s t h e success o f o b t a i n i n g f i x e s . When b o t h r e c e i v e r s were put i n 2D mode and used s i m u l t a n e o u s l y , t h e r a t i o of f i x e s of 3m over h a n d h e l d h e i g h t s was 1.5. S i n c e t h e d a t a a c q u i s i t i o n r a t e s s h o u l d be 11 seconds p e r f i x i n 2D f o r b o t h r e c e i v e r s , t h e d i s c r e p a n c y can be e n t i r e l y a t t r i b u t e d t o antenna h e i g h t . Conclusions The use o f a s i n g l e channel r e c e i v e r under a f o r e s t canopy 12 - 15-metres h i g h , f o r s i n g l e p o i n t p o s i t i o n i n g , i s n o t recommended. When under a canopy l e s s than 12-metres, i t i s recommended t h a t t h e antenna be e l e v a t e d , p r e f e r a b l y o v e r top o f t h e canopy. When i n stands of g r e a t e r than 2 0-metres i n h e i g h t , t h e r e i s no b e n e f i t i n r a i s i n g t h e antenna from 2-metres t o 5-metres. Procedures and equipment need t o be d e v e l o p e d t o ensure t h a t t h e antenna i s not damaged when a l o n g p o l e i s used. The r a t e o f d a t a c a p t u r e i n dynamic mode u s i n g 2D was i n c r e a s e d by 150 p e r c e n t when a 3-metre antenna h e i g h t was used v e r s u s 1.5-metre antenna h e i g h t . The d a t a i n d i c a t e t h a t t h e r e was no s i g n i f i c a n t d i f f e r e n c e i n o b t a i n i n g f i x e s under a wet o r d r y canopy f o r f i x e d p o s i t i o n s . The d a t a cannot be d i s t i n g u i s h e d i n t h e dynamic t e s t s , t o l e a r n i f a wet canopy a f f e c t e d t h e a c q u i s i t i o n r a t e s . However, i t i s f e l t t h a t t h e r e was no d i s c e r n a b l e d i f f e r e n c e .  The use o f 2D i n dynamic mode i n c r e a s e d t h e number o f p o s i t i o n f i x e s d u r i n g t h e same p e r i o d by 222 p e r c e n t over the use o f 3D. T h i s i n c r e a s e i s due i n p a r t t o an i n c r e a s e i n d a t a c a p t u r e i n h e r e n t i n t h e r e c e i v e r , b u t a l s o due t o the i n c r e a s e d l i k e l i h o o d of o b t a i n i n g a f i x because fewer s a t e l l i t e s a r e r e q u i r e d u s i n g 2D. When 2D mode i s s e l e c t e d , t h e u s e r must s u p p l y an a c c u r a t e e l e v a t i o n t o o b t a i n an a c c u r a t e p o s i t i o n . For single point p o s i t i o n i n g an e l e v a t i o n may be typed i n t o t h e r e c e i v e r . For k i n e m a t i c p o s i t i o n i n g i t i s not f e a s i b l e t o e n t e r t h e e l e v a t i o n whenever i t changes, u n l e s s t h e t e r r a i n i s v e r y uniform. Recommendat i o n s The use o f a s i n g l e channel r e c e i v e r under immature and mature c o a s t a l f o r e s t s s h o u l d not t o be pursued a t t h i s time. When a f u l l c o n s t e l l a t i o n o f s a t e l l i t e s i s p r e s e n t , and t h e i n e v i t a b l e improvements i n t e c h n o l o g y a r e made, t h i s study s h o u l d be r e p e a t e d . The use of a s i n g l e channel r e c e i v e r i n r e g e n e r a t e d s t a n d s up t o 14-metres i n h e i g h t deserves f u r t h e r s t u d y . With an e l e v a t e d antenna, t r a v e r s e s were easy t o complete. The study o f t h e a c c u r a c y o f t r a v e r s e s completed by GPS s h o u l d be pursued. Any f u r t h e r e x p e r i m e n t a t i o n s h o u l d i n v o l v e a more r i g o r o u s • e x p e r i m e n t a l d e s i g n . Most of t h e a n a l y s i s i n t h i s study i n v o l v e ad hoc methods. An ANOVA would d e f i n e f o r t h e u s e r , the f a c t o r s a f f e c t i n g GPS s i g n a l s . F u r t h e r t e s t i n g s h o u l d be d e s i g n e d t o d i s t i n g u i s h v a r i a t i o n of s a t e l l i t e a c q u i s i t i o n by 1) mapping of the v e g e t a t i o n through a f i s h eye photograph 2) e l e v a t i o n of s a t e l l i t e s 3) geometry o f  s a t e l l i t e s 4) h e a l t h of s a t e l l i t e s 5) biomass of canopy and 6) t e c h n o l o g y r e c e i v i n g the s i g n a l s . type of r e c e i v e r was  tested.  In t h i s study o n l y  one  CHAPTER 7 - DISCUSSION AND CONCLUSIONS Discussion The f i e l d o f g e o d e t i c p o s i t i o n i n g w i t h GPS i s moving a t a r a p i d pace. F o r example, t h e s i n g l e channel r e c e i v e r used i n t h i s s t u d y was r e c e i v e d i n May o f 1990. I t was one o f the f i r s t u n i t s o f the model l i n e produced. S i n c e then i t has gone t h r o u g h two upgrades, and now has been superseded by a 5-channel r e c e i v e r w i t h c l a i m s o f sub-metre a c c u r a c y d u r i n g d i f f e r e n t i a l p o s i t i o n i n g . The p o s t - p r o c e s s i n g s o f t w a r e has a l s o been c o m p l e t e l y r e w r i t t e n . S e v e r a l areas of GPS t h a t have changed s i g n i f i c a n t l y s i n c e t h e s t a r t o f t h i s study are: 1) DGPS - D i f f e r e n t i a l GPS. The U.S. m i l i t a r y has c o n f i r m e d t h a t SA w i l l be implemented t o prevent t h e use o f p r e c i s e GPS p o s i t i o n i n g by enemies o f t h e U n i t e d S t a t e s , and i t s allies. T h i s w i l l render autonomous p o s i t i o n i n g a c c u r a c i e s of 100 metres 95 p e r c e n t o f t h e time. To a c h i e v e h i g h e r a c c u r a c i e s , i n h e r e n t w i t h i n t h e system, d i f f e r e n t i a l p o s i t i o n i n g w i l l need t o be employed. GPS r e c e i v e r s a r e now o f f e r e d as a p l u g i n module f o r desktop and hand h e l d computers. Coupled w i t h modems (or r a d i o modems) r e a l - t i m e d i f f e r e n t i a l p o s i t i o n i n g i s now p o s s i b l e a t a r e a s o n a b l e c o s t . The U.S. Coast Guard i s committed t o u p g r a d i n g i t s network o f r a d i o beacons t o b r o a d c a s t d i f f e r e n t i a l GPS c o r r e c t i o n s . A n a t i o n w i d e network o f GPS c o m p a t i b l e beacons s h o u l d be i n p l a c e by 1996. The s e r v i c e w i l l be a v a i l a b l e up t o 200 m i l e s o f f s h o r e and a c c u r a c i e s s h o u l d be under 10metres. There i s a l s o the p o s s i b i l i t y o f sub-decimetre a c c u r a c y w h i l e u s i n g phase d i f f e r e n t i a l p o s i t i o n i n g w i t h i n harbours. The governments o f Canada and B r i t i s h Columbia a r e p l a n n i n g t o e s t a b l i s h an A c t i v e C o n t r o l System (ACS), f o r d i f f e r e n t i a l GPS. T h i s w i l l a l l o w u s e r s t o p e r f o r m  d i f f e r e n t i a l p o s i t i o n i n g r e l a t i v e t o a number of e s t a b l i s h e d control points. T h i s w i l l a l l o w u s e r s such as n a v i g a t o r s and s u r v e y o r s t o o b t a i n h i g h q u a l i t y d i f f e r e n t i a l information. S e v e r a l p r i v a t e concerns a l r e a d y o f f e r d i f f e r e n t i a l data f o r post-processing. New t e c h n i q u e s i n s u r v e y i n g , such as r a p i d - s t a t i c a r e e n a b l i n g u s e r s of GPS t o o b t a i n c e n t i m e t r e a c c u r a c i e s w i t h a s i t e o c c u p a t i o n time of o n l y minutes. The t a s k of p o s t p r o c e s s i n g d i f f e r e n t i a l data a few y e a r s ago r e q u i r e d a h i g h l y t r a i n e d t e c h n i c i a n . Today's r e c e i v e r s a r e b e i n g s h i p p e d w i t h menu d r i v e n s o f t w a r e t h a t v i r t u a l l y any GPS u s e r can use e f f e c t i v e l y . The R e c e i v e r Independent N u m e r i c a l Exchange (RINEX) format w i l l a l l o w u s e r s of r e c e i v e r s from d i f f e r e n t manufacturers t o exchange d a t a f o r differential positioning. The use of many of these t e c h n i q u e s w i l l not be a v a i l a b l e t o f o r e s t e r ' s a t t h e p r e s e n t time. R e a l - t i m e d i f f e r e n t i a l w i l l depend on a r a d i o l i n k between the base s t a t i o n and t h e remote u s e r . G i v e n t h a t most of the r a d i o f r e q u e n c i e s a r e a l r e a d y a l l o c a t e d and the d i f f i c u l t t e r r a i n i n B r i t i s h Columbia, the q u a l i t y of the s i g n a l i n many areas r e n d e r s r a d i o d a t a communications u n r e l i a b l e . However, i n t h e near f u t u r e , s a t e l l i t e based c e l l u l a r communications w i l l be a v a i l a b l e . Where t h e r e are enough GPS s a t e l l i t e s v i s i b l e f o r a p o s i t i o n , t h e r e s h o u l d a l s o be a communications s a t e l l i t e a v a i l a b l e t o b r o a d c a s t the d i f f e r e n t i a l c o r r e c t i o n s . Many communication s a t e l l i t e s have some p o s i t i o n i n g a b i l i t y . T h i s w i l l s t r e n g t h e n the amount of r a d i o n a v i g a t i o n i n f o r m a t i o n on the a i r w a v e s . The use of s a t e l l i t e s t o b r o a d c a s t d i f f e r e n t i a l c o r r e c t i o n s , however, begs t h e q u e s t i o n , "why use GPS i n the f i r s t p l a c e ? " I f one u s e r i s t o use d i f f e r e n t i a l c o r r e c t i o n s from a s a t e l l i t e t h a t i s b r o a d c a s t i n g over a q u a r t e r of the  g l o b e , then t h e remote u s e r needs t o b r o a d c a s t t h e approximate p o s i t i o n o f t h e remote r e c e i v e r t o t h e satellite. The s a t e l l i t e then may b r o a d c a s t t h e a p p r o p r i a t e c o r r e c t i o n parameters f o r t h a t a r e a o f t h e g l o b e . I f t h e r e i s two-way communications between t h e remote u s e r and t h e communications s a t e l l i t e , a range t o t h e s a t e l l i t e from t h e u s e r can be d e r i v e d . I f t h e communication s a t e l l i t e i s a c t i n g as a t r a n s p o n d e r f o r r a d i o s i g n a l s t h e r e i s no need to c a r r y a s e r i e s o f atomic c l o c k s . A communications s a t e l l i t e can be b u i l t and launched f o r l e s s c o s t than a GPS satellite. W i t h t h e promise o f SA, i t might be more c o s t e f f e c t i v e f o r a c i v i l agency t o l a u n c h i t s own c o n s t e l l a t i o n of s a t e l l i t e s f o r n a v i g a t i o n and communication. The g r e a t e s t p o t e n t i a l f o r t h e use o f DGPS i n f o r e s t r y i s i n post-computed c o r r e c t e d p o s i t i o n s . T h i s w i l l e l i m i n a t e t h e need f o r t h e e x t r a components r e q u i r e d f o r communications. However i t w i l l r e q u i r e g r e a t e r onboard d a t a s t o r a g e on t h e remote r e c e i v e r . DGPS ca be used e f f e c t i v e l y f o r e s t a b l i s h i n g c o o r d i n a t e s f o r t i e p o i n t s , road and p o l y g o n t r a v e r s e s and v i r t u a l l y any a e r i a l a p p l i c a t i o n . The r a p i d - s t a t i c s u r v e y i n g t e c h n i q u e r e q u i r e s a c o u p l e o f minutes of u n i n t e r r u p t e d s a t e l l i t e s i g n a l s . G i v e n t h e d i f f i c u l t y o f o b t a i n i n g even i n t e r m i t t e n t s i g n a l s under a canopy, t h i s t e c h n i q u e i s not f e a s i b l e f o r under-canopy a p p l i c a t i o n s a t t h e p r e s e n t time n o r f o r t h e f o r e s e e a b l e future. 2) Software improvements. The f i r s t s o f t w a r e s h i p p e d w i t h the M a g e l l a n r e c e i v e r was command l i n e d r i v e n w i t h no d a t a management c a p a b i l i t i e s o r m i s s i o n p l a n n i n g . The most r e c e n t v e r s i o n has pull-down menus w i t h s a t e l l i t e p r e d i c t i o n software included.  