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Adaptive finite‐dimensional optimal linear filtering of nD smooth Gaussian random fields

This paper deals with the optimal filtering problem of nD sampled, Gaussian random fields. The filtering algorithm is based on a state‐space signal model analytically derived from the assumption that the continuous Gaussian random field can be well approximated, almost everywhere, by a continuously differentiable nD surface. An appealing feature of the proposed optimal filter is that it is not based on nD strip processing schemes. The filtering algorithm has a structure which is recursive both with respect to the point‐to‐point scanning procedure of the sampled field and to the dimensionality of the estimate computed at each point. This greatly reduces the numerical complexity of the filtering scheme. The filtering algorithm requires the knowledge of some statistical parameters of the random field. For a greater generality, a procedure for the adaptive estimation of these parameters is also provided. Numerical results are reported to illustrate the applicability and performance of the proposed filter. Copyright © 2006 John Wiley & Sons, Ltd.