Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

A Quaternion-Based Robust Adaptive Spherical Simplex Unscented Particle Filter for MINS/VNS/GNS Integrated Navigation System

An improved filtering algorithm-robust adaptive spherical simplex unscented particle filter (RASSUPF) is proposed to achieve high accuracy, induce the amount of computation, and resist the influence of abnormal interference for the MINS/VNS/GNS integrated navigation system. This algorithm adopts spherical simplex unscented transformation (SSUT) to approximate the probability distribution, employs the spherical simplex unscented Kalman filter (SSUKF) to generate the importance sampling density of particle filter, and applies robust and adaptive estimation to control the influence of the abnormal information on the state model and the observation model. Simulation results demonstrate the proposed algorithm can effectively reduce the navigation error, improve the navigation positioning precision, and decrease the computation cost.