Efficient ARMA parameter estimation of non Gaussian processes by minimization of the Fisher information under cumulant constraints

The problem estimating the parameters of a non-causal ARMA system, driven by an unknown input noise with unknown 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 (FI) among PDFs matching the estimated cumulants up to 4th order. This minimization problem is hard to solve, so we use an over-parameterized PDF model, which is a gaussian mixture, and minimize the FI in this set. A new parameter estimation method is given and its robustness properties are detailed. The performances of the resulting identification scheme an compared to those of another higher order method.