2-4-3 
epoch change in the system’s coordinates allows for the 
distinct variation in the design matrix partial 
derivatives, enabling fast offset estimation, as shown in 
the figures below. 
In the tests presented here, the GPS/INS/CCD system, 
placed on a common rigid platform, was mounted on 
the top of a land vehicle. The GPS/INS lever arm 
offsets were 0, 0.95, -0.04 m in x, y and z INS body 
frame directions, respectively. The initial part (500 sec) 
of the van trajectory, used for testing the lever arm 
estimation is presented in Figure 1. For this test, the 
INS x-axis was oriented approximately towards south 
during the initial stationary period of about 50 sec; then 
the vehicle performed some maneuvers (for about 
200 sec) for the system’s calibration, as shown in 
Figure 1. 
-83.0418 -83.0416 -83.0414 -83.0412 -83.041 -83.0408 -83.0406 
longitude [deg] 
Figure 1. Vehicle trajectory, first 500 sec. 
The GPS/INS data were processed with the correct 
(pre-surveyed) lever arm offsets, and with the offsets set 
to 0, 0.50 and 0 m, respectively. The differences in the 
longitude and height of the center of the INS body 
frame between the solutions with correct and distorted 
lever arm offsets are plotted in Figures 2 and 3. These 
results indicate that the horizontal offsets can be 
recovered practically within just a few epochs while the 
vehicle starts maneuvering. The initial looping as shown 
in Figure 1, allowed for almost instantaneous recovery 
of the horizontal lever arm errors, while the vertical 
component was estimated after approximately 60 sec 
into the motion. Thus, if the lever arm offsets are not 
known precisely, and have to be estimated together with 
other components of the state vector, it is important to 
perform some maneuvers before the image collection 
starts, to allow for the system’s calibration. These 
maneuvers are also needed to bring the attitude 
(especially heading) errors down. 
Another test was performed on the same data set, with 
distorted lever arm offsets, but without the initial 
maneuvering (the data reduction started after the vehicle 
finished the initial 200-sec looping). The test results 
were compared with the solution based on the correct 
offsets. The comparison presented in Figures 4 and 5 
indicates again the importance of maneuvering for the 
fast lever arm recovery. Since the offset estimation 
started daring the low-dynamics motion, the partial 
derivatives changed much slower, as compared to the 
high-dynamics part of the trajectory in the previous test. 
The figures show that the horizontal components were 
recovered after approximately 100 sec (compare to just 
a few epochs while maneuvering), while the vertical 
component was recovered after ~300sec, as opposed to 
~70 sec as shown in Figure 3. 
x 10' 6 
s 
- 
- 
- 
- 
■ 
4.166 4.167 4.168 4.169 4.17 4.171 4.172 
GPS time of week [sec] x 1Q s 
Figure 2. Longitude difference between solutions with 
correct and incorrect lever arm components 
(10' 6 deg corresponds to ~10 cm). 
GPS time of week [sec] x 1Q s 
Figure 3. Height difference between solutions with 
correct and incorrect lever arm components.