Convergence analysis of adaptive filtering algorithms with singular data covariance matrix

The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algo...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 49; H. 2; S. 334 - 343
1. Verfasser: Eweda, E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.02.2001
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Adaptive filters
Algorithm design and analysis
Algorithms
Applied sciences
Convergence
Covariance matrix
Detection, estimation, filtering, equalization, prediction
Errors
Exact sciences and technology
Filtering algorithms
Information, signal and communications theory
Least squares approximation
Mathematical analysis
Regression analysis
Resonance light scattering
Signal and communications theory
Signal processing algorithms
Signal, noise
Steady-state
Studies
Telecommunications and information theory
Upper bound
Vectors (mathematics)
Theoretical study
Adaptive filtering
Adaptive signal processing
Covariance matrix
Algorithm
Convergence
Least mean squares methods
ISSN:1053-587X, 1941-0476
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Beschreibung
Zusammenfassung:The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algorithms. Both the signal and weight behavior of the algorithms are considered. The signal behavior is evaluated in terms of the moments of the excess output error of the filter. The weight behavior is evaluated in terms of the moments of the filter weight misalignment vector. It is found that the RLS and SRA diverge when the input covariance matrix is singular. The steady-state signal behavior of the LMS and SA can be made arbitrarily fine by using sufficiently small step sizes of the algorithms. Indeed, the long-term average of the mean square excess error of the LMS is proportional to the algorithm step size. The long-term average of the mean absolute excess error of the SA is proportional to the square root of the algorithm step size. On the other hand, the steady-state weight behavior of both the LMS and SA have biases that depend on the weight initialization. The analytical results of the paper are supported by simulations.
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ISSN:1053-587X
1941-0476
DOI:10.1109/78.902115