Compressive Estimation of a Spatial Gaussian Process

In this paper, we consider estimating the spatial variations of a field that can be represented by a Gaussian process, based on a small number of observations in a sensor network. We consider cases where the underlying dynamical model is unobservable and therefore the traditional filtering approaches are not able to estimate the field's hyper parameters. More specifically, we look at the Gaussian process with Gaussian radial basis, which is a good regression model for a smooth field. We then propose an integrated log-likelihood and sparsity-based estimator. Furthermore, we apply the random projections over the field to improve the RIC properties and the overall performance for the case of narrow Kernels. We also discuss the impact of different Gaussian field parameters on the estimation. Overall, the proposed framework can be applied to compressively sample and estimate any field that can be represented by Gaussian processes.