Two-dimensional non-Gaussian autoregressive model order determination

A two-dimensional (2-D) autoregressive (AR) model driven by a non-Gaussian zero-mean independent identically distributed 2-D sequence is considered. The input sequence is not observed. The signal observations may be contaminated by additive Gaussian noise. We consider the problem of model order determination using higher order cumulants of the 2-D signal. We show that the necessary information to determine the 2-D AR model order is implicitly contained in a specific cumulant matrix. The algorithm is based on the computation of three matrix ranks via singular value decomposition. The proposed approach is illustrated via computer simulations.