Identification of certain time-varying nonlinear Wiener and Hammerstein systems

Abstract

The problem of identification and tracking of time-varying nonlinear systems is addressed. In particular, the Wiener system that consists of a dynamic time-varying linear part followed by a fixed nonlinearity and the Hammerstein system in which the order of these two blocks is reversed are studied. The extended Kalman filter (EKF) algorithm is applied. It is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability, resulting in the algorithm CEKF. As indicated by means of numerical examples, this latter algorithm is less sensitive to the chosen initialization than the EKF. The proposed algorithms depend on certain second-order statistics that may be unknown in a typical scenario. A method for estimation of these quantities is proposed. It is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation.