Lower accuracy estimation of uniform rational approximation in georeferencing problems

Аuthors

Bakharev A. ^*, Mesyats A. ^**

S. P. Korolev Rocket and Space Corporation «Energia», 4A Lenin Street, Korolev, Moscow area, 141070, Russia

*e-mail: post@rsce.ru
**e-mail: aleksey.mesyats@rsce.ru

Abstract

This paper discusses the problem of determining the limitations of rational function sensor model. Rational function model (RFM) is a generalized sensor model; it approximates the complex rigorous sensor model by utilizing a multitude of parameters (coefficients).
Various algorithms exist for calculating RFM parameters based on different approaches, such as solving the linearized approximation problem and integral method. In a best-case scenario most of the algorithms perform similarly, providing decent results. However, for more complex shooting parameters calculation algorithms are affected by input data differently and provide varying approximation quality. Separating the model approximation limits from the algorithm constraints is not trivial.
For a polynomial fitting in the one-dimensional case the theorem of de la Vallee-Poussin can be used to obtain lower estimate on the accuracy of the best uniform approximation. This theorem was generalized to a wider class of functions including rational functions of a single argument. This paper proposes an approach of obtaining lower estimate of the accuracy of uniform approximation by rational functions of multiple arguments. This approach is based on the selection of a subset of the estimated region consisted of segments. For each of those segments the multiple argument problem can be substituted by a single argument problem. Next, the generalized theorem can be applied to find the lower estimate of the error of uniform approximation.
This approach is applied to the georeferencing problem. The method of estimating the influence of the scene extent on the approximation accuracy is described. The presented results are validated using the real remote sensing satellite data.

Keywords:

remote sensing, georeferencing, rational function model, approximation accuracy estimation

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