Appendix 3
STATE OF CALIFORNIA DEPARTMENT OF TRANSPORTATION
TECHNICAL REPORT DOCUMENTATION PAGE
TR0003 ( REV. 10/ 98)
1. REPORT NUMBER
CA04- 0289
2. GOVERNMENT ASSOCIATION NUMBER
3. RECIPIENT’S CATALOG NUMBER
5. REPORT DATE
December 2008
4. TITLE AND SUBTITLE
Carrier Phase Differential GPS aided INS for Snowplow
Guidance 6. PERFORMING ORGANIZATION CODE
Department of Electrical Engineering
10. WORK UNIT NUMBER
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Jay A. Farrell
Department of Electrical Engineering
University of California, Riverside
Riverside, CA 92521 USA
11. CONTRACT OR GRANT NUMBER
65A1078
13. TYPE OF REPORT AND PERIOD COVERED
Final Report
12. SPONSORING AGENCY AND ADDRESS
California Department of Transportation
Sacramento, CA 95819
14. SPONSORING AGENCY CODE
15. SUPPLEMENTAL NOTES
16. ABSTRACT
Snow Plow driver guidance system has two major components: a roadway relative position determination system
( RRPDS) and a human machine interface ( HMI). The RRPDS must maintain an estimate of the vehicle state
( i. e., position, velocity, heading, and heading rate) relative to the roadway with position accurate to a few
centimeters. The HMI presents the data from the RRPDS to the driver in a visually appealing and easily
perceivable format. This is a three phase effort with the objective of producing a Carrier Phase ( CP) Differential
Global Positioning System ( DGPS) aided Inertial Navigation System ( INS) implementation of the RRPDS that
is able to maintain centimeter level position accuracy along highways through mountain environments. The main
advantage of the system underdevelopment relative to previously demonstrated systems is that the CP DGPS
aided INS approach would not require any alterations of the highway infrastructure. Along the demonstration
corridor, the phase II effort demonstrated that: By the use of a single radio modem repeater and differential
correction prediction technology, differential corrections could be reliably received to achieve the desired level
of performance. Along the vast majority of the highway included in the demonstration, GPS signal reception
was sufficient to be able maintain the desired centimeter level system accuracy. The selected portion of the I80
did not include overpasses or overhead street signs due to limitations of the GPS receivers available to the
project during Phase II. To achieve this successful demonstration, the Phase II effort: evaluated alternative
methods for communication of the base station corrections, selecting the Freewave modem approach for the final
demonstration; studied the effect of modem repeaters on system performance and designed a modem/ repeater
configuration to support the demonstration; developed a Windows based HMI with enhanced features; and
advanced the state- of- the- art in GPS aided INS signal processing. In addition, we performed research on the
suitability of certain augmentation technologies, most notably Pseudolites, as they relate to the objectives of this
project.
17. KEY WORDS
GPS, Snow Plow Guidance, Carrier Phase
Correction, Differential Correction
18. DISTRIBUTION STATEMENT
No restrictions. This document is available to the
public through the National Technical Information
Service, Springfield, VA 22161
19. SECURITY CLASSIFICATION ( of this report)
Unclassified
20. NUMBER OF PAGES
45
21. PRICE
Division of Research
& Innovation
Report CA04- 0289
December 2008
Differential Carrier Phase GPS aided
Inertial Navigation for Snowplow
Guidance
Final Report
Appendix 3
Reproduction of completed page authorized
Appendix 3
Reproduction of completed page authorized
Differential Carrier Phase GPS aided Inertial Navigation
for Snowplow Guidance
Final Report
Report No. CA04- 0289
December 2008
Prepared By:
Department of Electrical Engineering
University of California, Riverside
Riverside CA 92521
Prepared For:
California Department of Transportation
Division of Research and Innovation, MS- 83
1227 O Street
Sacramento, CA 95814
DISCLAIMER STATEMENT
This document is disseminated in the interest of information exchange. The contents of this report
reflect the views of the authors who are responsible for the facts and accuracy of the data presented
herein. The contents do not necessarily reflect the official views or policies of the State of California
or the Federal Highway Administration. This publication does not constitute a standard, specification
or regulation. This report does not constitute an endorsement by the Department of any product
described herein.
For individuals with sensory disabilities, this document is available in Braille, large print,
audiocassette, or compact disk. To obtain a copy of this document in one of these alternate formats,
please contact: the Division of Research and Innovation, MS- 83, California Department of
Transportation, P. O. Box 942873, Sacramento, CA 94273- 0001.
C a l t r a n s P r o j e c t : 6 5 A 0 1 4 8
D i ® e r e n t i a l C a r r i e r P h a s e G P S a i d e d I n e r t i a l N a v i g a t i o n f o r
S n o w p l o w G u i d a n c e
F i n a l R e p o r t
J a y F a r r e l l
D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g
U n i v e r s i t y o f C a l i f o r n i a , R i v e r s i d e
R i v e r s i d e C A 9 2 5 2 1 , U S A
v : 9 0 9 - 7 8 7 - 2 1 5 9
f : 9 0 9 - 7 8 7 - 2 4 2 5
e : f a r r e l l @ e e . u c r . e d u
C a l t r a n s P o i n t o f C o n t a c t :
A s f a n d S i d d i q u i
9 1 6 - 6 5 4 - 6 9 9 4
1
C o n t e n t s
1 E x e c u t i v e S u m m a r y 3
2 I n t r o d u c t i o n 4
3 P r i o r s t a t u s 4
4 O b j e c t i v e s o f t h e P h a s e 1 5
5 E x p e r i m e n t a l R e s u l t s : I 8 0 D o n n e r s P a s s 5
6 B a s e S t a t i o n 1 9
6 . 1 C a l t r a n s B a s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9
6 . 2 B a s e a n d R o v e r S a t e l l i t e R e c e p t i o n D a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1
6 . 3 U C R B a s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3
7 P h a s e 1 R e s u l t s 4 3
8 C o n c l u s i o n s 4 4
9 C o n t a c t I n f o r m a t i o n 4 4
2
1 E x e c u t i v e S u m m a r y
T h e p r o j e c t i s c o n c e r n e d w i t h t h e d e v e l o p m e n t o f v e h i c l e n a v i g a t i o n s y s t e m s t o s e r v e a s t h e v e h i c l e
l o c a t i o n i n p u t f o r d r i v e r a s s i s t a n c e s y s t e m s f o r h i g h w a y m a i n t e n a n c e v e h i c l e s . T h e s e s y s t e m s w o u l d
h a v e v a l u e , f o r e x a m p l e , f o r s a f e t y o r l a w e n f o r c e m e n t v e h i c l e s t r a v e l i n g i n e x t r e m e f o g o r s n o w r e m o v a l
e q u i p m e n t o p e r a t i n g i n h e a v y s n o w f a l l . T h e o b j e c t i v e o f t h e n a v i g a t i o n s y s t e m i s t o r e l i a b l y m a i n t a i n
c m l e v e l a c c u r a c y f o r t h e v e h i c l e l o c a t i o n e s t i m a t e .
B a s e d o n p a s t s u c c e s s f u l d e m o n s t r a t i o n s a t C r o w s L a n d i n g o f d i ® e r e n t i a l c a r r i e r p h a s e g l o b a l p o -
s i t i o n i n g s y s t e m ( D C P G P S ) a i d e d i n e r t i a l n a v i g a t i o n s y s t e m s ( I N S ) m a i n t a i n i n g c m l e v e l a c c u r a c y f o r
v e h i c l e c o n t r o l a p p l i c a t i o n s , C a l t r a n s s u g g e s t e d t h a t t h e a p p r o a c h b e f u r t h e r d e v e l o p e d a n d t e s t e d t o
w o r k r e l i a b l y i n m o r e c h a l l e n g i n g e n v i r o n m e n t s , s u c h a s t h a t a t D o n n e r P a s s . A m a j o r o b j e c t i v e o f t h e
¯ r s t p h a s e o f t h i s p r o j e c t w a s a s i t e s u r v e y t o a s s e s s t h e f e a s i b i l i t y a n d c h a l l e n g e s o f w o r k i n g a t t h e
D o n n e r P a s s l o c a t i o n . T h a t a n a l y s i s i s c o n t a i n e d h e r e i n .
T h e m a i n c o n c l u s i o n s a r e
1 . T h e G P S s i g n a l a v a i l a b i l i t y i s s u ± c i e n t f o r t h e D C P G P S a i d e d I N S t o m a i n t a i n c m l e v e l a c c u r a c y ,
e x c e p t o n c e r t a i n s h o r t s e c t i o n s o f t h e t e s t e d r o a d w a y . T h e s e r o a d w a y s e c t i o n s a r e r e p e a t a b l e
b e t w e e n r u n s . T h i s r e p e a t a b i l i t y w a s a d e s i r e d o u t c o m e . T h e f a c t t h a t t h e r o a d w a y s e c t i o n s
a r e r e p e a t a b l e b e t w e e n r u n s m e a n s t h a t a t l e a s t o n e o f t h e a u g m e n t a t i o n m e t h o d s s u g g e s t e d i n t h e
o r i g i n a l p r o p o s a l ( e . g . , p s e u d o l i t e s , r o a d w a y a l t i t u d e , o r m a g n e t o m e t e r a l o n g i s o l a t e d r o a d s e c t i o n s )
o r a d v a n c e s i n G P S r e c e i v e r a n d s a t e l l i t e t e c h n o l o g y s h o u l d y i e l d a r e l i a b l e w o r k i n g s y s t e m a l o n g
t h e e n t i r e r o a d w a y f r o m S i e r r a v i l l e t o G r a s s V a l l e y .
2 . T h e C a l t r a n s b a s e s t a t i o n i n D o n n e r s P a s s i s s u ± c i e n t t o a l l o w t e s t i n g o f t h e a p p r o a c h a l o n g l i m i t e d
s e c t i o n s o f I 8 0 ; h o w e v e r , c e r t a i n s e c t i o n s o f t h e r o a d w a y d o n o t r e l i a b l y r e c e i v e t h e b a s e s t a t i o n
s i g n a l . T h i s s h o u l d b e ¯ x a b l e b y i n s t a l l i n g r e p e a t e r s .
T h e s e c o n c l u s i o n s a r e b a s e d o n a n a l y s i s o f e l e v e n d a t a s e t s a c q u i r e d a t d i ® e r e n t t i m e s a n d o n d i ® e r e n t
d a y s b e t w e e n A u g u s t 2 6 { A u g u s t 2 8 , 2 0 0 3 o n t h e I 8 0 b e t w e e n t h e S i e r r a v i l l e a n d G r a s s V a l l e y e x i t s .
B a s e d o n t h e s e c o n c l u s i o n s , f u t u r e p r o j e c t g o a l s a r e :
1 . t o i n v e s t i g a t e a n d d e v e l o p t h e a u g m e n t a t i o n m e t h o d s f o r u s e w i t h t h e D C P G P S a i d e d I N S ;
2 . t o i n v e s t i g a t e t h e u s e o f a d v a n c e d G P S a n d I N S t e c h n o l o g i e s ;
3 . t o m o d i f y t h e U C R D C P G P S a i d e d I N S s o t h a t i t i s a b l e t o r e c e i v e t h e d i ® e r e n t i a l c o r r e c t i o n d a t a
f r o m a n d o p e r a t e w i t h t h e C a l t r a n s b a s e s t a t i o n a t D o n n e r s P a s s ; a n d
4 . t o i n v e s t i g a t e a l t e r n a t i v e s o u r c e s o f d i ® e r e n t i a l c o r r e c t i o n s .
T h e o b j e c t i v e i s t o b e g i n s u c c e s s f u l d e m o n s t r a t i o n s o f t h e D C P G P S a i d e d I N S o n l i m i t e d s e c t i o n s o f t h e
I - 8 0 t h r o u g h D o n n e r P a s s i n t h e P h a s e I I o f t h e p r o j e c t . W e e x p e c t t o b e a b l e t o d e m o n s t r a t e o n l o n g e r
s e c t i o n s o f t h e I 8 0 t h r o u g h D o n n e r s a n d t o i m p r o v e p e r f o r m a n c e a n d r e l i a b i l i t y a s t h e a u g m e n t a t i o n
m e t h o d s a r e f u r t h e r i m p r o v e d a n d i n c o r p o r a t e d o v e r t h e d u r a t i o n o f t h i s p r o j e c t .
3
2 I n t r o d u c t i o n
S n o w p l o w s t y p i c a l l y o p e r a t e i n e x t r e m e e n v i r o n m e n t s i n t e r m s o f t e m p e r a t u r e , h u m i d i t y , v i b r a t i o n ,
a n d v i s i b i l i t y . I n e x t r e m e w h i t e o u t o r f o g c o n d i t i o n s , i t w o u l d b e u s e f u l t o p r o v i d e t h e d r i v e r i n f o r m a t i o n
a b o u t h i s r o a d w a y r e l a t i v e p o s i t i o n . A m a g n e t o m e t e r b a s e d r o a d w a y r e l a t i v e p o s i t i o n i n g s y s t e m d e v e l -
o p e d b y P A T H a n d A H M C T h a s p r e v i o u s l y b e e n d e m o n s t r a t e d i n t h e s n o w p l o w g u i d a n c e a p p l i c a t i o n
w i t h C a l t r a n s s p o n s o r s h i p . T h e e x i s t i n g a p p r o a c h h a s t w o m a i n c o m p o n e n t s . T h e ¯ r s t c o m p o n e n t i s a
m a g n e t o m e t e r b a s e d r o a d w a y - r e l a t i v e v e h i c l e p o s i t i o n s e n s o r . T h e s e c o n d c o m p o n e n t i s a d i s p l a y o f t h e
r o a d w a y r e l a t i v e p o s i t i o n t o t h e d r i v e r .
T h e u t i l i t y o f a s n o w p l o w / s n o w b l o w e r d r i v e r g u i d a n c e s y s t e m i s c l e a r . S u c h a s y s t e m c a n p r o v i d e t h e
d r i v e r w i t h r o a d w a y r e l a t i v e p o s i t i o n a n d v e l o c i t y i n f o r m a t i o n w h e n t h e d r i v e r ' s v i s u a l p e r c e p t i o n o f t h e s e
q u a n t i t i e s i s i m p a i r e d b y w e a t h e r c o n d i t i o n s . S u c h a d r i v e r g u i d a n c e s y s t e m h a s t w o m a j o r c o m p o n e n t s :
a r o a d w a y r e l a t i v e p o s i t i o n d e t e r m i n a t i o n s y s t e m ( R R P D S ) a n d a h u m a n m a c h i n e i n t e r f a c e ( H M I ) . T h e
R R P D S m u s t m a i n t a i n a n e s t i m a t e o f t h e v e h i c l e s t a t e ( i . e . , p o s i t i o n , v e l o c i t y , h e a d i n g , a n d h e a d i n g r a t e )
r e l a t i v e t o t h e r o a d w a y w i t h p o s i t i o n a c c u r a t e t o a f e w c e n t i m e t e r s . T h e H M I p r e s e n t s t h e d a t a f r o m
t h e R R P D S t o t h e d r i v e r i n a v i s u a l l y a p p e a l i n g a n d e a s i l y p e r c e i v e d f o r m a t . P r e v i o u s C A L T R A N S -
s u p p o r t e d p r o j e c t s h a v e d e m o n s t r a t e d a m a g n e t o m e t e r b a s e d s n o w - p l o w / s n o w b l o w e r R R P D S a n d a H M I .
P r e v i o u s C A L T R A N S r e s e a r c h u n d e r t h e P A T H p r o g r a m h a s d e v e l o p e d a n d d e m o n s t r a t e d a C P D G P S
a i d e d I N S R R P D S t h a t h a s b e e n s u c c e s s f u l l y d e m o n s t r a t e d i n l a t e r a l v e h i c l e c o n t r o l a p p l i c a t i o n s [ 2 , 4 ] .
C A L T R A N S r e s e a r c h u n d e r t h e P A T H p r o g r a m h a s a l s o d e v e l o p e d a n d d e m o n s t r a t e d a m a g n e t o m e t e r
a n d C P D G P S a i d e d I N S R R P D S t h a t h a s b e e n s u c c e s s f u l l y d e m o n s t r a t e d i n l a t e r a l v e h i c l e c o n t r o l
a p p l i c a t i o n s [ 5 , 7 ] . T h e m o t i v a t i o n f o r t h i s p r o j e c t i s t o a p p l y t h e C P D G P S a i d e d I N S R R P D S i n t h e
s n o w p l o w / s n o w b l o w e r a p p l i c a t i o n . T h e b e n e ¯ t o f t h i s a p p r o a c h i s t h a t t h e C P D G P S a i d e d I N S R R P D S
w o u l d r e q u i r e s i g n i ¯ c a n t l y l e s s c h a n g e s t o t h e r o a d w a y i n f r a s t r u c t u r e r e l a t i v e t o t h e m a g n e t o m e t e r o n l y
a p p r o a c h , t h e r e b y d e c r e a s i n g t h e i n s t a l l a t i o n a n d m a i n t e n a n c e c o s t s .
