On Minimax Robust Data Fusion.

Abstract

In this paper, minimax robust data fusion schemes based on discrete-time observations with statistical uncertainty are considered. The observations are assumed to be i.i.d and the decisions of all sensors independent when conditioned on the either of two hypotheses. The statistics of the observations are only known to belong to uncertainty classes determined by 2- alternating Choquet capacities. Both cases of fixed sample-size (block) data fusion and sequential data fusion are examined. For specific performance measures, three robust fusion rules: suboptimal, optimal and asymptotically optimal - as the number of sensors increases - are derived for the block data fusion case, and an asymptotically robust fusion rule is derived for the sequential data fusion case; these fusion rules are optimal in the class of rules employing likelihood ratio tests. In all situations the robust fusion rule makes use of likelihood ratios and thresholds which depend on the least-faborable probability distributions in the uncertainty class. In the limit of a large number of sensors, it is shown that the same threshold can be used by all sensors, which in turn simplifies the overall computation.