Most m a n u f a c t u r e r s now p r o v i d e d a t a c o n v e r s i o n s o f t w a r e t o a l l o w the user t o upload s p a t i a l data i n t o a v a r i e t y of GIS's. There i s a l s o a t t r i b u t e c a p t u r e s o f t w a r e t h a t s u p p o r t s most r e c e i v e r s . T h i s s o f t w a r e a l l o w s t h e u s e r t o t a g an a t t r i b u t e such as a c u l v e r t w i t h a time and p o s i t i o n . T h i s may be a c c o m p l i s h e d w i t h t h e use o f f u n c t i o n keys o r bar-codes. There i s a l s o t h e c a p a b i l i t y t o v i e w t h e p o s i t i o n o f t h e antenna as a c u r s o r on a computer v i d e o d i s p l a y . The s c r e e n background may c o n t a i n a g e o - r e f e r e n c e d image o f t h e a r e a b e i n g t r a v e r s e d o r a d i g i t i z e d map. 3) Permanent L i m i t a t i o n s - The l o n g l i f e span (7-10 y e a r s ) of a GPS s a t e l l i t e , t h e l a r g e c o s t o f each s a t e l l i t e , and t h e budget r e d u c t i o n s o c c u r r i n g i n t h e U.S. m i l i t a r y , suggest t h a t t h e r e i s l i t t l e chance o f r a p i d improvement i n the GPS s a t e l l i t e c o n s t e l l a t i o n . The o s c i l l a t o r s t h a t d r i v e the r a d i o s i g n a l s , t h e power o f t h e s i g n a l s , and t h e s a t e l l i t e c o n s t e l l a t i o n can be c o n s i d e r e d t o be a c o n s t a n t f o r t h e next decade. The a b i l i t y of t h e t r a n s m i t t e d s i g n a l s t o p e n e t r a t e a c l o s e d canopy w i l l remain a problem. There i s o p p o r t u n i t y f o r t h e R u s s i a n GLONASS s a t e l l i t e n a v i g a t i o n system t o be i n t e g r a t e d w i t h GPS. T h i s w i l l a l l o w f o r i n t e g r i t y checks o f t h e n a v i g a t i o n message b e i n g b r o a d c a s t by GPS s a t e l l i t e s . The u s e r w i l l a l s o have more s a t e l l i t e s above t h e h o r i z o n t o choose from. There a r e a l s o p r o p o s a l s t o e s t a b l i s h communication s a t e l l i t e s t o b r o a d c a s t s i g n a l i n t e g r i t y messages t o u s e r s and s u p p l y crude corrections for differential positioning. The most r a p i d advancement w i l l come i n t h e u s e r equipment. The p r i c e / p e r f o r m a n c e r a t i o i s r a p i d l y d e c l i n i n g . The u n i t c o s t o f t h e r e c e i v e r modules w i l l p r o b a b l y be h a l v e d a g a i n w i t h i n t h e next two y e a r s . The b i g g e s t advancement w i l l come w i t h t h e i n t e g r a t i o n of GPS modules w i t h o t h e r n a v i g a t i o n a l a i d s . F o r i n s t a n c e t h e r e i s a s m a l l gyro  c o s t i n g s e v e r a l hundred d o l l a r s t h a t can be used t o i n t e r p o l a t e p o s i t i o n s between GPS f i x e s . A GPS r e c e i v e r , combined w i t h a d i g i t a l compass, an i n e r t i a l n a v i g a t i o n u n i t and a r a d i o r e c e i v e r t o r e c e i v e d i f f e r e n t i a l c o r r e c t i o n s would approach a " b l a c k box". The box c o u l d t e l l you where you a r e w i t h i n a metre, how f a s t you a r e moving, and i n what direction. 4) A p p l i c a t i o n s i n F o r e s t r y - The a p p l i c a t i o n o f GPS t o f o r e s t management w i l l p r o b a b l y be i n t h e areas o f photogrammetry, mapping, and v e h i c l e n a v i g a t i o n . The c o s t of e s t a b l i s h i n g ground c o n t r o l f o r a e r i a l s u r v e y s can be g r e a t l y reduced i f not e l i m i n a t e d i f t h e a i r c r a f t uses GPS t o r e c o r d t h e p o s i t i o n of the camera. The use o f GPS f o r n a v i g a t i o n can p r o v i d e immediate b e n e f i t s f o r t h e p o s i t i o n i n g o f crews on l a r g e f i r e s , l o c a t i n g p r o j e c t a r e a s , growth and y i e l d p l o t s , and r o a d network navigation. T r a v e r s i n g l a r g e openings, t o g e t h e r w i t h a h i p c h a i n can e a s i l y be a c c o m p l i s h e d w i t h today's t e c h n o l o g y . When a f o r e s t canopy i s p r e s e n t , t h e use o f a t e l e s c o p i c range p o l e may be used, however the p o l e must e x t e n d t o t h e upper reaches o f t h e canopy. The  p r o b l e m of t h e canopy may be reduced i n t h e f u t u r e by  the use o f r e c e i v e r s s p e c i f i c a l l y d e s i g n e d f o r f o r e s t r y applications. P r e s e n t day r e c e i v e r s r e l y on o b t a i n i n g near s i m u l t a n e o u s r e a d i n g s from a t l e a s t f o u r s a t e l l i t e s w i t h an o m n i d i r e c t i o n a l antenna. The a u t h o r f e e l s t h a t i f an a r r a y of h i g h - g a i n antennae, each d i r e c t e d t o a s p e c i f i c s a t e l l i t e were used, t h e r e c e i v e r may l o c k onto v e r y weak s i g n a l s . I f s o p h i s t i c a t e d m o d e l i n g of the s a t e l l i t e o r b i t s were a c h i e v e d , ranges t o each s a t e l l i t e c o u l d be t a k e n i n seconds or minutes i n s t e a d of s i m u l t a n e o u s l y . I f t h e r e c e i v e r were s t a t i c , t h e r e c e i v e r c o u l d c a p t u r e enough d a t a over time t o c a l c u l a t e a p o s i t i o n . I t was f e l t t h a t d u r i n g t h e s t u d y  o p p o r t u n i t i e s of o b t a i n i n g s i g n a l s were m i s s e d due t o the l a c k of a channel b e i n g d e d i c a t e d t o each s a t e l l i t e . M u l t i c h a n n e l r e c e i v e r s w i l l h e l p t o c o r r e c t t h i s problem. The use of GPS i n may cases can reduce the c o s t of s u r v e y i n g p o s i t i o n s . The s a v i n g s can q u i c k l y d i s a p p e a r as the a c c u r a c y r e q u i r e d i n c r e a s e s and the time r e q u i r e d f o r a s o l u t i o n d e c r e a s e s . For a c c u r a c i e s i n the 25-metre range the u s e r may p u r c h a s e a r e c e i v e r f o r about $2000 and q u i c k l y average a number of f i x e s by p u s h i n g a b u t t o n . To o b t a i n a p o s i t i o n w i t h i n 10-metres two r e c e i v e r s are r e q u i r e d . This may be a r e c e i v e r owned by a s e r v i c e agency or the u s e r may p u r c h a s e a n o t h e r u n i t . The remote r e c e i v e r would need a s t o r a g e c a p a b i l i t y f o r p o s t - p r o c e s s i n g of the p o s i t i o n s obtained. A l t e r n a t i v e l y , a r a d i o l i n k would need t o be e s t a b l i s h e d to receive d i f f e r e n t i a l c o r r e c t i o n s i n r e a l time. I f the u s e r wanted to u p l o a d the p o s i t i o n s i n t o a GIS, onboard d a t a s t o r a g e would s t i l l be r e q u i r e d . I f the u s e r wanted t o o b t a i n a c c u r a t e p o s i t i o n s under a canopy, a t e l e s c o p i c range p o l e and e x t e r n a l antenna would need t o be purchased. I f the requirement was f o r sub-metre a c c u r a c y , r e a l - t i m e p o s i t i o n i n g would be u n r e a l i s t i c . C o n s i d e r a b l y more s t o r a g e c a p a c i t y would be r e q u i r e d at b o t h the base s t a t i o n and remote s t a t i o n s t o s t o r e the e x t r a data r e q u i r e d . I f the r e q u i r e m e n t was f o r s u b - c e n t i m e t r e a c c u r a c y , the u s e r would need t o be t r a i n e d i n d i f f e r e n t i a l p r o c e s s i n g . New i s s u e s would need t o be addressed such as the phase c e n t e r and o r i e n t a t i o n of the antenna. The modeling of e r r o r s from i o n o s p h e r i c and t r o p o s p h e r i c r e f r a c t i o n would need t o be i n c o r p o r a t e d i n t o the s o l u t i o n . The purchase of p o s t computed ephemiredes ( o r b i t a l data) would a l s o be r e q u i r e d . The c o s t of the equipment and the l e v e l of e x p e r t i s e would necessarily increase.  Conclusions A s i n g l e c h a n n e l GPS r e c e i v e r i s not adequate f o r o b t a i n i n g p o s i t i o n s under a f o r e s t e d canopy. A m u l t i p l e c h a n n e l r e c e i v e r w i l l p r o b a b l y be more s u c c e s s f u l i n o b t a i n i n g a p o s i t i o n f i x . However the q u a l i t y of the f i x may be degraded from the m a n u f a c t u r e r ' s s p e c i f i c a t i o n s . The d e g r a d a t i o n i s due t o ; 1) the s c a t t e r i n g and a t t e n u a t i o n of the s i g n a l by the f o r e s t canopy, and 2) the poor s a t e l l i t e c o n f i g u r a t i o n of u s i n g o n l y s a t e l l i t e s h i g h above the horizon. The second cause of d e g r a d a t i o n can be c o n t r o l l e d by o n l y r e c o r d i n g f i x e s when the c o n f i g u r a t i o n of s a t e l l i t e s y i e l d s a s t r o n g geometry, however the net e f f e c t w i l l i n many c a s e s , be the e x c l u s i o n of a l l f i x e s a t t a i n e d . Thus the r e c e i v e r cannot be used e f f e c t i v e l y under a canopy. The u t i l i t y of GPS can be r e a l i z e d where the antenna i s not o b s c u r e d by a f o r e s t canopy. A c t i v i t i e s t h a t o c c u r on wide road r i g h t - o f - w a y s and c l e a r c u t s are good c a n d i d a t e s f o r the use of GPS. Young stands where the e f f o r t of c a r r y i n g and e x t e n d i n g and c o l l a p s i n g a t e l e s c o p i c p o l e i s o f f s e t by the ease of c o l l e c t i n g p o s i t i o n a l i n f o r m a t i o n are a l s o a r e a s where GPS may be used. However, the p o l e must e x t e n d t o the h e i g h t of the topmost branches t o be of any b e n e f i t . The system may a l s o be used to t r a v e r s e c l e a r c u t s , i f a h i p c h a i n and compass i s a l s o c a r r i e d t o determine p o s i t i o n s during s i g n a l blockages. The f i r s t uses of GPS s h o u l d i n v o l v e equipment on a i r c r a f t . The view of the antenna t o the sky i s u s u a l l y u n o b s t r u c t e d when the antenna i s mounted atop a f i x e d wing, o r on the t a i l - b o o m of a r o t a r y - w i n g e d a i r c r a f t . S i n c e the c o s t of r e n t i n g a i r c r a f t i s h i g h , s m a l l g a i n s i n the e f f e c t i v e n e s s of the use of a i r c r a f t are worth p u r s u i n g . The a u t h o r f e e l s t h a t the use of GPS f o r a i r n a v i g a t i o n and c o l l e c t i o n of data would be c o s t e f f e c t i v e . T h i s can be a c h i e v e d by  enhanced n a v i g a t i o n t o areas o f study and automatic time and space t a g g i n g o f o b s e r v a t i o n s from t h e a i r c r a f t . F o r example, a mountain-pine b e e t l e f l i g h t may be p l a n n e d by e n t e r i n g c o o r d i n a t e s o f t h e study area i n t o t h e h e l i c o p t e r ' s n a v i g a t i o n system. T h i s w i l l a l l o w t h e p i l o t t o f l y d i r e c t l y t o the area i n question without having t o i n t e r p r e t maps. Any new i n f e s t a t i o n s encountered may have t h e i r p o s i t i o n s r e c o r d e d by t h e s i m p l e p r e s s i n g o f a b u t t o n . This w o u l d be f a r s u p e r i o r t o n a v i g a t i n g by a i r photographs and hand mapping t h e i n f e s t a t i o n s . The a c c u r a c y o f code based r e c e i v e r s w i l l u l t i m a t e l y be 100metres RMS i n autonomous mode. I n d i f f e r e n t i a l p o s i t i o n i n g , a u s e r can expect a c c u r a c i e s o f 6-10-metres RMS i n 3 dimensions. That i s , g i v e n an average o f 100 f i x e s on a g i v e n l o c a t i o n 63 o f them w i l l f a l l w i t h i n 8 metres o f t h e mean p o s i t i o n . N i n e t y - e i g h t p e r c e n t o f t h e f i x e s w i l l f a l l w i t h i n 16-metres o f t h e mean p o s i t i o n . However, i m p r o v i n g methods o f data c o l l e c t i o n and p r o c e s s i n g promise t o b r i n g higher accuracy f o r d i f f e r e n t i a l p o s i t i o n s w i t h s h o r t e r s i t e occupation times. GPS a l l o w s t h e d i r e c t c o l l e c t i o n o f time tagged s p a t i a l i n f o r m a t i o n i n a d i g i t a l format. This information i s v a l u a b l e f o r t h e o p e r a t i o n of v e h i c l e m o n i t o r i n g systems. P o s i t i o n a l d a t a c o u p l e d w i t h v e h i c l e performance d a t a w i l l a l l o w s u p e r v i s o r s t o e a s i l y determine o p e r a t o r p e r f o r m a n c e , e f f i c i e n c y and s a f e t y on a road network. Further t e s t i n g should i n v o l v e multi-channel r e c e i v e r s . Comparisons s h o u l d be made i n an o p e r a t i o n a l s e t t i n g w i t h competing t e c h n o l o g i e s . F o r i n s t a n c e t h e u p d a t i n g o f d i s t u r b e d areas w i t h GPS i n c l u d i n g q u a l i t a t i v e i n f o r m a t i o n g a t h e r e d by t h e f i e l d p e r s o n n e l , s h o u l d be compared w i t h Landsat, SPOT, a e r i a l photographs, and t i g h t - c h a i n e d traverses.  LITERATURE CITED Ewing, C E . and M.M. M i t c h e l l . 1970. I n t r o d u c t i o n t o geodesy. American E l s e v i e r P u b l i s h i n g Co. I n c . New York. F a r l e y , S.A., J u n k i n s D.R. 1990. The n a t i o n a l transformation. Program d e s c r i p t i o n s and u s e r i n s t r u c t i o n s f o r s o f t w a r e package. I n P r e l i m i n a r y proceedings. Moving t o NAD '83. Richmond, B.C. Canadian I n s t i t u t e of S u r v e y i n g and Mapping 40pp. Feess, B., J . I r o z , A S a t i n , B. Winn, C. Wiseman, B. Hermann, E. S w i f t , H. B e i s n e r , D. A l l a n , D. D a v i e s , M. Weiss, W. K l e p c z y n s k i and F. W i t h i n g t o n . 1987. GPS s a t e l l i t e - t o - u s e r range a c c u r a c i e s : a c a l i b r a t i o n experiment. N a v i g a t i o n . 34(3): 229-249 French, R.L. 1987. The e v o l v i n g r o l e s o f v e h i c u l a r n a v i g a t i o n . N a v i g a t i o n . J r n l . of t h e I n s t , o f Navigation. 3 4 ( 3 ) : 212-227. G e r l a c h F.L. and A.R. Jasumback. 1989. D i g i t i z i n g n a t u r a l r e s o u r c e s w i t h GPS. Paper p r e s e n t e d a t 12th Canadian Symposium on Remote Sensing, Vancouver, Canada. J u l y 10-14. 12pp. Hein, G.W., A. L e i c k and S. Lambert. 