Journal ArticleDOI
Almost sure convergence of a decreasing gain sign algorithm for adaptive filtering
TLDR
A rigorous proof of almost-sure convergence to the optimal filter is attained under a weak-ergodicity assumption that includes the case, important in practice, of correlated observations.Abstract:
The convergence analysis of a sign algorithm with decreasing gain, when governing the weights of an adaptive filter, is presented. The analysis is done in a noiseless case. A rigorous proof of almost-sure convergence to the optimal filter is attained under a weak-ergodicity assumption that includes the case, important in practice, of correlated observations. >read more
Citations
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Asymptotic Analysis of
TL;DR: The method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates, whereas previous stochastic analyses typically consider mean and mean square behavior.
Journal ArticleDOI
Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data
TL;DR: A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input and the mean square excess estimation error is shown to be the sum of the two terms with opposite dependencies on mu.
Journal ArticleDOI
Tracking analysis of the sign algorithm in nonstationary environments
Sung Ho Cho,V.J. Mathews +1 more
TL;DR: A tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented, and it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode.
Journal ArticleDOI
Asymptotic analysis of stochastic gradient-based adaptive filtering algorithms with general cost functions
TL;DR: Analysis of stochastic gradient based adaptive algorithms with general cost functions is carried out and almost sure behavior is considered, which means the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time.
Journal ArticleDOI
Optimum step size of sign algorithm for nonstationary adaptive filtering
TL;DR: The adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data and it is proved that the EAAE is the sum of two terms proportional to the algorithm step size mu and the other proportional to 1/ mu.
References
More filters
Journal ArticleDOI
A Stochastic Approximation Method
Herbert Robbins,Sutton Monro +1 more
TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Journal ArticleDOI
Adaptive filtering with binary reinforcement
TL;DR: It is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean-absolute error cost function.
Journal ArticleDOI
Comparison of the convergence of two algorithms for adaptive FIR digital filters
T. Claasen,W. Mecklenbrauker +1 more
TL;DR: It is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained.
Journal ArticleDOI
Some Considerations on the Design of Adaptive Digital Filters Equipped with the Sign Algorithm
N. Verhoeckx,T. Claasen +1 more
TL;DR: A new type of design graph is introduced, which characterizes the convergence pretty well and which is called "the elephant's ear," due to its typical shape, and some effects of non-Gaussian statistics of the received signal are considered.
Journal ArticleDOI
Convergence of an adaptive linear estimation algorithm
E. Eweda,Odile Macchi +1 more
TL;DR: In this paper, the convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations was shown to be almost sure.
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Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm
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Some Considerations on the Design of Adaptive Digital Filters Equipped with the Sign Algorithm
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