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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Bibliographic Details
Published in:Applied mathematics and computation Vol. 203; no. 1; pp. 186 - 193
Main Author: Nakamori, S.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.09.2008
Elsevier
Subjects:
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
Online Access:Get full text
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Description
Summary: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