Comparing Robustness of the Kalman, H_∞ , and UFIR Filters

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.