Multiple sensor fusion under unknown distributions

The sensor S_i, i = 1,2,..., N, of a multiple sensor system outputs Y⁽ⁱ⁾∈ ℛ, according to an unknown probability distribution P_Y(i)_|x, in response to input X ∈ ℛ. The problem is to design a fusion rule f:ℛ^N → 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* ∈ ℱ 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.