Hierarchical Parameter Estimation for Wiener-Hammerstein Systems

This paper proposes a new method to estimate the unknown parameters for stochastic nonlinear systems that can be described by Wiener-Hammerstein (W-H) mathematical models (L-N-L cascade). The key of this technique is to decompose the W-H structure into three sub-blocks. Afterwards, we apply the Recursive Extended Least Squares (RELS) estimator at each discrete-time in order to estimate the unknown parameters. Next, we put the output system under two matrix forms and from that, we determine the others parameters using the predicted intermediate variables. The convergence analysis of the W-H-RHPE algorithm is made using the differential equation approach and its performance is validated by treating a simulation example.