Comparing Robustness of the Kalman, H , and UFIR Filters

Yuriy S. Shmaliy, Frederic Lehmann, Shunyi Zhao, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


This paper provides a comparative analysis for robustness of the Kalman filter (KF), H filter derived using the game theory, and unbiased finite impulse response (UFIR) filter, which ignores the noise statistics and initial values. A comparison is provided for Gaussian models by studying the effects of errors and disturbing factors on the bias correction gain. It is shown that the rule of thumb of optimal filtering in terms of accuracy, UFIR < H = KF, typically does not hold in the real-world implying errors in the noise statistics, mismodeling, temporary uncertainties, and difficulties in filter tuning to optimal mode. Under such conditions, the filters are related to each other as KF H UFIR. A justification of this statement is provided analytically and confirmed by simulations and experimentally based on two-state polynomial and harmonic models.

Original languageEnglish
Pages (from-to)3447-3458
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number13
Publication statusPublished - 2018 Jul 1


  • H filter
  • Kalman filter (KF)
  • robustness
  • unbiased finite impulse response (UFIR) filter

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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