Least-Squares Estimation of the Common Pole-Zero Filter of Acoustic Feedback Paths in Hearing Aids

Abstract

In adaptive feedback cancellation both the convergence speed and the computational complexity depend on the number of adaptive parameters used to model the acoustic feedback paths. To reduce the number of adaptive parameters, it has been proposed to model the acoustic feedback paths as the convolution of a time-invariant common pole-zero filter and time-varying all-zero filters, enabling to track fast changes. In this paper, a novel procedure to estimate the common pole-zero filter of acoustic feedback paths is presented. In contrast to previous approaches which minimize the so-called equation-error, we propose to approximate the desired output-error minimization by employing a weighted least-squares procedure motivated by the Steiglitz--McBride iteration. The estimation of the common pole-zero filter is formulated as a semidefinite programming problem, to which a constraint based on the Lyapunov theory is added in order to guarantee the stability of the estimated pole-zero filter. Experimental results using measured acoustic feedback paths from a two microphone behind-the-ear hearing aid show that the proposed optimization procedure using the Lyapunov constraint outperforms existing optimization procedures in terms of modelling accuracy and added stable gain.