Robust H2-finite impulse response state observers for uncertain and disturbed systems with applications to quasi-periodic processes

In this article, we develop a robust H-2 optimal unbiased FIR (H-2-OUFIR) predictor and receding horizon (RH) H-2-OUFIR filter for uncertain and disturbed systems in the presence of measurement errors. The state observers are designed using a novel H-2-FIR approach by minimizing the squared Frobenius norm of the weighted error-to-error transfer function, where weights are related to errors. The bias-constrained RH H-2-FIR filtering algorithm using the linear matrix inequality is also obtained. The RH H-2-OUFIR filter is applied to uncertain and disturbed quasi-periodic harmonic systems, where the uncertainty is due to random sampling and the disturbance is Gauss-Markov. It is shown that the RH H-2-OUFIR filter outperforms in terms of accuracy and robustness the Kalman, OFIR, UFIR, and maximum likelihood FIR filters under sever disturbances and large timing error.

Automated summary

In this article, a robust H-2 optimal unbiased FIR predictor and filter are developed for uncertain and disturbed systems, demonstrating superior performance over existing filters under severe disturbances and large timing error.