Optimal smoothing for spherical Gauss-Markov Random Fields with application to weather data estimation

This paper considers the smoothing problem for inhomogeneous Gauss-Markov Random Fields on a spherical lattice. Various observation models are considered, such as the case of noisy, possibly correlated, observations available only on a subset of sites, or a variable number of process components being measured. A 2D recursive optimal smoothing algorithm is derived, with computational complexity of O(N2) where N is the number of sites, in line with known more common algorithms for inhomogeneous fields on rectangular lattices. An application of the method in weather forecasting using real data is presented, showing the capability of the proposed method.