Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.