Practical Active Noise Control Algorithms in Bayesian Inversion Framework

This paper approaches the problem of adaptive active noise control (ANC) as a Bayesian inverse problem. Initially, a forward model for the ANC system in the generic form usually used in the theory of inverse problems is derived. A vector of control system parameters is considered the problem's unknown variable. The unknown is assumed to be a multivariate random variable with a Gaussian prior probability density function. A data vector is formed using samples of the residual noise signal collected by a feedback microphone. Then, the standard Bayesian inversion method is applied to the forward model, resulting in a posterior probability density function for the unknown variable. We use the maximizer of this function to adjust the ANC system parameters. Both numerical results using computer simulation and empirical results using an experimental ANC setup confirm the efficiency of the proposed algorithm in practice.