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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