A Novel $H_2$ Approach to FIR Prediction Under Disturbances and Measurement Errors

A novel approach is proposed to $H_2$ finite impulse response (FIR) prediction in discrete-time state-space. The biased-constrained $H_2$ optimal unbiased FIR ( $H_2$ -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 $H_2$ FIR filtering algorithm using the linear matrix inequality is also designed. The $H_2$ -OUFIR predictor performance is investigated by simulations and experimentally in a comparison with the Kalman and unbiased FIR predictors.