Control Filter Estimation for Multichannel Active Noise Control Using Kronecker Product Decomposition

Abstract

Active noise control (ANC) algorithms have been developed within the adaptive algorithm framework. However, multichannel ANC systems, which include numerous reference sensors, control speakers, and error microphones, require a very long control filter converging time for control filter estimation. Traditional system identification methods, such as the Wiener filter method, are better suited for such systems because of their relatively shorter converging time. However, they require large amounts of data to achieve accurate statistical estimation. Therefore, this article proposes a control filter estimation method that requires only a short length of data. An iterative Wiener filter solution using Kronecker product decomposition for multichannel ANC systems converts the filter estimation process by breaking down the extensive control filter into multiple shorter control filters through Kronecker product decomposition. This decomposition effectively reduces the high-dimensional system identification problem into manageable low-dimensional ones. Numerical simulations demonstrate the superiority of the proposed method over conventional Wiener filter techniques, especially in scenarios when limited data are available for control filter estimation.