Improved discrete-time Kalman filtering within singular value decomposition

This study presents a new Kalman filter (KF) implementation useful in applications where the accuracy of numerical solution of the associated Riccati equation might be crucially reduced by influence of roundoff errors. Since the appearance of the KF in 1960s, it has been recognised that the factored...

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Vydáno v:	IET control theory & applications Ročník 11; číslo 15; s. 2412 - 2418
Hlavní autoři:	Kulikova, Maria V, Tsyganova, Julia V
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	The Institution of Engineering and Technology 13.10.2017
Témata:	Cholesky decomposition covariance matrices discrete time systems discrete‐time Kalman filtering error covariance matrix Kalman filter implementation Kalman filters KF implementation matrix factorisation method numerical stability numerical stability issues Research Article Riccati equation Riccati equations roundoff errors singular value decomposition square‐root algorithms SVD‐based KF variant SVD‐based strategy covariance matrices error covariance matrix discrete-time Kalman filtering Kalman filter implementation SVD-based strategy discrete time systems numerical stability issues numerical stability SVD-based KF variant Cholesky decomposition matrix factorisation method Riccati equations square-root algorithms roundoff errors Kalman filters Riccati equation singular value decomposition KF implementation
ISSN:	1751-8644, 1751-8652
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Popis
Shrnutí:	This study presents a new Kalman filter (KF) implementation useful in applications where the accuracy of numerical solution of the associated Riccati equation might be crucially reduced by influence of roundoff errors. Since the appearance of the KF in 1960s, it has been recognised that the factored form of the KF is preferable for practical implementation. The most popular and beneficial techniques are found in the class of square-root algorithms based on the Cholesky decomposition of error covariance matrix. Another important matrix factorisation method is the singular value decomposition (SVD) and, hence, further encouraging implementations might be found under this approach. The analysis presented here exposes that the previously proposed SVD-based KF variant is still sensitive to roundoff errors and poorly treats ill-conditioned situations, although the SVD-based strategy is inherently more stable than the conventional KF approach. In this study, the authors design a new SVD-based KF implementation for enhancing the robustness against roundoff errors, provide its detailed derivation, and discuss the numerical stability issues. A set of numerical experiments are performed for comparative study. The obtained results illustrate that the new SVD-based method is algebraically equivalent to the conventional KF and to the previously proposed SVD-based method, but it outperforms the mentioned techniques for estimation accuracy in ill-conditioned situations.
ISSN:	1751-8644 1751-8652
DOI:	10.1049/iet-cta.2016.1282