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- Isaksson, Alf
(författare)
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Analysis of Identified 2-D Noncausal Models
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- There are two approaches to the identification of noncausal autoregressive systems in two dimensions differing in the assumed noise model. For both approaches, the maximum likelihood estimator formulated in the frequency domain is presented. The Fisher information matrix is evaluated and found to be the sum of a block-Toeplitz and a block-Hankel matrix. The variance of the parameters, however, cannot be used for comparison of the two approaches, so the variance in the frequency domain is evaluated, 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 estimate is derived. If the number of parameters tends to infinity, it is shown that the two approaches give the same spectrum estimate variance. The question of which set of true spectra can be described by the respective approaches is discussed.
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- Isaksson, Alf
(författare)
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Frequency Domain Accuracy of Identified 2-D Causal Models
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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