The Algorithm of Adaptive Measurements Sampling for Satellite Navigation Equipment on High-orbit Spacecraft

G. V. Skorynina, A. V. Doronkin

Transactions of IAA RAS, issue 59, 14–18 (2021)

DOI: 10.32876/ApplAstron.59.14-18

Keywords: satellite navigation, high-orbit spacecraft, bad conditioning

Abstract

Since 2017 Kometa Corporation, JSC has been developing satellite navigation equipment for high-orbit spacecrafts. Algorithms of position and velocity evaluation for such equipment must operate in discontinuous navigational field when a number of visible navigational satellites is small, and relative location of spacecraft and navigational satellites changes slowly. These circumstances often lead to ill-conditioned problems of measurements processing. Position and velocity evaluation process in the algorithms for the above mentioned satellite navigation equipment consists of four stages: getting an initial approximation vector, collecting of smoothed measurements, getting a normal place, and normal places processing. At the stage of getting a normal place smoothed measurements are processed with the Least Squares Method. This stage is often associated with computational problems. The algorithm of adaptive measurements sampling is used to avoid bad conditioning in the algorithm of getting a normal place. In this algorithm conditioning is estimated every time when new smoothed measurements are obtained. One should start the algorithm of getting a normal place only if smoothed measurements processing is a well-conditioned problem. Specific methods for solving ill-conditioned problems often require a lot of auxiliary calculations and analysis of their results. It is not necessary for the algorithm of adaptive measurements sampling. This algorithm allows selecting duration of smoothed measurements collection automatically. According to simulation results the algorithm of adaptive measurements sampling ensures that the algorithm of getting a normal place will converge in approximately 98 percent cases. At the same time this algorithm provides required accuracy of position and velocity estimation.

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