One shot schemes for decentralized quickest change detection

  • Authors:

  • Olympia Hadjiliadis;Hongzhong Zhang;H. Vincent Poor

  • Affiliations:

  • Department of Mathematics, Brooklyn College and the Department of Computer Science, Graduate Center of the City University of NewYork, NewYork, NY and Department of Mathematics;Department of Mathematics, the Graduate Center of the City University of New York, New York, NY;Department of Electrical Engineering, Princeton University, Princeton, NJ

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

Quantified Score

Hi-index 754.90

Visualization

Abstract

This work considers the problem of quickest detection with N distributed sensors that receive sequential observations either in discrete or in continuous time from the environment. These sensors employ cumulative sum (CUSUM) strategies and communicate to a central fusion center by one shot schemes. One shot schemes are schemes in which the sensors communicate with the fusion center only once, via which they signal a detection. The communication is clearly asynchronous and the case is considered in which the fusion center employs a minimal strategy, which means that it declares an alarm when the first communication takes place. It is assumed that the observations received at the sensors are independent and that the time points at which the appearance of a signal can take place are different. Both the cases of the same and different signal distributions across sensors are considered. It is shown that there is no loss of performance of one shot schemes as compared to the centralized case in an extended Lorden min-max sense, since the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound. In the case of different signal distributions the optimal threshold parameters are explicitly computed.