Distributed Gaussian Process Regression Under Localization Uncertainty

In this paper, we propose distributed Gaussian process regression for resource-constrained distributed sensor networks under localization uncertainty. The proposed distributed algorithm, which combines Jacobi over-relaxation and discrete-time average consensus, can effectively handle localization uncertainty as well as limited communication and computation capabilities of distributed sensor networks. We also extend the proposed method hierarchically using sparse Gaussian process regression to improve its scalability. The performance of the proposed method is verified in numerical simulations against the centralized maximum a posteriori solution and a quick-and-dirty solution. We show that the proposed method outperforms the quick-and-dirty solution and achieves an accuracy comparable to the centralized solution.