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

Ting Cao,Huo-Tao Gao,Guo-Bao Ru,Yun Ling,Chun-Feng Sun

doi:10.1155/2020/1072824

Ting Cao, Huo-Tao Gao + Show 3 more

Open Access

https://doi.org/10.1155/2020/1072824

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Abstract

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.

Highlights

Nonlinear filtering and estimation based on Bayes framework have been widely applied in many fields, such as target tracking [1,2,3,4,5], navigation [5, 6] and positioning [7, 8], power system [9,10,11], and pattern recognition [12]
Filters in this approach have high precision, the computational burden is its primary obstacle to more widespread use. Another scheme is the global linearization [15] method, in which the differential inclusion theory represents the nonlinear system via a linear differential inclusion (LDI) model. is kind of method can effectively solve the problem of local linearization error in the local linearization method
E contribution of this paper is to propose a new class of CKFs with the spherical simplex rule to approximate the spherical integral and arbitrary order Gauss–Laguerre quadrature rule to solve the radial integral. e proposed filter is termed as spherical simplex Gauss–Laguerre quadrature cubature Kalman filter (SSGQKF). e SSGQKF would be a generalized form of spherical simplex-radial cubature Kalman filter (SSRCKF), and under single Gauss–Laguerre quadrature point evaluation, it coincides with the third-degree SSRCKF. e accuracy of the SSGQKF depends on the number of the simplex cubature points. e higher the number of simplex quadrature points, the better the accuracy

Summary

Introduction

Nonlinear filtering and estimation based on Bayes framework have been widely applied in many fields, such as target tracking [1,2,3,4,5], navigation [5, 6] and positioning [7, 8], power system [9,10,11], and pattern recognition [12]. Filters in this approach have high precision, the computational burden is its primary obstacle to more widespread use Another scheme is the global linearization [15] method, in which the differential inclusion theory represents the nonlinear system via a linear differential inclusion (LDI) model. The radial integral in both CKFs and SSRCKFs is solved by the moment matching method [22], which is ambiguous and does not provide the best possible solution available [23] To tackle this problem, Bhaumik and Swati proposed the cubature quadrature Kalman filter (CQKF) [24]. E contribution of this paper is to propose a new class of CKFs with the spherical simplex rule to approximate the spherical integral and arbitrary order Gauss–Laguerre quadrature rule to solve the radial integral.

Cubature Quadrature Kalman Filter

Spherical Simplex Gauss–Laguerre Quadrature Evaluation of Integrals

Findings

Simulations and Discussion

Conclusions