1989. I n t e g r a t e d p r o c e s s i n g o f GPS and g r a v i t y data. J r n l . o f S u r v e y i n g Engineering. 115(1): 15-33. Johannessen, R. 1987. I n t e r n a t i o n a l f u t u r e n a v i g a t i o n needs: o p t i o n s and concerns. J r n l . o f t h e I n s t , o f N a v i g a t i o n . 3 4 ( 4 ) : 279 -289 K n o e r n s c h i l d , G.F. 1 9 8 6 . G l o b a l p o s i t i o n i n g system f o r v e h i c l e n a v i g a t i o n and p o s i t i o n i n g r e p o r t i n g . Proceedings S o c i e t y of Automotive E n g i n e e r s . Piscataway, NJ. Oct. 1 9 8 6 . 8 6 1 0 5 9 : 2 1 9 - 222  L a c h a p p e l e , G. 1991. G l o b a l p o s i t i o n i n g system. Manual from GIS91 workshop #5 d u r i n g GIS91. Vancouver, B.C. F o r e s t r y Canada, P r o v i n c e o f B.C., D i g i t a l Mapping Group, R e i d C o l l i n s . 180pp. L e i c k , A. 1990. GPS s a t e l l i t e s u r v e y i n g . John W i l e y & Sons. Toronto. M a g e l l a n Systems Corp. 1990. S t a t i s t i c a l d e f i n i t i o n s o f f i x e r r o r s . I n t e r n a l memorandum. M a g e l l a n Systems Corp. 5pp. M a g e l l a n Systems Corp. 1990. M a g e l l a n GPS NAV 1000 PRO u s e r s g u i d e . M a g e l l a n Systems Corp. Monrovia CA. 195pp. M i n k e l , D.H. 1989. K i n e m a t i c GPS l a n d survey - d e s c r i p t i o n of o p e r a t i o n a l t e s t and r e s u l t s . J r n l . o f S u r v e y i n g Engineering. 115(1): 121-137 Mooney, F.W. 1985. T e r r e s t r i a l e v a l u a t i o n o f t h e GPS standard p o s i t i o n i n g s e r v i c e . J r n l . of the I n s t , of Navigation. 3 2 ( 4 ) : 351-369. Newcomer, D. 1990. GPS as a f a s t s u r v e y i n g t o o l . J r n l . o f the I n s t , o f N a v i g a t i o n . 116(2): 75-81 N o l a n , T.P., and M. C a r p e n t e r . 1988. The use o f d i f f e r e n t i a l N a v s t a r GPS t o a i d t h e v i s u a l l y handicapped. J r n l . o f Navigation. 4 1 ( 2 ) : 203-212. P a r k i n s o n , B. and K. F i t z g i b b o n . 1987. O p t i m a l l o c a t i o n s f o r p s e u d o l i t e s f o r d i f f e r e n t i a l GPS. N a v i g a t i o n . J r n l o f the I n s t , of N a v i g a t i o n . 3 3 ( 4 ) : 259-265. S t r a t t o n , A. 1987. Omega i n t h e l a n d environment. J r n l . o f Navigation. 4 0 ( 2 ) : 322-332 W e l l s , D.E. N. Beck, D. D e l i k a r a o g l o u , A. K l e u s b e r g , E . J . K r a k i w s k y , G. L a c h a p p e l l e , R.B. Langley, M. N a k i b o g l u , K.P. Schwarz, J.M. T r a n q u i l l a and P. V a n i c e k . 1986. Guide t o GPS P o s i t i o n i n g . Canadian GPS A s s o c i a t e s . F r e d e r i c t o n , NB.  W i l k i e D.D. 1990. Performance o f a backpack GPS i n a t r o p i c a l r a i n f o r e s t . Photogrammetric E n g i n e e r i n g and Remote S e n s i n g . 5 5 ( 1 2 ) : 1747-1749  APPENDIX A - VINCENTY INVERSE  Introduction: As s u g g e s t e d i n Chapter 1, t r a d i t i o n a l methods o f s u r v e y i n g c a l c u l a t e c o o r d i n a t e s i n two dimensions on a r e f e r e n c e plane. The t h i r d dimension, e l e v a t i o n , i s c a l c u l a t e d from a d i f f e r e n t r e f e r e n c e datum by d i f f e r e n t p r o c e d u r e s . Geodetic c o o r d i n a t e s , ( L a t i t u d e and Longitude) a r e based on a t h r e e dimensional world, but only describe the coordinates of a p o s i t i o n on t h e r e f e r e n c e e l l i p s o i d . The o r t h o m e t r i c h e i g h t ( h e i g h t above mean s e a - l e v e l ) , i s an a t t r i b u t e a s s i g n e d t o a position. The t a s k o f a GPS r e c e i v e r i s t o d e r i v e c o o r d i n a t e s on t h e e l l i p s o i d . The e l e v a t i o n i s g i v e n as t h e h e i g h t above e l l i p s o i d .  Objective The o b j e c t i v e o f t h i s s e c t i o n o f t h e study i s t o examine t h e e f f e c t o f convergence o f t h e m e r i d i a n s on t h e d i s t a n c e between two p o i n t s on t h e e a r t h ' s s u r f a c e . Convergence : On a s p h e r i c a l e a r t h , t h e d i s t a n c e between degrees o f l a t i t u d e i s e s s e n t i a l l y constant. The degrees o f l o n g i t u d e ( m e r i d i a n s ) converge a t t h e p o l e s . A t t h e equator, a l l meridians are p a r a l l e l . At the poles a l l the meridians converge t o a s i n g l e p o i n t . (Ewing and M i t c h e l l 1970). Assuming a s p h e r i c a l e a r t h , t h e convergence a n g l e f o r a UTM p r o j e c t i o n i s g i v e n by:  C = AB5[Asin(0)'  where : C - i s t h e a n g l e o f convergence. A - i s t h e d i f f e r e n c e i n l o n g i t u d e from t h e c e n t r a l meridian. <l> - i s t h e degree o f l a t i t u d e (Wong 1989) F o r e s t s u r v e y i n g w i t h a two man crew u s u a l l y depends on a f o r e s i g h t and b a c k s i g h t from each crew member. The f o r e s i g h t from t h e t a i l m a n s h o u l d d i f f e r by 180^ from t h e compassman o r l e a d i n g member o f the crew. T h i s i s t r u e f o r the crude compasses used and the s h o r t d i s t a n c e s between crew members. The s i g n i f i c a n c e o f convergence f o r g e o d e t i c p o s i t i o n i n g , i s t h e f o r w a r d and back azimuths do not d i f f e r by 180°. They d i f f e r from 180° by the amount o f convergence. The s i g n i f i c a n c e o f convergence on UTM c o o r d i n a t e s i s t h a t the UTM g r i d i s r e g u l a r w h i l e t h e meridians are c u r v i l i n e a r . The f e a t u r e s p r i n t e d on a map a r e d i s t o r t e d by the T r a n s v e r s e M e r c a t o r p r o j e c t i o n . Thus the UTM g r i d l i n e s r u n n i n g North-South a r e i n e r r o r w i t h r e s p e c t t o the l i n e s d e s i g n a t i n g l o n g i t u d e by t h e amount o f convergence. F i g u r e A-1 i l l u s t r a t e s convergence. The m e r i d i a n s o f l o n g i t u d e a r e shown w i t h the convergence e x a g g e r a t e d towards the N o r t h P o l e . An azimuth b e a r i n g w i t h r e f e r e n c e t o t r u e n o r t h from p o i n t A t o p o i n t B, on m e r i d i a n 123, i s AB. An a z i m u t h from p o i n t B, on m e r i d i a n 122 t o p o i n t A i s BA. However a n g l e BA i s not 180*^ g r e a t e r than a n g l e AB. The t h i n l i n e XY i s p a r a l l e l t o the m e r i d i a n 122. The a n g l e C i s the amount t h e two azimuths d i f f e r and i s d e f i n e d as t h e a n g l e o f convergence.  F i g u r e A-1 Convergence o f t h e m e r i d i a n s  Geodesies : The s h o r t e s t d i s t a n c e between any two p o i n t s on a sphere, describe a great c i r c l e . The s i g h t i n g o f a t h e o d o l i t e i n F i g u r e A-1, from p o i n t A t o B and B t o A would be i d e n t i c a l . The plumb o r normal from t h e l e v e l l e d t h e o d o l i t e s would i n t e r s e c t a t t h e c e n t r e of t h e e a r t h . The f o r e s i g h t b e a r i n g between t h e two p o i n t s would be i d e n t i c a l w i t h t h e backsight. The s h o r t e s t d i s t a n c e on an e l l i p s o i d d e s c r i b e s a n , a r c , o r a geodesic. The s u r f a c e normals o f two p o i n t s on t h e e l l i p s o i d a r e skewed t o one another; t h e normals do n o t i n t e r s e c t . T h e r e f o r e t h e s i g h t i n g o f a t h e o d o l i t e from p o i n t A t o p o i n t B does not r e c o r d t h e same a z i m u t h as t h e s i g h t i n g from p o i n t B t o p o i n t A. The d i f f e r e n c e i n azimuths between t h e two p o i n t s i s s l i g h t however. The d i f f e r e n c e f o r two p o i n t s s e p a r a t e d by 50 km amounts t o 0.02" i n an example i n Torge(1980). The amount o f convergence t h a t a f f e c t s azimuth c a l c u l a t i o n s , depends on the s e p a r a t i o n i n l o n g i t u d e as w e l l as t h e s c a l a r d i s t a n c e . Two p o i n t s l y i n g on t h e same m e r i d i a n , would n o t s u f f e r any convergence i n t h e azimuth.  Purpose: The m o t i v a t i o n f o r w r i t i n g t h e program G e o d i s t was t o c a l c u l a t e d i s t a n c e when g i v e n t h e l o n g i t u d e and l a t i t u d e o f two p o i n t s . T h i s c o u l d be used when c a p t u r i n g raw g e o d e t i c p o s i t i o n s from t h e r e c e i v e r . T h i s saves t r a n s f o r m i n g t h e g e o d e t i c p o s i t i o n s t o a mapping p l a n e . The f u n c t i o n may be used t o p e r f o r m d i f f e r e n t i a l c o r r e c t i o n s over s h o r t d i s t a n c e s . I t i s a l s o more convenient t o use l a t i t u d e and l o n g i t u d e when c a l c u l a t i n g d i s t a n c e s between p o s i t i o n s t h a t span two o r more UTM mapsheets o r UTM zones.  Method: The program G e o d i s t was w r i t t e n i n Turbo P a s c a l v e r s i o n 5.5. Topaz u n i t s were used f o r t h e menus and i n p u t s c r e e n s . The c a l c u l a t i o n s were based on C code as s u p p l i e d by P o i n t o n (1991), w h i c h were based on a paper by V i n c e n t y ( 1 9 7 5 ) . The GRS80 e l l i p s o i d model i s used. T h i s GRS80 e l l i p s o i d uses 6378 km f o r t h e semi-major a x i s , and 6357 km f o r t h e semi-minor a x i s . T h i s i s e s s e n t i a l l y t h e model used i n WGS84, w h i c h i s t h e n a t i v e e l l i p s o i d r e f e r e n c e system f o r GPS. ( L a c h a p e l l e 1991) The g e o d e t i c d i s t a n c e s v;ere c a l c u l a t e d u s i n g G e o d i s t . These were compared w i t h d i s t a n c e s c a l c u l a t e d from examples i n Torge (1980) . UTM t r a n s f o r m a t i o n s from g e o d e t i c c o o r d i n a t e s were c a l c u l a t e d from t h e program GSrugpc. T h i s program i s s u p p l i e d by t h e G e o d e t i c survey of Canada ( F a r l e y and J u n k i n s 1990). Results : The r e s u l t s o f t h e model as compared t o t h e example i n Torge(1980) a r e d i s p l a y e d i n T a b l e A-1. The f i r s t column i s the d i f f e r e n c e i n l a t i t u d e o r l o n g i t u d e o f t h e p o s i t i o n from 50*^ N and 123'-' W. The second and t h i r d columns a r e t h e d i s t a n c e s i n metres c a l c u l a t e d by Torge and G e o d i s t respectively. The l a s t column i s t h e d i f f e r e n c e between t h e Torge and G e o d i s t c a l c u l a t i o n s .  T a b l e A-1 Example by Torge compared t o G e o d i s t D i f f e r e n c e s i n d i s t a n c e s c a l c u l a t e d from g e o d e t i c p o s i t i o n s Delta  Torge(m)  Geodist(m)  Difference(m)  Lat 1 degree  111229  111229  0  Lat 1 minute  1853.8  1853.8  0  Lat 1 second  30.30  30.97  0.07  Long 1 degree  71696  71596  100  Long 1 minute  1194.9  1193.3  1.6  Long 1 second  19.92  19.21  0.71  Taken a t 50°  latitude.  123^  longitude  The model G e o d i s t , agrees w i t h i n 1 cm of the e l l i p s o i d a l a r c d i s t a n c e p a r a l l e l t o l o n g i t u d e of the example i n Torge. However the d i s t a n c e c a l c u l a t e d a l o n g an a r c of l a t i t u d e do not r e a d i l y agree. For one degree of l o n g i t u d e t h i s i s o n l y 0.1% e r r o r . At the one minute i n t e r v a l , the magnitude of the d i s c r e p a n c y decreases. At the one second i n t e r v a l of l o n g i t u d e , the e r r o r amounts t o 3.6% of the d i s t a n c e . F u r t h e r c a l c u l a t i o n w i t h G e o d i s t , e s t i m a t e s t h a t w i t h an i n t e r v a l of t h r e e degrees of l a t i t u d e , r e p r e s e n t i n g a d i s t a n c e of a p p r o x i m a t e l y 214 k i l o m e t r e s on the ground, the f o r w a r d and backward azimuths d i f f e r from 180° by 3°The i m p l i c a t i o n s f o r c a l c u l a t i n g d i s t a n c e s on the mapping p l a n e are i l l u s t r a t e d i n Table A-2. The r e s u l t s of G e o d i s t , are compared t o d i s t a n c e s between UTM c o o r d i n a t e s . The UTM c o o r d i n a t e s a r e c a l c u l a t e d by the program GSrugpc ( F a r l e y and J u n k i n s 1990). P o i n t s two t o s i x are c a l c u l a t e d as the d i s t a n c e from p o i n t one.  