A version of the geo-referencing of ground objects using single space snapshot

1Tkachenko, AI
1International Research and Training Center for Information Technologies and Systems of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kyiv, Ukraine
Space Sci. & Technol. 2020, 25 ;(4):38-44
Publication Language: Ukrainian
The problem of the positioning of unknown ground objects in a coordinate system related to the Earth (geo-referencing problem) is considered. The task was to use the single snapshot of the above-mentioned objects (markers) obtained with an onboard imaging camera of the spacecraft on the near-Earth orbit. The snapshot was transmitted to the ground-based services together with synchronous accompanying information for processing using the on-ground computer. The a priori accepted mathematical description of the Earth’s shape was attracted. Imaging of markers for geo-referencing was preceded by in-flight calibration, which is to clarify the mutual attitude of the camera and the onboard star tracker in the body of the spacecraft. Unlike statements of the above-mentioned problem and its solutions in known publications, here we started from a highly rough approximation of unknown coordinates of geo-referenced objects with errors at the 100 km level. At this base, the nonlinear equation of the Earth’s surface is replaced by a linearized equation to positioning errors of an unknown marker. The expression in the left part of this equation represents a projection of the vector of positioning errors onto the direction of the marker’s geocentric radius-vector. The above-mentioned equation is solved together with the vector equation of errors composed on the base of the photogrammetric collinearity condition. The system of four scalar equations of errors is wittingly nonsingular if the marker’s line of sight is non-orthogonal to the radius-vector of the marker.
               Simplifications made during the linearization of the equation of Earth’s shape essentially distort the estimation of the geo-referencing’s parameters. To dilute this effect, the method of geo-referencing based on using the fuzzy state observer is proposed. The method is realized as a sequence of cyclic operations. In each cycle, a relatively small elementary part of the marker’s positioning error is estimated using a fuzzy observer. The convergence of the estimation procedure makes it necessary to repeat up to thousands of elementary cycles to get acceptable accuracy of geo-referencing. This can be easily handled by computers in on-ground conditions.
                Accurate and unambiguous estimation of three coordinates of a geo-referencing object is possible when it has a low  height above the level surface.
Keywords: camera, convergence of the estimations, equation of the Earth’s surface, fuzzy observer, geo-referencing, spacecraft, star tracker
1. Lebedev D. V. (2014). On geographical coordinate determination of space images. J. Automation and Inform. Sci., Nо. 5, 71—79 [in Russian].
2. Lebedev D. V. (2016). On the coordinate determination of space images by coordinate data. J. Automation and Inform. Sci., Nо. 6, 120—132 [in Russian].
3. Piatak I. A. (2011). Problems of geo-referencing of the snapshots fulfilled by spacecraft. Dniepropetrovsk university. Ser. The Rocket and Space Technics, Nо. 14, 116—122 [in Russian].
4. Tkachenko A. I. (2015). On a geo-referencing of terrestrial objects using space snapshots. Kosm. nauka tehnol., 21, Nо. 2, 65—72 [in Russian].
5. Tkachenko A. I. (2018). Two algorithms for geo-referencing of the terrestrial objects using space snapshots. Kosm. nauka tehnol., 24, Nо. 3, 69—74 [in Russian].
6. Tkachenko A. I. (2019). Strenghtened convergence of estimations in the in-flight geometric calibration. Kosm. nauka tehnol., 25, Nо. 4, 41—47 [in Russian].