Adaptive crosstalk-resistant noise-cancellation using H infinity filters

Abstract

There are a great many methods of noise-cancelling available in the literature stretching back some 40 years. Despite the proliferation of papers, it is perhaps only in the past few decades where real-world examples have been successfully tried. Before noise-cancellation was discovered, there was only the seminal work of Wiener and Kalman which was not cancellation as such, but filtering in the traditional sense by finding an optimal way to perform this using least-squares type approaches and knowledge of noise statistics. Special cases of this approach include cross-coupled Kalman filters and cross-coupled recursive-least squares (RLS). Whereas Kalman (and Wiener) filtering minimise the mean-square error between a signal and its estimate, the H infinity approach here minimizes the worst possible effect of the noise terms in a parameter estimation scheme.