Low-Order Controllers for Active Noise Cancellation Based on Hankel Matrix Rank Minimization

Feedback active noise cancellation (ANC) has become a common tool to reduce unwanted noise in hearing devices. We discuss controller design approaches, which involve the approximation of high-order prototype controllers by low-order ones for resource-constrained applications. A drawback of conventional approaches is that the error introduced by the low-order approximation is not considered in the design of the prototype controller. Our concept is to mitigate this drawback using a novel algorithm which promotes prototype controllers that can be approximated with a low error. For this, we use the well-known nuclear norm heuristic. We describe the design process and provide empirical evidence of a performance improvement in applications where a low-order controller is required.