Online Secondary Path Modelling for Spatial Active Noise Control with Arbitrarily Spaced Arrays

Abstract: In this work we explore online secondary path modelling (SPM) in the context of spatial active noise control (ANC). Specifically, we are interested in the reduction of broadband noise over a three-dimensional region, without restrictions on microphone and loudspeaker array placement. As spatial ANC generally requires many channels, both ANC and SPM methods must have low computational cost. The SPM methods are intended to be used with a specific spatial ANC algorithm based on kernel interpolation. By incorporating SPM, the spatial ANC method is enabled to operate under timevarying secondary paths. Four SPM methods are considered in detail, of which three are based on the auxiliary noise technique. Descriptions of the algorithms are presented for the multichannel case, in addition to block-based implementations taking advantage of the fast Fourier transform to drastically reduce computational cost. Impulse responses to simulate a soundfield are recorded using a programmable robot arm. The algorithms are evaluated through simulations to show their respective strengths and weaknesses. It is found that the auxiliary noise based SPM methods have good convergence properties for both control filter and secondary path estimate, although the auxiliary noise’s degrading effect on the residual noise leads to a similar total noise reduction as the auxiliary noise free method. For all algorithms, the noise control performance worsens, and the convergence time increases by more than an order of magnitude, compared to when the secondary paths are known. It is verified that the kernel interpolation based spatial ANC method successfully reduces noise over a region even when used with online SPM.