FUSION METHODS FOR MULTIPLE SENSOR SYSTEMS WITH UNKNOWN ERROR DENSITIES

Consider that the sensor S-i, i = 1, 2,...,N, output y((i)) is an elem ent of R(d), according to an unknown probability density p(i)(y(i)\x), corresponding to an object with parameter x is an element of R(d). Fo r the system of N sensors, S-1, S-2,...,S-N, a training l-sample (x1,y 1), (x2,y2),...,(x is to minimized over a family of fusion rules F bas ed on the given l-sample. Let f is an element of F minimize I(f). In general, f cannot be computed since the underlying probability densit ies are unknown. Using V apnik's empirical risk minimization method, w e show that if F has finite capacity, then under bounded error conditi on, for sufficiently large sample, ($) over cap f can be obtained such that for arbitrarily specified epsilon > 0 and delta, 0 < delta < 1. We obtain similar conditions for the case when F is a set of Lipschitz continuous functions with a fixed constant, these conditions are appl icable to feedforward neural networks with a particular with a particu lar type of sigmoidal units. Then we identify sufficiency conditions f or the composite system (of fuser and sensors) to be better than the b est of the individual sensors. We then discuss linearly separable syst ems to identify objects from a finite class where ($) over cap f can b e computed in polynomial time using quadratic programming methods.