Robust stability analysis of H∞-SGQKF and its application to transfer alignment

Abstract

In this paper, the authors analyze the stochastic stability of the H∞ Sparse-grid Quadrature Kalman Filtering (H∞-SGQKF) used in nonlinear stochastic discrete-time systems with nonlinear state dynamic equation and nonlinear transition function. Using some standard results from estimation accuracy level of multidimensional sparse-grid theories as well as stochastic stability theories, we have developed the robust stability of nonlinear SGQKF under stochastic uncertainties. It is shown that estimation errors remain bounded if the system satisfies sufficient conditions, and that it is possible to improve stochastic stability by increasing system noise covariance matrixes, adjusting the noise robustness parameter γ and demonstrating the lower bound of noise robustness parameter. Finally, the H∞-SGQKF is applied to the design of Near-space hypersonic vehicle transfer alignment. The numerical simulation of the designed filter validates the effectiveness of the proposed filtering stochastic stability.