Table A-2 Comparison of distances from GSrugpc and Geodist Point  Latitude  Longitude  1  49:00 :00  123:00:00  2  49:01:00  3  Distance (m)  Geodist (m)  Difference (m)  123:00:00  1852.8  1853.5  0.7  49:00:01  123:00:00  30.9  31  0.1  4  49:00:00  123:01:00  1219.2  1217.8  1.4  5  49:00:00  123:00:01  21  0.7  6  49:01:00  123:01:00  20.3 2217.72  2217.63  0.9  A i l d i s t a n c e s a r e i n metres. The d i f f e r e n c e between c a l c u l a t i n g d i s t a n c e s from UTM c o o r d i n a t e s v e r s u s d i r e c t l y from g e o d e t i c c o o r d i n a t e s i s g e n e r a l l y l e s s than 1 metre. Only when t h e d i s t a n c e c a l c u l a t e d a l o n g an a r c o f l a t i t u d e o f one minute (1.2 km) does t h e d i s c r e p a n c y grow t o 1.4metres . Discussion: The d i s c r e p a n c i e s i n c a l c u l a t i n g t h e g e o d e s i c between t h e t e x t b o o k example found i n Torge, and t h e c a l c u l a t e d d i s t a n c e s i n G e o d i s t , a r e cause f o r concern. Since the r e s u l t s s t r o n g l y agree i n t h e d i s t a n c e a l o n g a m e r i d i a n (NS ) , i t i s f e l t t h a t t h e e f f e c t o f convergence may have been l e f t out o f t h e V i n c e n t y a l g o r i t h m . U n t i l t h e reason f o r t h e d i s c r e p a n c y i s found and c o r r e c t e d , t h e f u n c t i o n i n G e o d i s t s h o u l d o n l y be used f o r a p p r o x i m a t i o n s . When t h e d i s t a n c e s c a l c u l a t e d w i t h G e o d i s t , a r e compared t o t h o s e c a l c u l a t e d by t h e program GSrugpc, t h e d i s c r e p a n c y i s lessened.  F o r 1 minute o f  o n l y 0.04%.  l a t i t u d e , the discrepancy i s  F o r one second o f l o n g i t u d e however, t h e  d i s c r e p a n c y i s 3.5 %.  When a c o m b i n a t i o n  o f change i n t h e  l a t i t u d e and l o n g i t u d e o f one minute i s made, t h e  When t h e d i s t a n c e s c a l c u l a t e d w i t h G e o d i s t , a r e compared t o t h o s e c a l c u l a t e d by t h e program GSrugpc, t h e d i s c r e p a n c y i s lessened. F o r 1 minute o f l a t i t u d e , t h e d i s c r e p a n c y i s o n l y 0.04%. F o r one second of l o n g i t u d e however, t h e d i s c r e p a n c y i s 3.5 %. When a c o m b i n a t i o n o f change i n t h e l a t i t u d e and l o n g i t u d e of one minute i s made, t h e d i s c r e p a n c y i s o n l y 0.004%. A g a i n i t appears t h a t convergence may p l a y a r o l e i n t h e d i s c r e p a n c y . The UTM g r i d a l s o s u f f e r s from convergence o f t h e m e r i d i a n s . That i s t h e UTM g r a t i c u l e i s a t r i g h t a n g l e s , w h i l e t h e m e r i d i a n s of l o n g i t u d e a r e c u r v e d towards t h e p o l e s .  Conclusion: The V i n c e n t y i n v e r s e f u n c t i o n can be used t o a p p r o x i m a t e d i s t a n c e s and a z i m u t h s on t h e e a r t h ' s s u r f a c e u s i n g g e o d e t i c c o o r d i n a t e s . When i n c o r p o r a t e d i n t o t h e program G e o d i s t , t h e s e agree t o an a c c e p t a b l e degree on d i s t a n c e s o f a p p r o x i m a t e l y 2 0 k i l o m e t r e s . However, f o r s h o r t d i s t a n c e s , e s p e c i a l l y a l o n g an a r c of l a t i t u d e , t h e d i s c r e p a n c y i s u n a c c e p t a b l e as compared t o d i s t a n c e c a l c u l a t e d on a UTM g r i d . However, i f one keeps i n mind t h e map s c a l e t h a t GPS data s h o u l d be used a t , t h e program G e o d i s t i s u s e f u l f o r calculating distances.  Bibliography Ewing, C.E. and M.M. M i t c h e l l . 1970. I n t r o d u c t i o n t o geodesy. American E l s e v i e r P u b l i s h i n g Co. I n c . New York. F a r l e y , S.A., J u n k i n s D.R. 1990. The n a t i o n a l t r a n s f o r m a t i o n . Program d e s c r i p t i o n s and u s e r i n s t r u c t i o n s f o r software package. I n P r e l i m i n a r y p r o c e e d i n g s . Moving t o NAD '83. Richmond, B.C. Canadian I n s t i t u t e o f S u r v e y i n g and Mapping. 40pp. P o i n t o n , K. 1991. P e r s o n a l correspondence. M i n i s t r y o f Crown Lands. G e o d e t i c C o n t r o l U n i t . V i c t o r i a B.C.  Torge, W. 1980. Geodesy, an i n t r o d u c t i o n , de G r u y t e r . B e r l i n , New York. V i n c e n t y , T. 1975. D i r e c t and i n v e r s e s o l u t i o n s of g e o d e s i e s on the e l l i p s o i d w i t h a p p l i c a t i o n of n e s t e d e q u a t i o n s . Survey Review X X I I , 176: 88-93. Wong, F. 1989. Course notes f o r F435. F o r e s t I n v e n t o r y Systems. U n i v e r s i t y of B r i t i s h Columbia.  APPENDIX B - ORBITSET Introduction A program w r i t t e n i n Turbo P a s c a l t o p r e d i c t v i s i b i l i t y o f s a t e l l i t e s o f t h e G l o b a l P o s i t i o n i n g System (GPS). Objective : The purpose o f t h e p r o j e c t was t o w r i t e a program t o p r e d i c t the o r b i t s and v i s i b i l i t y of NAVSTAR (GPS) s a t e l l i t e s f o r a p e r s o n on t h e e a r t h ' s s u r f a c e . The m o t i v a t i o n s t o embark on t h i s p r o j e c t were: 1) The a u t h o r was unaware o f any IBM PC c o m p a t i b l e s o f t w a r e t h a t was n o n - p r o p r i e t a r y , and used t h e NASA s u p p l i e d o r b i t a l parameters. 2)  3) 4)  To a n a l y z e s i g n a l r e c e p t i o n under f o r e s t c a n o p i e s , i t was b e l i e v e d t h a t p o l a r p l o t s o f s a t e l l i t e t r a c k s would be r e q u i r e d . T h i s i n f o r m a t i o n would be needed t o a n a l y z e o v e r l a y s of s a t e l l i t e t r a c k s and t h e f i s h - e y e l e n s photographs of t h e canopy. T h i s would e n a b l e a study o f what was i n t e r f e r i n g w i t h t h e s a t e l l i t e signals. T a b l e s o f s a t e l l i t e e l e v a t i o n s were r e q u i r e d t o a n a l y z e s a t e l l i t e e l e v a t i o n and s i g n a l a v a i l a b i l i t y . A p r e d i c t i o n program was needed t o a l l o w t h e p l a n n i n g of d i f f e r e n t i a l p o s i t i o n i n g s e s s i o n s .  5)  The f l e x i b i l i t y of p r o v i d i n g f u t u r e r e p o r t s c a n o n l y be h a n d l e d by h a v i n g access t o source code. I t was f e l t t h a t i t would be advantageous t o have a program w r i t t e n i n a h i g h l e v e l language f o r easy maintenance.  6)  The program c o u l d p r o v i d e t h e core f o r a s a t e l l i t e p r e d i c t i o n program t h a t i n c o r p o r a t e d a d i g i t a l t e r r a i n model. The s a t e l l i t e a v a i l a b i l i t y would be d e t e r m i n e d  7)  a f t e r a n a l y z i n g t h e s p e c i f i c area t h e u s e r was i n t e r e s t e d i n , using l o c a l p h y s i c a l b a r r i e r s (e.g. mountains). I t a l s o may p r o v i d e a c o r e f o r a system f o r p o i n t i n g a h i g h - g a i n antenna a r r a y i n a f o r e s t environment. The t y p i c a l GPS antenna i s c u r r e n t l y o m n i d i r e c t i o n a l .  Method: The program was w r i t t e n i n Turbo P a s c a l v e r s i o n 5.5. TOPAZ (1990) u n i t s were used t o handle t h e d a t a f i l e s and c r e a t e the menus. The g r a p h i n g f u n c t i o n was w r i t t e n as a u n i t by m o d i f y i n g a program from Turbo P a s c a l Programmer's Toolkit(1989). The a l g o r i t h m f o r t h e c a l c u l a t i o n f o r t h e e l e v a t i o n a n g l e s was found i n P r a t t and B e s t i a n ( 1 9 8 6 ) . Methods f o r h a n d l i n g J u l i a n dates were found i n D u f f e t - S m i t h P.(1981). These a r e i n c l u d e d i n t h e a n n o t a t e d b i b l i o g r a p h y . The d a t a f o r t h e o r b i t a l parameters were found i n t h e NASA prediction bulletins. These can be a c q u i r e d by w r i t i n g t o the a d d r e s s i n Appendix B - I I I . Results : W h i l e w r i t i n g t h e program, t h e n u m e r i c a l example i n P r a t t and B o s t i a n (1986), was c o n t i n u o u s l y checked. The r e s u l t s of t h e P r a t t example a r e c o n t a i n e d i n Appendix B-I. The r e s u l t s f o r ORBITSET compare f a v o r a b l y as i n d i c a t e d i n T a b l e B-1.  Table B-1 Comparison of ORBITSET to Pratt Numerical example Program  Elevation (degrees)  Azimuth (degrees)  Pratt & Bostian  32.28  229.39  ORBITSET  32.4  229.24  T h i s example was f o r a geosynchronous s a t e l l i t e . r e s u l t s change v e r y l i t t l e on a d a i l y  The  cycle.  The GPS r e s u l t s were t e s t e d a g a i n s t t h e T r i m b l e SATVIZ^M program and t h e M a g e l l a n NAV 1000 PRO^M r e c e i v e r . The T r i m b l e almanac was c o l l e c t e d by a survey r e c e i v e r on J u l y 7, 1990. The i n a b i l i t y o f u p d a t i n g t h e SATVIZ program w i t h o u t owning a T r i m b l e r e c e i v e r was one o f t h e m o t i v a t i o n s f o r w r i t i n g ORBITSET. The almanac f o r t h e M a g e l l a n was c o l l e c t e d on November 25, 1990. S i n c e ORBITSET cannot work backwards i n t i m e , a t e s t t o compare s a t e l l i t e PRN 17 was made on August 10, 1990 w i t h NASA d a t a from a b u l l e t i n i s s u e d on August 3, 1990. The results are: August 10 1990  00:00 UTC Program  Elevation  Azimuth  (degrees)  (degrees)  SATVIZ  25  244  ORBITSET  25.5  244.05  Magellan  25  244  August  10 1990  02:00 UTC Program  Elevation  Azimuth  (degrees)  (degrees)  SATVIZ  74  296  ORBITSET  74 . 6  296  Magellan  75  297  S i n c e t h e M a g e l l a n r e c e i v e r had a much l a t e r almanac i t may have s u f f e r e d a problem i n working backwards i n t i m e . T h e r e f o r e another comparison f o r December 3, 1990 was made. December 3, 1990 16:00 UTC Program  Elevation (degrees)  Azimuth (degrees)  SATVIZ  31  242  ORBITSET  33.6  240.76  Magellan  34  243  December 3, 1990 18:00 UTC Program  Elevation  Azimuth  (degrees)  (degrees)  SATVIZ  80  317  ORBITSET  81.78  326  Magellan  80  320  Discussion: More t e s t i n g i s r e q u i r e d t o f u l l y e v a l u a t e t h e program. S i n c e t h e d a t a i n p u t f o r each program i s d i f f e r e n t , some v a r i a t i o n i s t o be expected. A few degrees i n e l e v a t i o n may be a cause f o r concern i n some a p p l i c a t i o n s . However, one degree o f e l e v a t i o n may r e p r e s e n t o n l y about 2 minutes o f t i m e f o r a s a t e l l i t e p a s s i n g h i g h overhead.  ORBITSET uses t h e s i x c l a s s i c a l K e p l a r i a n parameters. These are : Inclination - t h e i n c l i n a t i o n of the s a t e l l i t e o r b i t t o the equator. E c c e n t r i c i t y - t h e measure o f how out o f round t h e e l l i p s e is. Mean Anomaly - t h e angle c r e a t e d by t h e p o s i t i o n o f t h e s a t e l l i t e a t epoch ( p o i n t i n time) and t h e argument o f p e r i g e e i f t h e o r b i t was c i r c u l a r . Argijment of perigee - t h e angle c r e a t e d by t h e p o i n t where t h e o r b i t i s c l o s e s t t o t h e e a r t h and t h e p o i n t o f t h e a s c e n d i n g node. Right ascension of the ascending node - a n g l e on t h e e q u a t o r i a l p l a n e from t h e p o i n t o f A r i e s ( f i x e d i n space) and t h e a s c e n d i n g node. Mean Motion - t h e number o f o r b i t s p e r day. The n a v i g a t i o n message c o l l e c t e d by t h e r e c e i v e r s c o n t a i n s 16 parameters. T h i s i s needed t o model t h e s a t e l l i t e ' s o r b i t more p r e c i s e l y . These e x t r a parameters c o n s i d e r t h e e f f e c t s o f a n o n - s p h e r i c a l e a r t h and t h i r d body gravitational effects. I t i s updated every 90 minutes (Wells, 3± 1986). To t e s t t h e s e n s i t i v i t y o f t h e parameters t o time s e v e r a l graphs were produced f o r t h e P r a t t example. example uses a geosynchronous  Since the P r a t t  s a t e l l i t e i n a very s t a b l e  o r b i t , i t would be expected t o remain t h e same over millennia.  The s a t e l l i t e o r b i t was p r e d i c t e d , f o r t h e time  t h e o r b i t a l parameters were c a l c u l a t e d : December 27, 1978. I t was then r u n e v e r y year u n t i l 1988 on December 27. F i g u r e s B-1 and B-2 i l l u s t r a t e how t h e p r e d i c t i o n s t a r t s t o deteriorate.  F i g u r e B-1 S a t e l l i t e e l e v a t i o n above t h e h o r i z o n v s . Time. 1978  90  n  I  F  I  I  1  I  1  I  I  T  I  '  I  I  I  80 70 .§  60  ^ o  60  !  40  CD  O  §> 30 20 10 Q  I  0  I  I  6  I  I  I  1  I  I  12  I  I  I  I  I  18  Hours UTC for 1 2 / 2 7 / 7 8  I  I  L.  24  December  F i g u r e B-2 S a t e l l i t e e l e v a t i o n above t h e h o r i z o n v s . Time. 1988  90  T  1  1  1  1  1  1  1  ,  L.  1  1  1  1  1  1  1  1  1  1  I  I  I  1  1  1  1  L_  r-  80 70 c  .§  60  ^ o  60  CD  40  CD CD  ^  30  Q  20 10 0  J  0  6  J  L  12  _J  I  18  Hours UTC for 1 2 / 2 7 / 8 8  I  24  December  F u t u r e Developments: The program i s at the stage where i t can be used as a p l a n n i n g t o o l by a GPS u s e r . The a u t h o r would l i k e t o see developed: 1) Output f i l e s i n ASCII and modules and programs.  .DBF  format t o be r e a d by o t h e r  2) A p o l a r p l o t of each s a t e l l i t e t o be used f o r a n a l y z i n g data c o l l e c t i o n s i t e s . scales.  