A robust adaptive hybrid feedback cancellation scheme for hearing aids in the presence of outliers

It has been demonstrated that the Filtered-x Wilcoxon LMS (FxWLMS) based adaptive filter mitigates the effect of the outliers acquired by the microphone signal of hearing aids by minimizing the Wilcoxon norm and hence shows better cancellation performance than the existing Filtered-x LMS (FxLMS) algorithm. The prediction error method based adaptive feedback canceller (PEMAFC) reduces the bias present in the estimate of the feedback path due to the continuous adaptive filtering (CAF). However, the impulse response of the measured feedback path is close to zero for the first many samples due to the delay introduced by ADC converters and then contains few significant values, which results in slow convergence rate when an adaptive filter is used to model the same. To overcome this limitation, we propose a proportionate normalized WLMS (PNWLMS) algorithm based PEMAFC (P-PNWLMS) for feedback cancellation in hearing aid in the presence of outliers. Further, with an objective to improve the convergence rate and performance accuracy simultaneously, this paper proposes a novel convex PNWLMS (CPNWLMS) algorithm which incorporates convex combination of PNWLMS and WLMS algorithms. The weight update equations are derived for PEMAFC trained by PNWLMS (P-PNWLMS) and CPNWLMS (P-CPNWLMS) algorithms respectively. The results of the simulation study show improved performance of the proposed CPNWLMS based adaptive filter over its component filters.