Randomized Sensor Selection in Sequential Hypothesis Testing

TL;DR

This paper studies sensor selection strategies for sequential hypothesis testing, showing that optimal detection can often be achieved by observing only a small subset of sensors, even in complex scenarios.

Contribution

It introduces a class of simple, asymptotically optimal sequential tests that require observing at most two sensors for binary hypotheses and as many as the number of hypotheses for multiple hypotheses.

Findings

Fusion center needs to consider at most two sensors for binary hypotheses.

Optimal policy observes at most as many sensors as the number of hypotheses.

Proposed tests are easy to implement, asymptotically optimal, and computationally efficient.

Abstract

We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. We consider the class of sequential tests which are easy to implement, asymptotically optimal, and computationally amenable. For three distinct performance metrics, we show that, for a generic set of sensors and binary hypothesis, the fusion center needs to consider at most two sensors. We also show that for the case of multiple hypothesis, the optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses.