Pairwise Optimal Weight Realization-Acceleration Technique for Set-Theoretic Adaptive Parallel Subgradient Projection Algorithm

The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 54; H. 12; S. 4557 - 4571
Hauptverfasser: Yukawa, M., Yamada, I.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.12.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Acceleration
Adaptive algorithms
Adaptive filters
Adaptive parallel subgradient projection
Algorithms
Applied sciences
Computational complexity
Convergence
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Filtering algorithms
Half spaces
Information, signal and communications theory
Least squares methods
Mathematical analysis
Mathematical models
optimal weight design
Optimization
Projection
Projection algorithms
Resonance light scattering
set-theoretic adaptive filtering
Signal and communications theory
Signal processing algorithms
Signal, noise
Studies
Telecommunications and information theory
Transversal filters
Parallel algorithm
optimal weight design
Adaptive algorithm
Adaptive filtering
Parallel architectures
Affine transformation
Recursive algorithm
Computational complexity
Half space
Time variation
Adaptive parallel subgradient projection
set-theoretic adaptive filtering
Optimal design
Fast filter
Weighting
Least squares method
Transverse filter
Convergence rate
Noise immunity
Numerical simulation
Set theory
Fast algorithm
Newton method
ISSN:1053-587X, 1941-0476
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Zusammenfassung:The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r=1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.881225