Robust data fusion for multisensor detection systems

Minimax robust data fusion schemes for multisensor detection systems with discrete-time observations characterized by statistical uncertainty are developed and analyzed. Block, sequential, and serial fusion rules are considered. The performance measures used, and made robust with respect to the uncertainties, include the error probabilities of the hypothesis testing problem in the block fusion case and the error probabilities and expected numbers of samples or sensors in the sequential and serial fusion cases. For different sensor observation statistics, the minimax robust fusion rules are derived for two asymptotic cases of interest: when the number of sensors is large and when the number of times the fusion center collects the local (sensor) decisions is large. Moreover, for the case of identical sensor observation statistics and a large number of sensors, it is shown that there is no loss in optimality, if local tests using likelihood ratios and equal thresholds are used in the sequential fusion rule. In all situations, the robust decision rules at the sensors and the fusion center are shown to make use of likelihood ratios and thresholds that depend on the least-favorable probability distributions of the uncertainty class describing the statistics of sensor observations