T h e r e f o r e , t h e o b j e c t i v e o f t h e p r o j e c t d i s c u s s e d i n t h i s r e p o r t i s t o e v a l u a t e , d e v e l o p , a n d d e m o n s t r a t e
a n a l t e r n a t i v e r o a d w a y - r e l a t i v e v e h i c l e p o s i t i o n s e n s o r . T h e p r o j e c t w i l l u t i l i z e t h e s a m e d r i v e r d i s p l a y
a s t h e e x i s t i n g s y s t e m . T h e n e w r o a d w a y - r e l a t i v e v e h i c l e p o s i t i o n s e n s o r u t i l i z e s d i ® e r e n t i a l c a r r i e r p h a s e
G l o b a l P o s i t i o n i n g S y s t e m ( D C P G P S ) a n d i n e r t i a l m e a s u r e m e n t s .
3 P r i o r s t a t u s
U C R h a s p r e v i o u s l y d e m o n s t r a t e d a D C P G P S a i d e d I N S t h a t m a i n t a i n s c m a c c u r a c y p o s i t i o n e s t i -
m a t e s a t 1 5 0 H z s a m p l e r a t e [ 4 ] . T h i s s y s t e m w a s u s e d t o c o n t r o l t h e l a t e r a l p o s i t i o n o f a u t o m o b i l e s a t
l o w s p e e d s a t U C R a n d a t h i g h s p e e d s d u r i n g t e s t i n g a t t h e C r o w ' s L a n d i n g t e s t f a c i l i t y . N o t e t h a t t h e
D C P G P S a i d e d I N S d o e s n o t r e q u i r e a n y a l t e r a t i o n s t o t h e r o a d w a y .
U C R h a s a l s o p r o v i d e d s e v e r a l d e m o n s t r a t i o n s o f a m a g n e t o m e t e r a n d C P D G P S a i d e d I N S [ 1 , 2 ,
5 ] . T h i s s y s t e m a l s o m a i n t a i n e d c m a c c u r a c y p o s i t i o n e s t i m a t e s a t 1 5 0 H z . T h e n a v i g a t i o n s y s t e m i s
a b l e t o w o r k w i t h m a g n e t o m e t e r m e a s u r e m e n t s o n l y , w i t h D C P G P S m e a s u r e m e n t s o n l y , o r w i t h b o t h
m e a s u r e m e n t s s i m u l t a n e o u s l y . A n a d v a n t a g e o f t h i s m a g n e t o m e t e r a n d D C P G P S a i d e d I N S a p p r o a c h i s
t h a t s e n s o r r e d u n d a n c y m a k e s i t s i g n i ¯ c a n t l y m o r e r e l i a b l e t o s e n s o r f a i l u r e s t h a n a s i n g l e s e n s o r a p p r o a c h
c o u l d b e . A l s o , i n c o m p a r i s o n t o a m a g n e t o m e t e r o n l y a p p r o a c h , t h e c o m b i n e d s y s t e m d o e s n o t r e q u i r e
m a g n e t s e m b e d d e d i n t h e r o a d w a y a t a ¯ x e d 1 . 2 m s p a c i n g . I n s t e a d , m a g n e t s c o u l d b e w i d e l y s p a c e d
o n s e c t i o n s o f r o a d w a y w i t h a n o p e n v i e w o f t h e s k y a n d m o r e c l o s e l y s p a c e d o n l y a l o n g t h o s e r e g i o n s o f
t h e r o a d w a y w h e r e t h e s k y i s s i g n i ¯ c a n t l y o b s c u r e d ( e . g . , t u n n e l s ) .
4
4 O b j e c t i v e s o f t h e P h a s e 1
T h e o b j e c t i v e s s t a t e d f o r p h a s e 1 o f t h i s p r o j e c t w e r e :
I n i t i a l s i t e a n a l y s i s t e s t i n g . T h e o b j e c t i v e o f t h e i n i t i a l s i t e t e s t w a s t o d e t e r m i n e s e v e r a l s p e c i ¯ c c h a r -
a c t e r i s t i c s o f t h e t e s t s i t e a n d a n a l y z e w h e t h e r a n y o f t h e s e c h a r a c t e r i s t i c s p r e s e n t u n s u r m o u n t a b l e
b a r r i e r s t o t h e p r o j e c t ' s s u c c e s s . T h i s i n i t i a l t e s t w a s p e r f o r m e d u s i n g a s t a n d a r d a u t o m o b i l e w i t h
t h e n a v i g a t i o n s y s t e m a t t a c h e d t o t h e l u g g a g e r a c k . T h e c h a r a c t e r i s t i c s t o b e t e s t e d i n c l u d e : ( a )
G P S s i g n a l a v a i l a b i l i t y , ( b ) d i ® e r e n t i a l c o r r e c t i o n a v a i l a b i l i t y , a n d ( c ) h i g h w a y t r a j e c t o r y c h a r a c -
t e r i s t i c s . T h e r e s u l t s o f t h i s t a s k a ® e c t t h e r e s u l t s , o r d e r , a n d i m p o r t a n c e o f t h e r e m a i n i n g T a s k s .
U C R b o r r o w e d a T r i m b l e r a d i o m o d e m f r o m A H M C T t h a t w a s c a p a b l e o f r e c e i v i n g t h e C a l t r a n s
D G P S b a s e s t a t i o n m e s s a g e s t o e v a l u a t e c h a r a c t e r i s t i c ( b ) .
I n f r a s t r u c t u r e d e v e l o p m e n t : P u r c h a s e e q u i p m e n t . T h i s p r o j e c t r e q u i r e d d e v e l o p m e n t o f a d d i t i o n a l
s e t s o f G P S / I N S h a r d w a r e t o b e i n s t a l l e d o n t e s t v e h i c l e s . U n d e r t h i s t a s k w e d e ¯ n e d a n d p u r c h a s e d
t h e n e c e s s a r y p i e c e s o f e q u i p m e n t . W e h a v e c o n s t r u c t e d a d d i t i o n a l D C P G P S p r o t o t y p e s t h a t h a v e
b e e n u s e d f o r o n - v e h i c l e t e s t i n g .
I n f r a s t r u c t u r e d e v e l o p m e n t : V i b r a t i o n i s o l a t i o n a n d e n v i r o n m e n t p r o t e c t i o n e n c l o s u r e . T h e
e n c l o s u r e a n d v i b r a t i o n i s o l a t i o n s y s t e m w e r e p u r c h a s e d m o d i ¯ e d a n d t e s t e d .
I n f r a s t r u c t u r e d e v e l o p m e n t : S n o w p l o w G P S / I N S m o u n t i n g d e v e l o p m e n t . T h i s t a s k w i l l d e -
¯ n e , i m p l e m e n t , a n d t e s t t h e c a b l i n g , m o u n t i n g , a n d p o w e r r e q u i r e d t o t e s t t h e n a v i g a t i o n h a r d w a r e
o n a s n o w p l o w .
I n f r a s t r u c t u r e d e v e l o p m e n t : C P D G P S / I N S s o f t w a r e m o d i ¯ c a t i o n s a n d s y s t e m t e s t . T h e e x -
i s t i n g s o f t w a r e w a s m o d i ¯ e d t o a c c o m m o d a t e t h e h a r d w a r e c h a n g e s t h a t r e s u l t e d d u r i n g T a s k 2 .
I n f r a s t r u c t u r e d e v e l o p m e n t : S o f t w a r e m o d i ¯ c a t i o n s f o r t h e H M I . T h e e x i s t i n g H M I s o f t w a r e
w i l l b e m o d i ¯ e d t o a c c o m m o d a t e t h e C P D G P S a i d e d I N S s t a t e i n f o r m a t i o n .
T e s t : S n o w p l o w o n - v e h i c l e s y s t e m t e s t o f C P D G P S a i d e d I N S . T h i s t a s k w i l l t e s t t h e n a v i g a -
t i o n s y s t e m b a s i c o p e r a t i o n o n t h e s n o w p l o w . I n a d d i t i o n , t o c h e c k i n g t h e h a r d w a r e , c a b l i n g , a n d
p o w e r o p e r a t i o n , a n o b j e c t i v e i s t o v a l i d a t e t h e n a v i g a t i o n s y s t e m p e r f o r m a n c e w i t h t h e m o u n t i n g ,
v i b r a t i o n , a n d p o w e r s t a b i l i t y c h a r a c t e r i s t i c s o f t h e s n o w p l o w . T h i s w i l l b e p e r f o r m e d a t C r o w s
L a n d i n g t o f a c i l i t a t e a n y c h a n g e s t h a t m i g h t b e r e q u i r e d t o t h e m o u n t i n g d e s i g n .
