A Statistical Inverse Problem Approach to Online Secondary Path Modeling in Active Noise Control

This paper recasts the problem of online secondary path modeling in the form of a statistical inverse problem. A statistical and, in particular, a Bayesian approach towards secondary path modeling is developed and the computational issues that emerge from this approach are discussed. All signals and parameters are modeled as random variables and the degree of information concerning them is coded in their probability density functions. An abstract solution is formulated in the form of a probability density function for the secondary path model. For extracting point estimates, common statistical estimation methods are investigated. It is shown that maximum likelihood estimation is not stable; however, Bayesian method of maximum a posteriori gives a reliable solution. An adaptive algorithm is then developed to compute this solution in a computationally efficient manner. This algorithm has three advantages, compared to the traditional secondary path modeling algorithms. First, it does not cause any interference with the main active noise control algorithm. Second, it does not require any additive-noise to be injected into the secondary path. Third, it does not require any off-line initiation. The convergence of the proposed algorithm is analyzed theoretically. The validity of the theoretical results is investigated by using computer simulation. Finally successful integration of the proposed algorithm into a real-time ANC system is reported.