A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems

This article studies the problem for parameter identification of nonlinear dynamical systems (i.e., the Hammerstein–Wiener systems) with additive coloured noises. Based on the gradient search and the key term separation, a generalized extended stochastic gradient (GESG) algorithm is given for estimating the system parameters. To improve the computational efficiency, a data filtering based GESG algorithm and a data filtering based multi-innovation GESG algorithm are derived by applying the data filtering technique and the multi-innovation identification theory. Moreover, the proposed algorithms are proved to be convergent under proper conditions. Finally, the simulation results verify the theoretical analysis.