State estimation for jump markov nonlinear systems of unknown measurement data covariance

Ke Li, Shunyi Zhao, Choon Ki Ahn, Fei Liu

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable.

Original languageEnglish
Pages (from-to)1673-1691
Number of pages19
JournalJournal of the Franklin Institute
Issue number2
Publication statusPublished - 2021 Jan

Bibliographical note

Funding Information:
This work was supported by the National Natural Science Foundation of China ( 61973136 , 61833007 ).

Publisher Copyright:
© 2020 The Franklin Institute

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics


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