Parametric identification of ARMAX models with unknown forming filters

In this paper, we present the parameter estimation algorithm for the class of an extended ARMAX model containing a 'coloured' noise sequence, formed by an unknown finite-dimensional linear filter. This algorithm represents the extended versions of residual whitening method and least squares method, working in parallel, to identify the extended parameters obtained after the suggested linear model transformation. The strong consistency of the suggested method (convergence with probability one of the obtained extended parameters to their exact values) is proven. A good performance of the proposed method is illustrated by a numerical example with all polynomials containing unknown parameters.