about 2 compared to the ratio of 1:1. The height accuracy 
is not affected, as mentioned already. 
  
1 h? 1 
0,70,- oy —— 3677 997 3 (3) 
2Cp p*CN 2C p 
2.2 Reconstruction of the exterior orientation 
The functional model of the bundle adjustment is based on 
extended collinearity equations. The exterior orientation 
parameters are estimated only for so-called orientation 
images (OI), which are introduced at certain time intervals. 
Between the OI, the parameters of each individual image 
line are expressed as functions (e.g. polynomials) of the 
parameters of the neighbouring orientation images (Müller, 
1991). A variety of different parameter models for the 
reconstruction of the exterior orientation were applied in 
the past (see survey in Wu, 1986). The goal of each 
approach is the minimization of the interpolation error 
using as few parameters as possible. 
Investigations, based on simulated orbit data, showed that 
3rd order polynomial functions approximate the orbit quite 
accurately. Therefore the linear interpolation function, used 
in the bundle block adjustment program CLIC previously, 
was replaced by a Lagrange Polynomial (LP) approach (4). 
It, 
J 
nr (4) 
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P) - Y. P) 
i-0 
[; 3 
- 
In (4) the exterior orientation parameters P(t) at time t are 
expressed as a linear combination of the related parameters 
P(t) assigned to the n+1 neighbouring orientation images i 
at time t. The main characteristics of the LPs are: The LP 
coefficients are explicitly the (unknown) exterior orientation 
parameters of the orientation images; the LP order can 
easily be changed by the definition of the parameter n. The 
linear interpolation therefore remains applicable by setting 
n = 1. The complete extended collinearity equations are 
derived by replacing the exterior orientation elements X,, 
Yo Lo 9» €» K, in equations (2) by the related expres- 
sions (4). 
2.3 Introduction of offset and drift parameters 
In principle, the reconstruction of the exterior orientation of 
three-line-imagery is possible by means of photogrammetric 
measurements and ground control information only. 
However, precise position and attitude observations 
essentially improve the accuracy of point determination, 
especially if little or weak ground control information is 
available (Ebner et al., 1991). 
In case of MOMS-02/D2, 
information is available: 
» position and attitude data from an onboard Inertial 
Navigation System (INS), 
» position data from the Tracking Data Relay Satellite 
System (TDRSS), 
» position data from sophisticated orbit models. 
the following additional 
All these rather heterogeneous data of position and attitude 
have to be combined and transformed into a common 
coordinate system. 
460 
Basically, all measurements are affected by blunders, 
random and systematic errors. Blunders must be located 
and eliminated a priori by robust estimation methods. 
Random errors can be processed by least squares 
adjustment. The critical aspect is the influence of systematic 
errors. They should be described by the functional model. 
In our case the different systematic errors of the position 
and attitude data are modeled through additional unknown 
parameters. By limitation to constant and linear terms 
which, describe the main effects, twelve additional 
parameters, namely an offset and a drift parameter for each 
exterior orientation parameter, have to be estimated during 
the bundle adjustment. 
3. SIMULATIONS 
In the past a series of simulations was carried out for 
MOMS-02/D2 to analyze the effect of certain parameters 
on the accuracy of point determination and to give recom- 
mendations in the planning phase of the project concerning 
the technical design of the camera or additional measure- 
ments during the mission (Ebner et al, 1991; Ebner and 
Kornus, 1991). Based on these results, new simulations are 
performed to show the attainable accuracy using the 
extended functional model and realistic input information. 
In the following the input information and the results of the 
simulations are presented. 
3.1 Input information 
3.1.1 Camera and mission parameters The geometric 
configuration is established by the MOMS-02/D2 camera 
and mission specifications. The most conspicuous feature is 
the extremely small image angle, which results in a ratio 
between flying height and swath width of 8:1. This is an 
essential handicap for a precise geometric evaluation. 
The parameters used in the simulations are listed in table 1 
and match the nominal values of the project to a large 
extent. 
  
  
  
  
  
view direction of the lens forward nadir backward 
calibrated focal length [mm] 2372 660.0 2372 
pixel size [4m] 10.0 10.0 10.0 
ground resolution [m] 13.5 4.5 13.5 
convergency angle A« [deg] -21.9 0.0 21.9 
orbit height [km] 296 
orbit inclination [deg] 28.5 
swath width [km] 36 
strip length [km] 468 
  
  
  
  
Table 1: Simulation parameters 
The camera is mounted on top of the space shuttle, which 
will move along a 296 km high orbit with an inclination of 
28.5°. Besides the recording of single strips in normal (bay 
down) flight attitude of the shuttle, some orbits will be 
flown with a shuttle cross inclination of 30°. As shown in 
(Ebner et al., 1991) the accuracy of point determination can 
be improved by convergent sensor configuration either 
obtained by an instrumental sensor line convergency or by 
inclining the camera carrier in case of parallel sensor 
arrangement. 
  
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