Non-causal ARMA model identification by maximizing the kurtosis

The problem of estimating the parameters of a noncausal ARMA system, driven by an unobservable input noise is addressed. We propose a method based on a generalized version of the prediction error minimum variance approach and on the maximum kurtosis properties. Firstly, a spectrally equivalent (SE) model is identified with the generalized minimum variance approach. Secondly, the kurtosis allows us to identify the phase of the true model by localizing its zeros and poles from the SE model. Finally, we propose a new method which is a closed-loop form of the preceding method allowing to improve the accuracy of the parameter estimation and to obtain a better reconstruction of the estimated model phase. Simulation results seem to confirm the good behavior of the proposed methods compared to methods using higher order statistics.