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.
Bibliographical noteFunding Information:
Manuscript received February 16, 2011; revised July 13, 2011; accepted November 23, 2011. Date of publication December 09, 2011; date of current version July 19, 2012. This work was presented in part at the American Control Conference (ACC), San Francisco, CA,2011. This work was supported by the National Science Foundation through CAREER Award CMMI-0846547. Recommended by Associate Editor H. S. Chang.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering