Framework for Robust $H_{2}$-OFIR Filtering of Uncertain and Disturbed Systems With Data Errors

The novel theory of robust
a posteriori

$H_{2}$
optimal finite impulse response (OFIR) filtering is developed in linear discrete-time state-space for uncertain and disturbed systems under initial and measurement errors. The
$H_{2}$
-OFIR filter is derived using the backward Euler method by minimizing the squared Frobenius norm of the weighted error-to-error transfer function. A suboptimal
$H_{2}$
-OFIR filter is obtained via a linear matrix inequality, and recursive forms are shown for the resulting gain matrix. Based on simulations and experimental examples of uncertain and disturbed systems, it is shown that the
$H_{2}$
-OFIR filter is more robust than the OFIR, Kalman, maximum likelihood FIR, and unbiased FIR filters.