Multiple sensor fusion under unknown distributions

The sensor Si, i=1, 2, T20…, N, of a multiple sensor system outputs Y(i)∈R, according to an unknown probability distribution PY(i)∣X, in response to input X∈R. The problem is to design a fusion rule f :RN↦R, based on a training sample, such that the expected square error I( f )=E[(X−f (Y))2] is minimized over a family of functions F. In general, f ∗ϵF that minimizes I(.) cannot be computed since the underlying distributions are unknown. We consider sufficient conditions and algorithms to compute an estimator f̂ such that I( f̂ )−I( f ∗)<ε with probability 1−δ, for any ε>0 and 0<δ<1. We present a general method for obtaining f̂ based on the scale-sensitive dimension of F. We then review three recent computational methods based on the feedforward sigmoidal networks, the Nadaraya–Watson estimator, and the finite-dimensional vector spaces.