Recursive H∞ filtering: Computing gain using LMI for backward Euler method-based disturbed models

Abstract

Robust H_∞ filtering has been developed using the transfer function approach to provide estimates with guaranteed energy-to-energy performance. In this paper, we use a previously proven bounded real lemma corresponding to the backward Euler method-based disturbed models and show how to numerically compute the bias correction gain K for the recursive H_∞ filter, which is uniquely responsible for its performance. The unknown disturbance is viewed as a Gauss-Markov sequence with an uncertain coloredness factor. Since the error covariance is a quadratic function of K, two theorems are proved and two algorithms are developed to compute K using a linear matrix inequality. A comparison of the H_∞, Kalman, and unbiased finite impulse response (UFIR) filters is provided in terms of mean square error, robustness, and estimation quality. It is shown numerically and experimentally that the gain K of the H_∞ filter is between the Kalman gain and the UFIR filter gain, and that under certain conditions the H_∞ filter can outperform both of them.