Development and critical evaluation of robust H∞ filters

Abstract

This work presents a discrete convolution-based H∞ finite impulse response (H∞ FIR) filter. The a posteriori H∞ FIR filter is developed by minimizing the squared H∞ norm of the weighted disturbance-to-error transfer function, where the weights are related to errors. Since minimization isn’t reachable without numerical approximations, Linear Matrix Inequality (LMI) based algorithms are derived to compute the filter gain in batch form, also recursive (Kalman-like) forms of the filter are provided in this work. It is shown numerically and experimentally that for disturbed systems operating under measurement and initial errors, the developed H∞ FIR filter surpasses the Kalman filter in accuracy and has almost the same robustness as an unbiased FIR filter.