Minimax Robust Decentralized Detection in Parallel Sensor Networks

TL;DR

This paper investigates minimax robust decentralized detection in parallel sensor networks, demonstrating the possibility of detection without the joint stochastic boundedness property and generalizing previous work.

Contribution

It extends existing theories by showing robust detection is feasible without the joint stochastic boundedness property and relaxes the monotonicity requirement for sensor quantization functions.

Findings

Robust detection possible without joint stochastic boundedness.

Quantization functions at sensors need not be monotone.

Provided specific examples and discussed potential generalizations.

Abstract

Minimax robust decentralized detection is studied for parallel sensor networks. Random variables corresponding to sensor observations are assumed to follow a distribution function, which belongs to an uncertainty class. It has been proven that, for some uncertainty classes, if all probability distributions are absolutely continuous with respect to a common measure, the joint stochastic boundedness property, which is the fundamental rule for the derivations in Veerevalli's work, does not hold. This raises a natural question whether minimax robust decentralized detection is possible if the uncertainty classes do not own this property. The answer to this question has been shown to be positive, which leads to a generalization of the work of Veerevalli. Moreover, due to a direct consequence of Tsitsiklis's work, quantization functions at the sensors are not required to be monotone. For the proposed model, some specific examples have been provided and possible generalizations have been discussed.