Discrete Time q-Lag Maximum Likelihood FIR Smoothing and Iterative Recursive Algorithm

The finite impulse response (FIR) approach is known to be more robust than the Kalman approach. In this paper, we derive a batch <inline-formula><tex-math notation="LaTeX">q</tex-math></inline-formula>-lag maximum likelihood (ML) FIR smoother for full covariance mat...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 69; S. 6342 - 6354
Hauptverfasser: Zhao, Shunyi, Wang, Jinfu, Shmaliy, Yuriy S., Liu, Fei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 2021
Schlagworte:
Covariance matrices
Finite impulse response filters
FIR smoother
Iterative algorithms
Kalman filters
Kalman smoother
maximum likelihood
Maximum likelihood estimation
Signal processing algorithms
Smoothing methods
State space
UFIR smoother
ISSN:1053-587X, 1941-0476
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Zusammenfassung:The finite impulse response (FIR) approach is known to be more robust than the Kalman approach. In this paper, we derive a batch <inline-formula><tex-math notation="LaTeX">q</tex-math></inline-formula>-lag maximum likelihood (ML) FIR smoother for full covariance matrices and represent it with an iterative algorithm using recursions for diagonal covariance matrices. It is shown that, under ideal conditions of fully known model, the ML FIR smoother occupies an intermediate place between the more accurate Rauch-Tung-Striebel (RTS) smoother and the less accurate unbiased FIR smoother. With uncertainties and errors in noise covariances, ML FIR smoothing is significantly superior to RTS smoothing. It is also shown experimentally that ML FIR smoothing is more robust than RTS smoothing against measurement outliers.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2021.3127677