Asymptotically optimum tests for decentralized sequential testing in continuous time

We propose an asymptotically optimum test for the problem of decentralized sequential hypothesis testing in continuous time, in the case where the sensors have full local memory and no feedback from the fusion center. According to our scheme, the sensors perform locally repeated SPRTs and communicate, asynchronously, their one-bit decisions to the fusion center. The fusion center in turn uses the received information to perform a centralized SPRT in order to make the final decision. The expected time for a decision of the proposed scheme differs from the optimum continuous-time centralized SPRT only by a constant. This fact suggests order-2 asymptotic optimality of our test as compared to existing schemes that are optimal of order-1. Moreover, simulation experiments reveal that the performance of our scheme is significantly better than that of the discrete-time centralized SPRT.