Distributed Kalman filtering for Time-Space Gaussian Processes

Abstract

In this paper we address the problem of distributed Kalman filtering for spatio-temporal Gaussian Process (GP) regression. We start our analysis from a recent result that bridges classical non-parametric GP-based regression and recursive Kalman filtering. Inspired by results on distributed Kalman filtering, we propose two algorithms to perform distributed GP regression in sensor networks. In the first procedure each sensor estimates a local copy of the entire process by combining a classical average consensus information filter running among neighboring sensors with local Kalman filter which is optimal with respect to the partial information gathered by means of the consensus. The procedure, in the limit of the average consensus filter, is proven to be in one-to-one correspondence with the classical centralized Kalman procedure. To enhance the estimation performance, in the second algorithm neighboring nodes perform consensus among the partial state estimates. Finally, theoretical results are complemented with numerical simulations and compared with solutions available in the literature.