A Novel $H_2$ Approach to FIR Prediction Under Disturbances and Measurement Errors
Jorge A. Ortega-Contreras, Eli G. Pale-Ramón, Yuriy S. Shmaliy, Yuan Xu
Abstract
A novel approach is proposed to H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> finite impulse response (FIR) prediction in discrete-time state-space. The biased-constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> optimal unbiased FIR (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -OUFIR) predictor derived under disturbances and measurement errors is shown to have the maximum likelihood form and be equivalent to the OUFIR predictor under Gaussian noise. The derivation is provided using the backward Euler method by minimizing the squared weighted Frobenius norm. A bias-constrained suboptimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> FIR filtering algorithm using the linear matrix inequality is also designed. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -OUFIR predictor performance is investigated by simulations and experimentally in a comparison with the Kalman and unbiased FIR predictors.