Secondary-path models in adaptive-noise-control headphones

The Filtered-x-Least-Mean-Square (FxLMS) is an efficient algorithm for active-noise-control-headphones. It relies on a correct model Ŝ of the secondary-path S which, in the case of headphones, is above all determined by the acoustic path from the loudspeaker to the error-microphone. If the headphones are abruptly lifted or put on, the phase of S changes more than 90° and the formerly correct model Ŝ will suddenly be wrong and the FxLMS might diverge. This paper presents three methods how the divergence of the FxLMS can be avoided. All three methods rely on laboratory measurements under different conditions from tight headphones to completely lifted headphones. First, it is shown how a stable secondary-path model can be derived from the phase information of the measurements. For the second and third method, two secondary-path models are implemented. One for the tight use case and one for the lifted headphones. The current state of the secondary-path is then detected either via an online noise-cancelling-analysis or via an infrasonic test-signal. Comparison with existing approaches shows the robust stability and efficiency of the proposed methods.