Abstract
Abstract. Very high resolution optical satellites are imaging the object space by a combination of CCD-lines in one direction and by time, speed and satellite rotation in the other direction. The combination of the CCD-lines usually is known by pre-calibration. Remaining errors of the pre-calibration, also slightly depending upon the satellite movement and rotation, with few exceptions are usually small up to negligible. This may not be the case for the image component in the scan direction and the alignment of the line combinations - they are controlled by giros and stellar cameras. Stellar cameras are compensating giro drifts, but their recording frequency is limited as well as in general the accuracy of the satellite view direction. In addition the satellites may show a jitter caused by the fast rotation from one pointed area to another. Not all giros are able to record the jitter frequency. A limited accuracy of the view direction is causing systematic image errors in relation to the used mathematical model of geometric reconstruction. The systematic image errors can be determined theoretically by image orientation based on ground control points (GCPs), but usually not a satisfying number and distribution of GCPs is available. Another possibility is the analysis of the intersection of corresponding rays in a stereo model and an analysis of generated height models against reference height models. Here also free of charge available height models as the SRTM Digital Surface Model (DSM) or AW3D30 can be used. Several very high resolution satellite cameras have been analyzed; this includes images from WorldView-2, WorldView-4, Kompsat-3, Kompsat-1, Pleiades, Cartosat-1, ZY3, OrbView-3, QuickBird, IKONOS, ASTER, IRS-1C, SPOT, SPOT-5 HRS, EROS-B, IKONOS, QuickBird, OrbView and GeoEye but only results of the today more important satellites are shown in detail. For few satellites the systematic image errors can be ignored, but others require a correction which may be just a levelling of the DSM but also a higher degree of deformation up to a compensation of the satellite jitter effect. The used method cannot be named as calibration due to variation from image to image, only the character and size of deformation is typical for the used special optical satellite, but it depends also upon the operating conditions as fast satellite rotation. Due to the very high number of reference points in a DSM the determination of systematic image errors is independent upon random errors and also high frequent jitter can be determined with a standard deviation down to 0.1 ground sampling distance (GSD) or even better.
Highlights
The geometry of optical satellite systems including the camera and the orientation of the single CCD-lines requires a satisfying calibration, attitude accuracy and time interval for recording attitude information (Wang et al 2016), (Radhadevi et al 2016), (Tong et al 2014), (Jacobsen 2006a), (Jacobsen 2012), (Jacobsen 2017)
Across the scan direction the image geometry depends upon the CCD-line combination, while in the scan direction the accuracy depends upon the attitude which may be influenced by a satellite jitter
The systematic y-parallaxes cannot be used for the improvement of the achieved results; they only indicate some geometric problems which may be available in the other coordinate components. This is different for the systematic height model errors; they can be used after high pass filtering directly for the improvement of the generated height models
Summary
The geometry of optical satellite systems including the camera and the orientation of the single CCD-lines requires a satisfying calibration, attitude accuracy and time interval for recording attitude information (Wang et al 2016), (Radhadevi et al 2016), (Tong et al 2014), (Jacobsen 2006a), (Jacobsen 2012), (Jacobsen 2017). Digital Globe used an aerial block, flown with a Leica DMC, as ground control reference leading to 15502 indirect GCPs for the verification of the WorldView-4 calibration (Comp 2017). This is a higher effort not possible for everyone. Problems of the satellite pitch are influencing the point heights, so it is possible to determine it by comparison of a generated height model with a reference height model. Even only a validation is useful for a better estimation of the achieved quality of mapping results
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