P l o t s s h o u l d be a v a i l a b l e a t v a r i o u s  Other v a r i a b l e s t h a t a r e c a l c u l a t e d i n the program a r e : longsub l a t s u b - these are the ground t r a c k s of the satellites. They may be used t o p l o t the s a t e l l i t e ' s p a t h a l o n g a map of the e a r t h . a z i m u t h - the azimuth a n g l e of the s a t e l l i t e i n r e l a t i o n t o the u s e r ' s p o s i t i o n . P l o t s may be made t o h e l p t h e u s e r f i n d the p o s i t i o n of the s a t e l l i t e i n r e l a t i o n t o the u s e r . 3) Amalgamation of model w i t h a GIS d i g i t a l t e r r a i n model. T h i s would enable the u s e r t o produce a s i t e s p e c i f i c s a t e l l i t e window. 4) The p o s i t i o n a l d i l u t i o n of p r e c i s i o n (PDOP) s h o u l d be added t o t h e model. T h i s would i n d i c a t e the a c c u r a c y t h a t c o u l d be e x p e c t e d from a GPS s e s s i o n . The p r o j e c t suggested i n 3 c o u l d then be upgraded t o incorporate vegetation. of GPS  A GIS c o u l d be used t o p r o v i d e maps  a v a i l a b i l i t y based on l a n d forms and v e g e t a t i o n t y p e .  A f u r t h e r v e r s i o n c o u l d i n c o r p o r a t e t h e PDOP and e l e v a t i o n masks. Even w i t h a f u l l c o n s t e l l a t i o n o f s a t e l l i t e s a v a i l a b l e , t h i s c o u l d prove t o be a v a l u a b l e p l a n n i n g and research t o o l . The source code s h o u l d be c l e a n e d up by removing redundant code and f i n d i n g q u i c k e r a l g o r i t h m s . The bugs r e l a t e d t o s p u r i o u s e l e v a t i o n s s h o u l d be c o r r e c t e d . The s p u r i o u s e l e v a t i o n s a r e f e l t t o be from t h e o m i s s i o n o f a means o f d e t e r m i n i n g r i s e and s e t t i m e s f o r t h e s a t e l l i t e . A crude mask i s p r o v i d e d i n t h e program t h a t e x c l u d e s s a t e l l i t e s t h a t a r e on t h e o t h e r s i d e o f t h e e a r t h . The i n t e r f a c e can a l s o be made smoother. Upon c o m p l e t i o n o f t h e p r o j e c t i t was found t h a t v a r i o u s computer b u l l e t i n boards a r e i n e x i s t e n c e f o r t h e GPS community. A good p r o j e c t would be t o scan t h e v a r i o u s b u l l e t i n boards f o r a v a i l a b l e source code and e x e c u t a b l e programs. Conclusion: The program i s u s e f u l f o r a GPS u s e r t o p l a n d a i l y a c t i v i t y . A l t h o u g h some s p u r i o u s e l e v a t i o n s c r e e p i n t o t h e r e s u l t s , these a r e c o n f i n e d t o e l e v a t i o n s l e s s t h a n 15 degrees. I t i s f e l t t h a t s a t e l l i t e e l e v a t i o n s t h i s low s h o u l d be i g n o r e d as t h e s a t e l l i t e i s t o o c l o s e t o t h e h o r i z o n t o be used s u c c e s s f u l l y f o r p o s i t i o n i n g . The e l e v a t i o n mask however, can be changed by t h e u s e r . I t i s f e l t t h a t p r e d i c t i o n s w i l l be a c c u r a t e enough f o r p l a n n i n g purposes w i t h o r b i t a l parameters up t o a year o l d . The parameters s h o u l d however, be updated when a new s a t e l l i t e has been launched, o r when s a t e l l i t e o r b i t s have been a l t e r e d .  The s t r u c t u r e d f e a t u r e of Turbo P a s c a l s h o u l d  allow  m o d i f i c a t i o n o f t h e program t o support o t h e r f u n c t i o n s produce more v a r i e d  reports.  and  Bibliography D u f f e t - S m i t h , P. 1981. P r a c t i c a l astronomy w i t h your c a l c u l a t o r . Cambridge U n i v e r s i t y P r e s s . London. Second e d i t i o n . 188pp. A good g u i d e w i t h n u m e r i c a l examples f o r c a l c u l a t i n g J u l i a n dates. A l s o u s e f u l f o r r o t a t i o n matrices f o r converting between c o o r d i n a t e - o r d i n a t e systems. L a c h a p e l l e , G. 1991. G l o b a l p o s i t i o n i n g system. GPS workshop at GIS91, Vancouver, B.C. 180 pp. C o n t a i n s many e x c e r p t s from W e l l s , st, (1986) . Each page i s d e s i g n e d t o be used as an overhead t r a n s p a r e n c y . A l s o i n c l u d e s some notes t a k e n d u r i n g workshop. Morgan, W.L. and G.D. Gordon. 1989. Communications s a t e l l i t e handbook. John W i l e y and Sons. Toronto. 900pp. The b i b l e o f s a t e l l i t e communications. Compendium o f formulae and c o n s t a n t s . Some FORTRAN code i n c l u d e d but not used. N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n (NASA). 1990. NASA P r e d i c t i o n B u l l e t i n s . G r e e n b e l t , MD. 9pp. Free b u l l e t i n s c o n t a i n i n g t h e K e p l a r i a n s a t e l l i t e parameters.  Now a v a i l a b l e on e l e c t r o n i c b u l l e t i n  P r a t t , T. and C.W. B o s t i a n . 1986. S a t e l l i t e John W i l e y and Sons. Toronto. 472pp.  boards.  communications.  Was e s s e n t i a l f o r d e v e l o p i n g t h e program. P r o v i d e s a n u m e r i c a l example on pg 31. An e r r o r was found i n a r o t a t i o n a l m a t r i x i n e q u a t i o n 2.47. The p r e c i s i o n o f t h e i r c a l c u l a t i o n s a l s o may be q u e s t i o n e d .  TOPAZ. 1990. User's g u i d e and r e f e r e n c e manual. S o f t w a r e S c i e n c e I n c . B r i s b a n e , C a l i f o r n i a . 399pp. U s e f u l Turbo P a s c a l u n i t s f o r h a n d l i n g data i n .dbf format. A l s o used f o r b u i l d i n g menus. Source code not i n c l u d e d . Turbo P a s c a l . 1989. R e f e r e n c e guide, v e r s i o n 5.5. B o r l a n d I n t e r n a t i o n a l . S c o t t s V a l l e y , C a l i f o r n i a . 468pp. V e r s i o n 5.5.  V e r s i o n 6.0  and Turbo P a s c a l f o r Windows a r e  now a v a i l a b l e . Rugg, T. and P. Feldman. 1989. Turbo P a s c a l programmer's t o o l k i t . Que C o r p o r a t i o n . Carmel I n d i a n a . 53 9pp. Used f o r g r a p h i n g the r e s u l t s . Code i s commented and s u g g e s t e d m o d i f i c a t i o n s are found i n the book. Source code included. W e l l s , D.E. N. Beck, D. D e l i k a r a o g l o u , A. K l e u s b e r g , E . J . K r a k i w s k y , G. L a c h a p p e l l e , R.B. Langley, M. N a k i b o g l u , K.P. Schwarz, J.M. T r a n q u i l l a and P. V a n i c e k . 1986. Guide t o GPS P o s i t i o n i n g . Canadian GPS A s s o c i a t e s . F r e d e r i c t o n , NB. 544pp. Comprehensive guide. However too c o n c i s e t o be u s e f u l f o r a specific  topic.  APPENDIX B- I PRATT SOLUTION  Reference : P r a t t T., and C.W. B o s t i a n , 1986. S a t e l l i t e  communications  John W i l y & Sons. T o r o n t o . N u m e r i c a l example on page 30. Epoch : UT December 27, 1978 J u l i a n Date: 2443869.5 I n i t i a l parameters: 42164.765 km. 0.001181 0.802 116.636 138.167 84 .178  semimajor a x i s eccentricity inclination mean anomaly arg of perigee RA o f A s c e n d i n g node  ratio degrees degrees degrees degrees  User's l o c a t i o n : Latitude  37:13:44  degrees N  Longitude  80:26:17  degrees W  Results; Subsat l a t  -0.7736 degrees  c a l c u l a t e d by P r a t t  Subsat l a t  -0.775  p u b l i s h e d i n almanac  Subsat l o n g  116.2342 degrees  c a l c u l a t e d by P r a t t  Subsat l o n g  116.0230 degrees  p u b l i s h e d i n almanac  degrees  Elevation Azimuth  32.2 8 degrees 229.39 degrees  Appendix B-II Orbitset Users guide  Getting  started:  The d i s k c o n t a i n s t h e f i l e s : ORBITSET.EXE ORBITSET.OVR ORBITSET.DBF ORBIT.DBF DEADSATS.DBF The f i r s t two f i l e s c o n t a i n the e x e c u t a b l e code. To s t a r t the program type ORBITSET <enter>. ORBITSET.DBF i s a f i l e i n dBase format t h a t c o n t a i n s configuration information. ORBIT.DBF i s a f i l e i n dBase format t h a t c o n t a i n s t h e o r b i t d a t a f o r each s a t e l l i t e . I n c l u d e d a r e t h e K e p l a r i a n parameters. DEADSATS.DBF c o n t a i n s d a t a r e g a r d i n g t h e i d e n t i f i c a t i o n o f each s a t e l l i t e . I t provides a cross reference of i d e n t i f i e r s from d i f f e r e n t o r g a n i z a t i o n s . I t i s used by t h e Import f a c i l i t y t o weed out unusable s a t e l l i t e s . I t i s also used by Import t o a s s i g n t h e s a t e l l i t e pseudorandom n o i s e number (PRN). Menus The menus can be stepped through by p r e s s i n g t h e space b a r , u s i n g t h e arrow keys t o h i g h l i g h t the s e l e c t i o n . The <enter> key i s then p r e s s e d . A l t e r n a t i v e l y , t h e hot key may be used. The hot key corresponds t o t h e f i r s t l e t t e r o f t h e  menu s e l e c t i o n . F o r example, t o choose Setup i n t h e main menu, t h e u s e r would p r e s s S. Changing  configuration  At t h e main menu type S o r h i g h l i g h t SETUP and p r e s s <enter>. The date o f t h e setup can be changed by t y p i n g E o r h i g h l i g h t i n g E d i t and p r e s s i n g <enter>. The program d e f a u l t s t o o v e r t y p e mode. The setup can be named. The l o n g i t u d e i s n e g a t i v e f o r p o s i t i o n s West o f Greenwich. To e x i t t h e module, c u r s o r p a s t t h e l a s t f i e l d u n t i l t h e c u r s o r l a n d s on t h e menu. A l t e r n a t i v e l y one may p r e s s Page Down t o e n t e r t h e menu. To e x i t type Q u i t . A l l l a t i t u d e s a r e North. The program a l s o a l l o w s t h e u s e r t o s e l e c t t h e window o f time f o r t h e p r e d i c t i o n . This i s useful i n reducing the c l u t t e r on t h e graph. UTC i s a 24 hour c l o c k based on t h e Greenwich M e r i d i a n . I t i s commonly known as Greenwich Mean Time. P a c i f i c Standard Time i s e i g h t hours b e h i n d UTC. The mask a n g l e can be changed by t h e u s e r . The program r e q u i r e s t h a t t h e s t a r t and s t o p times d i f f e r by a t l e a s t two h o u r s . Editing  Bulletins  The c o n t r o l keys a r e t h e same as those f o r e d i t i n g t h e c o n f i g u r a t i o n . A s a t e l l i t e may be d i s a b l e d by p r e s s i n g D i s a b l e when t h e s a t e l l i t e i s on t h e s c r e e n . The d i s a b l e key i s a t o g g l e . P r e s s i n g D when t h e s a t e l l i t e i s d i s a b l e d enables i t . By d i s a b l i n g a s a t e l l i t e i t w i l l not appear on the p r e d i c t i o n .  D i s a b l e d s a t e l l i t e s can be d e l e t e d from t h e database by u s i n g t h e C l e a n f u n c t i o n . A prompt w i l l ask i f t h e u s e r wishes t o continue w i t h the d e l e t i o n . The o r b i t a l parameters can be e n t e r e d by hand from t h e NASA prediction bulletin. To e n t e r t h e e d i t mode, c u r s o r o v e r t o E d i t o r p r e s s E. Importing  par^met^rs  An a l t e r n a t i v e t o e n t e r i n g t h e numbers by hand i s t o import them from a f i l e . The parameters may be i m p o r t e d from a t w o - l i n e K e p l e r parameter f i l e . The d a t a may be downloaded from one o f t h e b u l l e t i n boards l i s t e d i n Appendix C. The Import f a c i l i t y i s found i n t h e B u l l e t i n menu. The f i l e s s u p p l i e d by t h i s program a r e NASA90.dat and NASA831.dat. The import f a c i l i t y a l l o w s t h e u s e r t o m a i n t a i n a dead satellite file. T h i s f i l e s t o r e s i d e n t i f i e r s and t h e s t a t u s of each s a t e l l i t e . I f t h e s a t e l l i t e i s tagged as "DEAD" i t i s s k i p p e d by t h e import program. M a r g i n a l s a t e l l i t e s a r e r e a d i n t o t h e database. The number o f r e c o r d s i n t h e b u l l e t i n i s n o t appended by t h e import f a c i l i t y . The user must add r e c o r d s t o t h e ORBIT.DBF file. T h i s can be done by u s i n g t h e Add f u n c t i o n i n t h e B u l l e t i n menu. The e a s i e s t way i s t o use Add, and p r e s s Page Down on t h e keyboard t o add a s a t e l l i t e . The import f u n c t i o n o v e r w r i t e s the e x i s t i n g Orbit.dbf f i l e . The NASA parameters can be used f o r up t o a y e a r w i t h no apparent d e g r a d a t i o n i n o r b i t p r e d i c t i o n . The u s e r may f i n d however, t h a t t h e s a t e l l i t e c o n s t e l l a t i o n i s c o n t i n u o u s l y changing. The b u l l e t i n needs maintenance as new s a t e l l i t e s are l a u n c h e d and o l d e r ones f a i l . The u s e r w i l l need t o d e l e t e some s a t e l l i t e s t h a t a r e i n o p e r a b l e and e n t e r  p a r a m e t e r s from new s a t e l l i t e s as they become a v a i l a b l e . P r e s e n t l y , t h e r e i s no way t o c o r r e l a t e the s a t e l l i t e c a t a l o g number as a s s i g n e d by NASA, w i t h the s a t e l l i t e PRN number. There i s a l i s t i n g of the p r e s e n t i d e n t i f i e r s i n A p p e n d i x C.  