## Estimation of 2-D ARMA model parameters by using equivalent AR approach

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, vol.342, no.1, pp.39-67, 2005 (Journal Indexed in SCI)  • Publication Type: Article / Article
• Volume: 342 Issue: 1
• Publication Date: 2005
• Doi Number: 10.1016/j.jfranklin.2004.08.002
• Title of Journal : JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
• Page Numbers: pp.39-67
• Keywords: 2-D ARMA model, 2-D equivalent AR model, parameter estimation, SPECTRAL ESTIMATION, RECURSIVE SOLUTION, LINEAR PREDICTION, FIELDS

#### Abstract

In this paper, the problem of estimating the parameters of a two-dimensional autoregressive moving-average (2-D ARMA) model driven by an unobservable input noise is addressed. In order to solve this problem, the relation between the parameters of a 2-D ARMA model and their 2-D equivalent autoregressive (EAR) model parameters is investigated. Based on this relation, a new algorithm is proposed for determining the 2-D ARMA model parameters from the coefficients of the 2-D EAR model. This algorithm is a three-step approach. In the first step, the parameters of the 2-D EAR model that is approximately equivalent to the 2-D ARMA model are estimated by applying 2-D modified Yule-Walker (MYM) equation to the process under consideration. Then, the moving-average parameters of the 2-D ARMA model are obtained solving the linear equation set constituted by using the EAR coefficients acquired in the first step. Finally, the autoregressive parameters of the 2-D ARMA model are found by exploiting the values obtained in first and second steps. The performance of the proposed algorithm is compared with other 2-D ARMA parameter and spectral estimation algorithms available in the technical literature by means of three different criteria. As a result of this comparison, it is shown that the parameters and the corresponding power spectrums estimated by using the proposed algorithm are converged to the original parameters and the original power spectrums, respectively. (C) 2004 The Franklin Institute. Published by Elsevier Ltd. All fights reserved.