Recursive identification of the Hammerstein model based on the Variational Bayes method

The estimation of the Hammerstein system by using a noniterative learning schema is considered, and a novel algorithm based on the Variational Bayes method is presented. To best emulate the original distribution of the system parameters within the set of those with feasible moments, the loss functional is constructed to optimally approximate the true distribution by a product of independent marginals. To guarantee the uniqueness of the model parameterization, the hard equality constraint is imposed on the selected parameter mean value. In our adopted recursive scenario, the transmission of the approximated moments via iterative cycles is avoided by propagating the sufficient statistics associated with the overparameterized model, which is linear in unknown parameters. Moreover, this propagation penalizes the difference of the updated parameters from the previous ones rather than from the initial guess. Due to access to the sufficient statistics and the suitably chosen marginals, the solution we propose is produced in closed form.