The performance surface in filtered nonlinear mean-square estimation

This brief investigates the properties of the performance surface for the problem of linearly constrained nonlinear mean-square estimation of a random sequence. The problem studied has direct application to the study of active noise control systems when the transducers are driven into nonlinear behavior. A deterministic expression is derived for the mean-square error (MSE) surface as a function of the nonlinearity parameter for Gaussian inputs. It is demonstrated that the surface is unimodal, and expressions are determined for the optimum weight vector and for the minimum MSE.