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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Veröffentlicht in:IET control theory & applications Jg. 11; H. 15; S. 2412 - 2418
Hauptverfasser: Kulikova, Maria V, Tsyganova, Julia V
Format: Journal Article
Sprache:Englisch
Veröffentlicht: The Institution of Engineering and Technology 13.10.2017
Schlagworte:
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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Beschreibung
Zusammenfassung: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