Multidimensional Multiple-Order Complex Parametric Model Identification

This paper presents a way to access both the multiple-order and parameters of a multidimensional complex number autoregressive (AR) model through matrix factorization. The principle of this technique consists of the transformation of the multidimensional model to a pseudo simple-input simple-output AR model, then performing factorization of the covariance matrix of the data. This factorization then leads to a recursive form of the parameter and order estimation. This paper makes two principal contributions. The first is a generalization of one dimensional factored form algorithm, and the second is that it makes it possible to access all the possible different orders and parameters of a multidimensional complex number AR model of any dimension, whereas classical approaches are limited to at most four-dimensional models. Computer simulation results are provided to illustrate the behavior of this method.