3-D AR model order selection via rank test procedure

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 (p₁,p₂,p₃) 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