Weighted robust adaptive filtering in Krein space and its application in active noise control

Robust adaptive filtering ensures the minimization of the transfer function from the disturbance to the estimation error, and thus guarantees the robustness against the worst-case disturbance in the system. However, a more general approach is given in this paper by employing frequency weighting, which offers flexibility in determining robustness sensitivity in certain frequency of interest. Using the projection in Krein space, we developed a weighted recursive H_∞ filtering that computes the stationary point of certain weighted quadratic form corresponding to an H_∞ norm of a transfer operator T(F). The solution is applied to the active noise cancellation problem, where it is used in ensuring the control signal to be inside the nominal frequency range of the actuators, and avoiding the nonlinearity effect caused by saturation. Experimental result shows the advantage of this weighted form. The proposed algorithm offers an alternative means in dealing with the wideband noise and actuator nonlinearity.