Multidimensional Multiple-Order Complex Parametric Model Identification

• Published in: IEEE transactions on signal processing 2008-10, Vol.56 (10), p.4574-4582
• Main Authors: Kouame, D., Girault, J.-M.
• Format: Article
• Language: English
• Subjects: Additive noise; Algorithms; Applied sciences; Autoregressive; Complex numbers; Computer simulation; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Engineering Sciences; Exact sciences and technology; Factorization; Image processing; Information, signal and communications theory; Mathematical models; Miscellaneous; multidimensional; Multidimensional systems; Neodymium; order; parameter; Parameter estimation; Parametric statistics; Recursive; Recursive estimation; Signal and communications theory; Signal and Image processing; Signal processing; Signal, noise; Spectral analysis; Telecommunications and information theory; Transformations
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.928088

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.