On sample-based implementation of non-smooth decision fusion functions

A number of optimal fusion functions have been derived in the literature for multiple detection systems based on a complete knowledge of the detector distributions. In several practical systems, however, only measurements are available. A general result was recently shown that any fusion function with a suitable Lipschitz property derived under the complete knowledge of the distributions can be converted into a measurement-based one. While this result subsumes the well-known cases of independent and correlated detectors, it is not applicable to discontinuous fusion rules which often arise in practice. In this paper, we show that any fusion function with bounded variation can be converted into a measurement-based one with a somewhat weaker guarantee. These fusion functions subsume Lipschitz as well as several discontinuous fusion functions. In particular we show that given a sufficiently large sample, the measurement-based fusion function performs almost as well as the optimal one with an arbitrarily specified confidence.