Spatial Gaussian Process Regression With Mobile Sensor Networks

This paper presents a method of using Gaussian process regression to model spatial functions for mobile wireless sensor networks. A distributed Gaussian process regression (DGPR) approach is developed by using a sparse Gaussian process regression method and a compactly supported covariance function. The resultant formulation of the DGPR approach only requires neighbor-to-neighbor communication, which enables each sensor node within a network to produce the regression result independently. The collective motion control is implemented by using a locational optimization algorithm, which utilizes the information entropy from the DGPR result. The collective mobility of sensor networks plus the online learning capability of the DGPR approach also enables the mobile sensor network to adapt to spatiotemporal functions. Simulation results are provided to show the performance of the proposed approach in modeling stationary spatial functions and spatiotemporal functions.

[1]  Guido Sanguinetti,et al.  Bayesian Multitask Classification With Gaussian Process Priors , 2011, IEEE Transactions on Neural Networks.

[2]  Nicholas R. Jennings,et al.  A Decentralized, On-line Coordination Mechanism for Monitoring Spatial Phenomena with Mobile Sensors , 2008 .

[3]  Carl E. Rasmussen,et al.  In Advances in Neural Information Processing Systems , 2011 .

[4]  Iain Murray.  Introduction To Gaussian Processes , 2008 .

[5]  Randy A. Freeman,et al.  Decentralized Environmental Modeling by Mobile Sensor Networks , 2008, IEEE Transactions on Robotics.

[6]  Sonia Martínez,et al.  Distributed Interpolation Schemes for Field Estimation by Mobile Sensor Networks , 2010, IEEE Transactions on Control Systems Technology.

[7]  Aníbal Ollero,et al.  A cooperative perception system for multiple UAVs: Application to automatic detection of forest fires , 2006, J. Field Robotics.

[8]  Aníbal R. Figueiras-Vidal,et al.  Marginalized Neural Network Mixtures for Large-Scale Regression , 2010, IEEE Transactions on Neural Networks.

[9]  Cyrill Stachniss,et al.  Learning gas distribution models using sparse Gaussian process mixtures , 2009, Auton. Robots.

[10]  Naomi Ehrich Leonard,et al.  Collective Motion, Sensor Networks, and Ocean Sampling , 2007, Proceedings of the IEEE.

[11]  George J. Pappas,et al.  On trajectory optimization for active sensing in Gaussian process models , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Andreas Krause,et al.  Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies , 2008, J. Mach. Learn. Res..

[13]  Lehel Csató,et al.  Sparse On-Line Gaussian Processes , 2002, Neural Computation.

[14]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[15]  Zongmin Wu,et al.  Compactly supported positive definite radial functions , 1995 .

[16]  Neil D. Lawrence,et al.  Fast Forward Selection to Speed Up Sparse Gaussian Process Regression , 2003, AISTATS.

[17]  Hugh F. Durrant-Whyte,et al.  Modeling and decision making in spatio-temporal processes for environmental surveillance , 2010, 2010 IEEE International Conference on Robotics and Automation.

[18]  M. Opper.  Sparse Online Gaussian Processes , 2008 .

[19]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[20]  M. V. Ramana,et al.  Capturing vertical profiles of aerosols and black carbon over the Indian Ocean using autonomous unmanned aerial vehicles , 2007 .

[21]  R. Schaback.  Creating Surfaces from Scattered Data Using Radial Basis Functions , 1995 .

[22]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[23]  Joonho Lee,et al.  Swarm intelligence for achieving the global maximum using spatio-temporal Gaussian processes , 2008, 2008 American Control Conference.

[24]  Stephen A. Billings,et al.  State-Space Reconstruction and Spatio-Temporal Prediction of Lattice Dynamical Systems , 2007, IEEE Transactions on Automatic Control.

[25]  Jorge Cortés,et al.  Distributed Kriged Kalman Filter for Spatial Estimation , 2009, IEEE Transactions on Automatic Control.

[26]  Amaury Lendasse,et al.  OP-ELM: Optimally Pruned Extreme Learning Machine , 2010, IEEE Transactions on Neural Networks.

[27]  D. Nychka,et al.  Covariance Tapering for Interpolation of Large Spatial Datasets , 2006 .

[28]  Mac Schwager,et al.  Decentralized, Adaptive Coverage Control for Networked Robots , 2009, Int. J. Robotics Res..