Fast Kalman-Like Optimal Unbiased FIR Filtering With Applications

• Published in: IEEE transactions on signal processing Vol. 64; no. 9; pp. 2284 - 2297
• Main Authors: Shunyi Zhao, Shmaliy, Yuriy S., Fei Liu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cost function; Finite impulse response filters; Kalman filter; Kalman filters; Mean square error methods; Mean square errors; optimal FIR filter; Robustness; Signal processing algorithms; State-space; tracking; unbiased FIR filter; Uncertainty
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2016.2516960

In this paper, an optimal unbiased finite impulse response (OUFIR) filter is proposed as a linking solution between the unbiased FIR (UFIR) filter and the Kalman filter (KF). We first derive the batch OUFIR estimator to minimize the mean square error (MSE) subject to the unbiasedness constraint and then find its fast iterative form. It is shown that the OUFIR filter is full horizon (FH) and that its estimate converges to the KF estimate by increasing the horizon length N. As a special feature, we note that the FH OUFIR filter operates almost as fast as the KF. Several other critical properties of the OUFIR filter are illustrated based on simulations and practical applications. Similar to the UFIR filter, and contrary to the KF, the OUFIR filter is highly insensitive to the initial conditions. It has much better robustness than KF against temporary model uncertainties. Finally, the OUFIR filter allows for ignoring system noise, which is typically not well known to the engineer.