Multiple sensor fusion under unknown distributions

The sensor S-i, i = 1, 2,..., N, of a multiple sensor system outputs Y-(i) is an element of R, according to an unknown probability distribution P-Y(i\ X), in response to input X is an element of R. The problem is to design a f usion rule f:R-N bar right arrow R, based on a training sample, such that t he expected square error I(f)= E[(X-f(Y))(2)] is minimized over a family of functions F. In general, f* is an element of F that minimizes I(.) cannot be computed since the underlying distributions are unknown. We consider suf ficient conditions and algorithms to compute an estimator (f) over cap such that I((f) over cap) - I(F*) < epsilon with probability 1 - delta, for any epsilon > 0 and 0 < delta < 1. We present a general method for obtaining ( f) over cap based on the scale-sensitive dimension of F. We then review thr ee recent computational methods based on the feedforward sigmoidal networks , the Nadaraya-Watson estimator, and the finite-dimensional vector spaces. (C) 1998 The Franklin Institute. Published by Elsevier Science Ltd.