Asymptotic optimality of multicenter Voronoi configurations for random field estimation

IEEE Transactions on Automatic Control

Volumn 54, Issue 1, 2009, Pages 153-158

  Graham, Rishi ^a   Cortés, Jorge ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Linear unbiased minimum variance estimator (LUMVE)

Indexed keywords

AGENTS; MOBILE AGENTS; WIRELESS NETWORKS; WIRELESS TELECOMMUNICATION SYSTEMS;

ASYMPTOTIC OPTIMALITY; DISTRIBUTED COORDINATION ALGORITHMS; ERROR VARIANCES; INCENTER; KRIGING; LINEAR UNBIASED MINIMUM VARIANCE ESTIMATOR (LUMVE); MAXIMUM ERRORS; MEASUREMENT LOCATIONS; MULTI-AGENT NETWORKS; NETWORK CONFIGURATIONS; OBJECTIVE FUNCTIONS; OPTIMIZATION PROBLEMS; PREDICTION VARIANCES; RANDOM FIELDS; SPATIAL PROCESS; SPATIAL STOCHASTIC; STATISTICAL TECHNIQUES; TECHNICAL NOTES; VORONOI;

SENSOR NETWORKS;

EID: 59649106137     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2007179     Document Type: Article

References (16)

1. M. E. Johnson, L. M. Moore, and D. Ylvisaker, "Minimax and maximin distance designs," J. Stat. Planning Inference, vol. 26, pp. 131-148, 1990.
2. N. A. C. Cressie, Statistics for Spatial Data. New York: Wiley, 1993.
3. M. L. Stein, Interpolation of Spatial Data. Some Theory for Kriging New York: Springer Verlag, 1999.
4. F. Pukelsheim, Optimal Design of Experiments. Philadelphia, PA: SIAM, 2006, vol. 50.
5. E. P. Liski, N. K. Mandal, K. R. Shah, and B. K. Sinha, Topics in Optimal Design. New York: Springer Verlag, 2002, vol. 163.
6. J. S. Willcox, J. G. Bellingham, Y. Zhang, and A. B. Baggeroer, "Performance metrics for oceanographic surveys with autonomous underwater vehicles," IEEE J. Oceanic Eng., vol. 26, pp. 711-725, 2001.
7. K. M. Lynch, I. B. Schwartz, P. Yang, and R. A. Freeman, "Decentralized environmental modeling by mobile sensor networks," IEEE Trans. Robotics, vol. 24, no. 3, pp. 710-724, Jun. 2008.
8. S. Martínez, "Distributed representation of spatial fields through an adaptive interpolation scheme," in Proc. Amer. Control Conf., New York, NY, 2007, pp. 2750-2755.
9. N. E. Leonard, D. Paley, F. Lekien, R. Sepulchre, D. M. Fratantoni, and R. Davis, "Collective motion, sensor networks, and ocean sampling," Proc. IEEE, Special Issue Networked Control Syst., vol. 45, no. 1, pp. 48-74, Jan. 2007.
10. A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2 ed. New York: Wiley, 2000.
11. J. Cortés and F. Bullo, "Coordination and geometric optimization via distributed dynamical systems," SIAM J. Control Optim., vol. 44, no. 5, pp. 1543-1574, 2005.
12. R. Graham and J. Cortés, "Asymptotic Optimality of Multicenter Voronoi Configurations for Random Field Estimation," University of California, Santa Cruz, CA, Tech. Rep. ams2007-10, 2007 [Online]. Available: http://www.ams.ucsc.edu/research/report?ID=480
13. P. Abrahamsen, "A Review of Gaussian Random Fields and Correlation Functions," Norwegian Computing Center, Oslo, Norway, Tech. Rep. 917, 1997 [Online]. Available: http://publications.nr.no/917_Rapport.pdf
14. S. S. Wilks, "Certain generalizations in the analysis of variance," Biometrika, vol. 24, no. 3/4, pp. 471-494, 1932.
15. D. S. Bernstein, Matrix Mathematics. Princeton, NJ: Princeton University Press, 2005.
16. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides. Dordrecht, The Netherlands: Kluwer, 1988, vol. 18.