Improvement in adaptive noise canceling using a nonlinear filter based on the Pontryagin minimum principle (Q1105547)

Consider the following filtering problem: suppose that a signal \(x_ 2(t)\) is corrupted by an interference \(x_ 1(t)\) and that noisy observations of both \(x_ 1(t)\) and \(x_ 1(t)+x_ 2(t)\) are available; the model for \(x_ 1(t)\) and \(x_ 2(t)\) is a linear time-varying system the coefficients of which are unknown, and one wants to estimate the signal. The author constructs a framework under which the estimation problem becomes an optimization problem which is solved by the Pontryagin minimum principle; he also explains some tools which make possible the implementation of the procedure in real time. Results of simulation are given and it is shown that the proposed filter has better performance than the least mean square algorithm.