Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link SUMMARYThis paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias-constrained optimal finite impulse response filtering algorithm for linear discrete time-invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite-horizon and full-horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade-off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full-horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate.

Parameter estimation of Markov‐switching Hammerstein systems using the variational Bayesian approach

“…Specifically, linear time‐invariant modelling methods have been well developed. Many linear dynamic model structures have been considered, such as the equation‐error model [7], the output‐error model [8, 9], the linear state space model [10] and so on.…”

Receding horizon observer for linear time-varying systems

“…Shmaliy (2010); Y.S. Shmaliy (2012); Zhao et al (2017a) (and references therein) derived an optimal FIR estimator that proved to be less sensitive to noise than the Kalman filter. Zhao et al (2017b) has derived an optimal FIR filter for time-variant systems and Ahn and Shmaliy (2018) considered the time-invariant case such that the achieved results are more robust than the Kalman filter design.…”