Identification of Multichannel AR Models with Additive Noise: a Frisch Scheme Approach

A new approach for estimating multichannel AR (M-AR) models from noisy observations is proposed. It relies on the so-called Frisch scheme, whose rationale consists in finding the solution of the identification problem within a locus of solutions compatible with the second order statistics of the noisy data. Once that the locus of solutions has been defined, it is necessary to introduce a suitable selection criterion in order to identify a single solution. The criterion proposed in the paper is based on the comparison of the theoretical statistical properties of the residual of the noisy M-AR model with those computed from the data. The results obtained by means of Monte Carlo simulations show that the proposed algorithm outperforms some existing methods.