SO. T h i s i n i t i a t e s the p r e d i c t i o n . Press G o r h i g h l i g h t GO and <enter>. T h i s r e s u l t i s g r a p h i c a l output, w i t h s a t e l l i t e e l e v a t i o n v e r s u s t i m e . The graph may be p r i n t e d on a dotmatrix printer. TâMe T h i s f u n c t i o n p r i n t s out a t a b l e of s a t e l l i t e e l e v a t i o n s v e r s u s time. I t does no e r r o r c h e c k i n g w i t h r e g a r d s t o the printer. I t uses one page of output f o r every s a t e l l i t e t h a t i s enabled. The header g i v e s the s t a r t time i n UTC, and date of the c o n f i g u r a t i o n . The pseudorandom n o i s e code (PRN) i s g i v e n i n the f i r s t column. The time, g i v e n i n UTC, i n d e c i m a l hours i s the second column. The e l e v a t i o n , i n degrees above the u s e r ' s h o r i z o n , i s g i v e n i n the t h i r d column. The time increment i s the same as t h a t used t o produce the graph. That i s , t h e r e a r e n i n e t y - s i x d i v i s i o n s , whatever the time frame. The r e s u l t i s a f i n e r r e s o l u t i o n of time f o r a s h o r t e r p r e d i c t i o n time. The time frame i s chosen i n the Setup c o n f i g u r a t i o n . U s i n g ORBITSET Once the program i s run, the u s e r w i l l n o t i c e t h a t t h e s c r e e n w i l l be c l u t t e r e d w i t h s a t e l l i t e t r a c k s . The s h o u l d determine t h e i r l o c a l time from UTC. This i s f o r P a c i f i c Standard Time. For example 23:00 UTC i s 15:00 l o c a l o r 3:00 PM PST. The s a t e l l i t e s t h a t a r e  user UTC - 8 23-8= below  the h o r i z o n d u r i n g the u s e r ' s planned use of GPS may be d i s a b l e d . T h i s i s done by t o g g l i n g the D i s a b l e key i n t h e B u l l e t i n module. The u s e r w i l l a l s o f i n d the graph much e a s i e r t o r e a d i f the times a r e chosen t o c o i n c i d e w i t h the times of t h e p l a n n e d field collection.  Appendix  B-III  To r e c e i v e  f r e e NASA o r b i t a l parameters w r i t e t o :  NASA P r e d i c t i o n B u l l e t i n s u b s c r i p t i o n s C o n t r o l C e n t e r Support S e c t i o n Code 513.2 P r o j e c t O p e r a t i o n s Branch NASA Goddard Space F l i g h t Center G r e e n b e l t , MD 2 0771 The u s e r s h o u l d r e q u e s t t h e NAVSTAR GPS subset o f p r e d i c t i o n bulletins.  NASA p r e d i c t i o n b u l l e t i n s a r e a l s o a v a i l a b l e from t h e computer b u l l e t i n boards: C e l e s t i a l Remote CP/M 9600 baud F i l e t o download: BULLETIN.TXT Datalink 9600 baud M a i n l y f o r r e m o t e l y sensed images from t h e U.S. space program. The  Eyeballer baud data b i t s 1 s t o p b i t no p a r i t y  D e d i c a t e d t o t h e s u r v e y i n g community. I n f o r m a t i o n on E y e b a l l e r may be o b t a i n e d by w r i t i n g : D a v i d L. Hough Associated Consulting Inc. North Decateur Boulevard Las Vegas, Nevada (702)647-9265 I f on b i t n e t y o u may use t h e CANSPACE s e r v e r . To s u b s c r i b e t o CANSPACE send t h e message: SUB CANSPACE yourfirstname t o LISTSERV@UNB.CA  yourlastname  C r o s s r e f e r e n c e f o r GPS NASA C a t a l o g u e Number  satellites  S a t e l l i t e PRN  GPS D e s c r i p t i o n  4 7 6 8 5 9 11  GPS-OOOl GPS-0002 GPS-0003 GPS-0004 GPS-0005 GPS-0006 GPS-0008  * * marginal * * * exceeds specs  13 12 3 14 2  GPS-0009 exceeds specs GPS-OOlO exceeds specs GPS-0011 exceeds specs GPS-BII-01 GPS-BII-02  16 19  GPS-BII-03 GPS-BII-04  17 18 20 21  GPS-BII-05 GPS-BII-06 GPS-BII-07 GPS-BII-08  15  GPS-BII-09  23 24  GPS-BII-10 GPS-BII-11  * i n a c t i v e s a t e l l i t e s a t time of p r i n t i n g ( i e . dead) BII s a t e l l i t e s a r e those t h a t a r e capable o f s e l e c t i v e a v a i l a b i l i t y (SA). Sources: L a c h a p e l l e  (1991). NASA P r e d i c t i o n B u l l e t i n ( 1 9 9 1 )  M a g e l l a n 1000 NAV PRO r e c e i v e r almanac.  APPENDIX C - GPSDXF Description:  GPSDXF i s a program t o c o n v e r t d a t a f i l e s from t h e M a g e l l a n NAV 10 0 PRO (TM) GPS r e c e i v e r i n t o .DXF format.  The d a t a  i n p u t i s r e s t r i c t e d t o data f i l e s c r e a t e d w i t h t h e M a g e l l a n Systems C o r p o r a t i o n , RE4MAT, u t i l i t y u s i n g t h e U n i v e r s a l Transverse Mercator  (UTM) o p t i o n .  F o r i n s t r u c t i o n s on t h e  use o f t h e program, r e f e r t o Appendix C - I .  Introduction :  Data can be downloaded from t h e b u f f e r o f t h e M a g e l l a n Nav 1000  P r o GPS r e c e i v e r .  The r e c e i v e r may a l s o be connected  to an I B M ™ c o m p a t i b l e p e r s o n a l computer f o r a d a t a l o g g i n g session.  The raw GPS data can be r e f o r m a t t e d w i t h t h e  s o f t w a r e RE4MAT, s u p p l i e d by M a g e l l a n Systems. c o n v e r t e d and w r i t t e n t o an ASCII f i l e . program s u p p l i e d by t h e manufacturer.  The d a t a i s  CS87 i s a n o t h e r I t i s used t o p e r f o r m  s t a t i s t i c a l a n a l y s i s o f t h e raw d a t a from t h e r e c e i v e r .  The  s o f t w a r e does n o t have a s a t i s f a c t o r y c a p a b i l i t y o f viewing, or p l o t t i n g t h e r e s u l t s .  I t also only provides  average  p o s i t i o n s i n l a t i t u d e and l o n g i t u d e , w i t h e l e v a t i o n g i v e n as h e i g h t above t h e e l l i p s o i d .  It  was  the  these  program  software  limitations GPSDXF  is  intended  R-E4MAT  program.  f i l e .  That  points, output Aided  or  calculation then  be  into  other  further  s t a t i s t i c a l  user  view  to  and  the  the  format  labels  for  resultant  various  Computer  Information  provide  ample  scaling,  functions.  the  f i l e  programs  the  by  . DXF  The  Geographic  write The  output  produce  into  should  analysis.  edit  as  to  TALLY.  bones"  to  imported  writes  to  "bare  or  author  program data  made  plotting  statistics  read  a  programs  also  the  the  polygons..  programs  and  GPSDXF,  or  easily  These  editing  program  be  is was  lines  (CAD)  (GIS).  convert  attempt  should  motivated  companion  output  construct  Drafting  viewing,  The  no  the  to  The  is,  f i l e  Systems  and  that  of  each  TALLY.DBF.  such  The  f i l e  summary  as  This  f i l e  spreadsheets  program  TALLY,  can  for  allows  the  TALLY.DBF.  Purpose :  The  program  GPSDXF  is  the  program  RE4MAT  into  choose  to  produce  be  viewed  session  averages  is  program  may  various  scales.  printed  on  used  an  convert  .DXF f i l e .  may  be  a  .DBF  averages  A  to  a  session  be  used  written  to  to  the  plot  screen  Epson  FX  image  UTM f i l e s  format. A  The  the  f i l e  the  compatible  may  to  plot  9-pin  by  also  analysis  of  summary  of  A  TALLY.DBF.  positions of  user  s t a t i s t i c a l  and p r i n t e d .  produced  the can  The  screen be  printer.  sent  at to  .  Method:  The program was  w r i t t e n i n Turbo P a s c a l  TOPAZ v e r s i o n 3.0 f i l e s and  (1989) v e r s i o n  5.5.  (1990) u n i t s were used t o h a n d l e the  data  c r e a t e menus.  as a u n i t by m o d i f y i n g Programmer's T o o l k i t  The program was IBM  compatible  The g r a p h i n g  f u n c t i o n was  a program from Turbo P a s c a l (1989).  developed and t e s t e d on an AST computer.  t e x t mode and was  Bravo 485/25  The program makes use of c o l o u r i n  t e s t e d on a VGA  screen.  To t e s t  r e s u l t s of each program the f i l e C0403-3.GPS was f i l e was The  raw  written  the  used.  a n a l y z e d w i t h CS87 as s u p p l i e d by the m a n u f a c t u r e r . f i l e was  then c o n v e r t e d u s i n g RE4MAT w i t h the NAD27-  A l a s k a datum and h e i g h t above g e o i d .  A second f i l e  was  c r e a t e d u s i n g NAD27-Alaska and h e i g h t above e l l i p s o i d . r e s u l t i n g f i l e s were then a n a l y z e d u s i n g GPSDXF. f i l e was  The  c r e a t e d u s i n g RE4MAT.  The o r i g i n a l f i l e  A  The  third  was  c o n v e r t e d w i t h WGS84 as the datum, and h e i g h t above ellipsoid,  The  f o r the e l e v a t i o n .  s t a t i s t i c a l c a l c u l a t i o n s were based on f o r m u l a e from an  i n t e r n a l memorandum from M a g e l l a n  Systems.  Results :  The r e s u l t s o f each program a r e d i s p l a y e d i n F i g u r e s C-1 and C-2.  Although  t h e o r i g i n a l data f i l e c o n t a i n e d  the program CS87 o n l y used 159.  161 f i x e s  The program RE4MAT  s u c c e s s f u l l y read a l l 161 f i x e s and wrote them t o t h e f i l e C0403-3.UTM.  GPSDXF read a l l 161 f i x e s c o n t a i n e d i n t h e  f i l e C0403-3.UTM.  The a v e r a g e d p o s i t i o n g i v e n by CS87 cannot be r e a d i l y compared w i t h t h a t c a l c u l a t e d by GPSDXF.  CS87 o n l y p r i n t s  r e s u l t s i n l a t i t u d e and l o n g i t u d e u s i n g WGS84, w h i l e GPSDXF o n l y c a l c u l a t e s p o s i t i o n s i n UTM. for  coordinates  The datum u s u a l l y chosen  i n UTM v/as NAD-27-Alaska.  The a v e r a g e e l e v a t i o n s between the two programs cannot be r e a d i l y compared, when t h e h e i g h t above g e o i d i s s e l e c t e d i n the RE4MAT program.  The average e l e v a t i o n s i n F i g u r e s C-1  and C-2 d i f f e r by more than 17-metres. h e i g h t above e l l i p s o i d . method n a t i v e t o GPS. users.  Height  CS87 o n l y uses t h e  The h e i g h t above e l l i p s o i d i s t h e However i t i s not u s e f u l t o map  above t h e g e o i d ,  l e v e l ) i s t h e most u s e f u l .  (height above mean s e a -  A n a l y s i s o f GPS s e s s i o n C0403-3 by CS87 s o f t w a r e . datum used. H e i g h t above e l l i p s o i d  F I L E  N A M E :  O U T L I E R  L I M I T  (M)  OF  SAMPLES  NO.  OF  GOOD  AVE  SAMPLES  L A T I T U D E 1 7  AVE  L O N G I T U D E  123  3  AVE  A L T .  :  1 0 0 0  E X C E E D I N G  P O S I T I O N  49  only.  C 0 4 0 3 - 3 . G P S  NO.  KNOWN  ALSKA  NOT  O U T L I E R  U S E D :  M I N ,  FOR  C A L C U L A T I O N  M I N ,  F I X  ERRORS  NORTH  SEC)  4 3 . 1 7 7 4 4 8 0 7 5 0 7 2 1 1 A B O V E / B E L O W  OF  SEC)  1 2 . 3 5 0 1 8 5 1 2 9 4 3 9 5 2 (DEG,  0  1 5 9  A V A I L A B L E  (DEG,  L I M I T :  ( + / - )  W G S - 8 4  WEST E L L I P S O I D  M E T E R S :  STANDARD  D E V .  OF  SCATTER  X-COMPONENT,  METRES  :  STANDARD  D E V .  OF  SCATTER  Y-COMPONENT,  METRES  :  STANDARD  D E V .  OF  SCATTER  A L T - C O M P O N E N T ,  METRES  1 7 . 3 1 0 3 7 5 9 4 4 6 2 3 4 1  5 . 2 8 7 9 0 0 1 5 7 0 2 6 4 7 8 2 8 . 3 5 8 2 3 8 2 2 3 0 3 2 9 1 :  2 4 . 7 3 8 8 6 9 3 6 8 2 7 8 9 4  2- D I M E N S I O N A L  RMS  D E V I A T I O N ,  M E T R E S :  2 8 . 8 4 7 0 3 7 3 3 8 0 8 6 6 5  3 - D I M E N S I O N A L  RMS  D E V I A T I O N ,  M E T R E S :  3 8 . 0 0 2 1 4 7 5 8 1 4 5 1 2  2 - D I M E N S I O N A L  MEAN  R A D I A L  D E V I A T I O N ,  M E T R E S :  2 2 . 4 0 4 1 4 9 5 4 6 4 7 0 0 2  2 - D I M E N S I O N A L  MEAN  R A D I A L  D E V I A T I O N ,  M E T R E S :  3 2 . 1 5 5 3 7 9 7 0 7 9 4 3 6 7  CEP  R E L A T I V E  TO  AVERAGE  P O S I T I O N  METRES  :  1 7 . 6 1 5 5 9 1 8 9 7 8 9 9  SEP  R E L A T I V E  TO  AVERAGE  P O S I T I O N  METRES  :  2 8 . 6 5 4 5 7 5 4 1 1 7 7 0 6 5  A n a l y s i s o f GPS s e s s i o n C0403-3 by GPSDXF s o f t w a r e . ALSKA datum used. E l e v a t i o n g i v e n as h e i g h t above g e o i d . GPS Data File:  C:\GPS\DATA\C0403-3.UTM  Number o f r e c o r d s : 161 Zone  Analysis  Average N o r t h i n g  10  Collection  Datum: ALSKA (m)  From: 3:50:55 - 4:20:56 UTC  Average E a s t i n g  (m)  496794  5459139  Average Elevation(m) 34.61  RMS  Standard D e v i a t i o n (m) Easting  d a t e : 04/04/91  (m)  5.2 6  2- D i m e n s i o n a l :  28.73  Northing  28.33  3- D i m e n s i o n a l :  37.85  Elevation  24.75  Mean R a d i a l  Deviation(m)  Mean PDOP:  5.38 9.0  2- D i m e n s i o n a l :  22.34  Mean  3- D i m e n s i o n a l :  32.10  Highest PDOP  Circular  E r r o r Probable(m)  18.11  SNR  Lowest SNR 9  5.73  S p h e r i c a l E r r o r Probable(m) 28.4  A n a l y s i s o f GPS s e s s i o n C0403-3 by GPSDXF s o f t w a r e . ALSKA datum used. E l e v a t i o n g i v e n as h e i g h t above e l l i p s o i d . GPS Data A n a l y s i s File: C:\GPS\DATA\C0403-3G.UTM C o l l e c t i o n d a t e : 04/04/91 Number o f r e c o r d s : 161 Datum: ALSKA From: 3:50:55 - 4:20:56 UTC Zone Average N o r t h i n g (m) Average E a s t i n g (m) Average E l e v a t i o n ( m ) 10 5459139 496794 17.06 Standard D e v i a t i o n (m) RMS (m) Easting 5.26 2- D i m e n s i o n a l : 28.73 Northing 28.33 3- D i m e n s i o n a l : 37.85 Elevation 24.71 Mean R a d i a l Deviation(m) 2- D i m e n s i o n a l : 22.34 3- D i m e n s i o n a l : 32.06  Mean PDOP: Mean SNR Highest PDOP  C i r c u l a r E r r o r Probable(m) 18.11  5.38 9.0 5.73  Lowest SNR 9  S p h e r i c a l E r r o r Probable(m) 28.32  F i g u r e C-3B Same f i l e as i n C-3A b u t w i t h WGS84 e l l i p s o i d . GPS Data  Analysis  File: C:\GPS\DATA\C0403-3W.UTM C o l l e c t i o n d a t e : 04/04/91 Number o f r e c o r d s : 161 Datum: ALSKA From: 3:50:55 - 4:20:56 UTC Zone Average N o r t h i n g (m) Average E a s t i n g (m) Average E l e v a t i o n ( m ) 10 5459336 4967704 17.06 Standard D e v i a t i o n (m) RMS (m) Easting 5.28 2- D i m e n s i o n a l : 28.64 Northing 28.24 3- D i m e n s i o n a l : 37.78 Elevation 24.71 Mean R a d i a l Deviation(m) 2- D i m e n s i o n a l : 22.28 3- D i m e n s i o n a l : 32.00 C i r c u l a r E r r o r Probable(m) 17 . 