VECTOR-SPACE METHODS FOR SENSOR FUSION PROBLEMS

In a multiple sensor system, the sensor S-j, j = 1, 2, ..., N, outputs Y-(j) is an element of R in response to input X is an element of [0,1 ], according to an unknown probability distribution P-y(j/X). The prob lem is to estimate a fusion function f:R-N bar arrow right [0, 1], bas ed on a training sample, such that the expected square error is minimi zed over a family of functions F that constitutes a finite-dimensional vector space. The function f that exactly minimizes the expected err or cannot be computed since the underlying distributions are unknown, and only an approximation (f) over cap to f is feasible, We estimate the sample size sufficiently to ensure that an estimator (f) over cap that minimizes the empirical square error provides a close approximati on to f with a high probability. The advantages of vector space metho ds are twofold: (1) the sample size estimate is a simple function of t he dimensionality of F and (2) the estimate (f) over cap can be easily computed by the well-known least square methods in polynomial time. T he results are applicable to the classical potential function method a s well as to a recently proposed class of sigmoidal feedforward neural networks. (C) 1998 Society of Photo-Optical instrumentation Engineers .