Efficient order recursive LS algorithms for 2D SAR model fitting

Three fast, recursive, in-order, least-squares (LS) algorithms are presented to estimate efficiently the two-dimensional simultaneous autoregressive (SAR) model parameters and to determine the model orders at the same time. The algorithms are for a causal model with a nonsymmetric half plane neighborset, a semicausal model with a symmetric half plane neighborset, and a noncausal model with the corresponding neighborset being a rectangle plane centered at (0,0). The first two algorithms are conventional LS estimation algorithms while the last one is a consistent LS estimation scheme. The computational complexities of the algorithms are all proportional to m^5/2, where m is the number of estimated parameters. Numerical examples are given to show the correctness and efficiency of the algorithms