The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
885 
^2 = 
^ © 
1 
’ F yf b - R "b' F f = 
yf>f 
7* 0 0 ' 
o fi o 
0 0 
9x6 
1 
o 
O 
o- 
F 13 = 
0 0 
0 0 
’ F = ~ R b ’ F = 
(4X o o ■ 
0 (ufo 0 
F F 
£0) d 1 ea, f 
9x6 
o 
O 
i 
F = 0 F = 0 
1 22 v 6x6 > 1 33 w 
6x6 ’ 
If more items in Equations (1) and (5) are considered in the 
error model, the KF will perform more elegantly. If the noise in 
Equations (3) and (7) is zero, d R and h R will be same to d b and b h 
respectively. In this paper, only the d R and d m for the gyroscope 
(and b R for accelerometer) are modeled for the stochastic error. 
So the error dynamic equation of the KF with 15 inertial sensor 
error states is given as Equation (11). 
Xv/ 
>u 
F n 
^3 
1 
\v/ 
Xf 
= 
0 
F22 
0 
0 
Xf 
+ 
*7 
K 
0 
0 
^33 
0 
x m 
*• 
0 
0 
0 
'A 
H 
5? 
(11) 
where 
X »~'- C l J ^13 = 
0 0 
0 0 
F F F 
£<O d £0) m £<0, f j 9x9 
Feco d Fto m ^b ’ p — 
0 A 0 
, I-, denotes 
the 3-order identity matrix, and other parameters are same to 
those in Equation (10). 
3. EXPERIMENT AND ANALYSIS 
In the experiment, aerial GPS/INS data was collected in 
September 2005 with a tactical grade IMU and dual frequency 
GPS receivers by the POS AV 510 system from Applanix. The 
gyroscope drifts in the IMU are of the order of 0.1 deg/h and the 
accelerometer biases are lOOug. The data rate of the IMU is 
250Hz and 10Hz for the GPS. The GPS/INS integration 
software package Throstle™, which supports loosely-coupled 
and tightly-coupled models and different stochastic error 
models, was used to process the data with the three error models 
proposed in the paper. In the data processing, the loosely 
coupled model for the Extended Kalman Filter (EKF) is used, 
which is a common coupling method for the aerial GPS/INS 
integration because the GPS observation condition in aerial 
applications is much better than that in the land-based 
applications. Firstly the differential GPS positioning was 
processed with GPS high precision positioning software Caravel 
PP™ at a 1 Hz data rate because this data rate is high enough for 
the GPS/INS coupling. The positioning result was compared to 
another GPS positioning software Graf/Nav™, and the 
difference is less than 10 cm for the 200km baseline. The 
trajectory of the test flight is shown in Figure 1. Then the 
positioning result of Caravel PP was put into Throstle for the 
loose coupling with three stochastic models. The configurations 
of three tests are listed in Table 1. The data was processed also 
by POSPac™ to compare the result of Throstle. 
Figure 1. The trajectory of the test flight. 
Items 
model 1 
model 2 
model 3 
Gyro drift random walk 
~T~ 
V 
V 
Acce. bias random walk 
V 
V 
V 
Gyro scale factor 
V 
V 
Acce. scale factor 
V 
V 
Gyro drift first-order 
V 
Markov process 
Table 1. The configurations of the three stochastic models. 
The first test is processed with model 1 which uses 6 error states, 
i.e. 3 random walks for the gyroscope drifts and 3 random walks 
for the accelerometer biases. In order to check the performance 
of the KF with different stochastic models, the backward 
filtering and the smoothing were not implemented. The 
innovation (predicted residual) and measurement residual are 
shown in the Figures 2 and 3. The estimated errors of position 
(the output of the EKF) are shown in Figure 4. The estimated 
sensor errors are shown in Figures 5 and 6. The standard 
deviations of position and attitude are shown in Figures 7 and 8. 
The difference of the positions between the GPS differential 
positioning result (Caravel PP) and GPS/INS coupling result 
(Throstle) is shown in Figure 9. The difference of the attitude 
between the Throstle solution and the POSPac solution is shown 
in Figure 10. 
Figure 2. The innovation of the Filter with model 1.