Accuracy, Efficiency and Stability Analysis of Sparse-grid Quadrature Kalman Filter in Near Space Hypersonic Vehicles

As a recently developed sampling strategy, Sparse-grid quadrature rule has been paid more attention within nonlinear estimation for its high accuracy and low computation cost. Through the Taylor series expansion, the accuracy of Sparse-grid Quadrature Kalman Filter (SGQKF) is analyzed and compared with Quadrature Kalman Filter (QKF). In addition, the computational complexity is analyzed to evaluate the efficiency of SGQKF. The SGQKF asymptotic stability behavior is analyzed by introducing an unknown instrumental diagonal matrix. The theoretical analysis shows that the SGQKF is computationally much more efficient than QKF with the same even higher accuracy; consequently the curse of dimensionality for high dimensional problems can be effectively alleviated. Sufficient conditions for bounded stability are established and it is proved that the estimation error of SGQKF nonlinear systems is exponentially asymptotic. The performance of SGQKF is demonstrated by transfer alignment with large azimuth misalignment angle for Near-space hypersonic vehicle (NSHV), and the simulation results are used to illustrate the benefits of state estimation and modified noise covariance matrix. Our framework is deterministic.