International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 Inte 
is no ground truth, there is no absolute solution; however, using Mos 
4.0 Cross-Site Tie Points Selection Singular Value Decomposition (SVD) we can obtain an optimal soft 
solution. Equation 8 represents the rigid transformation, in GIS 
Selecting tie points from original images is extremely difficult which the transformation matrix B (representing rotation and caps 
due to perspective distortion sce Figure 13 (left). Orthophotos translation) is calculated from cross-site tie points. poin 
   
can remove such distortion and rotation, see Figure 13(right). 
This can help the human operator identify tie points. 
  
  
  
  
  
   
  
        
| (FAZ XY. ed) (4) 
The extracted rocks and their measurement uncertainty can be 2 ; S ; ; 
matched by considering the localization uncertainty of rovers. vz adX e a,dY Y a,dZ € a,dX, ta, dX + add, (5) 
Figure 14 shows an example; there are two sites (red/blue) and +a, dw + add + a,dx ; 
two sets of landmarks. Some landmarks are only distinguishable PX (6) 
from one site. X s(A47 PAY! 47 PV (I) 
P, = BP, (8) 
where (x,y) is the image coordinate of the tie points Wel 
(X,Y.Z) is the object coordinate of the tie points fol 
(Xs, Ys,Zs) is the camera coordinate robo 
(o,0,K) is the camera attitude mate 
Figure 13. Cross-site tie points on original image (left) and v, V are the residuals of the observation time 
orthophotos (right) a1.o, A are coefficients, a function of (Xs,Y s,Zs, G0) in cl 
X is the unknown vector (X, Y.Z,X«, Ys,Zs. 0,0,K) land: 
P is the weight matrix maxi 
B is the matrix of rigid transformation autoi 
co P,, P5 are homogeneous coordinates of tie points 
After the bundle adjustment, the new camera position can be 
used to renew the rover's location. This 
5. RESULTS Map 
The above algorithms have been developed and tested on 
several sets of data, including 1997 Mars Pathfinder IMP data, 
1999 Silver Lake simulation data, 2002 FIDO simulation data, Atiy: 
2003 PORT simulation data, and finally, 2004 Mars local 
Exploration Mission (MER) data. 9(6), 
Figure 14. Matching of cross-site landmarks Bell, 
Rove 
By pairing landmarks located within ranges defined by Geor 
measurement and localization uncertainty, the parameter of 
localization uncertainty can be estimated as: Betk: 
landr 
251-: 
arg max count (|. — I< (u, + 4, +4, )) (3) 4 
"i row 
comp 
Mack 
where a, b denote site a and site b 
Li, ly; are the coordinates of landmarks a-i and b-j Cozn 
u,; and uy; are landmark measurement uncertainty positi 
uy is relative localization uncertainty between a and b © | 9(2), 
Eu : n SAEC à 5 i weeds = 
The corresponding pairs of landmarks can be used as cross-site Figure 15. Traverse map of Gusev Crater site Davis 
tie points. This normally needs human veri fication. s : did 
In MER mission, we have supported the science and Analy 
43 Bundle Adjustment and Rover Localization engineering team by providing maps in near real-time. Up to 
: s now, we have produced large-scale terrain maps generated from Desoi 
Bundle adjustment to improve rover localization results consists DIMES of both the MER-A Gusev Crater site and the MER-B navig 
of three steps: in-site bundle-adjustment (to remove the within- Meridiana Planum site. For surface operations, more than m Mach 
site inconsistence), cross-site rigid transformation (to improve orthophotos and DEMS have been provided for MER-A (Figur Fürst: 
initial parameters), and cross-site bundle-adjustment (to refine 15) and around 7 orthophotos and DEMs have been made Rr sn 
parameters iteratively). MER-B (Figure 16). We have also made initial maps for S eu 
interesting craters including the Eagle, Bonneville, Fram. ensu 
  
The bundle adjustment shown in Equation 7 is derived from Missoula, and Endurance craters. 
observation equation 4 and error equations 5 and 6. Since there 
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