Framework for Robust H2-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.

Automated summary

This paper develops a novel theory of robust a posteriori H-2 optimal finite impulse response (OFIR) filtering for uncertain and disturbed systems. The H-2-OFIR filter is derived by minimizing the squared Frobenius norm of the weighted error-to-error transfer function using the backward Euler method. Simulation and experimental examples demonstrate that the H-2-OFIR filter outperforms other filters in terms of robustness.