Recursive nonparamettic estimation of nonlinear systems of Volterra type

Abstract

A large class of non linear input-output systems is here represented by means of Volterra series. These series are completely specified when their coefficients, called Volterra kernels, are known. Almost sure consistent estimates of Volterra kernels are presented in two fundamental steps. Firstly the almost sure convergence of a recursive kernel estimator of the joint density of the strongly mixing (or po-dependent) input-output process is obtained. Secondly the "explosive" behavior of the previous estimator in a neighborhood of the true, input-output functional is established, Volterra kernels are obtained by a projection criterion. Some simulation results are provided.