Adaptive sparse grid quadrature filter for nonlinear estimation

Abstract

This dissertation explores novel adaption algorithms for sparse grid quadrature filter (SGQF) for nonlinear estimation and their application to aerospace estimation problems. The proposed adaptation algorithms intend to improve the performance of SGQF in terms of computational efficiency and optimality. The proposed adaptation techniques are level adaptation algorithm and bump-up strategy. The new SGQFs with adaptation techniques are named adaptive sparse grid quadrature filter (ASGQF) and Bump-up sparse grid quadrature filter (B-SGQF) respectively. Accuracy level of the sparse grid quadrature filter is an important tuning factor that affects desired performance. The proposed ASGQF autonomously adjusts the accuracy level of the sparse grid quadrature rule by increasing the level gradually until an adaptation criterion is satisfied. The adaptation criterion is derived based on a quadrature error estimator. The adaptation criterion of first level adaptation algorithm is determined by estimated quadrature error and statistical standard deviation of transformed random variable approximated by sparse grid quadrature. The second level adaptation algorithm is modified from first level adaptation to focus on improvement of filter performance. This modification is based on the hypothesis that the degradation of estimation performance of filter is due to the false correction in update step from the quadrature error. The level adaptation algorithm suggests proper accuracy level depending on noise level of system model as well as severity of nonlinearity. By the adaptation that suggests proper accuracy level depending on severity of nonlinearity, the ASGQF reduces the computational burden by using a low level under feasible conditions without performance degradation. The B-SGQF is able to maintain consistency of filters in spite of existence of the quadrature error which tends to break consistency in update step by bump-up strategy based on quadrature error. By artifici...