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4
Targets of Known Coordinates
Position (j)
GPS antenna
PN
Figure 4: The test field for calibrating the VISAT system
Where (Xy, Y}, Z}) and (X, Y,, Z,) are the left and the right
camera perspective coordinates of image(i) as obtained from
the bundle adjustment, and R, 1s the rotation matrix
between the c-frame and the m-frame as obtained from the
bundle adjustment.
» interpolating the perspective center coordinate of the
cameras and the attitude information at the time of exposure.
This requires the camera to be synchronized with the
GPS/INS data.
» merging the data necessary for the georeferencing
process with the image data. The georeferencing data are
contained in the header in front of each stereo-pair
5. ACCURACIES ACHIEVABLE WITH
THE VISAT SYSTEM
The object coordinates are obtained from the VISAT system
through a fourteen parameter transformation (two scales, two
translation vectors, and two rotation matrices) from the c-
frame to the m-frame. As the position and the orientation of
the two cameras are known at the time of exposure, an
intersection procedure can be performed using the
georeferencing formula in its final form as given in equation
8
m mi : b
P" o ms (0 * Rp (0 (Sí AR, +r Ü 8)
It is clear from the georeferencing procedure that the
accuracy of the 3-D coordinates is a function of a complete
processing chain. This, involves system synchronization,
GPS positioning, INS position/attitude determination,
system calibration, accuracy of cameras, and geometry.
As a first step in obtaining the contribution of each of these
factors, a standard error analysis through error propagation
is performed. The propagation of equation 8 after neglecting
the second order terms results in the following equation:
m
INS
RU @- @si. dr] Sis SR] 4
dr." = Orel) + SR, . (si . anb ro ad) +
si. dR" vas sas 9)
Equation 9 contains three major group of errors that
contribute to the final accuracy of the 3-D coordinates
derived from the VISAT system. They are the INS/GPS
position errors, the INS orientation errors, and the
calibration and target pointing errors. Table 1 summarizes
the way each term in equation 9 contributes to the final
accuracy of the 3-D coordinates. The table indicates that the
major error sources are the INS/GPS position errors, the
system synchronization errors, and the target pointing
errors. The only potential error which was not included in
equation 9 is the instability of the cameras with respect to
the navigation sensors. This instability will add more errors
b b : : ;
through Sa and 8dR , specifically when its magnitude
exceeds the noise level of the INS gyros. In general, the
1. : b. rs : b
variation in da is not as critical as that in ôdR,- The
effects of camera instability on the final accuracy of the 3-D
coordinates has still to be tested. In the remainder of this
section, the contribution of each factor will be discussed
using recent lab and field test data.
The synchronization effect appears in both the interpolated
m ; i m
vector rius (0 and the rotation matrix R. (t). In order to
reach the required accuracy of the VISAT system, the
synchronization should be accurate to few milliseconds ( one
millisecond is equivalent to 1.6 cm positional error for a
velocity of 60 km/h). The system synchronization will be
performed using the PPS from the GPS receiver. The PPS
interrupts the computer every second. The interrupt handler
gets a computer time tick with a resolution of 53
microseconds from the programmable time chip of the PC.
The computer time tick will be used to solve the ambiguous
time offset between the GPS time and the computer time.
245
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