Robust Parametric Identification for ARMAX Models with Non-Gaussian and Coloured Noise: A Survey

In this paper the Cramer-Rao information bound for ARMAX (Auto-Regression-Moving-Average-Models-with-Exogenuos-inputs) under non-Gaussian noise is derived. It shown that direct application of Least Squares Method (LSM) leads to incorrect (shifted) parameter estimates. This inconsistency can be corrected by implementation parallel usage MLMW (Maximum Likelihood with Whitening) procedure, applied all measurable variables model, and a nonlinear residual transformation using on distribution density noise, participating in Moving Average structure. The design corresponding parameter-estimator, realizing suggested MLMW-procedure discussed details. method asymptotically optimal, is, reaches bound. If belongs some given class, then Huber approach (min-max version MLM) may effectively applied. A numerical example illustrates approach.