Invariant Sequential Detection and Recognition of Targets in Distributed Systems

The sequential testing of many hypotheses is important for a variety of applications including detection and recognition of targets by multiple-resolution-element radar and infrared systems. In this paper, we consider a distributed multisensor system in which each sensor tests a finite number of composite hypotheses in a sequential manner. Then the decisions are transmitted to a fusion center, which combines them to improve the performance of the system. First, we study the behavior of an invariant sequential test for many composite hypotheses assuming that distributions of observations under each hypothesis are not exactly known due to the presence of nuisance parameters. In particular, we show that, under certain general conditions, the proposed sequential test is asymptotically optimal in the sense that it minimizes any positive moment of the stopping time distribution when error probabilities are small. Then, general results are applied to the problem of target detection-identification in a multi-sensor, multi-channel system. We consider two statistical models which frequently arise in the target detection area. The first model is related to the detection of a non-fluctuating target in the presence of clutter with unknown mean and variance. The second problem is detection of a slowly fluctuating target in white Gaussian noise with unknown variance. Finally, we use a nonsequential fusion rule for fusion of local decisions. This fusion rule waits until all the local decisions in all sensors are made and then fuses them. It is optimal in the sense of maximizing the average probability of correct target detection-identification for a given false alarm rate. ∗Supported in part by the U.S. ONR grants N00014-99-1-0068 and N00014-95-1-0229. †Supported in part by ONR via grant N00014-00-1-0677 and by NSF via Grant ECS-9734285. ‡Supported in part by the U.S. ONR grants N00014-99-1-0068 and N00014-95-1-0229.