Gradient-based recursive parameter estimation for a periodically nonuniformly sampled-data Hammerstein–Wiener system based on the key-term separation

The identification of the Hammerstein–Wiener (H-W) systems based on the nonuniform input–output dataset remains a challenging problem. This article studies the identification problem of a periodically nonuniformly sampled-data H-W system. In addition, the product terms of the parameters in the H-W system are inevitable. In order to solve the problem, the key-term separation is applied and two algorithms are proposed. One is the key-term-based forgetting factor stochastic gradient (KT-FFSG) algorithm based on the gradient search. The other is the key-term-based hierarchical forgetting factor stochastic gradient (KT-HFFSG) algorithm. Compared with the KT-FFSG algorithm, the KT-HFFSG algorithm gives more accurate estimates. The simulation results indicate that the proposed algorithms are effective.