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Information Fusion Methods Based on Physical Laws
January 2005 (vol. 27 no. 1)
pp. 66-77
We consider systems whose parameters satisfy certain easily computable physical laws. Each parameter is directly measured by a number of sensors, or estimated using measurements, or both. The measurement process may introduce both systematic and random errors which may then propagate into the estimates. Furthermore, the actual parameter values are not known since every parameter is measured or estimated, which makes the existing sample-based fusion methods inapplicable. We propose a fusion method for combining the measurements and estimators based on the least violation of physical laws that relate the parameters. Under fairly general smoothness and nonsmoothness conditions on the physical laws, we show the asymptotic convergence of our method and also derive distribution-free performance bounds based on finite samples. For suitable choices of the fuser classes, we show that for each parameter the fused estimate is probabilistically at least as good as its best measurement as well as best estimate. We illustrate the effectiveness of this method for a practical problem of fusing well-log data in methane hydrate exploration.

[1] M. Anthony and P.L. Bartlett, Neural Network Learning: Theoretical Foundations. Cambridge Univ. Press, 1999.
[2] T.M. Apostol, Mathematical Analysis. Addison-Wesley, 1974.
[3] P. Billingsley, Probability and Measure, second ed. New York: John Wiley and Sons, 1986.
[4] Scientific Results from JAPEX/JNOC/GSC Mallik 2L-38 Gas Hydrate Research Well, Mackenzie Delta: Geological Survey of Canada Bulletin 544, Geological Survey of Canada, S.R. Dallimore, T. Uchida, and T.S. Collett, eds., 1999.
[5] B.V. Dasarathy, Decision Fusion. Los Alamitos, Calif.: IEEE CS Press, 1994.
[6] D. Haussler, “Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications,” Information and Computation, vol. 100, pp. 78-150, 1992.
[7] Multiple Classifier Systems, J. Kittler and F. Roli, eds., Berlin: Springer-Verlag, 2002.
[8] A. Krzyzak, T. Linder, and G. Lugosi, “Nonparametric Estimation and Classification Using Radial Basis Function Nets and Empirical Risk Minimization,” IEEE Trans. Neural Networks, vol. 7, no. 2, pp. 475-487, 1996.
[9] K.A. Kvenvolden, “A Primer on the Geological Occurrence of Gas Hydrate,” Gas Hydrates: Relevance to World Margin Stability and Climate Change, J.P. Hemriet and J.Mienert, eds., vol. 137, pp. 9-30, 1998.
[10] G. Mavko, T. Mukerji, and J. Dvorkin, The Rock Physics Handbook: Tools for Seismic Analysis in Porus Media. Cambridge Univ. Press, 1998.
[11] M. Miyairi, K. Akihisa, T. Uchida, T.S. Collett, and S.R. Dallimore, “Well-Log Interpretation of Gas-Hydrate-Bearing Formations in the JAPEX/JNOC/GSC Mallik 2L-38 Gas Hydrate Research Well,” Scientific Results from JAPEX/JNOC/GSC Mallik 2L-38 Gas Hydrate Research Well, Mackenzie Delta: Geological Survey of Canada Bulletin 544, pp. 281-293, 1999.
[12] D. Pollard, Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.
[13] B.L.S. Prakasa Rao, Nonparametric Functional Estimation. New York: Academic Press, 1983.
[14] N.S.V. Rao, “Multiple Sensor Fusion under Unknown Distributions,” J. Franklin Inst., vol. 336, no. 2, pp. 285-299, 1999.
[15] N.S.V. Rao, “Projective Method for Generic Sensor Fusion Problem,” Proc. IEEE/SICE/RSJ Int'l Conf. Multisensor Fusion and Integration for Intelligent Systems, pp. 1-6, 1999.
[16] N.S.V. Rao, “Simple Sample Bound for Feedforward Sigmoid Networks with Bounded Weights,” Neurocomputing, vol. 29, pp. 115-122, 1999.
[17] N.S.V. Rao, “Finite Sample Performance Guarantees of Fusers for Function Estimators,” Information Fusion, vol. 1, no. 1, pp. 35-44, 2000.
[18] N.S.V. Rao, “On Design and Performance of Metafusers,” Proc. Workshop Estimation, Tracking, and Fusion, pp. 259-268, 2001.
[19] N.S.V. Rao, “On Fusers that Perform Better than Best Sensor,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 8, pp. 904-909, Aug. 2001.
[20] N.S.V. Rao, “Multisensor Fusion under Unknown Distributions: Finite Sample Performance Guarantees,” Multisensor Fusion, A.K. Hyder, E. Shahbazian, and E. Waltz, eds., Kluwer Academic, 2002.
[21] N.S.V. Rao, “Nearest Neighbor Projective Fuser for Function Estimation,” Proc. Int'l Conf. Information Fusion, 2002.
[22] N.S.V. Rao, E.M. Oblow, C.W. Glover, and G.E. Liepins, “N-Learners Problem: Fusion of Concepts,” IEEE Trans. Systems, Man, and Cybernetics, vol. 24, no. 2, pp. 319-327, 1994.
[23] L.G. Valiant, “A Theory of the Learnable,” Comm. ACM, vol. 27, no. 11, pp. 1134-1142, 1984.
[24] V. Vapnik, Estimation of Dependences Based on Empirical Data. New York: Springer-Verlag, 1982.
[25] V.N. Vapnik, The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995.
[26] P.K. Varshney, Distributed Detection and Data Fusion. Springer-Verlag, 1997.

Index Terms:
Information fusion, distribution free bounds, covering numbers, sensor fusion, Vapnik-Chervonenkis theory, physical laws, methane hydrates exploration.
Citation:
Nageswara S.V. Rao, David B. Reister, Jacob Barhen, "Information Fusion Methods Based on Physical Laws," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 1, pp. 66-77, Jan. 2005, doi:10.1109/TPAMI.2005.12
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