Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 4065–4081 | Cite as

A Kullback–Leibler-Based IMM Information Filter for the Jump Markov System with Unknown Noise

  • Chen ShenEmail author
  • Wei Huang
Short Paper


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.


Cubature 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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Information and Electronic EngineeringZhejiang Gongshang UniversityHangzhouChina
  2. 2.China Ship Development and Design CenterWuhanChina

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