Sampled Wiener Time Delay System Identification

This brief presents an iterative identification method for a sampled Wiener output error (OE) model with an integer time delay dynamics against stochastic noise. Considering the output nonlinearity as an unknown function to be estimated by using a kernel regression, two iterative least squares (ILS) algorithms are established for evaluating the discrete-time linear model parameters and the coefficients of the nonlinear function simultaneously. For consistent estimation, a noise-free output response is predicted through an auxiliary model method. Meanwhile, two crucial parameters, namely the time delay and a kernel bandwidth, are determined by using a two-dimensional linear search strategy. In addition, the rate of convergence of parameter estimation is enhanced by introducing an adaptive set of forgetting factors. Using the statistical theory of stochastic processes, the asymptotic convergence is analyzed through a mathematical proof. Simulation and experimental results are included to demonstrate the efficacy and advantage of the proposed algorithm.