Improvement in adaptive noise canceling using a nonlinear filter based on the pontryagin minimum principle

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