NDLI: Improved discrete-time Kalman filtering within singular value decomposition

Content Provider	IET Digital Library
Author	Kulikova, Maria V. Tsyganova, Julia V.
Abstract	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.
Starting Page	2412
Ending Page	2418
Page Count	7
ISSN	17518644
Volume Number	11
e-ISSN	17518652
Issue Number	Issue 15, Oct (2017)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/11/15
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2016.1282
Journal	IET Control Theory & Applications
Publisher Date	2017-06-05
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Cholesky Decomposition Covariance Matrices Discrete Control System Discrete Time System Discrete-time Kalman Filtering Error Covariance Matrix Kalman Filter Kalman Filter Implementation KF Implementation Linear Algebra Matrix Factorisation Method Numerical Analysis Numerical Stability Numerical Stability Issues Riccati Equation Roundoff Error Signal Processing Theory Singular Value Decomposition Square-root Algorithm SVD-based KF Variant SVD-based Strategy
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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