Time-Varying Volterra System Identification Using Kalman Filtering

Most nonlinear system identification methods based on Volterra model assume that the underlying system is time-invariant. In this paper, a novel identification method for time-varying Volterra systems (TVVS) is proposed. We view this problem from a different perspective in the sense that the system identification problem is converted to a state estimation problem of a dynamic system. The time-varying Volterra kernels are governed by a Gauss-Markov stochastic difference equation upon which a state-space representation of time-varying Volterra systems is built. The state transition matrix and noise covariance of the underlying state equations are usually unknown. Therefore, we develop a method to estimate these unknown quantities. Finally, a Kalman filtering scheme is utilized to identify and track the time-varying Volterra system. Simulation examples are given to illustrate the better performance of the proposed method as compared with other adaptive identification methods such as the LMS and RLS algorithms.