A Kullback–Leibler-Based IMM Information Filter for the Jump Markov System with Unknown Noise
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This paper is concerned with the state estimation of the jump Markov system with the unknown measurement noise. The proposed algorithm is derived under the framework of Interacting Multiple Model approach, and the recently reported Kullback–Leibler (KL) divergence-based scheme is used for estimation fusion. To facilitate KL divergence-based scheme, the information state and Wishart distribution are, respectively, used to describe the state and the unknown precision matrix of the measurement noise. Specifically, at both the mixing and estimation fusion stages, the KL divergence-based fusion scheme is adopted to fuse the information matrices, information state vectors, and parameters of the Wishart distribution from all the modes. At mode-conditioned filtering stage, parallel noise adaptive cubature information filters are designed to recursively estimate the information states, information matrices, and the Wishart distributed noise parameters. Simulation results prove the efficacy of the proposed approach.
KeywordsCubature information filter Interacting Multiple Model Kullback–Leibler divergence Jump Markov system
This work was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ18F030003 and Research Program of Department of Education of Zhejiang Province under Grant No. Y201635593. The authors are also grateful to the reviewers for their thorough reviews of this article.
- 2.M. J. Beal, Variational algorithm for approximate Bayesian inference, Ph.D dissertation, University of London (2003)Google Scholar
- 4.K.P.B. Chandra, D. Gu, I. Postlethwaite, Cubature information filter and its applications. in Proceedings of American Control Conference, (San Francisco, June 29–July 1 2011), pp. 3609–3614Google Scholar
- 8.Y. Huang, Y. Zhang, N. Li, J. Chambers, A robust Gaussian approximate filter for nonlinear systems with heavy tailed measurement noises, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (Shanghai, March 20–25, 2016), pp. 4209–4213Google Scholar
- 15.G. Liu, G. Tian, Central difference information filter with interacting multiple model for robust maneuvering object tracking, in Proceedings of the IEEE International Conference on Information and Automation, (Lijiang, Aug. 8–10, 2015), pp. 2142–2147Google Scholar
- 19.F. Tronarp, R. Hostettler, S. Sarkka, Sigma-point filtering for nonlinear systems with non-additive heavy-tailed noise, in Proceedings of 19th International Conference on Information Fusion, (Heidelberg, Germany, July 5–8, 2016), pp. 1859–1866Google Scholar