This chapter provides an overview of interesting phenomena pertaining to the learning capabilities of stochastic-gradient adaptive filters, and in particular those of the least-mean-squares (LMS) algorithm. The phenomena indicate that the learning behavior of adaptive filters is more sophisticated, and also more favorable, than was previously thought, especially for larger step-sizes. The discu...

A novel approach for the least-mean-square (LMS) estimation algorithm is proposed. Rather than using a fixed convergence parameter μ, this approach utilizes a time-varying LMS parameter μn. This technique leads to faster convergence and provides reduced mean-squared error compared to the conventional fixed parameter LMS algorithm. The algorithm has been tested for noise reduction and estimation...

Positive results are proved here about the ability of numerical simulations to reproduce the exponentialmean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step si...

In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared with a non-cooperative agent which represents the average of the network. The analysis provides conditions under which diversity in the filter parameters is be...

In this paper, a stochastic mean square version of Lax’s equivalence theorem for Hilbert space valued stochastic differential equations with additive and multiplicative noise is proved. Definitions for consistency, stability, and convergence in mean square of an approximation of a stochastic differential equation are given and it is shown that these notions imply similar results as those known ...

In this paper, the Acoustic Echo Cancellation (AEC) are investigated by using Finite Impulse Responses Adaptive Filter with the analysis of Mean Square Error (MSE) and its convergence property. It is the result of a project in the course Fundamental of Signal Processing at Chongqing University of Posts and Telecommunications. It focuses on Normalized Least Mean Square (NLMS) algorithm of adapti...

Absfracf-This paper presents a general approach to the derivation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and convergence is in the mean-square sense. The method of derivation is based on the integral representation of such processes. It covers both the...

This paper is devoted to the convergence analysis of stochastic θ-methods for nonlinear neutral stochastic differential delay equations (NSDDEs) in Itô sense. The basic idea is to reformulate the original problem eliminating the dependence on the differentiation of the solution in the past values, which leads to a stochastic differential algebraic system. Drift-implicit stochastic θ-methods are...

This paper addresses the iterative learning control problem under random data dropout environments. The recent progress on iterative learning control in the presence of data dropouts is first reviewed from 3 aspects, namely, data dropout model, data dropout position, and convergence meaning. A general framework is then proposed for the convergence analysis of all 3 kinds of data dropout models,...

In this work, a new class of stochastic gradient algorithm is developed based on q-calculus. Unlike the existing q-LMS algorithm, the proposed approach fully utilizes the concept of q-calculus by incorporating time-varying q parameter. The proposed enhanced q-LMS (Eq-LMS) algorithm utilizes a novel, parameterless concept of error-correlation energy and normalization of signal to ensure high con...