Adaptive sparse grid quadrature filter for spacecraft relative navigation

Abstract

This paper explores a novel adaptive sparse grid quadrature filter. The sparse grid quadrature approach has been recently developed for nonlinear estimation problems to alleviate the curse-of-dimensionality issue of the Gauss-Hermite quadrature filter. Accuracy level of the sparse grid quadrature filter is an important tuning factor that affects desired performance. The proposed filter autonomously adjusts the accuracy level of the sparse grid quadrature rule in both prediction and update steps by increasing the level gradually until an adaptation criterion is satisfied. The adaptation criterion is derived based on a quadrature error estimator. The nestedness property of sparse grid quadrature rule enables efficient computation in adaptation by reusing quadrature points of the previous level sparse grid quadrature. An application to spacecraft relative navigation has been made to demonstrate the adaptive spare grid quadrature filter outperforming the extended Kalman filter and the unscented Kalman filter. (C) 2013 IAA. Published by Elsevier Ltd. All rights reserved.