A Recursive Restricted Total Least-Squares Algorithm

We show that the generalized total least squares (GTLS) problem with a singular noise covariance matrix is equivalent to the restricted total least squares (RTLS) problem and propose a recursive method for its numerical solution. The method is based on the generalized inverse iteration. The estimati...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 62; no. 21; pp. 5652 - 5662
Main Authors: Rhode, Stephan, Usevich, Konstantin, Markovsky, Ivan, Gauterin, Frank
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Algorithms
Computer Science
Computer simulation
Covariance matrices
Covariance matrix
Engineering Sciences
Estimates
Generalized total least squares (GTLS)
Least squares approximations
Least squares method
Mathematical model
Mathematical models
Noise
recursive estimation
restricted total least squares (RTLS)
Signal and Image Processing
Signal processing algorithms
subspace tracking
system identification
total least squares (TLS)
Transaction processing
Vectors
recursive estimation
restricted total least squares (RTLS)
total least squares (TLS)
system identification
generalized total least squares (GTLS)
subspace tracking
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Description
Summary:We show that the generalized total least squares (GTLS) problem with a singular noise covariance matrix is equivalent to the restricted total least squares (RTLS) problem and propose a recursive method for its numerical solution. The method is based on the generalized inverse iteration. The estimation error covariance matrix and the estimated augmented correction are also characterized and computed recursively. The algorithm is cheap to compute and is suitable for online implementation. Simulation results in least squares (LS), data least squares (DLS), total least squares (TLS), and restricted total least squares (RTLS) noise scenarios show fast convergence of the parameter estimates to their optimal values obtained by corresponding batch algorithms.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2350959