Sequential Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks

In this technical note, we formulate a fully Bayesian approach for spatio-temporal Gaussian process regression such that multifactorial effects of observations, measurement noise and prior distributions are all correctly incorporated in the predictive distribution. Using discrete prior probabilities and compactly supported kernels, we provide a way to design sequential Bayesian prediction algorithms in which exact predictive distributions can be computed in constant time as the number of observations increases. For a special case, a distributed implementation of sequential Bayesian prediction algorithms has been proposed for mobile sensor networks. An adaptive sampling strategy for mobile sensors, using the maximum a posteriori (MAP) estimation, has been proposed to minimize the prediction error variances. Simulation results illustrate the practical usefulness of the proposed theoretically-correct algorithms.