Iterative Maximum Likelihood FIR Estimation of Dynamic Systems with Improved Robustness

Shunyi Zhao, Yuriy S. Shmaliy, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In this paper, an iterative maximum likelihood (ML) finite impulse response (FIR) filter is proposed for discrete-time state estimation in dynamic mechanical systems with better robustness than the Kalman filter (KF). The ML FIR filter and the error covariance matrix are derived in batch forms and further represented with fast iterative algorithms to have a clearer insight into the ML FIR filter performance. Provided that all of the model parameters are known, the ML FIR filter has an intermediate accuracy between the robust unbiased FIR (UFIR) filter and the KF. Under the uncertainties in not exactly known noisy environments, the ML FIR filter performs much better than the KF. A fundamental feature of the ML FIR estimate is that it develops gradually from the UFIR estimate on small horizons to the KF estimate on large horizons. Properties of the ML FIR filter are learned in more detail based on the drifting stochastic resonator and rotary flexible joint.

Original languageEnglish
Pages (from-to)1467-1476
Number of pages10
JournalIEEE/ASME Transactions on Mechatronics
Issue number3
Publication statusPublished - 2018 Jun

Bibliographical note

Funding Information:
Manuscript received December 27, 2016; revised April 12, 2017, September 27, 2017, and January 30, 2018; accepted March 13, 2018. Date of publication March 28, 2018; date of current version June 12, 2018. Recommended by Technical Editor M. Basin. This work was supported in part by the National Natural Science Foundation of China under Grant 61603155 and in part by the 111 Project under Grant B12018. (Corresponding authors: Shunyi Zhao and Yuriy S. Shmaliy.) S. Zhao is with the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, Jiangsu 214122, China (e-mail:

Publisher Copyright:
© 1996-2012 IEEE.


  • Dynamic mechanical system
  • Kalman filter (KF)
  • finite impulse response (FIR) filter
  • maximum likelihood (ML)
  • state estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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