Distributed Chernoff Test: Optimal decision systems over networks

In this work, we propose two different sequential and adaptive hypothesis tests, motivated from classic Chernoff's test, for both decentralized and distributed setup of sensor networks. In the former setup, the sensors can communicate via central entity i.e. fusion center. On the other hand, in the latter setup, sensors are connected via communication link, and no central entity is present to facilitate the communication. We compare the performance of these tests with the optimal consistent sequential test in the sensor network. In decentralized setup, the proposed test achieves the same asymptotic optimality of the classic one, minimizing the expected cost required to reach a decision plus the expected cost of making a wrong decision, when the observation cost per unit time tends to zero. This test is also asymptotic optimal in the higher moments of decision time. The proposed test is parsimonious in terms of communications as the expected number of channel uses required by each sensor, in the regime of vanishing observation cost per unit time, to complete the test converges to four.In distributed setup, the proposed test is evaluated on the same performance measures as the test in decentralized setup. We also provide sufficient conditions for which the proposed test in distributed setup also achieves the same asymptotic optimality as the classic one. Like the proposed test in decentralized setup, under these sufficient conditions, the proposed test in distributed setup is also asymptotic optimal in the higher moments of time required to reach a decision in the sensor network. This test is parsimonious is terms of communications in comparison to the state of art schemes proposed in the literature for distributed hypothesis testing.