1 March 1997 Nadaraya-Watson estimator for sensor fusion
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Abstract
In a system of N sensors, the sensor Sj , j=1,2, . . . ,N, outputs Y(j ) ? [0,1], according to an unknown probability density pj (Y(j |)uX), corresponding to input X P ?[0,1]. A training n-sample (X1 ,Y1),(X2 ,Y2), . . . ,(Xn ,Yn) is given where Yi5(Y i (1) ,Y i (2) , . . . , Y i(N)) such that Y i (j ) is the output of Sj in response to input Xi . The problem is to estimate a fusion rule f :[0,1]N? [0,1], based on the sample, such that the expected square error I (f ) = ?[X-f(Y)]2p(Y|X)dY(1) dY(2). . . dY(N)dx is minimized over a family of functions F with uniformly bounded modulus of smoothness, where Y=(Y(1),Y(2), . . . ,Y(N)). Let f* minimize I (.) over F ; f* cannot be computed since the underlying densities are unknown. We estimate the sample size sufficient to ensure that Nadaraya-Watson estimator f satisfies P[I(f )- I (f*)> ?.] ? for any ?>0 and ?, 0
Nageswara S. V. Rao, Nageswara S. V. Rao, } "Nadaraya-Watson estimator for sensor fusion," Optical Engineering 36(3), (1 March 1997). https://doi.org/10.1117/1.601136 . Submission:
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