Receding Horizon ₂-FIR Filtering for Uncertain Disturbed Systems With Initial and Data Errors

Receding 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. Note to Practitioners—Monitoring and control of modern automation systems require accurate discrete-time algorithms. The standard techniques such as Kalman filter are applicable under ideal conditions and have poor performance otherwise. The discrete convolution-based batch FIR filters are more accurate and robust. Under industrial uncertainties, disturbances, initial errors, and data errors, FIR filters are able to extract features of dynamic processes with high accuracy. They can also be combined with convolutional neural networks.