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Ian Dowman
Given the replacement sensor model's polynomial and C, instead of the original rigorous sensor model and Cy. the
user performs the desired ground point solution with error propagation by simply substituting C, for Cg and
B, for B, when implementing equation [4]. (Note that the polynomial is used to generate the a priori M, and
that B Als easily computed either analytically or numerically from the polynomial) Because relationship [7] is
satisfied, the resultant "replacement" solution and error propagation will be nearly identical to the “original” solution
and error propagation. Note that when there is more than one block of images with correlated support data errors, the
actual C, or C, utilized in equation [4], contains the appropriate individual C A or C, correlated blocks down its
diagonal.
Operationally, the system that generates the replacement sensor model performs the following sequential steps for each
image:
e Generates the ground-to-image (rational) polynomial from the original rigorous sensor model.
e Defines the components of the adjustment vector A and generates its corresponding error covariance matrix C A
from the original rigorous sensor model’s support data error covariance Cs . This step is actually performed in
common for all images that have correlated sensor support data errors.
e Generates all appropriate identifiers associated with the above.
* Outputs the replacement sensor model and its supporting data to the user community. Regarding the adjustment
vector's error covariance matrix, only the upper triangular portion is required for each group of correlated (same
pass) images. The particular C, is duplicated (or "pointed" to) in the support data for each of these images.
The performance of the replacement sensor model with rigorous error propagation ( C A) has been verified to-date
with a limited set of real imagery/support data, and a more extensive set of simulated imagery/support data. The
following results for one simulated scenario are representative.
5.3 Test results
A space-born sensor was emulated using a simulated frame camera with seven sensor error parameters consisting of
position, attitude, and focal length errors. A focal length and vertical ground sample distance of 3 m were assumed.
Images were 10k x 10k pixels. Six images were simulated, three from each of two passes. The sensor support data
errors were modeled as time correlated errors for images from the same pass. Figure 1 illustrates the imaging
geometry for this scenario and figure 2 the corresponding image footprints and horizontal location for the two ground
points for solution. The elevations above the local tangent plane for the two ground points were 1000 m and 300 m,
respectively. Table 2 presents the sensor support data error characteristics for images 4-6. Support data error standard
deviations were ten times larger for images 1-3.
y A sensor height 225 nm A 100000 m
1 4 y
2 | x1 ground point 1
3 | x2 ground point 2
elev angle 1 = 34 | | images
2 35 | 1-3 (approx)
8 36 1 8 ——
! 4 » x1 a
elev angle 4 = 45 ! X x2 »
5 45 | | X
6 45 | | > images
I | i 4-6 (approx)
same pass images |
5 seconds apart * |
Figure 1. Imaging Geometry Figure 2. Image Footprints
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 263