T r a j e c t o r y C u r v e F i t t i n g . T h e g u i d a n c e i n f o r m a t i o n t o b e g i v e n t o t h e d r i v e r w i l l b e d e t e r m i n e d
b a s e d o n t h e v e h i c l e p o s i t i o n d e t e r m i n e d b y t h e n a v i g a t i o n s y s t e m a n d s t o r e d t r a j e c t o r y i n f o r m a -
t i o n . T h i s t a s k u s e d t h e d a t a f r o m t e s t i n g i n t h e D o n n e r P a s s t o d e v e l o p a n a p p r o p r i a t e c u r v e ¯ t
t o t h e d a t a d e s c r i b i n g t h e l a n e t r a j e c t o r y .
5 E x p e r i m e n t a l R e s u l t s : I 8 0 D o n n e r s P a s s
O n - s i t e t e s t i n g w a s p e r f o r m e d o n t h e I 8 0 i n D o n n e r s P a s s d u r i n g t h e w e e k o f A u g u s t 2 5 - 2 9 , 2 0 0 3 .
T h e i n t e n t o f t h i s s e t o f e x p e r i m e n t s w a s t o a c q u i r e G P S d a t a a l o n g t h e I 8 0 s o t h a t w e c o u l d p e r f o r m
a n o ® - l i n e a n a l y s i s o f t h e e x p e c t e d a c c u r a c y o f e s t i m a t e d p o s i t i o n u s i n g e i t h e r D C P G P S o r D C P G P S -
a i d e d - I N S . D a t a w a s a c q u i r e d i n b o t h t h e E a s t - b o u n d a n d W e s t - b o u n d l a n e s . I n e a c h l a n e , d a t a w a s
5
N a m e D i r e c t i o n D a t e T i m e
2 4 8 9 5 9 W B 8 / 2 6 / 2 0 0 3 1 4 : 1 0
2 5 1 3 5 3 E B 8 / 2 6 / 2 0 0 3 1 4 : 5 0
2 5 2 3 7 0 E B 8 / 2 6 / 2 0 0 3 1 5 : 1 0
2 5 4 9 0 3 W B 8 / 2 6 / 2 0 0 3 1 5 : 4 0
2 5 5 4 1 7 E B 8 / 2 6 / 2 0 0 3 1 5 : 5 8
2 5 6 0 6 5 W B 8 / 2 6 / 2 0 0 3 1 6 : 1 0
2 5 6 6 6 6 W B 8 / 2 6 / 2 0 0 3 1 6 : 1 9
2 5 7 4 7 0 E B 8 / 2 6 / 2 0 0 3 1 6 : 3 3
3 1 8 9 6 9 W B 8 / 2 7 / 2 0 0 3
3 2 1 9 3 2 E B 8 / 2 7 / 2 0 0 3
3 2 4 5 0 9 W B 8 / 2 7 / 2 0 0 3
T a b l e 1 : S u m m a r y o f d a t a r u n s .
a c q u i r e d a t d i ® e r e n t t i m e s o f t h e d a y o n v a r i o u s d a y s . T h i s a l l o w s a c c u r a c y a n a l y s i s f o r v a r i o u s s a t e l l i t e
c o n ¯ g u r a t i o n s . T h e t i m e , d a t e , d i r e c t i o n , a n d ¯ l e n a m e f o r e a c h d a t a s e t i s s h o w n i n T a b l e 1
T h i s s e c t i o n c o n t a i n s a n a l y t i c p r e d i c t i o n s o f t h e p o s i t i o n e r r o r e x p e c t e d t o b e a c h i e v e d a l o n g t h e I 8 0
i n t h e v i c i n i t y o f D o n n e r P a s s . T h e a n a l y t i c p r e d i c t i o n s a r e m a d e u s i n g c o v a r i a n c e p r o p a g a t i o n m e t h o d s
a s d e s c r i b e d i n [ 1 , 6 ] . T h e p r e d i c t i o n s a r e c a l c u l a t e d o ® - l i n e u s i n g o n l y t h e s a t e l l i t e s o b s e r v a b l e t o t h e
r e c e i v e r d u r i n g e a c h r u n . T h e r e f o r e , t h e p r e d i c t i o n s d o n o t u s e s a t e l l i t e s i f t h e r e i s n o t a d i r e c t a n d
u n b l o c k e d l i n e o f s i g h t b e t w e e n t h e r e c e i v e r a n d t h e s a t e l l i t e . T h e I 8 0 t h r o u g h D o n n e r P a s s r e s u l t s i n
s i g n i ¯ c a n t b l o c k a g e o f s a t e l l i t e s i g n a l s d u e t o t h e m o u n t a i n o u s t e r r a i n a n d t r e e s n e a r t h e h i g h w a y .
T h i s a n a l y s i s d o e s n o t a c c o u n t f o r b a s e s t a t i o n c o r r e c t i o n a v a i l a b i l i t y . T h e e s s e n t i a l a s s u m p t i o n i s
t h a t b a s e c o r r e c t i o n s a r e a v a i l a b l e f o r a n y s a t e l l i t e t h e r o v e r n e e d s t o u s e . I f b a s e s i g n a l s a r e n o t r e l i a b l y
a v a i l a b l e , t h e n t h e p e r f o r m a n c e o f b o t h t h e G P S - o n l y a n d t h e C P D G P S - a i d e d - I N S w o u l d b e w o r s e t h a n
i n d i c a t e d . A v a i l a b i l i t y o f b a s e c o r r e c t i o n i n f o r m a t i o n i s d i s c u s s e d i n a s u b s e q u e n t s e c t i o n .
F i g u r e s 1 { 6 s h o w d a t a f o r w e s t b o u n d r u n s . F i g u r e s 7 { 1 1 s h o w d a t a f o r e a s t b o u n d r u n s . T h e t o p
r o w o f g r a p h s i n e a c h ¯ g u r e p r e d i c t s t h e s i z e o f t h e p o s i t i o n e r r o r f o r c a l c u l a t i o n s u s i n g o n l y G P S
c a r r i e r p h a s e m e a s u r e m e n t s . T h e s i z e o f t h e p o s i t i o n e r r o r d e p e n d s o n t h e 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 f o r
w h i c h t h e r e c e i v e r c a n m e a s u r e d a t a . T h i s c o n s t e l l a t i o n c h a n g e s w i t h t i m e a n d l o c a t i o n . I 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 i s i n s u ± c i e n t , t h e n n o s o l u t i o n i s p o s s i b l e . I n t h e ¯ g u r e s , ¾ T i n d i c a t e 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 p o s i t i o n e r r o r t a n g e n t t o t h e c e n t e r l i n e a n d ¾ N i n d i c a t e 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 p o s i t i o n
e r r o r p e r p e n d i c u l a r t o t h e c e n t e r l i n e . T h e b o t t o m r o w o f g r a p h s i n e a c h ¯ g u r e p r e d i c t s t h e s i z e o f t h e
p o s i t i o n e r r o r t h a t w o u l d b e o b t a i n e d u s i n g a D C P G P S a i d e d I N S a p p r o a c h .
S e v e r a l c o m m e n t s a p p l y g e n e r a l l y t o t h e r e s u l t s .
1 . T h e e ® e c t o f t h e o v e r p a s s e s a n d a g r i c u l t u r e i n s p e c t i o n s t a t i o n i s c l e a r l y e v i d e n t i n t h e D C P G P S
e r r o r p l o t s , b u t a l m o s t c o m p l e t e l y r e m o v e d i n t h e D C P G P S a i d e d I N S r e s u l t s .
2 . T h e g r e a t m a j o r i t y o f t h e t i m e , t h e D C P G P S a i d e d I N S e r r o r s a r e p r e d i c t e d t o b e s u b s t a n t i a l l y l e s s
t h a n 1 0 c m . T h e D C P G P S a i d e d I N S e r r o r s i n a g i v e n d i r e c t i o n o n l y a p p r o a c h a n d t h e n e x c e e d 1 0
c m i f t h e D C P G P S a i d i n g s i g n a l s f r o m t h a t d i r e c t i o n a r e l o s t f o r a s i g n i ¯ c a n t p e r i o d o f t i m e .
3 . T h e p r e d i c t e d e r r o r c o m p o n e n t s a r e d e p e n d e n t o n b o t h t h e G P S s a t e l l i t e c o n ¯ g u r a t i o n ( n u m b e r o f
s a t e l l i t e s i n v i e w a n d t h e i r l o c a t i o n s i n t h e s k y ) a n d t h e v e h i c l e l o c a t i o n a l o n g t h e r o a d w a y . T h e
6
a r e a s w h e r e t h i s i s m o s t o b v i o u s a r e n e a r t h e a g r i c u l t u r e i n s p e c t i o n s t a t i o n a n d o n t h e w e s t b o u n d
l a n e s b e t w e e n D o n n e r S u m m i t a n d K i n g v a l e . S u c h l o c a l i z e d a r e a s c a n b e a d d r e s s e d t h r o u g h t h e
a u g m e n t a t i o n m e t h o d s s u g g e s t e d i n t h e o r i g i n a l p r o p o s a l ( i . e . , a l t i t u d e a i d i n g , m a g n e t o m e t e r a i d i n g ,
o r p s e u d o l i t e s ) . T h e n e x t p h a s e o f t h i s r e s e a r c h p r o j e c t i s t o a n a l y z e t h e p e r f o r m a n c e a n d f e a s i b i l i t y
o f e a c h t y p e o f a i d i n g s i g n a l f o r t h i s a p p l i c a t i o n .
