On the relationship between kriging and state estimation

Interpolation of sampled random spatial processes is of interest to hydrologists. The interpolation task requires the determination of an underlying process that may be confounded by both process noise and data measurement error. One approach that has appeared in the hydrologic literature is universal kriging. Universal kriging interpolates a discrete stationary spatial process obtained by polynomial filtering through spatial differencing of the original nonstationary process. The interpolation procedure of kriging is presented within the more general framework of state estimation. The paper analyzes the assumptions and limitations of kriging within state estimation and discusses some of the concerns of practitioners which have arisen in recent papers.