Square-root algorithms of RLS Wiener filter and fixed-point smoother in linear discrete stochastic systems

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are in...

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Vydáno v:	Applied mathematics and computation Ročník 203; číslo 1; s. 186 - 193
Hlavní autor:	Nakamori, S.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY Elsevier Inc 01.09.2008 Elsevier
Témata:	Algebra Algebraic geometry Covariance information Discrete-time systems Exact sciences and technology Finite differences and functional equations Global analysis, analysis on manifolds Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Square-root algorithms Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Wiener–Hopf equation Discrete-time systems Wiener–Hopf equation Covariance information Square-root algorithms Wiener Hopf equation Error estimation Decomposition method Discrete system Difference equation Stochastic system Variance Direct method Fix point Least squares method Factorization method Numerical stability Transcendental equation Filtering Recurrence relation Numerical linear algebra Recursive algorithm Numerical analysis Linear system Matrix inversion Applied mathematics Symmetric matrix Positive definite matrix Discrete time Riccati equation Wiener-Hopf equation
ISSN:	0096-3003, 1873-5649
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Popis
Shrnutí:	This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the round-off errors, in the case of the small value of the observation noise variance, under a single precision computation, the auto-variance function becomes asymmetric and the estimators tend to be numerically instable. From this viewpoint, in the proposed square-root RLS Wiener estimators, in each stage updating the estimates, the auto-variance function of the filtering estimate is expressed in a symmetric positive semi-definite matrix and the stability of the RLS Wiener estimators is improved. In addition, in the square-root RLS Wiener estimation algorithms, the variance function of the state prediction error is expressed as a symmetric positive semi-definite matrix in terms of the UD factorization method.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2008.04.026