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are discrepancy vectors; and P and P, are weight matrices, the former relating to image coordinate observation precision, the 
latter to the constraint function(s). Depending on the model adopted, the *additional parameters', x;, might comprise “drift” 
terms, ‘calibration’ parameters or orbital perturbation terms. 
Eqs. 2 represent a form of the photogrammetric bundle adjustment, or least-squares multi-image orientation/ triangulation 
adjustment, which provides a 3D ground point determination for DTM extraction or feature positioning. Under the 
assumption that there are two or more overlapping images with appropriate imaging geometry, the success to be expecting in 
applying this modified bundle adjustment will be heavily dependent on a number of factors, for example the triangulation 
geometry, the number of ground control and pass points, the precision of the image coordinate observations and the degree 
to which the orbital parameters of the satellite and attitude of the sensor (i.e. x" . y? ) Ze and R,) are known a priori. 
Up until the time of launch of the /konos 1m satellite in September 1999, all earth observation satellites familiar to the 
remote sensing community lacked the provision of precise orbital information, thus precluding the straightforward 
implementation of tight platform orientation and position constraints via Eqs. 2. Instead, alternative constraint formulations 
were employed. These included a dynamic modelling of the German MOMS-2P 3-line imaging system (deployed on the Mir 
Space station), whereby orbital constraints (position only) were applied (Ebner et al., 1996); and adoption of the concept of 
multiple projection centres or ‘orientation images’, again for the triangulation of MOMS imagery, by Ebner et al. (1992) and 
Fraser & Shao (1996). Prior to the launch of MOMS-02, which undertook two missions in the early and mid 1990s, similar 
triangulation models had been formulated and applied for SPOT imagery (e.g. Westin, 1990) and /RS-1C (Radhadevi et al., 
1998). 
Given the provision of GPS and star trackers on both the 7konos satellite and the two future 1m satellites, Earlybird and 
Orbview III, there have been expectations in the photogrammetric and remote sensing communities of the possibility of 
implementing Eqs. 2 to the fullest metric extent, since the EO of each scan line will be known to about 2-3m in position and 
2-3 arc seconds in attitude. This suggests, even before rigorous analysis, that point positioning accuracies of 2-3m in 
planimetry and height will be achievable, given a strong intersection geometry (e.g. base-to-height ratio of 0.8 to 1) and 
image mensuration to a precision of 1 pixel or better. 
It is therefore understandable why 1m satellite imagery is seen to hold such great potential for topographic mapping and the 
revision of topographic databases. As mentioned, however, it is not clear whether the precise ephemeris data for 1m 
satellites will be made available to the remote sensing community. Hence, there is the prospect that alternative constraint 
functions to straightforward position and attitude data will still be required in the application of Eqs. 2 for ground point 
triangulation. Moreover, the level of triangulation precision referred to above may therefore not be achievable. The strong 
dependence of the bundle adjustment formulation of Eqs. 2 on sufficiently precise preliminary EO values suggests that 
alternative formulations to the collinearity equation model need to be examined. 
3.3 Image Mensuration Precision 
Any discussion of the accuracy potential of multi-image restitution is incomplete without reference to the precision of image 
coordinate mensuration. After all, triangulation accuracies achieved ulilising automated tie point connection and refined 
area-based image matching to 0.1 pixel precision can be expected to be three times better than those achieved with feature- 
based matching to 0.3 pixel, and an order of magnitude superior to results obtained with image coordinate observations to 1 
pixel accuracy. Nevertheless, in the following discussion this aspect is not touched upon when the results of applying 
different triangulation models are discussed. As it happens, image mensuration accuracies of between 0.3 and 0.5 pixels 
were obtained in the practical experiments mentioned in the following discussion, and such observational precision can be 
anticipated in controlled practical applications. It can only be presumed that the same will be true for 1m satellite imagery. 
4 ALTERNATIVE MODELS 
4.1 Multiple Projection Centre Model 
In the absence of the continuous sensor attitude data and sensor orbital parameters, a re-parameterisation of the collinearity 
equations, Eqs. 1 is required. Individual EO elements (X,Y, Z; and the attitude angles forming R;) are replaced by time 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part B7. Amsterdam 2000. 455