7
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 1 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n , u s i n g
G P S o n l y , t h e r e a r e s e v e r a l s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e s i g n i ¯ c a n t
p o s i t i o n i n g e r r o r s . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e
D C P G P S a i d e d I N S w o u l d m a i n t a i n l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e r u n . T h i s r u n s t a r t s a t t h e
S i e r r a v i l l e o n - r a m p a n d c o n t i n u e s t o t h e v i c i n i t y o f B i g B e n d .
8
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 2 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 2 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a s h o r t r u n n e a r T r u c k e e . T h e
t o p r o w o f ¯ g u r e s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n , f o r t h e G P S
o n l y s o l u t i o n , t h e r e a r e s e v e r a l s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g t h e s a t e l l i t e s i g n a l s c a u s e
s i g n i ¯ c a n t p o s i t i o n i n g e r r o r s . L o c a t i o n s w h e r e t h e s i g n a l s a r e b l o c k e d b y t h e o v e r p a s s e s a n d a g r i c u l t u r e
i n s p e c t i o n s t a t i o n a r e c l e a r l y v i s i b l e . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s a t e l l i t e
c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e
r u n , e x c e p t f o r t h e p o r t i o n g o i n g t h r o u g h t h e a g r i c u l t u r a l i n s p e c t i o n s t a t i o n w h e r e t h e a c c u r a c y p a r a l l e l
t o t h e r o a d c e n t e r l i n e g r o w s t o m o r e t h a n 5 0 c m .
9
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 3 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 3 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a s h o r t r u n n e a r T r u c k e e . T h e
t o p r o w o f ¯ g u r e s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n , f o r t h e G P S
o n l y s o l u t i o n t h e r e a r e s e v e r a l s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s c a u s e s i g n i ¯ c a n t
p o s i t i o n i n g e r r o r s . T h e e ® e c t o f s i g n a l s b e i n g b l o c k e d b y t h e o v e r p a s s e s a n d a g r i c u l t u r e i n s p e c t i o n
s t a t i o n a r e c l e a r l y v i s i b l e . T h e b o t t o m r o w o f ¯ g u r e s s h o w s t h a t f o r t h e s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e
D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e r u n .
1 0
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 4 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 4 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n b e t w e e n D o n n e r L a k e a n d
K i n g v a l e . T h e t o p r o w o f ¯ g u r e s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n ,
t h e r e a r e a f e w s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e s i g n i ¯ c a n t p o s i t i o n i n g
e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f F i g u r e s s h o w s t h a t f o r t h e s a m e s e c t i o n o f r o a d
a n d s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m
e r r o r f o r t h e e n t i r e r u n .
1 1
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 5 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 5 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n b e t w e e n S e i r r a v i l l e a n d
G r a s s V a l l e y . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n ,
t h e r e a r e m a n y s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e s i g n i ¯ c a n t p o s i t i o n i n g
e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s e c t i o n o f r o a d a n d
s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r
f o r a l m o s t t h e e n t i r e r u n . T h e o n l y l o c a t i o n w h e r e t h e D C P G P S a i d e d I N S s o l u t i o n e x c e e d s 1 0 c m e r r o r
i s b e t w e e n t h e a g r i c u l t u r e i n s p e c t i o n s t a t i o n a n d t h e s u b s e q u e n t o v e r p a s s .
1 2
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ ¬ OAgv. e Irnpsaps. s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 6 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a w e s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 6 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n b e t w e e n S e i r r a v i l l e a n d
G r a s s V a l l e y . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n ,
t h e r e a r e m a n y s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e s i g n i ¯ c a n t p o s i t i o n i n g
e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s e c t i o n o f r o a d a n d
s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r
f o r a l m o s t t h e e n t i r e r u n . T h e o n l y l o c a t i o n s w h e r e t h e D C P G P S a i d e d I N S s o l u t i o n e x c e e d s 1 0 c m o f
e r r o r i s n e a r t h e a g r i c u l t u r e i n s p e c t i o n s t a t i o n a n d n e a r t h e C i s c o G r o v e o v e r p a s s .
1 3
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
F i g u r e 7 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a n e a s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 7 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n f r o m G r a s s V a l l e y t o C i s c o
G r o v e . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n , t h e
p o s i t i o n e r r o r s p r e d i c t e d f o r t h e G P S o n l y p o s i t i o n s o l u t i o n a r e a l w a y s l e s s t h a n 2 0 c m . T h e b o t t o m
r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s e c t i o n o f r o a d a n d s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S
a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e r u n .
1 4
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley F i g u r e 8 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a n e a s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 8 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n f r o m G r a s s V a l l e y t o S i e r -
r a v i l l e . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e d u r i n g t h i s r u n , t h e r e
a r e s e v e r a l s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e s i g n i ¯ c a n t p o s i t i o n i n g
e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r t h e s a m e s e c t i o n o f r o a d a n d
s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r
f o r t h e e n t i r e r u n .
1 5
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley F i g u r e 9 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a n e a s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 9 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a r u n f r o m V i s t a P o i n t t o S i e r -
r a v i l l e ( i . e . , n e a r T r u c k e e ) . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n a v a i l a b l e
d u r i n g t h i s r u n , t h e r e a r e t w o s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s c a u s e
s i g n i ¯ c a n t p o s i t i o n i n g e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s t h a t f o r t h e s a m e
s e c t i o n o f r o a d a n d s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n s u b s t a n t i a l l y
l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e r u n .
1 6
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley F i g u r e 1 0 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a n e a s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 1 0 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a n e a s t b o u n d r u n f r o m K i n g v a l e
t o S i e r r a v i l l e ( i . e . , n e a r T r u c k e e ) . T h e t o p r o w o f g r a p h s s h o w t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n
a v a i l a b l e d u r i n g t h i s r u n , t h e r e a r e s e v e r a l s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s
c a u s e s i g n i ¯ c a n t p o s i t i o n i n g e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t
f o r t h e s a m e s e c t i o n o f r o a d a n d s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n
s u b s t a n t i a l l y l e s s t h a n 1 0 c m e r r o r f o r t h e e n t i r e r u n .
1 7
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s N , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS− only s T , m
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s N , m
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley
0 10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
GPS aided INS s T , m
arclength ( km)
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ ¬ OCivsecrop aGsrsove
¬ Grass Velley F i g u r e 1 1 : P r e d i c t e d p o s i t i o n e r r o r s t a n d a r d d e v i a t i o n f o r a n e a s t b o u n d r u n . E r r o r u s i n g o n l y D C P G P S
i s s h o w n o n t h e t o p r o w . E r r o r u s i n g D C P G P S a i d e d I N S i s s h o w n o n t h e b o t t o m r o w . T h e l e f t c o l u m n
i n d i c a t e s t h e e r r o r n o r m a l t o t h e l a n e c e n t e r l i n e . T h e r i g h t c o l u m n i n d i c a t e s t h e e r r o r p a r a l l e l t o t h e
l a n e c e n t e r l i n e . N o t e t h a t t h e e r r o r a x i s i s l i m i t e d t o a m a x i m u m o f 0 . 5 m . E r r o r s e x c e e d i n g 0 . 5 m . a r e
n o t s h o w n .
F i g u r e 1 1 c o n t a i n s f o u r s u b ¯ g u r e s t h a t i n d i c a t e p e r f o r m a n c e f o r a n e a s t b o u n d r u n f r o m K i n g v a l e
t o S i e r r a v i l l e ( i . e . , n e a r T r u c k e e ) . T h e t o p r o w o f g r a p h s s h o w s t h a t f o r t h e s a t e l l i t e c o n ¯ g u r a t i o n
a v a i l a b l e d u r i n g t h i s r u n , t h e r e a r e m a n y s e c t i o n s o f r o a d w a y w h e r e o b s t a c l e s b l o c k i n g s a t e l l i t e s i g n a l s
c a u s e s i g n i ¯ c a n t p o s i t i o n i n g e r r o r s f o r t h e G P S o n l y s o l u t i o n . T h e b o t t o m r o w o f g r a p h s s h o w s t h a t f o r
t h e s a m e s e c t i o n o f r o a d a n d s a m e s a t e l l i t e c o n ¯ g u r a t i o n , t h e D C P G P S a i d e d I N S w o u l d m a i n t a i n l e s s
t h a n 1 0 c m e r r o r f o r a l m o s t t h e e n t i r e r u n .
