Arma model identification using higher order statistics and fisher information concepts

The problem of estimating the parameters of a non causal ARMA system, driven by an unknown input noise with unknown symmetrical probability density function (PDF) is addressed. A maximum likelihood approach is proposed in this paper. The main idea of our approach is that the assumed PDF of the input noise is the PDF minimizing the Fisher information among PDFs matching the estimated cumulants of 2nd and 4th order. This minimization problem is hard to solve, so we use an over-parameterized PDF model, which is a gaussian mixture. We obtain two different models for the classes of sub-Gaussian and super-Gaussian PDFs. For this latter class, we get the most robust estimator in Huber's sense, among these generated by this class. A new parameter estimation method is given and its robustness and optimality properties are detailed. The performances of the resulting identification scheme are compared to those of another higher order method.