64  Mean PDOP: Mean SNR H i g h e s t PDOP  5.38 9.0 5.73  Lowest SNR 9  S p h e r i c a l E r r o r Probable(m) 28.06  The r e s u l t s i n F i g u r e C-3 a r e based on h e i g h t above t h e e l l i p s o i d but s t i l l u s i n g NAD27-Alaska as t h e datum. e l e v a t i o n s compare f a v o r a b l y .  The  When t h e r e s u l t s o f CS87, a r e  compared w i t h t h o s e from GPSDXF, when WGS84 and h e i g h t above e l l i p s o i d a r e used, t h e most f a v o r a b l e comparison s h o u l d be made.  However i t appears t o be no b e t t e r than u s i n g t h e  NAD27-Alaska datum.  The s t a t i s t i c s c a l c u l a t e d by each  program a r e summarized i n Table C-1. Table C-1 Comparison of results from GPSDXF and CS87 i n analyzing GPS data  Elev STD E STD N STD E l e v RMS RMS M Rad M Rad CEP SEP  CS87 ellip 17 .31 5.29 28.36 24.74 28.85 38.00 22.40 32.15 17.62 28.65  GPSDXF geoid 34 .61 5.26 28.33 24 .75 28 .73 37.87 22.34 32.10 18,11 28 .40  ellip 17.06 5.26 28.33 24.71 28.73 37.85 22.34 32.06 18.11 28.32  WGS84 17 .06 5.28 28.24 24.71 28.64 37.78 22.28 32.00 17 . 64 28.06  A l l measurements a r e i n metres. Average D i f f e r e n c e i n % 0.52% D i f f e r e n c e i s between GPSDXF/geoid and CS87 STD - s t a n d a r d d e v i a t i o n RMS - r o o t mean square M Rad - mean r a d i a l e r r o r CEP - c i r c u l a r e r r o r p r o b a b l e SEP - s p h e r i c a l e r r o r p r o b a b l e  difference 17 .3 -0.03 -0.03 + 0.01 -0.12 -0.13 -0.06 -0.05 + 0.49 -0.25  Discussion :  The program CS87 performs the s t a t i s t i c a l c a l c u l a t i o n s raw d a t a from the r e c e i v e r .  on  GPSDXF performs a l l  c a l c u l a t i o n s on the product of the program RE4MAT.  The  raw  d a t a i s t r a n s f o r m e d and c o o r d i n a t e s are u s u a l l y based on a datum d i f f e r e n t from t h a t used i n CS87. concerned  The u s e r i s u s u a l l y  w i t h the p o s i t i o n i n g e r r o r on a mapping p l a n e .  Thus the s t a t i s t i c s performed by GPSDXF a r e more r e l e v a n t , because they d e a l w i t h c o o r d i n a t e s on a mapping p l a n e  (UTM).  The d i f f e r e n c e s i n the e x p r e s s i o n of e r r o r o r p r e c i s i o n , between the two programs i s n e g l i g i b l e . d i s c r e p a n c i e s o c c u r when d i f f e r i n g  The  largest  models a r e used ( i . e .  r e f e r e n c e p o i n t f o r e l e v a t i o n ) , r a t h e r than t r a n s f o r m e d  data  a n a l y z e d by d i f f e r e n t programs.  The program RE4MAT c o n t a i n s a g e o i d s e p a r a t i o n model.  The  p o s i t i o n on the e a r t h ' s s u r f a c e i s c a l c u l a t e d on  an  e l l i p s o i d based on WGS84 w i t h i n a GPS  I f the u s e r  receiver.  r e q u e s t s the d i s p l a y of p o s i t i o n s i n any o t h e r system UTM,  h e i g h t above g e o i d ) , the r e c e i v e r must p e r f o r m  transformation.  (e.g.  a  To c a l c u l a t e the h e i g h t above the g e o i d ,  the program o r r e c e i v e r must model the s e p a r a t i o n between the g e o i d and e l l i p s o i d .  S i n c e the r e c e i v e r works f o r  p o s i t i o n s anywhere i n the w o r l d , the s e p a r a t i o n model must n e c e s s a r i l y be crude.  The u s e r would a c h i e v e more a c c u r a t e  e l e v a t i o n s by c a l c u l a t i n g t h e h e i g h t above e l l i p s o i d , and applying a l o c a l geoid separation to the e l e v a t i o n .  F u t u r e Developments:  The program c u r r e n t l y o n l y p r o v i d e s UTM c o o r d i n a t e s i n a .DXF format.  I t may be d e s i r a b l e t o c o n v e r t o t h e r  formats  such as l o n g i t u d e and l a t i t u d e as can be s u p p l i e d by RE4MAT.  The program c u r r e n t l y c o n v e r t s o n l y d a t a f i l e s as s u p p l i e d by t h e RE4MAT program.  The next s t e p i s t o c a p t u r e t h e data  i n t h e raw form as s u p p l i e d by t h e r e c e i v e r i t s e l f . A l l t r a n s f o r m a t i o n s s h o u l d be performed by a program where t h e s o u r c e code i s a v a i l a b l e t o t h e u s e r .  C u r r e n t l y , Magellan  Systems Corp. does not p r o v i d e t h e a l g o r i t h m s f o r t h e transformations.  A n o t h e r development would be t o w r i t e an i n t e g r a t e d package f o r t h e a n a l y s i s o f t h e GPS d a t a .  T h i s would i n c l u d e :  - r e a d i n g raw d a t a from t h e r e c e i v e r . - p e r f o r m i n g s t a t i s t i c a l f u n c t i o n s on t h e p o s i t i o n s obtained. - p e r f o r m i n g d i f f e r e n t i a l c o r r e c t i o n s on p o s i t i o n s . - p l o t t i n g p o i n t s t o the screen. - p l o t t i n g t o paper. - e d i t i n g p o i n t s , e i t h e r manually  o r by a s t a t i s t i c a l  test.  Conclusions :  The program GPSDXF i s a u s e f u l program t o c o n v e r t i n t o other formats.  I t c o n t a i n s more f e a t u r e s and  p r o d u c t i v i t y b e n e f i t s than t h e s o f t w a r e Systems.  GPS data  s u p p l i e d by M a g e l l a n  The .DXF format a l l o w s p l o t t i n g by v a r i o u s CAD and  GPS packages.  The GPSUTM.DBF f i l e i s i n a format t h a t can  be r e a d by v a r i o u s database and spreadsheet packages.  The  d i s c r e p a n c i e s i n the r e p o r t i n g of the e r r o r s a r e  n e g l i g i b l e between t h e two programs. 0.52 p e r c e n t  overall.  The d i f f e r e n c e i s o n l y  Bibliography TOPAZ. 1990. U s e r ' s guide and r e f e r e n c e manual. Science Inc. Brisbane, C a l i f o r n i a . Turbo P a s c a l . 1989. Reference g u i d e , v e r s i o n 5.5. I n t e r n a t i o n a l . Scotts Valley, C a l i f o r n i a .  Software Borland  Rugg T, and P. Feldman. 1989. Turbo P a s c a l programmer's t o o l k i t . Que C o r p o r a t i o n . Carmel I n d i a n a .  A p p e n d i x C-I  Uger'g  guide  Getting started:  The program d i s k e t t e c o n t a i n s s i x  files:  GPSDXF.EXE GPSDXF.OVR GPSDXFCF.DBF GPSUTM.DBF TALLY.EXE TALLY.DBF  The  first  two f i l e s c o n t a i n t h e e x e c u t a b l e code.  The f i l e  GPSDXFCF.DBF c o n t a i n s c o n f i g u r a t i o n i n f o r m a t i o n t o r u n t h e program.  The f i l e c o n t a i n s such i n f o r m a t i o n as t h e d e f a u l t  p a t h and f i l e n a m e  The  extensions.  f i l e GPSUTM.DBF c o n t a i n s a l l t h e d a t a found i n t h e f i l e  p r o v i d e d by t h e program RE4MAT.  The g r a p h i n g module  the p o s i t i o n s t o p l o t from t h i s f i l e .  reads  F o r a complete  l i s t i n g o f t h e f i e l d s , r e f e r t o Appendix C - I I .  The  f i l e TALLY.DBF i s appended w i t h s t a t i s t i c a l summary  i n f o r m a t i o n every time t h e s t a t i s t i c s module i s used.  The  program TALLY a l l o w s t h e user t o view and e d i t t h e r e c o r d s in  t h e f i l e TALLY.DBF.  To use t h e program l o a d a l l t h e f i l e s i n t o a s i n g l e directory.  To s t a r t t h e program t y p e GPSDXF.  Menus  The menus can be s t e p p e d t h r o u g h by p r e s s i n g t h e space b a r , u s i n g t h e arrow keys t o h i g h l i g h t t h e s e l e c t i o n . E n t e r key i s p r e s s e d . used.  Then t h e  A l t e r n a t i v e l y , t h e hot key may be  The hot key c o r r e s p o n d s t o t h e f i r s t l e t t e r o f t h e  menu s e l e c t i o n .  F o r example, t o choose C o n f i g u r e i n t h e  main menu, t h e u s e r would p r e s s C.  Changing the configuration:  At t h e main menu t y p e E o r p r e s s <enter> when E d i t i s highlighted. Editing:  To e d i t t h e f i e l d s t h e keys a r e s i m i l a r t o Wordstar o r dBase.  An example o f t h e more u s e f u l f u n c t i o n and k e y s :  Function  Key  Beginning of l i n e  Home  End o f l i n e  End  Delete l i n e  Ctrl-Y  D e l e t e c h a r a c t e r under c u r s o r  Delete  Next  field  Enter  Skip  fields  Page Down  Escape  Ctrl-Q  Escape  ESC  Fields :  Path: T h i s i s t h e v a l i d DOS p a t h t o t h e d e s i r e d i n p u t  file.  Examples i n c l u d e : \gps\data \  The program does a v a l i d a t i o n check on t h e p a t h  entered.  Input f i l e : T h i s i s t h e f i l e produced by t h e program RE4MAT as s u p p l i e d by M a g e l l a n .  The o p t i o n s  selected i n the  program RE4MAT must be s e l e c t e d t o produce a f i l e i n t h e U n i v e r s a l T r a n s v e r s e M e r c a t o r (UTM) format. does no e r r o r c h e c k i n g  The program  i n the reading of the f i l e .  The f i l e  may be s e l e c t e d from a d i r e c t o r y l i s t i n g by p r e s s i n g t h e F2 key.  I f t h e u s e r chooses t o supply t h e name o f t h e f i l e by  t y p i n g i t i n , t h e e x t e n s i o n must a l s o be s u p p l i e d .  Extension: I t i s suggested t h a t when u s i n g t h e program RE4MAT, t h e e x t e n s i o n The  .UTM be used f o r t h e output f i l e s .  e x t e n s i o n may be changed however, as r e q u i r e d , i n t h e  program GPSDXF t o match t h e output f i l e from RE4MAT.  The  program d i s p l a y s o n l y those f i l e s t h a t c o n t a i n t h e e x t e n s i o n s u p p l i e d by t h e u s e r , when F2 i s used.  Output f i l e : T h i s i s t h e f i l e t o be c r e a t e d by t h e program. The  d e f a u l t i s g i v e n as t h e i n p u t f i l e b u t w i t h a .dxf  and/or .dbf e x t e n s i o n .  The user may s u p p l y a n o t h e r name.  I t must be a v a l i d DOS name w i t h o u t program s u p p l i e s t h e e x t e n s i o n .  the extension.  The  The program checks i f t h e  f i l e w i t h a .dxf e x t e n s i o n a l r e a d y e x i s t s , and i f so, w i l l respond w i t h an i n q u i r y t o o v e r w r i t e t h e e x i s t i n g f i l e .  It  w i l l not check i f a f i l e of t h e same name, w i t h a .dbf extension,  exists.  GO!: Performs t h e c o n v e r s i o n t o t h e f i l e i n t h e c o n f i g u r e menu.  formats as s e l e c t e d  S t a t i s t i c s : C a l c u l a t e s r e l e v a n t s t a t i s t i c s on a s e t o f f i x e s on t h e same p o s i t i o n . A l s o p r o v i d e s t h e maximum and average PDOP and s i g n a l q u a l i t y . To p r i n t t h e r e p o r t p r e s s P r i n t . View: A l l o w s t h e user t o view t h e i n p u t f i l e . The f i l e viewed i s GPSUTM.DBF. T h i s f i l e i s o v e r w r i t t e n on every conversion. A l l o w s t h e user t o view t h e f i l e on a r e c o r d by r e c o r d o r t a b l e format. Plot: E n t e r s t h e SEEPLOT menu system f o r p l o t t i n g t h e p o s i t i o n s t o s c r e e n and t o paper. Quit: A l l o w s t h e user t o e x i t t h e program and r e t u r n t o DOS. A l l f i l e s used by t h e program a r e saved and c l o s e d upon exit.  U s i n g GPSDXF:  Once the c o n f i g u r a t i o n i s completed the u s e r s h o u l d c u r s o r , o r escape, t o the main menu.  Help may  be o b t a i n e d by  s e l e c t i n g HELP from the main menu o r p r e s s i n g F l . p e r f o r m the c o n v e r s i o n , GO s h o u l d be s e l e c t e d . DOS,  To  To e x i t t o  EXIT s h o u l d be chosen.  The program w i l l r e a d a maximum of two hundred p o s i t i o n s . This corresponds  t o the maximum number of f i x e s i n the  b u f f e r of the M a g e l l a n r e c e i v e r .  The  f i l e TALLY i s o n l y  l i m i t e d by the space on the d i s k .  The program w i l l o n l y p r o v i d e s t a t i s t i c s o r p l o t c u r r e n t l y converted data f i l e .  To view another  the file,  the  u s e r must e d i t the C o n f i g u r e menu and c o n v e r t the d e s i r e d file. U s i n g SEEPLOT:  The SEEPLOT module a l l o w s the u s e r t o p l o t the p o s i t i o n s of the c u r r e n t f i l e onto the s c r e e n . are shown on the s c r e e n .  The d e f a u l t c o n d i t i o n s '  The u s e r s e l e c t s GO t o p e r f o r m  p l o t w i t h the d e f a u l t parameters of a u t o s c a l e and pop d i s p l a y a l l the p o i n t s at once.  or  a  The  A u t o s c a l e s e l e c t i o n , ensures t h a t a l l the  f i l e w i l l be d i s p l a y e d . d i m e n s i o n t h a t has  The  fixes in  program c a l c u l a t e s  the most s p r e a d and  p l o t on the  l a r g e s t dimension.  