1 8
6 B a s e S t a t i o n
6 . 1 C a l t r a n s B a s e
D i ® e r e n t i a l C a r r i e r P h a s e G P S r e q u i r e s a b a s e s t a t i o n . T h e r e i s a C a l t r a n s G P S b a s e s t a t i o n i n t h e
v i c i n i t y o f t h e I 8 0 i n D o n n e r s P a s s . I t i s a T r i m b l e 4 7 0 0 W i n C O R S r e c e i v e r l o c a t e d a t
3 9 : 1 9 : 1 8 : 7 s N o r t h L a t i t u d e a n d 1 2 0 : 2 0 : 1 1 : 7 W e s t L o n g i t u d e .
T h e r e c e i v e r b r o a d c a s t s C M R f o r m a t d i ® e r e n t i a l c o r r e c t i o n s v i a a T r i m b l e T r i m t a l k 4 5 0 s r a d i o w i t h a
c e n t e r f r e q u e n c y o f 4 5 3 . 8 8 7 5 M H z a n d a 1 2 . 5 k H z c h a n n e l s p a c i n g . T h e b a u d r a t e i s 1 2 0 0 - 9 6 0 0 b p s . T h i s
b a s e h a s a n e x p e c t e d r a n g e o f 1 0 k m l i n e - o f - s i t e a t 0 . 5 W . I t i s r e p e a t e r c a p a b l e .
F i g u r e s 1 2 { 2 2 s h o w d a t a i n d i c a t i v e o f d i ® e r e n t i a l c o r r e c t i o n r e c e p t i o n v e r s u s a r c l e n g t h . E a c h ¯ g u r e
c o n t a i n s t h r e e g r a p h s o f d a t a i n d i c a t i n g t h e t i m e d e l a y b e t w e e n r e c e p t i o n o f c o n s e c u t i v e b a s e c o r r e c t i o n s .
I d e a l l y , o n e c o r r e c t i o n s h o u l d b e r e c e i v e d p e r s e c o n d . D e l a y s o f 2 o r 3 s e c o n d s c a n b e a c c o m m o d a t e d
e a s i l y . D e l a y s o f m o r e t h a n 7 s e c o n d s a r e p r o b l e m a t i c . I n e a c h ¯ g u r e , t h e t o p t w o p l o t s a r e t h e s a m e d a t a ,
j u s t p l o t t e d w i t h d i ® e r e n t s c a l e s . T h e t o p g r a p h h a s a s c a l e t h a t i n c l u d e s a l l d a t a p o i n t s . T h e s e c o n d
g r a p h h a s a v e r t i c a l r a n g e b e t w e e n 0 a n d 6 , t o m o r e c l e a r l y i n d i c a t e t h e d i s t r i b u t i o n o f d a t a i n t h i s r a n g e .
T h e t h i r d p l o t i s a h i s t o g r a m o f t h e d a t a . T h i s d a t a s h o w s t h a t e a c h r u n c o n t a i n e d a t s e v e r a l i n s t a n c e s o f
b a s e c o r r e c t i o n s n o t b e i n g r e c e i v e d f o r a t l e a s t 1 0 s . F o r t u n a t e l y , t h e b a d b a s e s t a t i o n r e c e p t i o n a p p e a r s
t o o c c u r a t n e a r l y t h e s a m e a r c l e n g t h f o r t h e v a r i o u s r u n s . T h e r e f o r e , t h i s i s s u e m a y b e a d d r e s s a b l e b y
a d d i n g b a s e s t a t i o n r e p e a t e r s ( o ® t h e h i g h w a y ) a l o n g t h e r o a d w a y .
1 9
5 10 15 20 25 30
0
50
100
Number of seconds from last measurement
Time, s
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
5 10 15 20 25 30
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
Time between base corrections, s
counts
>
F i g u r e 1 2 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 0
1 2 3 4 5 6
0
10
20
30
Number of seconds from last measurement
Time, s
¬ Overpass
¬ Ag. Insp.
¬ Overpass
1 2 3 4 5 6
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
50
100
150
200
Time between base corrections, s
counts
>
F i g u r e 1 3 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 1
1 2 3 4 5 6 7 8
0
10
20
Number of seconds from last measurement
Time, s
¬ Overpass
¬ Ag. Insp.
¬ Overpass
1 2 3 4 5 6 7 8
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
100
200
300
Time between base corrections, s
counts
>
F i g u r e 1 4 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 2
12 14 16 18 20 22 24 26
0
10
20
30
Number of seconds from last measurement
Time, s
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
12 14 16 18 20 22 24 26
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
100
200
300
Time between base corrections, s
counts
>
F i g u r e 1 5 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 3
5 10 15 20 25 30 35
0
20
40
60
80
Number of seconds from last measurement
Time, s
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
5 10 15 20 25 30 35
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
800
Time between base corrections, s
counts
>
F i g u r e 1 6 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 4
5 10 15 20 25 30 35
0
20
40
60
80
Number of seconds from last measurement
Time, s
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
5 10 15 20 25 30 35
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
Time between base corrections, s
counts
>
F i g u r e 1 7 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
w e s t b o u n d r u n .
2 5
2.5 3 3.5 4 4.5 5 5.5
0
50
100
Number of seconds from last measurement
Time, s
¬ Cisco Grove
¬ Overpass
2.5 3 3.5 4 4.5 5 5.5
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
50
100
Time between base corrections, s
counts
>
F i g u r e 1 8 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
e a s t b o u n d r u n .
2 6
0 5 10 15 20 25 30 35
0
20
40
60
80
Number of seconds from last measurement
Time, s
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
Time between base corrections, s
counts
>
F i g u r e 1 9 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
e a s t b o u n d r u n .
2 7
31 32 33 34 35 36 37 38 39 40 41
0
10
20
30
Number of seconds from last measurement
Time, s
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
31 32 33 34 35 36 37 38 39 40 41
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
100
200
300
400
Time between base corrections, s
counts
>
F i g u r e 2 0 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
e a s t b o u n d r u n .
2 8
15 20 25 30 35 40
0
10
20
30
Number of seconds from last measurement
Time, s
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
15 20 25 30 35 40
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
Time between base corrections, s
counts
>
F i g u r e 2 1 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
e a s t b o u n d r u n .
2 9
5 10 15 20 25 30 35 40
0
20
40
60
80
Number of seconds from last measurement
Time, s
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
5 10 15 20 25 30 35 40
0
2
4
6
Time, s
Arclength, km
1 2 3 4 5 6 7 8 9 10
0
200
400
600
800
Time between base corrections, s
counts
>
F i g u r e 2 2 : T i m e d e l a y b e t w e e n s u b s e q u e n t D G P S c o r r e c t i o n u s i n g t h e C a l t r a n s b a s e s t a t i o n . T h i s i s a
e a s t b o u n d r u n .
3 0
6 . 2 B a s e a n d R o v e r S a t e l l i t e R e c e p t i o n D a t a
F i g u r e s 2 3 { 3 3 s h o w t h e s h o w a n a l y t i c p r e d i c t i o n s o f a c c u r a c y , p r e v i o u s l y s h o w n i n F i g u r e s 1 { 1 1 a l o n g
w i t h g r a p h s s h o w i n g t h e n u m b e r o f s a t e l l i t e s a v a i l a b l e t o t h e r o v e r a n d t h e n u m b e r o f s a t e l l i t e c o r r e c t i o n s
r e c e i v e d f r o m t h e b a s e b y t h e r o v e r , e a c h a s a f u n c t i o n o f a r c l e n g t h .
N o t e t h a t t h e a n a l y t i c p r e d i c t i o n s o f a c c u r a c y a s s u m e t h a t b a s e s t a t i o n c o r r e c t i o n s a r e c o n t i n u o u s l y
a v a i l a b l e , e v e n t h o u g h t h e y a r e n o t . H o w e v e r , t h e b a s e s i g n a l a v a i l a b i l i t y i s s u e s h o u l d b e ¯ x a b l e w i t h
r a d i o m o d e m r e p e a t e r s .
T h e s e ¯ g u r e s i n d i c a t e t h a t t h e G P S s i g n a l d r o p o u t s o c c u r a t r e p e a t a b l e l o c a t i o n s . T h e r e f o r e , e i t h e r
m a g n e t o m e t e r o r p s e u d o l i t e a i d i n g w o u l d o n l y b e r e q u i r e d n e a r t h o s e l o c a t i o n s a n d w o u l d b e e x p e c t e d
e x p e c t e d t o ¯ x t h e i s s u e s r e l a t e d G P S s i g n a l d r o p o u t s .
