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Figure 1: Control point distribution 
extended collinearity equation must be 
determined via camera calibration. These 
include the interior orientation elements 
and the parameters Ao, Ao, Ax, AX, AY and 
AZ for the forward- and backward-looking 
channels. For the processing of the MOMS- 
02/D2 data, the inclination angle of Aq = 
+21.457° was the only parameter of these 
six to have a non-zero value. 
In order to achieve a solution for the 
collinearity equations at each scan line, 
a re-parameterization of the exterior 
orientation elements by time dependent 
polynomial functions is adopted. 
Quadratic functions have been used for 
stereo restitution of both SPOT (Kratky, 
1989) and MOMS-02/D2 imagery (Dorrer et 
al, 1995), whereas for the triangulation 
of MOMS-02 three-line imagery Lagrange 
polynomials:Jof “third order "have been 
proposed "(Ebner et ‘al, 1992; EKornus et 
al,” 1995). Under ‘the Tlatter approach, 
which has been adopted in this 
investigation, exterior orientation 
elements are recovered for so-called 
orientation images (OIs) at. given scan- 
line intervals. The Lagrange polynomials 
then model the assumed smooth variation 
of sensor position and attitude over each 
interval of m scan lines between adjacent 
OIs. For a third-order curve the model is 
given as: 
Bis S Pr Ti —= Q) 
i=0l-1 jz0l4 f; 71; 
j*i 
where; Ps;í(t), at time: €. is; à linear 
Internati 
onal Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
combination of PÍít:) at the four 
neighbouring OIs. 
One of the perceived advantages of the 
Lagrange polynomial approach is that the 
interpolation is dependent upon only the 
nearest one or two OIs on each side of a 
given scan line for first- to third-order 
interpolation. Thus, fór a third-order 
approximation, four OIs are employed, 
whereas for a  first-order model the 
interpolation would be linear between two 
OIs. One of the aims of the present work 
was to investigate the impact of the 
order of the function on triangulation 
accuracy. 
For the bundle adjustment of the MOMS- 
02/D2 imagery, the following observation 
equation set was employed: 
y — Att TBi-DL5 P 
vonoq qt, wep 
v, = Az me (3) 
Vu = I du Pia 
um fo wi] cP, 
th 
where A indicates the coefficient matrix 
of the unknown exterior orientation 
parameters t; B is the coefficient matrix 
of the ground coordinate vector x; tz and 
tp are. the vectors of shift and drift 
terms whose coefficient matrices are 
given by Cg -and- C; vj,. 1; and P; are 
residual and discrepancy vectors, and 
weight matrices, respectively. The weight 
matrices Px, Ptg and Prp are primarily 
employed to allow the associated