This paper studies the application of the linear least-mean-square (LMS) algorithm with leakage to a system having a memoryless saturation-type nonlinearity. This approach represents an interesting alternative to the nonlinear LMS (NLLMS) algorithm. The major drawback to implement the latter is that the model parameters of the system nonlinearity must be known. In contrast, the linear LMS algorithm with leakage does not require such knowledge. It permits to approximate the performance of the NLLMS by properly selecting a constant leakage factor value. To cope with an eventual change of the environment, a strategy for a variable leakage is also proposed. Several numerical simulations are presented with the aim of ratifying the feasibility of the proposed approach

On the LMS algorithm with constant and variable leakage factor in a nonlinear environment

A Model of Temporal Adaptation in Fly Motion Vision

This article develops a new adaptive filter algorithm intended for use in active noise control systems where it is required to place gain or power constraints on the filter output to prevent overdriving the transducer, or to maintain a specified system power budget. When the frequency-domain version of the least-mean-square algorithm is used for the adaptive filter, this limiting can be done directly in the frequency domain, allowing the adaptive filter response to be reduced in frequency regions of constraint violation, with minimal effect at other frequencies. We present the development of a new adaptive filter algorithm that uses a penalty function formulation to place multiple constraints on the filter directly in the frequency domain. The new algorithm performs better than existing ones in terms of improved convergence rate and frequency-selective limiting.

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An active noise control algorithm with gain and power constraints on the adaptive filter

Real-time feedback control of flow-induced cavity tones—Part 2: Adaptive control

The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-X LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [ldquorobustness of the filtered-X LMS algorithm - part I: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz Matricesrdquo of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set.

Robustness of the Filtered-X LMS Algorithm— Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty

The performance surfaces of two classes of minimum effort adaptive filter are studied. Eigenvalue spreads of the cost functions of minimum weight vector norm and minimum output variance algorithms are examined for both estimation and feedforward control applications. Results support the widespread practical use of the "leaky LMS" algorithm. >

Performance surfaces of minimum effort estimators and controllers

An analysis of the behavior of adaptive filters designed around practically useful, minimum effort cost functions is presented. It is shown that equivalent transfer functions can be derived for both a conventional minimum variance system and for an estimator whose controlling algorithm attempts to minimize the norm square of the filter's weight vector, this latter system being exactly equivalent to the leaky LMS (least mean squares) algorithm. Although the equivalent transfer functions are generally time variant, they assume time invariant form for several important classes of reference signal. In such cases the equivalent transfer function can be used to predict both transient and steady state aspects of the adaptive estimator's performance, as demonstrated for the particularly important case of synchronous periodic estimation. >

P. Darlington

Papers

Performance surfaces of minimum effort estimators and controllers

Equivalent transfer functions of minimum output variance mean-square estimators