Distributed Interpolation Schemes for Field Estimation by Mobile Sensor Networks

We introduce a procedure to adapt local interpolations to represent spatial fields as they are measured by a mobile sensor network. The scheme incorporates new sensor (synchronous) measurements in a similar fashion to a Kalman filter-like recursion. We derive necessary conditions that allow the distributed computation of the recursion and present an algorithm that makes use of agreement rules that satisfy them. We show how the nearest neighbor interpolation scheme is compatible with the motion coordination algorithm for region coverage proposed in. Finally, we illustrate the performance of the algorithms in simulation.

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

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

[3]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[4]  Francesco Bullo,et al.  Esaim: Control, Optimisation and Calculus of Variations Spatially-distributed Coverage Optimization and Control with Limited-range Interactions , 2022 .

[5]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

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

[7]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[8]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[9]  Bernhard Maschke,et al.  Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems , 2010 .

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

[11]  Vijay Gupta,et al.  Distributed estimation and control in networked systems , 2007 .

[12]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[13]  Francesco Bullo,et al.  Optimal sensor placement and motion coordination for target tracking , 2006, Autom..

[14]  J. Speyer.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1979 .

[15]  Richard M. Murray,et al.  Approximate distributed Kalman filtering in sensor networks with quantifiable performance , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[16]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[17]  Jason Speyer,et al.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[18]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[19]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..