Sara Tressens

A Nonparametric VSS NLMS Algorithm

The aim of a variable step size normalized least-mean-square (VSS-NLMS) algorithm is to try to solve the conflicting requirement of fast convergence and low misadjustment of the NLMS algorithm. Numerous VSS-NLMS algorithms can be found in the literature with a common point for most of them: they may not work very reliably since they depend on several parameters that are not simple to tune in practice. The objective of this letter is twofold. First, we explain a simple and elegant way to derive VSS-NLMS-type algorithms. Second, a new nonparametric VSS-NLMS is proposed that is easy to control and gives good performances in the context of acoustic echo cancellation

A New Robust Variable Step-Size NLMS Algorithm

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.

Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice

A variable regularized affine projection algorithm (VR-APA) is introduced, without requiring the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal and it satisfies certain error energy bounds. Second, the time-varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. Although we first derive the VR-APA for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time-varying system following a first-order Markov model. We also find expressions for the power of the steady-state error vector for the VR-APA and the standard APA with no regularization parameter. Particularly, we obtain quite different results with and without using the independence assumption between the a priori error vector and the measurement noise vector. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations. An important conclusion is that the former independence assumption can lead to very inaccurate steady-state results, especially when high values of the projection order are used

A Fast Robust Recursive Least-Squares Algorithm

We present a fast robust recursive least-squares (FRRLS) algorithm based on a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing a cost function subject to a time-dependent constraint on the norm of the filter update. Although the characteristics of the exact solution to this problem are known, there is no closed-form solution in general. However, the approximate solution we propose is very close to the optimal one. We also present some theoretical results regarding the asymptotic behavior of the algorithm. The FRRLS is then tested in different environments for system identification and acoustic echo cancellation applications.

A Family of Robust Algorithms Exploiting Sparsity in Adaptive Filters

We introduce a new family of algorithms to exploit sparsity in adaptive filters. It is based on a recently introduced new framework for designing robust adaptive filters. It results from minimizing a certain cost function subject to a time-dependent constraint on the norm of the filter update. Although in general this problem does not have a closed-form solution, we propose an approximate one which is very close to the optimal solution. We take a particular algorithm from this family and provide some theoretical results regarding the asymptotic behavior of the algorithm. Finally, we test it in different environments for system identification and acoustic echo cancellation applications.

Optimum Variable Explicit Regularized Affine Projection Algorithm

A variable regularized affine projection algorithm (VR-APA) is introduced, which does not require the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal, providing robust behavior against perturbations and model uncertainties. Second, the time varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. At each time step, it needs knowledge of the power of the estimation error vector, which can be estimated by averaging observable quantities. Although we first derive it for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time varying system following a first order Markov model. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations

A Robust Adaptive Filtering Algorithm Against Impulsive Noise

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we will derive a robust variable step-size NLMS algorithm which optimizes the square norm of the a posteriori error subject to the constraint on the norm of the filter change. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.

Author's Reply to “Comments on `Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice' ”

Muralidhar et al. point out that when the VR-APA is applied in echo cancellation it will diverge during the presence of a near-end signal or a silence period. We provide an explanation for the behavior of the algorithm and show that a double-talk detector makes the VR-APA suitable for this application.