2.2 Test solutions and their analyses 
The following solutions were obtained and compared: (1) 
free INS navigation solution, (2) free INS solution supported 
by DOVs (3) GPS/INS solution (“true” reference), (4) free 
INS solution supported by DOVs and ZUPTs (land-based 
only), (5) GPS/INS solution supported by DOVSs (gravity- 
enhanced reference solution). 
  
  
  
  
  
  
  
  
  
DOV (ArcSec) and Position Error (Meter) in East-West Direction 5 
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2D 500 1000 .-1500. 2000 . 2500 © 3000 300 40000 
Epoch From 322970 To 326798 [Second] 
Figure 2. East- West DOV and corresponding position error 
(mean DOV (pt) was used) bounded by +36. 
2.3. DOV effects on gyro and accelerometer errors 
Figures 3a and 3b illustrate the actual DOV signature along 
the land-based trajectory, and the gravity errors in N, E and 
D directions, estimated by the Kalman filter in the case when 
only normal gravity was used in the compensation procedure 
(solution 3). Figure 4 displays the difference between the true 
and the estimated DOVs, and the difference in the third 
component, the gravity disturbance, which is the actual 
difference between the two estimates (solution 3 and 5) since 
the gravity disturbance is not compensated for together with 
DOVs, for the airborne data set. For clarity, note that once 
DOVs are compensated for, they are fixed to a sigma of +I 
arcsec in the GPS/INS filter, and only the gravity disturbance 
is estimated. 
  
  
  
  
  
  
  
  
DOVv: Arcsec 
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; = North-South (xi) with mean=0.3arcsec 
; *** East-West (eta) with mean=6.0arcsec | 
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mmm mm bh hee en demas = 
a 1 : : : : ^st 
0 | 1 1 | 1 I | 
0 500 1000 1500 2000 — 2500. 3000 3500 4000 
Start Epoch: 322970 End Epoch: 326799 
Figure 3a. DOV for land-based GPS/INS dataset. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
Gravity Disturbance N,E,D: Arcsec 
  
  
  
  
  
Arcsec 
  
  
  
| i | i i j 
500 1000 . 1500 2000 20 3000 3500 4000 
Start Epoch: 322970 End Epoch; 326799 ; 
  
Figure 3b. DOVs and gravity disturbance (D) estimated by 
GPS/INS filter with no DOV compensation (solution 3); 
land-based data set. 
Figures 3a-b and Table ! show the difference between the 
estimated DOVs and the true DOVs at the level of ~8 arcsec. 
Clearly, the estimated DOVs are substantially different from 
the true values, indicating that the estimates absorb some 
signal from other parameters in the state vector. This 
suggests that introducing DOVs directly may remove 
noticeable errors in tilt and possibly in gyro and 
accelerometer error estimates, as these components are 
correlated. Indeed, further analysis of the differences 
between the IMU errors obtained with the two solutions (3 
and 5), with and without DOVs, indicates that direct DOV 
compensation affects the sensor error estimates. Figures 5-6, 
for example, illustrate the accelerometer bias and its RMS 
estimated by GPS/INS filter with no DOV compensation, 
and Figure 7 displays the difference between the 
accelerometer bias from Figure 5 and the one estimated by 
the filter where DOV compensation was included. Figure 8 
illustrates the corresponding RMS improvement due to the 
DOV compensation. 
Gravity Disturhance N,E,D: Arcsec 
  
15 
  
  
  
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35 | | l | | | | | 
0 . 500 1000 1500 2000 2500 3000 3500 4000 4600 
Start Epoch: 161319 End Epoch: 165700 
Figure 4. Difference between the true and the estimated 
(solution 3) DOVs; D is the difference between the gravity 
disturbance estimated by solutions (3) and (5); 
airborne data set. 
   
Interna 
Error 
| AccBi 
AccBi 
AccBi 
AccSI 
AccSI 
AccSI 
GyroE 
GyroE 
GravE 
GravE 
GravE 
AccBi 
| AccBi 
AccBi 
AccSF 
AccSF 
AccSF 
GyroB 
GyroB 
Gyro 
GravE 
GravE 
  
GravE 
Tabl 
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