ANALYSIS OF IDENTIFIED 2-D NONCAUSAL MODELS

There are two approaches to the identification of noncausal autoregres sive systems in two dimension differing in the assumed noise model. Fo r both approaches, the maximum likelihood (ML) estimator is presented, which is formulated in the frequency domain. General theory for the M L-method states that the estimation error is asymptotically normally d istributed, the covariance being the inverse of the Fisher information matrix. The Fisher matrix is evaluated and found to be the sum of a b lock-Toeplitz and a block-Hankel matrix. The variance of the parameter s, however, cannot be used for comparison of the two approaches. We, t herefore, evaluate the variance in the frequency domain, assuming that the true system in each case can be described by a model of that type , possibly high-order. In particular, the variance of the spectrum est imate is derived. If the number of parameters tend to infinity, it is shown that the two approaches give the same spectrum estimate variance . Keeping in mind that the results are obtained under the assumption t hat the true system can be described by the model, a key question, the refore, is which set of true spectra can be described by the respectiv e approaches.