Summary

This paper addresses the field of stereophonic acoustic echo cancelation (SAEC) by adaptive filtering algorithms Recently, simplified versions of the fast transversal filter (SFTF)-type algorithm has been proposed In this paper, we propose two major contributions In the first contribution, we propose two new FTF-type algorithms with low complexity and good convergence speed characteristics These two proposed algorithms are mainly on the basis of a forward prediction scheme to estimate the so called dual Kalman gain, which is inherent in the filtering part update This computation complexity is achieved by the introduction of new relations for the computation of the likelihood variables that are simple and lead to further simplifications on the prediction part of the two proposed algorithms In the second contribution, we propose to adapt then apply these four new SFTF-type algorithms, (the two proposed algorithms in this paper and their original versions) in the SAEC applications A fair comparison of the proposed algorithms with the original SFTF and the normalized least mean square algorithms, in mono and SAEC applications, is presented Copyright © 2014 John Wiley & Sons, Ltd

New efficient adaptive fast transversal filtering (FTF)‐type algorithms for mono and stereophonic acoustic echo cancelation

In this paper, we present new versions of numerically stable fast recursive least squares (NS-FRLS) algorithms. These new versions are obtained by using some redundant formulae of the fast recursive least squares (FRLS) algorithms. Numerical stabilization is achieved by using a propagation model of first order of the numerical errors. A theoretical justification for these versions is presented by formulating new conditions on the forgetting factor. An advanced comparative method is used to study the efficiency of these new versions relatively to RLS algorithm by calculating their squared norm gains ratio (SNGR). The simulation over a very long duration for a stationary signal did not reveal any tendency to divergence.

Error propagation analysis of fast recursive least squares algorithms

Migration of the identified system poles for a dynamical system indicates changes in its global properties. In civil engineering structures, these changes are most often due to changes in global stiffness or damping parameters associated with both environmental effects as well as deterioration of the structure. In structures that employ automated feedback control systems to mitigate unwanted vibrations, feedback control laws and state estimators (if used) are reliant upon a theoretical or identified model of the plant. Any loss in fidelity between the plant model and its actual condition will result in degradation of the controller performance. Low-cost, wireless control networks that by nature are more likely to utilize state-estimation, are therefore more vulnerable to problems associated with property changes in the system. In this paper, recursive identification of system poles is proposed for use in a wireless sensing network engaged in feedback control. Because it is based on system poles, the algorithm is ideally suited for adaptive control methods that update control and estimation gains as system properties change. The algorithm proposed is based on the fast transversal filter and is designed to minimize computation as well as data transmission requirements to optimally utilize the distributed data that is stored within a low-power wireless sensor network.

Near real-time system identification in a wireless sensor network for adaptive feedback control

In this paper, we present new version of numerically stable fast recursive least squares (NS-FRLS) algorithm. This new version is obtained by using some redundant formulae of the fast recursive least squares (FRLS) algorithms. Numerical stabilization is achieved by using a propagation model of first order of the numerical errors. A theoretical justification for this version is presented by formulating new conditions on the forgetting factor. An advanced comparative method is used to study the efficiency of this new version relatively to RLS algorithm by calculating their normalized square norm gain error (NGE). We provide a theoretical justification for this version by formulating new conditions on forgetting factor. It will be followed by an analytical analyze of the convergence of this version and we show, both theoretically and experimentally, their robustness. The simulation over a very long duration for a stationary signal did not reveal any tendency to divergence.

Analysis of Fast Recursive Least Squares Algorithms for Adaptive Filtering

The O(7N) implementation of the fast transversal filter (FTF) for recursive least-squares (RLS) adaptive filtering is known to be numerically unstable. Stabilization methods for this algorithm employing error feedback can be difficult to tune and do not work for aggressive choices of the forgetting factor X. A numerically-stable FTF algorithm employing leakage correction has been introduced that overcomes many of these difficulties. In this paper, we analyze the stability characteristics of this new algorithm. Our analysis employs a linearized model of the errors in the states of the adaptive filter. Through our analysis, we prove that for positive leakage factors v/sub 1/ in the range 0/spl Lt/v/sub 1/</spl lambda//sup /spl kappa//, where /spl kappa/ is the duty cycle of the leakage-based update, the algorithm is numerically stable. Simulations indicate the accuracy of the analysis and the stable behavior of the algorithm.

Analysis of the stabilized FTF algorithm with leakage correction

A derivation of fundamental fast transversal filter equations comes to a 7M fast RLS algorithm for system identification. Yet, this algorithm is not stable due to numerical errors resulting from implementation on a hardware with finite precision arithmetic. The known stabilization methods with feedback of numerical errors require a judicious choice of the feedback gains and depend on the properties of the exciting sequence, as simulations have shown. A new method to stabilize the algorithm is introduced that does not depend on the characteristics of the excitation signal. By inserting leakage factors in the filter equations, a steady contraction of error components is reached. >

S. Binde

Papers

A numerically stable fast transversal filter with leakage correction