the en- 
  
ude data. 
| to about 
otometric 
le adjust- 
Sigma (2) [m] 
o 
m 
0 
  
Sigma (2) [m] 
ordinates 
s (above) 
PD have 
| by com- 
ultaneous 
ith >60% 
ers of the 
bal block 
processed 
aordinary 
plete im- 
ion, 60m 
achieved. 
ect of im- 
any over- 
in a block 
| that the 
X4 Mars is 
3.4 Mars rotation parameters 
In case of the global PD, special emphasize is given to the 
Mars rotation parameters, which define the link between 
the Mars-fixed object coordinate system as the reference 
frame for photogrammetry, and the inertial Earth equator 
and equinox of J2000 coordinate system as the reference 
frame for orbit determination. By combining image and 
radio tracking data, as described in section 2, the Mars 
rotation parameters may be treated as estimation param- 
eters within the bundle adjustment. 
The Mars-fixed system is aligned with the Mars equator 
where the prime meridian is defined by the small crater 
Airy-0. The orientation of the Mars equator and the so- 
called TAU vector is described by the right ascension a 
and declination 6 of the Mars north pole with respect to 
the Farth mean equator and equinox of J2000. Here, the 
IAU vector is defined as the intersection line of the planes 
described by the Earth equator of J2000 and the Mars 
equator (Davies et al. 1992). The rotation of planet Mars 
is described by the parameter W giving the angle between 
the IAU vector and the point where the prime meridian 
through the crater Airy-0 intersects the Martian equator. 
Therefore, three elementary rotations are required for the 
transformation from J2000 coordinates to the Mars-fixed 
equator and prime meridian coordinates (Fig. 3): 
1°* rotation around the z-axis by an angle (90° +a) that 
is equal to the right ascension of the IAU vector, 
2"4 rotation around the z'-axis by an angle (90° — 6) 
that is equal to the angle between the Mars equator 
and the Earth equator 
3'4 rotation around the z"-axis by an angle (—W). 
Earth equator 
(J2000) 
  
Figure 3: Orientation of the north pole and prime meridian 
of Mars with respect to the Earth equator and equinox of 
J2000 
Neglecting nutation, the right ascension «, declination 6, 
and W are generally expressed as linear polynomials 
a(t) =a0 + aT 
é(t) =6&6 +êT (8) 
W(t) = Wo + Wd 
601 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
  
  
    
   
  
   
     
    
   
   
   
   
     
     
    
   
   
   
  
   
   
  
  
   
   
    
    
    
  
  
     
   
  
   
   
   
    
   
    
    
   
    
   
   
   
in time, where the subscript o refers to the orientation of 
the Mars rotation axis at the reference epoch J2000 and T' 
is the ephemeris time in Julian centuries since that epoch. 
The parameters Wo and W denote the longitude of the 
prime meridian with respect to the IAU vector at J2000 
and the rotation rate, while d gives the ephemeris time in 
days elapsed since that epoch. Note that à and é arise 
from precession and might be expressed as functions of 
the Mars precession rate (db). The parameters that affect 
the transformation from the inertial to the body-fixed sys- 
tem may therefore be combined to a planetary rotation 
parameter vector w = (ao, 60, (ab), Wo, W)T. 
It can be seen from Fig. 4 that the accuracies of the Mars 
rotation parameters in the global block adjustment can be 
improved up to factor 4. Further information on this topic 
is given by Ohlhof (1995). 
30 
oO 
£ 
© 
10 —+ 
[09] 
0 
fg) 
a, 
d 
& HW 
J . 
Y a 
COMES 
AT Si 
zz 
~ 
Figure 4: Standard deviations a priori und a posteriori 
of the Mars rotation parameters ((V)["/cy], oo["], 6o["], 
Wo[°-1000], W[”"/d - 1000]) for the global Mars block 
4 PRACTICAL TEST USING MOMS-02/D2 
DATA 
4.1 MOMS-02/D2 Experiment 
During the 2"? German spacelab mission D2, success- 
fully flown in April/May 1993, the Modular Optoelectronic 
Multispectral Stereo Scanner MOMS-02 acquired digital 
high resolution, multispectral and 3-fold stereoscopic im- 
agery of the earth surface. 
The optical system of MOMS-02 consists of a stereo mod- 
ule and a multispectral module. The 3 lenses of the stereo 
module with 1 CCD sensor array .(Fairchild 191) each 
provide 3-fold along track stereo scanning with different 
ground resolutions. The nadir looking CCD array (4.5m 
ground pixel size) comprises 2 arrays with 6000 sensor el- 
ements each, which are optically combined to 1 array with 
9000 active sensor elements. The other CCD arrays of 
the stereo module consist of 6000 active sensor elements 
(13.5m ground pixel size). 
To verify the concept of orbital constraints in the pho- 
togrammetric restitution of MOMS-02 imagery, one imag- 
ing sequence with 3 image strips and 32 120 rows each cov- 
ering 430 x 37 km? in North-West Australia (orbit #75B) 
has been selected.