A family of robust low-complexity adaptive filtering algorithms for active control of impulsive noise

Active noise control (ANC) is a technique used to achieve noise cancellation in physical spaces and has a wide range of applications. A key challenge in ANC systems is designing an adaptive filter that balances noise cancellation performance with computational efficiency. This paper presents two sets of robust adaptive filtering algorithms to address this challenge. The first set involves decomposing the adaptive filter's coefficient vector into a linear combination of two sets of shorter sub-filters using the Kronecker product. This decomposition reduces the size of the matrices and vectors involved in the ANC algorithm. To handle impulsive noise, we employ a class of robust estimators and define several cost functions under the recursive least-squares criterion, resulting in an adaptive control algorithm with two groups of alternately updating equations. We also analyze the low-rank property of the proposed adaptive filter in controlling impulsive noise. To further reduce computational complexity, we integrate the dichotomous coordinate descent scheme into the Kronecker product decomposition-based robust ANC method, forming a second set of algorithms. The effectiveness of the proposed algorithms is demonstrated through simulations.