3 1
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
GPS
GPS aided INS
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
GPS
GPS aided INS
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run248960
F i g u r e 2 3 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 2
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run254904
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 4 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 3
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run256066
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 5 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 4
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run256667
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 6 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 5
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run318970
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 7 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 6
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ Ag. Insp.
¬ Overpass
¬ Donner Lake
¬ Donner Summit
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Westbound Run324510
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 8 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 7
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Eastbound Run251354
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 2 9 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 8
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
10
20
Num. sat rvr
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Eastbound Run252371
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 3 0 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
3 9
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Eastbound Run255418
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 3 1 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
4 0
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat base
I80 Donners Pass Eastbound Run257471
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 3 2 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
4 1
0 5 10 15 20 25 30 35 40
0
0.2
0.4
s N , m
0 5 10 15 20 25 30 35 40
0
0.2
0.4
arclength ( km)
s T , m
0 5 10 15 20 25 30 35 40
0
5
10
Num. sat rvr
¬ Overpass
¬ C. Truckee
¬ Overpass
¬ Vista Point
¬ Donner Summit
¬ Overpass
¬ Kingvale
¬ Cisco Grove
¬ Overpass
¬ Grass Velley
0 5 10 15 20 25 30 35 40
0
2
4
6
Num. sat base
I80 Donners Pass Eastbound Run321933
GPS
GPS aided INS
GPS
GPS aided INS
F i g u r e 3 3 : T o p { N u m b e r o f s a t e l l i t e D G P S c o r r e c t i o n s r e c e i v e d f r o m t h e b a s e a s a f u n c t i o n o f a r c l e n g t h .
S e c o n d f r o m t o p { N u m b e r o f s a t e l l i t e m e a s u r e m e n t s r e c e i v e d a t t h e r o v e r v e r s u s a r c l e n g t h . S e c o n d
f r o m b o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p e r p e n d i c u l a r t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . B o t t o m { P o s i t i o n i n a c c u r a c y e x p e c t e d i n d i r e c t i o n p a r a l l e l t o t h e l a n e c e n t e r a s a f u n c t i o n
o f a r c l e n g t h . N o t e t h a t t h e s c a l e o f t h e b o t t o m t w o g r a p h s i s a r t i ¯ c i a l l y l i m i t e d t o 0 . 5 m . C u r v e s t h a t
e x c e e d t h e a x i s l i m i t s m a y h a v e p o s i t i o n i n a c c u r a c y s i g n i ¯ c a n t l y g r e a t e r t h a t 0 . 5 m .
4 2
6 . 3 U C R B a s e
F o r s e t t i n g u p a t e m p o r a r y D G P S b a s e s t a t i o n , i f n e c e s s a r y i n t h e f u t u r e , t h e r e i s N a t i o n a l G e o d e t i c
S u r v e y m a r k e r l o c a t e d a l o n g t h e f r o n t a g e r o a d a b o v e D o n n e r L a k e . I t i s i m p l a n t e d i n a l a r g e s t o n e a b o u t
1 0 m s o u t h o f t h e r o a d a l o n g t h e c u r v e b e l o w t h e o v e r l o o k . I t i s w e l l m a r k e d . T h e r e i s s p a c e a d j a c e n t t o
i t t o p a r k a c a r , i f r e q u i r e d f o r p o w e r . T h e N A D 8 3 c o o r d i n a t e s a n d m a r k e r i n f o r m a t i o n a r e
L a t i t u d e 3 9 : 1 9 : 2 . 0 6 6 5 1 N
L o n g i t u d e 1 2 0 : 1 9 : 3 . 6 0 2 8 2 W
E l l i p s e h e i g h t 2 0 4 6 . 2 4 m
G e o d . h e i g h t - 2 3 . 1 9 m
P I D K S 0 1 0 7
D e s t i n a t i o n V 1 2 0 1
E C E F X - 2 , 4 9 5 , 0 2 9 . 5 0 5 m
E C E F Y - 4 , 2 6 6 , 7 1 0 . 4 3 0 m
E C E F Z 4 , 0 2 0 , 9 2 2 . 8 0 9 m
T h e m a r k e r w a s l o c a t e d o n t h e a f t e r n o o n a n d e v e n i n g o f A u g u s t 2 7 , 2 0 0 3 . T h e U C R b a s e s t a t i o n w a s
s e t u p o n t h e m a r k e r . I t b r o a d c a s t c o r r e c t i o n s u s i n g a F r e e w a v e s p r e a d s p e c t r u m m o d e m . T h e D C P G P S
a i d e d I N S w o r k e d v e r y w e l l i n t h e v i c i n i t y o f t h e b a s e s t a t i o n . S e v e r a l r u n s o f t h e D C P G P S a i d e d
I N S w e r e a t t e m p t e d o n t h e I 8 0 i n t h e v i c i n i t y o f T r u c k e e ; h o w e v e r , t h e m o d e m s i g n a l w a s t o o w e a k t o
b e r e l i a b l y r e c e i v e d . F u t u r e o n - s i t e t e s t w i l l a t t e m p t t o u s e t h e C a l t r a n s b a s e s t a t i o n w i t h t h e U C R
D C P G P S a i d e d I N S .
7 P h a s e 1 R e s u l t s
T h e o b j e c t i v e s s t a t e d f o r p h a s e 1 o f t h i s p r o j e c t w e r e :
I n i t i a l s i t e a n a l y s i s t e s t i n g . O u r a s s e s s m e n t i s t h a t t h e r e a r e n o i n s u r m o u n t a b l e b a r r i e r s t o s u c c e s s f u l
d e m o n s t r a t i o n o f c a r r i e r p h a s e G P S a i d e d I N S a l o n g t h e I 8 0 i n t h e v i c i n i t y o f D o n n e r s P a s s . T h e
d a t a c o n t a i n e d h e r e i n d e m o n s t r a t e t h a t t h e n u m b e r o f a v a i l a b l e G P S s a t e l l i t e s i s s u ± c i e n t t o
m a i n t a i n t h e I N S a c c u r a c y a s s u m i n g t h a t c e r t a i n t e c h n i c a l c h a l l e n g e s c a n b e o v e r c o m e :
² G P S s i g n a l s m a y b e b l o c k e d b y t e r r a i n o r m a n - m a d e f e a t u r e s . T h e s e l o c a t i o n s c a n b e a d d r e s s e d
b y l o c a l a u g m e n t a t i o n o r e n h a n c e d r e c e i v e r t e c h n o l o g y .
² T h e b a s e s i g n a l i s n o t c u r r e n t l y r e l i a b l y r e c e i v e d . T h i s c a n b e a d d r e s s e d e i t h e r b y u s e o f
m o d e m r e p e a t e r s , c e l l p h o n e m o d e m s , o r c o r r e c t i o n p r e d i c t i o n m e t h o d s .
I n f r a s t r u c t u r e d e v e l o p m e n t : P u r c h a s e e q u i p m e n t . L e i c a G P S r e c e i v e r s , f r e e w a v e m o d e m s , a n d
Y H - T e k I M U ' s w e r e p u r c h a s e d a n d t h e i n t e g r a t e d s y s t e m w a s c o n s t r u c t e d t o s u p p o r t t h e p r o j e c t .
I n f r a s t r u c t u r e d e v e l o p m e n t : V i b r a t i o n i s o l a t i o n a n d e n v i r o n m e n t p r o t e c t i o n e n c l o s u r e . T h e
e n c l o s u r e a n d v i b r a t i o n i s o l a t i o n s y s t e m w e r e p u r c h a s e d m o d i ¯ e d a n d t e s t e d .
I n f r a s t r u c t u r e d e v e l o p m e n t : S n o w p l o w G P S / I N S m o u n t i n g d e v e l o p m e n t . P A T H a n d U C R c o l -
l a b o r a t e d t o m o u n t t h e h a r d w a r e o n a S n o w p l o w t h a t w a s o n l o a n t o P A T H .
I n f r a s t r u c t u r e d e v e l o p m e n t : C P D G P S / I N S s o f t w a r e m o d i ¯ c a t i o n s a n d s y s t e m t e s t . T h e e x -
i s t i n g s o f t w a r e w a s m o d i ¯ e d t o a c c o m m o d a t e t h e h a r d w a r e c h a n g e s t h a t r e s u l t e d d u r i n g T a s k 2 .
4 3
I n f r a s t r u c t u r e d e v e l o p m e n t : S o f t w a r e m o d i ¯ c a t i o n s f o r t h e H M I . P A T H ' s H M I s o f t w a r e w a s
m o d i ¯ e d b y P A T H t o a c c o m m o d a t e t h e C P D G P S a i d e d I N S s t a t e i n f o r m a t i o n .
