Design of FIR-Type Filtering Algorithms for Markov Jump Linear Systems

Shunyi Zhao, Yuhang Zhu, Choon Ki Ahn, Peng Shi, Fei Liu

Research output: Contribution to journalArticlepeer-review


To design a finite impulse response (FIR) filter for Markov jump linear systems (MJLSs), a fundamental problem is to avoid constructing the extended state-space model without knowing the mode sequence. This article proposes a new FIR filtering algorithm for MJLSs to address this problem. Under each mode, the variational inference approximates the posterior distribution as a product of Gaussian distribution and inverse gamma distribution by minimizing the Kullback–Leibler divergence. A recursion is then derived over a predefined estimation horizon, where the influence of abandoning the measurements beyond the horizon is compensated. By setting the estimation horizon length as a fixed number, the recursion achieved becomes a new FIR filter for MJLSs, while a new suboptimal Bayesian estimator appears when the horizon length is determined as the full horizon. A Newtonian tracking example as well a three degree-of-freedom hover model is presented to demonstrate that the proposed FIR method has good immunity against unpredicted modeling uncertainties at the cost of extra computational resources and memories, and its full-horizon form does not show this feature and may lose to some exiting algorithms when the underlying model is accurate.

Original languageEnglish
Article number3330827
Pages (from-to)1853-1864
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number3
Publication statusPublished - 2024 Mar 1

Bibliographical note

Publisher Copyright:
© 2024 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.


  • Bayesian inference
  • Markov jump linear systems (MJLSs)
  • finite impulse response (FIR)
  • state estimation
  • variational inference

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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