Frequency domain accuracy of identified 2-D causal models

A study is made of parametric estimation of 2-D transfer functions using the least-squares method which is the dominant method for causal systems. The analysis concentrates on the frequency-domain accuracy of the estimated models. There exist results for the accuracy of the parameter estimates. The parameters are asymptotically Gaussian distributed. The variance of the polynomial in the frequency domain can be expressed using these results for the parameters. This, however, gives no insight into the dependence on the true transfer function. An illuminating result is obtained if the model order tends to infinity. The limiting results show good correspondence with Monte-Carlo simulations for small data sets obtained with low model orders