3 Geo-Referencing
Figure 3. Illustration of Geo-referencing
In mobile mapping, the vehicle is
continuously moving or the
position of the vehicle is changing with respect to time. Besides, every sensor and device has it’s
own local coordinate system. For example, GPS output is based on WGS84 coordinates system,
Laser data is based on it’s own local coordinate system, the origin of which lies at the laser
scanning head and so on for other sensors and devices. The major problem is to identify the
spatial position of the objects scanned by the laser at any time while the vehicle is moving with
reference to a common coordinate system, which is called Geo-referencing. It involves the
integration of all the sensors and devices to a common coordinate system, which is the (local)
mapping coordinate system. The integration process mainly involves the computation of fixed
rotation and shift vectors between the INS body and sensors. As the GPS and INS are physically
located in two different places, we also need to know the shift vector between the GPS and INS.
Refer (Manandhar and Shibasaki, 2000) for details on individual sensor calibration.
The general mathematical model (Cramer et al., 1998) for direct geo-referencing when the GPS
and INS are physically offset is given in equation 1.
where,
Equation 2
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Any object point vector at time t in mapping coordinate system
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Equation 3
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GPS measured point vector at time t in mapping coordinate system
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A variable, 3 x 3 Rotation Matrix at time t from INS body (INS coordinate
system) to Mapping Frame. This is direct observation value at time t by
INS. The HISS system is calibrated so as to give the output in WGS84
coordinate system.
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Equation 4 |
Image vector in Image Coordinate System
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Equation 5
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Offset from INS to the CCD in body frame, obtained by direct measurement.
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Equation 6 |
Offset from INS to GPS in body frame, obtained by direct measurement.
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A fixed, 3 x 3 Rotation Matrix between CCD camera and INS body in
INS coordinate system. The computation of this rotation matrix is given
below:
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We get rotation matrix and shift vector between the CCD and local coordinate system from
outdoor camera calibration. During the calibration process we observe the GPS/INS position
together with acquisition of the calibration target images. We have defined a local coordinate
system for measuring the calibration targets by the total station. While defining the local
coordinate system, the orientation of the x, y, and z-axis were set following the map coordinate
system, so that the rotation between the two coordinate systems is a 3x3 unit matrix. Thus we
can approximate that the rotation between the CCD camera and the local coordinate system is
the rotation between the CCD camera and mapping coordinate system. The transformation from
local coordinate system to mapping coordinate system is given by equation 7. This is a two-
dimensional affine transformation.
Equation 7
The initialization process of INS aligns the horizontal plane and finds the north direction and the
output is calibrated to give the rotation with respect to the map coordinate system. Thus the
rotation output from the HISS (INS/GPS) is the rotation from the INS body to the Mapping
coordinate system.
Now, we have both the rotation of the CCD camera and INS body with respect to the mapping
coordinate system. From this two information, we can compute the fixed rotation between the
CCD and INS with respect to mapping coordinate system by using the three equations illustrated
in figure 4.
Figure 4. Illustration of computation of Fixed Rotation between the Sensor and INS
Since, we need to geo-reference laser coordinates, we have to know the relation between the
laser coordinate system and the mapping coordinate system. However, one major problem in
outdoor experiment is to identify a specific reflected laser from the object point (or calibration
target). The laser data we get is just a cloud of points and it’s too difficult to know which
particular point or points is the one reflected by the target. Thus in order to overcome this
problem, we based our integrated calibration on CCD calibration. We converted the laser
coordinate system to CCD coordinate system (image coordinate system) with some
assumptions. This is achieved by using the equations 8 and 9.
Equation 8
where,
Equation 9
In this system, the laser and CCD camera are housed in the same frame. Thus, both of these two
sensors rotate together with respect to INS and other devices. We assumed that the imaging
plane of CCD and Laser are orthogonal to each other and from the coordinate systems defined
for laser and CCD, we can write the rotation from laser to CCD as [0 0 –90] along X, Y and Z
axis. The shift between the laser and CCD are physically measured.
Thus we modify equation 1 to equation 10. We use this equation to compute every object
coordinate measured by laser with respect to the map coordinate system.
Equation 10
Using above mathematical model for geo-referencing, we have integrated laser range data from
three sensors. The fourth sensor, which is placed vertically up on top of the vehicle is used for
deriving the horizontal profile of the vehicle.
