“Fuzzy” estimating of the in-flight geometric calibration parameters

The goal of this work is to study opportunities to improve an accuracy and reliability of in-flight geometric calibration of the spacecraft imaging complex using known and unknown landmarks. Here calibration is interpreted as making more precise the mutual angular position of onboard imaging camera and a star tracker in a spacecraft body. It is an obligatory part of an optical-electronic complex preparation for imaging and geo-referencing of ground objects. The received snapshots, the readings of star tracker and GPS are processed on the ground. In calibration the use is made of known and unknown landmarks. There exist methods of in-flight geometric calibration based on forming measuring equations of various physical origin. These equations are solved by the least square method. Usually snapshots of known landmarks are used but there could be problem solutions with unknown landmarks involved. This work suggests the approach to solving the in-flight geometric calibration problem using formulas of fuzzy observer rather than the least square method. In many cases such approach allows one to weaken the negative impact of disturbances and sensor errors onto accuracy of estimating calibration parameters. The essential feature of the observer realization process is its recursive character. The obtained estimates are made more precise not by a manifold of received snapshots at once, but by each snapshot successively. Such approach allows us to improve convergence of estimates. As in this case the estimated parameters of calibration are constant there is no need for a stage of prognosis peculiar for such algorithm and only update procedure is used. Presentation and arguments are provided with a sufficient volume of computer simulation and analysis of its results. They confirm the above mentioned advantages of fuzzy observer as compared with the least square method for in-flight geometric calibration. © 2019 by Begell House Inc.