Frequency domain accuracy of identified 2-D causal AR-models

The author studies parametric estimation of 2-D autoregressive models using the least squares method. The analysis is concentrated on the frequency domain accuracy of the estimated models. First results for the accuracy of the parameter estimates are discussed. The estimates are asymptotically Gaussian distributed. The variance of the estimated model evaluated in the frequency domain can be expressed using these results for the parameters. This, however, gives no insight of the dependence on the true transfer function. An illuminating result is obtained if one lets the model order tend to infinity. The limiting results show good correspondence with Monte-Carlo simulations even for small data sets, using low model orders