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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