Generalized Polynomial Chaos-based Ensemble Kalman Filtering for Orbit Estimation

Abstract

In this paper a novel framework is proposed to carry out state and parameter estimation of a general nonlinear stochastic dynamical system in a prediction-correction fashion. The uncertainties in the initial states and parameters are propagated using generalized polynomial chaos expansion technique to compute the predicted estimates of states and parameters. Once the measurements are available, a nonlinear estimator is developed to update the predicted estimates in ensemble filtering framework. The methodology is then applied to estimate the states and uncertain parameters of a satellite for Low Earth Orbit (LEO) navigation using Global Positioning System (GPS) measurements. The results obtained from generalized polynomial chaos expansion-based ensemble filter are compared with that obtained from the unscented Kalman filter and the particle filter in terms of accuracy and computational efficiency.