In a multiple sensor system, the sensor S{sub}j, j=1,2,..., N, outputs Y{sup}(j)∈R in response to input X∈[0,1], according to an unknown probability distribution P{sub}Y{sup}(j){sub}｜{sub}X. The problem is to estimate a fusion functionf:R{sup}N→[0,1], based on a training sample, such that the expected square error is minimized over a family of functions , J that constitutes a finite-dimensional vector space. The function f* that exactly minimizes the expected error cannot be computedsince the underlying distributions are unknown, and only an approximation f to f* is feasible. We estimate the sample size sufficiently to ensure that an estimator f that minimizes the empirical square error provides a close approximation to f* with ahigh probability. The advantages of vector space methods are twofold: (1) the sample size estimate is a simple function of the dimensionality of J and (2) the estimate f can be easily computed by the well-known least square methods in polynomial time. The results are applicable to the classical potential function method as well as to a recently proposed class of sigmoidal feedforward neural networks.
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