Distributed Sequential Detection for Gaussian Shift-in-Mean Hypothesis Testing
For multi-agent networks performing sequential hypothesis testing, this work provides a distributed algorithm with theoretical guarantees on error performance and stopping times, though it is an incremental extension of existing consensus+innovations methods to a specific problem.
This paper proposes a distributed sequential probability ratio test (SPRT) algorithm for Gaussian shift-in-mean hypothesis testing in multi-agent networks. The algorithm achieves desired error probabilities and finite-time termination, with asymptotic performance approaching that of the optimal centralized detector in terms of large deviation exponents and expected stopping times.
This paper studies the problem of sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network. A sequential probability ratio test (SPRT) type algorithm in a distributed framework of the \emph{consensus}+\emph{innovations} form is proposed, in which the agents update their decision statistics by simultaneously processing latest observations (innovations) sensed sequentially over time and information obtained from neighboring agents (consensus). For each pre-specified set of type I and type II error probabilities, local decision parameters are derived which ensure that the algorithm achieves the desired error performance and terminates in finite time almost surely (a.s.) at each network agent. Large deviation exponents for the tail probabilities of the agent stopping time distributions are obtained and it is shown that asymptotically (in the number of agents or in the high signal-to-noise-ratio regime) these exponents associated with the distributed algorithm approach that of the optimal centralized detector. The expected stopping time for the proposed algorithm at each network agent is evaluated and is benchmarked with respect to the optimal centralized algorithm. The efficiency of the proposed algorithm in the sense of the expected stopping times is characterized in terms of network connectivity. Finally, simulation studies are presented which illustrate and verify the analytical findings.