A recursive prediction error algorithm for identification of certain time-varying nonlinear systems

The tracking problem in identification of certain classes of time-varying nonlinear systems is addressed. In particular, a Hammerstein type system which consists of a nonlinear part, given on a state space description, followed by a time-varying linear part is considered. A Recursive Prediction Error Method, RPEM combined with a method for on-line adjustment of the forgetting factor is proposed. This algorithm does not require estimation of the statistics of the noise and the dynamics of the true system. It is shown how the proposed scheme can be used for identification of certain nonlinear time varying acoustic echo paths. Thus, the suggested algorithm is applicable to for instance, conference telephony and mobile telephone handsfree.