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Modelling and Simulation in Engineering
Volume 2017 (2017), Article ID 2783781, 11 pages
Research Article

A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking

College of Science, National University of Defense Technology, Changsha, Hunan 410073, China

Correspondence should be addressed to Lijun Peng

Received 4 January 2017; Revised 15 June 2017; Accepted 24 July 2017; Published 11 September 2017

Academic Editor: Ming-Cong Deng

Copyright © 2017 Lijun Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.