i n both dimensions.  The  p l o t may  largest  I t centres not be  display.  The  a l l o w s the u s e r t o s t e p t h r o u g h  p o s i t i o n s one  at a time.  T h i s may  default  moving.  a p o s i t i o n may  time, when on a s t a t i o n a r y p l a t f o r m . u s e r may  It  drift  Alternatively,  choose t o d i s p l a y a l l the p o i n t s i s t o d i s p l a y the p o i n t s  the  be u s e f u l , f o r example,  t o i n d i c a t e which d i r e c t i o n a v e h i c l e was a l s o be u s e f u l , to examine how  the  suitable  scale for future  option  centred  on the bottom of  T h i s w i l l enable the u s e r to s e l e c t a  Point  the  When the p l o t i s shown, the s p r e a d i n  the l a r g e s t d i m e n s i o n i s d i s p l a y e d screen.  the  uses the  d i m e n s i o n t o c a l c u l a t e the s c a l e t o be used.  the  at once.  a l l at once.  may  with the The  Appendix C - I I Database s t r u c t u r e s Database s t r u c t u r e f o r GPSUTM.DBF GPSUTM Record = Record Boolean; Deleted LongInt; _STATION LongInt; _HOUR LongInt; _MIN LongInt; _SEC LongInt; _UTMZONE LongInt; _EASTING LongInt; _NORTHING _ELEVATION : L o n g I n t ; LongInt; _MODE S t r i n g [ 2] _SAT1 S t r i n g [ 2] _SAT2 S t r i n g [ 2] _SAT3 S t r i n g [ 2] _SAT4 S t r i n g [ 2] _SIG1 S t r i n g [ 2] _SIG2 S t r i n g [ 2] _SIG3 S t r i n g [ 2] _SIG4 Real; _PDOP S t r i n g [ 2] _MONTH S t r i n g [ 2] _DAY S t r i n g [ 2] _YEAR String[10] ; _DATE String[ £ ] _DATUM end;  width width width width width width width width width  6} 2} 2} 3} 2} 7} 8} 7} 1}  {width= 6,decimals =4}  { Date f i e l d }  NOTE:  The f i l e GPSUTM.DBF c o n t a i n s i n f o r m a t i o n t h a t i s n o t i n c l u d e d i n t h e .DXF f i l e . conversion.  GPSUTM i s o v e r w r i t t e n on every  I t i s found i n t h e same DOS d i r e c t o r y as t h e  program GPSDXF.exe.  A copy o f t h e f i l e GPSUTM, u s i n g t h e  i n p u t f i l e name w i t h t h e .dbf e x t e n s i o n i s w r i t t e n t o t h e same d i r e c t o r y t h a t t h e i n p u t data f i l e  resides.  Database s t r u c t u r e f o r TALLY.DBF type TALLY Record = Record Deleted Boolean; FILE S t r i n g [ 12] RECORDS Longint; MEASTING Real; MNORTHING Real; MEANELEV Real; STDX Real; STDY Real; STDZ Real; RMS 2 Real; RMS3 : Real; CEP : Real; SEP : Real; HIGHPDOP Real; LOWESTSNR : Real; AVGSNR : Real; AVGPDOP : Real;  { { { { { { { { { { { { { { {  width width width width width width width width width width width width width width width  = = = = = = = = = = = = = = =  7} 12, 12, 7, 12, 12, 12, 12, 12, 12, 12, 12, 8, 8, 12,  decimals decimals decimals decimals decimals decimals decimals decimals decimals decimals decimals decimals decimals decimals  = = = = = = = = = = = = = =  3} 3} 3} 7} 7} 7} 7} 7} 7} 7} 7} 4} 4} 7}  APPENDIX D  GLOSSARY OF TERMS  Almanac - The i n f o r m a t i o n r e c e i v e d from the s a t e l l i t e s t h a t c o n t a i n s the o r b i t a l parameters o f t h e s a t e l l i t e s . The d a t a c o n t a i n e d i n the almanac can be used t o p r e d i c t the p o s i t i o n s of the s a t e l l i t e s . This allows t h e r e c e i v e r t o determine which s a t e l l i t e s t o use f o r positioning. A z i m u t h - Measure o f a r c , i n degrees, i n a c l o c k w i s e d i r e c t i o n from t r u e n o r t h . C a r r i e r - A r a d i o wave h a v i n g a t l e a s t one c h a r a c t e r i s t i c (e.g. frequency, a m p l i t u d e , phase) w h i c h may be v a r i e d from a known r e f e r e n c e v a l u e by m o d u l a t i o n . I n GPS t h e c a r r i e r frequency i s 10.23 MHz.. Datum - The frame o f r e f e r e n c e f o r a c o o r d i n a t e system. L a t i t u d e and l o n g i t u d e a r e c o o r d i n a t e s on an e l l i p s o i d model o f t h e e a r t h . The parameters t h a t d e s c r i b e t h e e l l i p s e (semi-major and semi-minor axes ) and the p o i n t o f o r i g i n o f t h e e l l i p s e d e f i n e a datum e.g. Meades Ranch, Kansas f o r NAD27, c e n t r e o f the g r a v i t y o f t h e e a r t h f o r NAD83. DOP - d i l u t i o n o f : Q r e c i s i o n . A g e n e r a l term, used t o d e s c r i b e expected p o s i t i o n i n g v a r i a n c e s based on t h e s t r e n g t h o f t h e geometry o f t h e t r i a n g u l a t i o n , s e e PDOP. E l l i p s o i d - an e l l i p s e r o t a t e d on i t s minor a x i s through a r e v o l u t i o n . The e l l i p s o i d a l model t h a t i s used f o r Earth i s often c a l l e d a spheroid. Ephemeris - the p a t h o r t r a j e c t o r y o f t h e s a t e l l i t e around the e a r t h . The p a t h i s d e s c r i b e d by an e q u a t i o n r e q u i r i n g 14 parameters. The ephemeris parameters b r o a d c a s t by a s a t e l l i t e i s c a l l e d the b r o a d c a s t ephemeris. E r r o r e l l i p s e - The terms used t o d e s c r i b e t h e a c c u r a c y o f a p o s i t i o n vary according t o f i e l d of study. A f r e q u e n t l y used term i n s u r v e y i n g i s t h e e l l i p s e o f s t a n d a r d d e v i a t i o n . I t can be extended t o t h r e e dimensions as a r o t a t i o n a l e l l i p s o i d . F o r example, g i v e n a degree o f c o n f i d e n c e r e q u i r e d , an e l l i p s e can be m a g n i f i e d t o encompass a p r o b a b i l i t y o f 0.9 ( L e i c k  1990). T h i s method o f d e s c r i p t i o n o f e r r o r i s u s e f u l when t h e p o s i t i o n f i x e s do not suggest a c i r c u l a r normal d i s t r i b u t i o n . The e r r o r e l l i p s e i s t h e most r i g o r o u s method of d e s c r i b i n g t h e e r r o r , b u t i s n o t t h e most c o n v e n i e n t . (Lachappele 1991). G e o d e s i c - an a r c on t h e s u r f a c e o f an e l l i p s o i d . The s h o r t e s t d i s t a n c e c a l c u l a t e d on t h e e l l i p s o i d a l s u r f a c e of t h e e a r t h between two g e o d e t i c c o o r d i n a t e s ( l a t i t u d e and l o n g i t u d e ) G e o i d - bounding e q u i p o t e n t i a l s u r f a c e o f t h e e a r t h . Every f a c e t o f t h e s u r f a c e i s normal t o g r a v i t y . E s s e n t i a l l y mean s e a - l e v e l . G e o i d a l h e i g h t - t h e e l e v a t i o n above t h e g e o i d o r mean s e a level. T h i s i s t h e e l e v a t i o n used by f o r e s t e r s . E l l i p s o i d a l h e i g h t i s t h e h e i g h t above t h e e l l i p s o i d . E l l i p s o i d a l h e i g h t i s t h e e l e v a t i o n c a l c u l a t e d by GPS. GDOP - g e o m e t r i c d i l u t i o n of p r e c i s i o n . The sum o f t h e e x p e c t e d v a r i a n c e s i n time. E a s t i n g , N o r t h i n g and e l e v a t i o n , see PDOP. Ionospheric r e f r a c t i o n - a s i g n a l t r a v e l i n g through the i o n o s p h e r e (which i s non homogeneous and d i s p e r s i v e medium) e x p e r i e n c e s a p r o p a g a t i o n time d i f f e r e n t from t h a t w h i c h would o c c u r i n a vacuum. Phase advance depends on e l e c t r o n content and a f f e c t s c a r r i e r s i g n a l s . Group d e l a y depends on d i s p e r s i o n i n t h e i o n o s p h e r e as w e l l , and a f f e c t s s i g n a l m o d u l a t i o n (codes). Kinematic p o s i t i o n i n g - r e f e r s to a p p l i c a t i o n s i n which a t r a j e c t o r y o f an o b j e c t i s determined. M u l t i p a t h e r r o r - i s an e r r o r r e s u l t i n g from i n t e r f e r e n c e between r a d i o waves which have t r a v e l l e d between t h e t r a n s m i t t e r and t h e r e c e i v e r by two paths o f d i f f e r e n t e l e c t r i c a l lengths. Outage - t h e o c c u r r e n c e i n time and space o f a GPS D i l u t i o n of P r e c i s i o n (DOP) v a l u e exceeding a s p e c i f i e d v a l u e . PDOP - P o s i t i o n a l D i l u t i o n of P r e c i s i o n . A s c a l a r t h a t i s used t o m u l t i p l y t h e UERE t o d e r i v e t h e e x p e c t e d RMS e r r o r o f a p o s i t i o n . U s u a l l y thought o f as an i n d e x o f the s t r e n g t h o f t h e geometry o f t h e s a t e l l i t e c o n s t e l l a t i o n used t o determine a p o s i t i o n . A PDOP o f 3 would be v e r y good, 6 a c c e p t a b l e , 10 u n d e s i r a b l e . The PDOP i s t h e sum of t h e expected v a r i a n c e s i n t h e  N o r t h i n g E a s t i n g and E l e v a t i o n , based on the p o s i t i o n of the u s e r , i n r e l a t i o n t o the p o s i t i o n of the satellites. PPM  - p a r t s per m i l l i o n . One ppm i n the p o i n t p o s i t i o n i n g mode i s the rms of one m i l l i o n t h of the l e n g t h of the geocentric p o s i t i o n vector. (1 ppm- 6.4m.). In the r e l a t i v e p o s i t i o n i n g mode i t i s u s u a l l y assumed t o be t h e e r r o r / l e n g t h of the b a s e l i n e .  P r e c i s i o n and A c c u r a c y - As i n d i c a t e d i n the i n t r o d u c t i o n , t h e s e terms f o r t h i s study are assumed t o be the same. Pseudorandom n o i s e code - (PRN). Any group of b i n a r y sequences t h a t e x h i b i t n o i s e l i k e p r o p e r t i e s , the most i m p o r t a n t of which i s the sequence has a maximum auto c o r r e l a t i o n at z e r o l a g . The PRN code number i s u s u a l l y used t o d i s t i n g u i s h s a t e l l i t e s e.g. PRN 3 i s s a t e l l i t e 3. Pseudo-range - the t i m e d i f f e r e n c e t o c o r r e l a t e a r e p l i c a of the GPS code g e n e r a t e d by the r e c e i v e r w i t h the r e c e i v e d GPS code, s c a l e d i n t o the d i s t a n c e by the speed of l i g h t . T h i s time s h i f t i s the d i f f e r e n c e between the time of s i g n a l r e c e p t i o n (measured i n the r e c e i v e r time frame) and the time of e m i s s i o n (measured i n the s a t e l l i t e time frame). The range then must be c o r r e c t e d by removing the t i m i n g e r r o r between the two clocks. R e l a t i v e A c c u r a c y : The a c c u r a c y of a p o s i t i o n of a r e c e i v e r w i t h r e s p e c t t o another r e c e i v e r at a known l o c a t i o n . R e l a t i v e p o s i t i o n i n g - the d e t e r m i n a t i o n of r e l a t i v e (as opposed t o a b s o l u t e ) p o s i t i o n s between two or more r e c e i v e r s which are t r a c k i n g the same s i g n a l s . Also called differential positioning. R e p e a t a b l e A c c u r a c y - The  a c c u r a c y t h a t a u s e r can use  return to a p o s i t i o n previously RMS  determined by  to  GPS.  - r o o t mean square. The s t a n d a r d e r r o r of e s t i m a t e . E s s e n t i a l l y the s t a n d a r d d e v i a t i o n of o b s e r v a t i o n s t h a t were r e g r e s s e d t o e s t i m a t e a p o i n t p o s i t i o n .  S a t e l l i t e c o n f i g u r a t i o n - the s t a t e of the s a t e l l i t e c o n s t e l l a t i o n at a s p e c i f i c time, r e l a t i v e t o a s p e c i f i c user.  S a t e l l i t e c o n s t e l l a t i o n - t h e arrangement i n space o f t h e complete s e t o f s a t e l l i t e s o f a system l i k e GPS. SA - ^ e l e c t i v e a v a i l a b i l i t y implements a q u i c k c h a n g i n g a l g o r i t h m t o d i t h e r i n f o r m a t i o n coming from t h e satellites. T h i s w i l l be i n t h e form o f c l o c k o r o r b i t a l e r r o r s . T h i s w i l l deny u n a u t h o r i z e d u s e r s o f the system t o a c c u r a c i e s o f g r e a t e r than 100-metres i n p o s i t i o n i n r e a l - t i m e . The e f f e c t o f SA c a n be l e s s e n e d i f not e l i m i n a t e d by d i f f e r e n t i a l p o s i t i o n i n g . S t a t i c p o s i t i o n i n g - p o s i t i o n i n g a p p l i c a t i o n s i n which the p o s i t i o n s o f t h e p o i n t s a r e determined, w i t h o u t r e g a r d to t h e they may o r not have. T h i s a l l o w s t h e use o f v a r i o u s a v e r a g i n g t e c h n i q u e s t h a t improve a c c u r a c y by f a c t o r s o f over 1000. UERE - User E q u i v a l e n t Range E r r o r . The c o n t r i b u t i o n from an e r r o r source i n measurement u n i t s (metres) t o t h e c a l c u l a t i o n o f t h e range o f t h e u s e r ' s antenna t o a satellite. T h i s v a l u e i s m u l t i p l i e d by PDOP t o d e t e r m i n e t h e expected RMS e r r o r o f a p o s i t i o n WGS84 - W o r l d £eodetic System. The c o o r d i n a t e system used by GPS. E s s e n t i a l l y i d e n t i c a l t o t h e r e f e r e n c e e l l i p s o i d used i n NADS3. However t h e o b s e r v a t i o n s used i n t h e adjustment used t o d e s c r i b e t h e s t a t i o n s may be different.  

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