Binary Hypothesis Testing by Two Collaborating Observers: A Fresh Look

TLDR: This work considers the binary hypothesis testing problem with two observers and presents three different approaches to address the problem, taking into account the asymmetric and random stopping times of the observers.

Abstract: We consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations are collected by two observers. The observations are statistically related to the true state of nature. Given the observations, the objective of both observers is to find out what is the true state of nature. We present three different approaches to address the problem. In the first (centralized) approach, the observations collected by both observers are sent to a central coordinator where hypothesis testing is performed. In the second approach, each observer performs hypothesis testing based on locally collected observations. At every time step decision information is exchanged until consensus is achieved. In the third approach, sequential hypothesis testing problem is formulated for each observer. The sequential hypothesis testing problem is solved for each observer using locally collected observations. Taking into account the asymmetric and random stopping times of the observers, a consensus algorithm has been designed. Numerical study has been done to assess the performance of the three approaches.