<4D6963726F736F667420576F7264202D2039374F323230315FA668B0D1A6D2AFB8475053B0CABA41A977A6ECBA74BAE2AA6BA4A7ACE3A8735FB2C433BD675F> 183-194 979 183 Journal of Photogrammetry and Remote Sensing Volume 13, No.3, Sepetmber 2008, pp. 183-194
GPS

(1) RTZD RTZD(2)
(3)

1.
(Peal-Time Kinematic, RTK)

184 97 9
2.
2.1
(Double difference)

( ) gh ij
gh g g h h gh gh gh gh ij i j i j ij ij ij ijR T I N vλ λ
Φ Φ = − − + = + − − +
gh ij
gh g g h h gh gh gh ij i j i j ij ij ijR T I v
ρ ρ ρ ρ ρ ρ= − − + = + + +
ij
gh λ
gh ijN gh
ijΦ
GPS
ij m n
gh gh gh gh gh gh ij m n m n ij m n ij m n ij m n ij m n ijR N I T vλ λ
Φ Φ = = + + + +

+ (4)
, 1 2 gh gh gh ij m n ij ijN mN nN= + ,
gh ij m nI
(m)
+ =
+
(1)(2)(3)

gh wijN L1
1 gh ijN


m (m) 0
2 2 2 /1( )(1 e ) 2
d D mσ σ −
wijN
L1
1, 2, 2 1/ /I I f f =

GPS L1, L2 1 2/ 77 / 60f f = −
77m = ,
60n = − (3)
77, 60 1 77, 60
(77 60 )
gh gh gh ij ij ij
gh gh gh gh ij ij wij ijR N N T
λ
λ λ ε −
gh ijT (2001)
1 1 1 1 1[( ) ( )] 2 cos cos cos cosh g h g
j j i i
= − + − (8)
(8)(7) gh ijT
gh ijT MF z= × (9)
(9)z
'z 0 (m)


l
m
2 iσ
(Accompanying) n × n Ci (n
)

2
1
m
2 iσ Ci
Q
2 1, {1,..., }i i mσ ≅ ∈

Yeh, 2005)
BC B Q (12)

(m=4)



/ ( , , / 2) ( , ,1 / 2)
χ α α
1 2d d


1
RTZD
1
1 1
EΔ , NΔ TWD97(Taiwan
Datum 97, 1997 )
RTZD
1 1 1u u uz a E b N c= Δ + Δ + (15)
1uz RTZD 1uEΔ
iuNΔ 1uNΔ

RTZD

error) ( Mean, Sigma,

2006 3 13 21:03 21:13
CSRF()SPP0
3 1
2
RTZD
RTZD



L1
RTZD)

2 RTZD
1

2
3
0 200 400 600 Time (epochs)
-0.10
-0.05
0.00
0.05
0.10
-0.10
-0.05
0.00
0.05
0.10
8 NTPU
RTZD


3 5
(Mean)(Sigma)(RMSE,
(MRS)
(cm) RMSE Sigma Mean
SBL 1.53 0.44 -1.46
MRS 1.51 0.44 -1.45
(cm) RMSE Sigma Mean
SBL 2.97 2.29 -1.89
MRS 1.81 0.34 -1.77
(cm) RMSE Sigma Mean
SBL 4.88 4.03 2.76
MRS 2.87 1.99 2.86
2007 4 19 17:00 17:10
CSRF()SPP0SINPNTPU
XINU 9
6 7~8 GDOP
3.0 ~ 3.3 CSRF XINU 2 Hz
1 Hz 15.0°
7
CSRF_SINP

