Parameter estimation algorithms for multivariable Hammerstein CARMA systems

This paper considers parameter identification problems for multivariable Hammerstein controlled autoregressive moving average (CARMA) systems. We transform a multivariable Hammerstein CARMA system into a new identification model which contains a set of bilinear parameter vectors, i.e., two sets of parameter vectors. To solve the difficulty of estimating the two sets of parameter vectors, this paper constructs two different forms of the identification model in each of which the output is linear about one set of parameter vectors, and presents an extended stochastic gradient algorithm to interactively estimate the two sets of parameter vectors by using the hierarchical identification principle. The proposed hierarchical identification algorithm has a higher computational efficiency than the over-parametrization model based stochastic gradient algorithm. The simulation results indicate that the proposed algorithm is effective, and an example of modeling a photovoltaic array system with the multivariable Hammerstein model is given.