3-D AR Model Order Selection via Rank Test Procedure

Abstract : This paper deals with the problem of three dimensional AutoRegressive (3-D AR) model order estimation. We show that the information for the 3-D AR model order is implicitly contained in an appropriate matrix rank built from the AutoCorrelation Function (ACF) of the underlying 3-D Gaussian process. Exploiting this property, we develop an algorithm to estimate the order corresponding to the Quarter-Space (QS) region of support. The proposed method is based upon a Rank Test Procedure (RTP) using Singular Value Decomposition (SVD) and solving nonlinear system equations. Numerical simulations are presented to illustrate the performances of the proposed algorithm.