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The International Archives of the Photogrammetrv. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
EO polynomials of the reference strip starts from zero. For the 
other non-reference strips, it starts from the offsets. The initial 
value of the EO polynomial coefficients can be figured out by 
least-squares fitting of the line-by-line telemetry EO data. 
3. BUNDLE ADJUSTMENT OF HiRISE STEREO IMAGES 
This bundle adjustment integrates HiRISE EO parameters and tie 
points on HiRISE stereo images. EO parameters have been 
retrieved from the SPICE kernel and stored line by line. A 
hierarchical-matching algorithm has been developed at the 
Mapping and GIS Laboratory at The Ohio State University (OSU) 
for mapping purposes. The tie points are automatically selected 
from the matched terrain points on stereo images to make sure 
they are evenly distributed. These tie points will be included in 
the bundle adjustment as measurements after the interior 
orientation procedure. 
Different types of measurements will form observation equations 
separately. For image tie points, they are related to the ground 
coordinates and EO parameters via the collinear equations: 
x | J ll (X t -X c l ) + af l2 <r i -r i ) + a , i3 {Z,-Z c l ) Q 
' a i 3l (X i -X c i ) + a i n (Y i -Y c i ) + a‘ i3 (Z i -Z c i ) (5) 
{ . a' 2 \(X j -X c J + a' 22 (Yj - YT) + a‘ 23 (Z i -Z c ¡) Q 
a' 31 (X t - X%) + a' 32 (i' - 7 C ) + a' 33 (Z. - Z c ,) 
where X i is the along-track coordinate of the detector on the 
focal plane of the f h point which can be calculated using 
HiRISE interior orientations; y i is the corresponding 
cross-track image coordinate; X t ,Y j ,Z j are the ground 
coordinates of the i' h point; X°¡,Y C j9 Z c t are the position 
of the perspective center of the sensor at the i' h point; 
a' n ...a l 33 are the elements of the rotation matrix formed by 
the sensor pointing angles, and f is the focal length of the 
sensor. 
The EO parameters in Equation 4 determined through sensor 
modeling are treated as weighted parameters to form a set of 
pseudo observation equations, such that 
pseudo observation + correction - parameter = 0 (6) 
These equations are combined into the bundle adjustment system. 
The adjustment is based on the least-squares principle 
minimizing the sum of the weighted square of the residuals of the 
observations and the pseudo observations. Since Equation 5 is 
non-linear, linearization should be applied. Therefore the solution 
must be iterative. The initial values of the EO polynomial 
coefficients are from the least-squares fitting of telemetry EO 
data. The initial ground positions of tie points are obtained 
through an intersection using telemetry EO data. 
In this bundle adjustment system, tie points are used as 
measurements and telemetry EO parameters serve as pseudo 
measurements; 36 EO polynomial coefficients and ground tie 
point coordinates are unknowns. One tie point contributes to 4 
measurements and 3 unknowns, therefore at least 36 tie points 
are needed to make the problem solvable. 
4. DATA PROCESSING RESULTS AT MER SITES 
4.1 Bundle Adjustment without Ground Control 
The MRO mapping data used in this study includes HiRISE 
stereo images and MRO trajectory data including the positions of 
the camera perspective center and pointing angles. Table 1 
summarizes the main properties of the stereo images used in this 
study. 
Site Name 
Victoria Crater 
Husband Hill 
Stereo 
Left 
Right 
Left 
Right 
Acquisition Time 
10/03 
11/14 
12/12 
11/22 
(M/D/Y) 
/2006 
/2006 
/2006 
/2006 
Convergence Angle 
9.8 degrees 
19.8 degrees 
Image Size 
5000 by 4096 
5000 by 4096 
No. of Tie Points 
136 
178 
Table 1. Sites studied in this research 
Victoria Crater and Husband Hill, where the twin rovers in the 
2003 Mars Exploration Rover (MER) mission are doing their 
surface exploration, were selected as mapping areas in this study. 
The planned comparison with ground mapping products and 
further integration with ground data was the reason those sites 
were chosen. Also, those two sites represent two typical 
geological characteristics on the Martian surface. Husband Hill is 
a hilly area with a lot of topographical variations while Victoria 
Crater is 800 meters in diameter with a very smooth crater wall 
and flat sandy surface outside the crater ring. MRO trajectory 
data is extracted using Spacecraft, Planet, Instrument, C matrix