T e s t : S n o w p l o w o n - v e h i c l e s y s t e m t e s t o f C P D G P S a i d e d I N S . D u e t o P A T H ' s i n v o l v e m e n t i n
v a r i o u s d e m o n s t r a t i o n s i n 2 0 0 3 , t h e w o r k a n d f u n d i n g f o r t h i s t a s k w e r e d e l a y e d t o 2 0 0 4 . I n e a r l y
S e p t e m b e r 2 0 0 4 , t e s t i n g w a s p e r f o r m e d o n a s n o w p l o w a t t h e P A T H f a c i l i t y . T h e t e s t r e q u i r e d s u r -
v e y i n g o f a b a s e l o c a t i o n a t P A T H o n S e p t e m b e r 7 , 2 0 0 4 . T e s t i n g w a s p e r f o r m e d o n S e p t e m b e r 8 - 9 ,
2 0 0 4 . T e s t i n g s h o w e d t h e n e e d f o r p o w e r s t a b i l i z a t i o n h a r d w a r e w i t h i n t h e G P S / I N S s y s t e m d u e t o
p o o r p o w e r q u a l i t y o n t h e s n o w p l o w . O t h e r w i s e , t h e G P S / I N S p e r f o r m e d a t t h e s a m e p e r f o r m a n c e
l e v e l s o n t h e s n o w p l o w a s i t h a d i n p r e v i o u s v e h i c l e d e m o n s t r a t i o n s .
T r a j e c t o r y C u r v e F i t t i n g . M a t l a b s o f t w a r e w a s d e v e l o p e d t o p e r f o r m t h e c u r v e ¯ t t i n g t a s k . T h e
s o f t w a r e r e c e i v e s a s i n p u t t h e l a t i t u d e , l o n g i t u d e , a n d h e i g h t d a t a f r o m a p r i o r r u n w h e n t h e
v e h i c l e w a s d r i v e n a l o n g t h e d e s i r e d t r a j e c t o r y . T h e s o f t w a r e p e r f o r m s a c u r v e ¯ t w h i c h s m o o t h s
t h e d a t a a n d o u t p u t s t h e p a r a m e t e r s o f t h e c u r v e ¯ t . T h e s e p a r a m e t e r s a r e u s e d b y t h e G P S / I N S
s o f t w a r e o n f u t u r e r u n s t o c o m p u t e t h e s t a t e o f t h e v e h i c l e r e l a t i v e t o t h e s t o r e d t r a j e c t o r y .
8 C o n c l u s i o n s
T h i s r e p o r t d i s c u s s e s r e s u l t s o f P h a s e I o f t h e p r o j e c t 6 5 A 0 1 4 8 a n d i n c l u d e s d e t a i l e d a n a l y s i s o f d a t a
c o l l e c t e d o n t h e I 8 0 i n t h e v i c i n i t y o f D o n n e r P a s s ( i . e . , b e t w e e n S i e r r a v i l l e a n d G r a s s V a l l e y . T h e r a w
d a t a , a s e x p e c t e d , s h o w s t h a t t h e r e a r e l o c a l s t r e t c h e s o f t h e I 8 0 w h e r e t h e C a l t r a n s b a s e s t a t i o n s i g n a l
i s n o t r e l i a b l y r e c e i v e d a t a n e a r 1 H z r a t e a n d t h a t t h e r e a r e s t r e t c h e s o f t h e I 8 0 w h e r e a s u ± c i e n t c o n -
s t e l l a t i o n o f G P S s i g n a l s a r e n o t r e l i a b l y r e c e i v e d . T h e s e s t r e t c h e s a p p e a r t o b e l o c a l i z e d a n d r e p e a t a b l e .
T h e r e f o r e , t h e b a s e s t a t i o n r e c e p t i o n i s s u e s h o u l d b e ¯ x a b l e u s i n g r a d i o m o d e m r e p e a t e r s . T h e G P S
s i g n a l r e c e p t i o n s h o u l d b e a d d r e s s a b l e b y t h e a u g m e n t a t i o n m e t h o d s o r i g i n a l l y p r o p o s e d ( e . g . , m a g n e -
t o m e t e r , r o a d w a y a l t i t u d e , p s e u d o l i t e , o r u l t r a t i g h t a i d i n g ) o r b y a d v a n c e s i n G P S r e c e i v e r t e c h n o l o g y
t h a t a r e c u r r e n t l y e i t h e r p r o p o s e d o r a l r e a d y i n p r o g r e s s . U s e o f t h e s e m e t h o d s w i l l b e i n v e s t i g a t e d i n
t h e P h a s e I I o f t h e p r o j e c t .
9 C o n t a c t I n f o r m a t i o n
N a m e O r g a n i z a t i o n P h o n e e - m a i l
J a y F a r r e l l U C R 9 0 9 - 7 8 7 - 2 1 5 9 f a r r e l l @ e e . u c r . e d u
M i k e J e n k i n s o n C a l t r a n s 9 1 6 - 6 5 7 - 3 8 6 7 M i k e J e n k i n s o n @ d o t . c a . g o v
T y L a s k y A H M C T 5 3 0 - 7 5 2 - 6 3 6 6 t a l a s k y @ u c d a v i s . e d u
A s f a n d S i d d i q u i C a l t r a n s 9 1 6 - 6 5 4 - 6 9 9 4 A s f a n d S i d d i q u i @ d o t . c a . g o v
K i n Y e n A H M C T 5 3 0 - 7 5 2 - 6 9 5 7 k s y e n @ m e r c u r y . a h m c t . u c d a v i s . e d u
D a v e A l l e n I n s t r u m e n t s 4 8 0 - 5 1 0 - 4 9 0 2
M a t t A l l e n I n s t r u m e n t s 4 8 0 - 9 9 4 - 1 3 0 6
D a n M c M a n n A l l e n I n s t r u m e n t s 7 6 0 - 2 7 1 - 4 6 8 1
4 4
R e f e r e n c e s
[ 1 ] F a r r e l l , J . A . a n d B a r t h , M . , T h e G l o b a l P o s i t i o n i n g S y s t e m a n d I n e r t i a l N a v i g a t i o n , M c G r a w - H i l l
( I S B N - 0 - 0 7 - 0 2 2 0 4 5 - X ) , 1 9 9 9 .
[ 2 ] F a r r e l l , J . A . a n d B a r t h , M . , \ I n t e g r a t i o n o f G P S - a i d e d I N S i n t o A V C S S " , C a l i f o r n i a P a t h R e s e a r c h
R e p o r t U C B - I T S - P R R - 2 0 0 0 - 2 2 . A u g u s t , 2 0 0 0 .
[ 3 ] F a r r e l l , J . a n d G i v a r g i s . T . , \ D i ® e r e n t i a l G P S R e f e r e n c e S t a t i o n A l g o r i t h m : D e s i g n a n d A n a l y s i s "
I E E E T r a n s a c t i o n s o n C o n t r o l S y s t e m s T e c h n o l o g y . V o l . 8 ( 3 ) , M a y 2 0 0 0 , p p . 5 1 9 - 5 3 1 .
[ 4 ] F a r r e l l , J . , G i v a r g i s . , T . a n d B a r t h , M . , \ R e a l - t i m e D i ® e r e n t i a l C a r r i e r P h a s e G P S - A i d e d I N S , " I E E E
T r a n s a c t i o n s o n C o n t r o l S y s t e m s T e c h n o l o g y . V o l . 8 ( 4 ) , J u l y 2 0 0 0 , p p . 7 0 9 - 7 2 1 .
[ 5 ] F a r r e l l , J . , T a n , H . - S . a n d Y a n g , Y , \ C a r r i e r P h a s e G P S - a i d e d I N S b a s e d V e h i c l e L a t e r a l C o n t r o l , "
s u b m i t t e d A S M E J o u r n a l o f D y n a m i c s S y s t e m s , M e a s u r e m e n t , a n d C o n t r o l , M a y 7 , 2 0 0 1 , 3 9 m . s .
[ 6 ] F a r r e l l , J . , \ S t a t e E s t i m a t i o n , " s u b m i t t e d t o E l e c t r i c a l E n g i n e e r i n g H a n d b o o k , W . - K . C h e n ( e d . ) ,
A p r i l 2 0 0 1 , 2 0 m . s . , A c a d e m i c P r e s s .
[ 7 ] Y . Y a n g a n d J . A . F a r r e l l , \ M a g n e t o m e t e r a n d D i ® e r e n t i a l C a r r i e r P h a s e G P S a i d e d I N S f o r A d -
v a n c e d V e h i c l e C o n t r o l , " I E E E T r a n s . R o b o t i c s a n d A u t o m a t i o n , 1 9 ( 2 ) : 2 6 9 - 2 8 3 , 2 0 0 3
4 5