Comparing the extended and the sigma point Kalman filters for orbit determination modeling using GPS measurements

Abstract

The purpose of this work is to compare the extended Kalman filter (EKF) against the nonlinear sigma point Kalman filter (SPKF) for the satellite orbit determination problem, using GPS measurements. The comparison is based on the levels of accuracy improvement of the orbit dynamics model. The main subjects for the comparison between the estimators are accuracy of models and results. Based on the analysis of such criteria, the advantages and drawbacks of each estimator are presented. In this work, the orbit of an artificial satellite is determined using real data from the Global Positioning System (GPS) receivers. In orbit determination of artificial satellites, the dynamic system and the measurements equations are of nonlinear nature. It is a nonlinear problem in which the disturbing forces are not easily modeled. The problem of orbit determination consists essentially of estimating parameter values that completely specify the body trajectory in the space, processing a set of information (measurements) related to this body. Such observations can be collected through a ground tracking network on Earth or through sensors, like space GPS receivers onboard the satellite. The EKF implementation in orbit estimation, under inaccurate initial conditions and scattered measurements, can lead to unstable or diverging solutions. For solving the problem of nonlinear nature, convenient extensions of the Kalman filter have been sought. In particular, the unscented transformation was developed as a method to propagate mean and covariance information through nonlinear transformations. The Sigma Point Kalman Filter (SPKF) appears as an emerging estimation algorithm applied to nonlinear systems, without needing linearization steps. In this orbit determination case shady the focus is to gradually improve the dynamical model, which presents highly nonlinear properties, and to know how it affects the performance of the estimators. Therefore, the EKF (the most widely used real time estimation algorithm) as well as the SPKF (supposedly one of the most appropriate estimation algorithm for nonlinear systems) performance evaluation is justified. The aim of this work is to analyze the new nonlinear estimation technique, the SPKF, in an actual orbit determination problem with actual measurements data from GPS, and to compare it with a widely used technique, the EKF, pinpointing the main differences between both the algorithms.