An adaptive filter for noise cancelling

The author introduces a nonlinear filter for adaptive noise cancelling. The derivation and convergence properties of the filter are presented. The performance, as measured by the signal-to-noise ratio between the signal and its estimate, is compared to that of the commonly used least-mean-square (LMS) algorithm. It is shown, through simulation, that the proposed canceller has, on the average, better performance than the LMS canceller. It is based on the Pontryagin minimum principle and the method of invariant imbedding, and its computational time is about 10% that of the LMS in the cases studied, which is a substantial improvement