RTZD

-0.05
0
0.05
0.1
-0.20
-0.10
0.00
0.10
0.20
0.30

7
10 RTZD (CSRF_NTPU)
11 RTZD (CSRF_SINP)
12 RTZD (CSRF_SPP0)
(cm) RMSE Sigma Mean
SBL 4.02 0.49 -4.00
MRS 3.98 0.32 -3.97
0 200 400 600 Time (epochs)
-0.10
-0.05
0.00
0.05
0.10
-0.10
-0.05
0.00
0.05
0.10
-0.10
-0.05
0.00
0.05
0.10
-0.1
-0.05
0
0.05
0.1
(cm) RMSE Sigma Mean
SBL 5.10 0.94 -5.01
MRS 4.16 0.46 -4.14
(cm) RMSE Sigma Mean
SBL 9.38 2.32 -9.10
MRS 1.37 1.29 -0.46
YMSM TPSODYSSEY_E TPSCR3_GGD
12
(km) 8.8 20.8 37.2 12.3 12.3
3.3 NTPU_XINU
NTPU_XINU
2007 4 15 23:35 23:40
NTPU()CSRFSPP0SINP
YMSM 15
3.0 ~ 3.3 CSRF XINU 2 Hz
1 Hz 15.0°
12
NTPU_SPP0 NTPU_YMSM
NTPU SPP0
(37.2 km) NTPU YMSM
NTPU 60.9 m
YMSM 784.0 m RTZD
RTZD 20
21 XINU
22
23

-0.16
-0.12
-0.08
-0.04
0.00
0.04
80% 23


13 15

-0.1
-0.05
0
0.05
0.1
-0.1
-0.05
0
0.05
0.1
-0.1
-0.05
0
0.05
0.1
-0.1
-0.05
0
0.05
0.1
-0.1
-0.05
0
0.05
0.1
22 XINU
23 XINU
13 XINU (N)
(cm) RMSE Sigma Mean
SBL 3.44 0.73 -3.37
MRS 3.38 0.26 -3.37
14 XINU (E)
(cm) RMSE Sigma Mean
SBL 0.98 0.74 -0.65
MRS 0.82 0.37 -0.73
15 XINU (H)
(cm) RMSE Sigma Mean
SBL 2.93 2.34 1.74
MRS 2.76 2.04 -1.87

“Simplified formulae for the BIQUE estimation
of variance components in disjunctive
observation groups.” Journal of Geodesy, Vol. 74,
No. 6, pp. 447-457.
Dai, L., Han, S., Wang, J., and Rizos, C. (2003),
“Comparison of interpolation algorithms in
network-based GPS techniques.” Navigation, Vol.
50, No. 4, pp. 277-293.
Goad, C. C. and Yang, M. (1997), “A new approach
to precision airborne GPS positioning for
photogrammetry.” Photogrammetric Engineering
1067-1077.
Hu, G. R., Khoo, H. S., Goh, P. C., and Law, C. L.
(2003), “Development and assessment of GPS
virtual reference stations for RTK positioning.”
Journal of Geodesy, Vol. 77, No. 5-6, pp.
292-302.
John Wiley & Sons, Inc., Hoboken.
Wu, J. and Yeh, T. F. (2005), “Single-epoch
weighting adjustment of GPS phase observables.”
Navigation, Vol. 52, No. 1, pp. 39-47.
194 Journal of Photogrammetry and Remote Sensing Volume 13, No. 3, Sepetmber 2008
Research on GPS Kinematic Positioning with Multiple
Reference Stations
ABSTRACT The distance-dependent GPS errors, notably atmospheric refraction, reduce the success rate of
epoch-by-epoch ambiguity resolution, and limit the GPS positioning accuracy, especially for medium- to long-range baselines. Using multiple reference stations to model (or interpolate) the distance-dependent biases between the reference station and a rover can extend the distance or improve the positioning accuracy. The objective of this research is to find out the relative tropospheric zenith delays (RTZD) between different reference stations by using known coordinates and to provide rovers with interpolated corrections for more precise positioning. The project consists of three major steps: (1) finding out the RTZDs between reference stations, (2) modeling the RTZDs; (3) kinematic positioning. In the first step, a pseudo observation equation of RTZD is added in order to reduce the impact of RTZD on ambiguity resolution. In the second step, different model is used according to the numbers of reference stations. These two steps are the emphases of this investigation. The proposed method needs only one to three epochs to resolve ambiguities, so the effects of cycle slip or data gap are not very serious. A multiple reference stations network located in north Taiwan is used in this research. There are six permanent GPS stations in this network. Test result indicates that if the RTZDs between different reference stations can be resolved successfully, and a proper interpolation model is used, it is possible to improve the positioning accuracy.
Keywords: Multiple reference stations, GPS kinematic positioning, Tropospheric zenith delay
1 Graduate Student, Department of Civil Engeneering, National Central University 2 Professor, Centor for Space and Remote Sensing Research, National Central
University 3 Ph. D. Candidate, Department of Civil Engeneering, National Central University