A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking. (11th September 2017)

• Record Type: Journal Article
• Authors: Peng, Lijun; Duan, Xiaojun; Zhu, Jubo
• Other Names: Deng Ming-Cong Academic Editor.
• Is Part Of: Modelling and simulation in engineering. Volume 2017(2017)
• Publication Date: 2017-09-11
• Subjects: Engineering -- Simulation methods -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.004
• DOI: 10.1155/2017/2783781
• Languages: English
• ISSNs: 1687-5591

Abstract

Abstract : A new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak's quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential drawback that some cubature points generated by Smolyak's rule have negative weights, which may result in instability for the computation. A relative-weight-ratio criterion based sparse Gauss-Hermite rule is presented in this paper, in which cubature points are kept symmetric in the input space and corresponding weights are guaranteed to be positive. The generation of the new sparse cubature points set is simple and meaningful for practice. The difference between our new sparse Gauss-Hermite cubature rule and other cubature rules is analysed. Simulation results show that, compared with Kalman filter with those types of full tensor-product based Gauss-Hermite rules, our new sparse Gauss-Hermite cubature rule based Kalman filter can lead to a substantially reduced number of cubature points, more stable computation capability, and maintaining the accuracy of integration at the same time.