Determination of the Two-Dimensional ARMA Model Order Using Rank Test Based Approach

Determination of the order of a two-dimensional (2-D) ARMA model is a key first step toward the goal of modeling a process. In this paper, a rank test approach for 2-D ARMA model order determination is proposed. This method shows that the information of AR and MA orders are implicitly contained in two different correlation matrices and the AR and MA orders of the 2-D ARMA model can be independently determined before parameter estimation. In the proposed method, the model is assumed causal, stable, linear, and spatial shift-invariant with P₁times P₂ quarter plane (QP) support. Analysis and simulation results demonstrate the applicability of this approach.