The International Archives of the Photogramme try, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
2. SYSTEMATIC ERROR CORRECTION MODEL FOR 
THE UAV AIRBORNE GPS/INS 
The UAV airborne GPS/INS integrated navigation system is a 
position and azimuth determining system composed of GPS 
receiver and Inertial Measurement Unit (IMU), it can be used to 
obtain the moving vehicle’s spatial three-dimensional position 
and attitude data. 
2.1 Coordinate System Transformation 
The original attitude data {0, (j), (//) acquired from UAV 
airborne IMU is the corresponding coordinate axes’ angles 
between IMU Coordinates System and Navigation Coordinates 
System (moving); while the exterior orientation elements of the 
images (<p,0),K) is the corresponding coordinate axes’ 
angles between image Coordinates System and terrestrial 
photogrammetry coordinates system. Therefore, we must first 
transform the UAV airborne IMU attitude data (0,(f),y/) 
from navigation coordinates system (moving) to terrestrial 
photogrammetry coordinates system in order to obtain the 
exterior orientation elements of the images(Baumker, 2002). 
Figure 1 shows the concrete conversion process. 
Figure 1. The flow chart of coordinate transformation for UAV 
attitude data 
2.2 Deviation Angle Error 
For apparatus installation technology’s reasons, the axes of 
IMU coordinates system aren’t exactly parallel to that of 
camera coordinates system when installing. Generally there 
exists exiguous angle deviation ( < 3° ) between the 
corresponding axes of this two coordinates. We call it deviation 
angle error usually (Figure 2). In Figure 2, X b ,y b ,Z b 
respectively represents three axes of IMU coordinate system, 
and X c ,y c ,Z c respectively represents three axes of camera 
coordinate system. Camera coordinates system separately 
rotates (X z ^ GC v > CC X around the z axis> y axis and x axis 
relatively to IMU coordinate system. This group of deviation 
angle error can’t be determined directly by the conventional 
measurement method, so other methods are needed to use to 
obtain them. 
Figure 2. Deviation angles from camera coordinate to IMU 
coordinate 
2.3 Deviation Angle Error Correction Model 
Images’ exterior orientation elements obtained after coordinate 
system transformation are still affected by the deviation angle 
error. This error can’t be acquired through the conventional 
measurement method, so the images which have known exterior 
orientation elements can be utilized to obtain this error 
indirectly. First, one calibration region which has enough 
quantity and precision ground control points is selected to 
proceed calibration flight, then the exterior orientation element 
of each image is calculated by the conventional method. Finally, 
the best estimated value of the deviation angle error 
((X x ,(X y ,(X z ) is calculated using the exterior orientation 
elements computed above and the original attitude data 
obtained from IMU. The concrete computing process is as 
follows. 
I According to this group of deviation angle 
error (CC X , Ct y , OL z ) , the rotation matrix R b from camera 
coordinate system c to IMU coordinate system b is established. 
And because (X (X CX are all less than 3° , this matrix 
z y X 9 7 
can be simplified according to the related knowledge of inertial 
navigation(Skaloud, 2003). 
S* 
= Rfa ) )R x (a i )Rfa i ) 
cosa, 
0 
-sina,' 
1 
0 
0 
cosa, 
-sina, 
0' 
0 
1 
0 
0 
cosa. 
-sina, 
sin a, 
cosa, 
0 
sina, 
0 
cosa, 
0 
sina. 
cosa. 
0 
0 
1 
f 
} j 
J 
1 -a, -a, 
a, 1 -a, 
a, a„ 1 
(1) 
II According to the flow chart of coordinate transformation 
in Figure 1, the rotation matrix from camera coordinate 
system c to terrestrial photogrammetry coordinate system L is 
set up. R b is the rotation matrix from IMU coordinate system 
to terrestrial photogrammetry coordinates system. Thus, we can 
get formula (2) and (3). 
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