Abstract

This paper considers the problem of estimating the parameters of two-dimensional moving average random fields. We first address the problem of expressing the co- variance matrix of non-symmetrical half-plane, noncausal, and quarter-plane moving average random fields, in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed form expression for the Cramer-Rao lower bound on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the moving average model is de- veloped. The algorithm initially fits a two-dimensional autoregressive model to the observed field, then uses the estimated parameters to compute the moving average model. A maximum-likelihood algorithm for estimating the MA model parameters is also presented. The performance of the proposed algorithms is illustrated by Monte-Carlo simulations, and is compared with the Cramer-Rao bound.

Citations