Formulation of distortion error for the line-of-sight (LOS) vector adjustment model and its role in restitution of SPOT imagery

A recently developed line-of-sight (LOS) vector adjustment model is an effective geopositioning method for pushbroom images. A requirement for this method is that a predicted orbit be close to a true orbit. Although the method has proven very effective for SPOT 5, which has an accurate orbital control system, it was an open question whether or not the method could be effective for a satellite system with poor orbital accuracy. In this paper, a distortion error is defined and formulated as a common criterion for testing orbital requirements of a pushbroom system from the perspective of the LOS vector adjustment model. Using the distortion error, it is shown that a satellite system, even with poor locational accuracy comparable to SPOT 3-4, meets the orbital requirements as long as the maximum topographic height in the landscape is less than 4 km against the height level of the control points. A test was performed using three SPOT images and only five ground control points (GCPs). Results indicated that the root mean squared errors (RMSEs) of horizontal residual errors calculated from 30 check points were less than 10 m. The achieved accuracy of three-dimensional object-point determination was 6 m in the X-dimension and 7 m in both Y- and Z-dimensions. The conclusion can be drawn that the orbital requirements of this method can accommodate most space-borne systems, and therefore the LOS vector adjustment model is effective for SPOT and comparable pushbroom imagery.