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Online Stochastic Convergence Analysis of the Kalman Filter

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  • Matthew B. Rhudy
  • Yu Gu

Abstract

This paper presents modifications to the stochastic stability lemma which is then used to estimate the convergence rate and persistent error of the linear Kalman filter online without using knowledge of the true state. Unlike previous uses of the stochastic stability lemma for stability proof, this new convergence analysis technique considers time-varying parameters, which can be calculated online in real-time to monitor the performance of the filter. Through simulation of an example problem, the new method was shown to be effective in determining a bound on the estimation error that closely follows the actual estimation error. Different cases of assumed process and measurement noise covariance matrices were considered in order to study their effects on the convergence and persistent error of the Kalman filter.

Suggested Citation

  • Matthew B. Rhudy & Yu Gu, 2013. "Online Stochastic Convergence Analysis of the Kalman Filter," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-9, November.
    • Handle: RePEc:hin:jnijsa:240295
    DOI: 10.1155/2013/240295
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    Cited by:

    1. Quanmin Zhu & Dingli Yu & Dongya Zhao, 2017. "An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 451-461, February.
    2. Weihua Wang & Rong Fu, 2023. "Stability Analysis of EKF-Based SOC Observer for Lithium-Ion Battery," Energies, MDPI, vol. 16(16), pages 1-18, August.

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