In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.

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In this paper, we propose distributed Gaussian process regression (GPR) for resource-constrained distributed sensor networks under localization uncertainty. The proposed distributed algorithm, which combines Jacobi over-relaxation (JOR) and discrete-time average consensus (DAC), 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 GPR to improve its scalability. The performance of the proposed method is verified in numerical simulations against the centralized maximum a posteriori (MAP) solution and a quick-and-dirty solution. We show that the proposed method outperforms the quick-and-dirty solution and achieve an accuracy comparable to the centralized solution.

In this paper, we design and analyze a class of multiagent systems that locate peaks of uncertain static fields in a distributed and scalable manner. The scalar field of interest is assumed to be generated by a radial basis function network. Our distributed coordination algorithms for multiagent systems build on techniques from adaptive control. Each agent is driven by swarming and gradient ascent efforts based on its own recursively estimated field via locally collected measurements by itself and its neighboring agents. The convergence properties of the proposed multiagent systems are analyzed. We also propose a sampling scheme to facilitate the convergence. We provide simulation results by applying our proposed algorithms to nonholonomic differentially driven mobile robots. The extensive simulation results match well with the predicted behaviors from the convergence analysis and illustrate the usefulness of the proposed coordination and sampling algorithms.

This paper considers visual feature selection to implement position estimation using an omnidirectional camera. The localization is based on a maximum likelihood estimation (MLE) with a map from optimally selected visual features using Gaussian process (GP) regression. In particular, the collection of selected features over a surveillance region is modeled by a multivariate GP with unknown hyperparameters. The hyperparameters are identified through the learning process by an MLE, which are used for prediction in an empirical Bayes fashion. To select features, we apply a backward sequential elimination technique in order to improve the quality of the position estimation with compressed features for efficient localization. The excellent results of the proposed algorithm are illustrated by the experimental studies with different visual features under both indoor and outdoor real-world scenarios.