Analysis of GNSS navigation accuracy assessment in geostationary orbit using recursive algorithms

Abstract

The article considers the problems of ensuring the assessment of the accuracy of determining the coordinates and velocities of a spacecraft in near-Earth orbit using global navigation satellite systems. The main attention is paid to the analysis of the Kalman filter efficiency under the conditions of systematic errors of the ephemeris of navigation spacecraft, time correlation of noise and the geometric factor typical of geostationary orbits. It is shown that traditional models of accuracy assessment based on the error covariance matrix often do not correspond to the real errors due to simplified assumptions about noise statistics and ignoring systematic errors. A method for increasing the reliability of the accuracy assessment is proposed, combining a simplified Kalman filter with a parallel calculation of the extended covariance matrix that takes into account the systematic errors of the ephemeris. This approach allows preserving the computational efficiency of the main algorithm, while adjusting the accuracy assessment without a significant increase in the load on the onboard systems. The simulation results confirm the correspondence of the adjusted assessment to the actual errors of the spacecraft coordinates and velocities. The results are relevant for satellite navigation in high orbits.