Receding Horizon H2-FIR Filtering for Uncertain Disturbed Systems With Initial and Data Errors

horizon (RH) finite impulse response (FIR) filters (observers) are used in model predictive and state feedback control. For such applications, we develop a robust RH H-2 suboptimal FIR (RH H-2-FIR) filter under the conditions when an uncertain system is also disturbed, and the initial and data errors are not necessarily Gaussian. The RH H-2-FIR filter is obtained by minimizing the squared Frobenius norm of the weighted error-to-error transfer function, where the weights are related to the errors. The filter developed is tested by a quasi periodic disturbed process with an uncertain system matrix. Based on numerical examples and experimental data, it is shown that the RH H-2-FIR filter outperforms the optimal FIR, Kalman, maximum likelihood FIR, and unbiased FIR (UFIR) filters. It is also almost as robust as the UFIR filter.

Automated summary

This article proposes a robust RH H-2-FIR filter for uncertain system disturbances and demonstrates its superiority in quasi-periodic disturbed processes.