Multiple sensor fusion under unknown distributions

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In a system of N sensors, the sensor {ital S{sub i}}, i = 1, 2 ..., N, outputs {ital Y}{sup (i)} {element_of} {Re}, according to an unknown probability distribution P{sub Y{sup (i)}}{vert_bar}X, corresponding to input X {element_of} {Re}. A training {ital n}-sample (X{sub 1}, Y{sub 1}), (X{sub 2},Y{sub 2}), ..., (X{sub n},Y{sub n}) is given where {ital Y{sub i}} = (Y{sub i}{sup (1)},Y{sub i}{sup (2)},...,Y{sub i}{sup (N)}) such that Y{sub i}{sup (j)} is the output of S{sub j} in response to input X{sub i}. The problem is to design a fusion rule expected square error: I({ital f}) = {integral}[X - ... continued below

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11 p.

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Rao, N.S.V. October 1, 1996.

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Description

In a system of N sensors, the sensor {ital S{sub i}}, i = 1, 2 ..., N, outputs {ital Y}{sup (i)} {element_of} {Re}, according to an unknown probability distribution P{sub Y{sup (i)}}{vert_bar}X, corresponding to input X {element_of} {Re}. A training {ital n}-sample (X{sub 1}, Y{sub 1}), (X{sub 2},Y{sub 2}), ..., (X{sub n},Y{sub n}) is given where {ital Y{sub i}} = (Y{sub i}{sup (1)},Y{sub i}{sup (2)},...,Y{sub i}{sup (N)}) such that Y{sub i}{sup (j)} is the output of S{sub j} in response to input X{sub i}. The problem is to design a fusion rule expected square error: I({ital f}) = {integral}[X - f (Y)]{sup 2}dP{sub y{vert_bar}X}dPx, where Y=(Y{sup (1)}, Y{sup (2)},..., Y({sup N)}),is minimized over a family of functions {ital F}. Let f{sup *} minimize I(.) over {ital F}; in general, f{sup *} cannot be computed since the underlying distributions are unknown. We consider sufficient conditions based on smoothness and/or combinatorial dimensions of {ital F} to ensure that an estimator {cflx {ital f}} satisfies P[I({cflx {ital f}}) - I(f{sup *}) > {epsilon}] < {delta} for any {epsilon} > 0 and 0 < {delta} < 1. We present two methods for computing {cflx {ital f}} based on feedforward sigmoidal networks and Nadaraya-Watson estimator. Design and performance characteristics of the two methods are discussed, based both on theoretical and simulation results.

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11 p.

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OSTI as DE96014690

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  • Workshop on foundations of information/decision fusion, Arlington, VA (United States), 7-9 Aug 1996

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  • Other: DE96014690
  • Report No.: CONF-9608144--1
  • Grant Number: AC05-96OR22464
  • Office of Scientific & Technical Information Report Number: 391704
  • Archival Resource Key: ark:/67531/metadc682720

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  • October 1, 1996

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  • July 25, 2015, 2:20 a.m.

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  • Jan. 22, 2016, 12:18 p.m.

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Rao, N.S.V. Multiple sensor fusion under unknown distributions, article, October 1, 1996; Tennessee. (digital.library.unt.edu/ark:/67531/metadc682720/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.