Filtered error adaptive IIR algorithms and their application to active noise control

This paper is concerned with systems in which the output error of an adaptive IIR filter is subsequently filtered, eg, an active noise control system where a transfer function models the path between the injection point of the cancellation noise and the point where the residual error is measured. We propose a family of algorithms suited to this type of scenarios, deriving conditions for their deterministic convergence. The analysis of the convergence is particularized to the Filtered-U Recursive LMS algorithm, a popular scheme whose global convergence has never been proved formally. Finally, some results based on real measurements are also presented.