Topics in Decentralized Detection By

In this thesis we obtain several new results in the areas of decentralized sequential detection and robust decentralized detection. In the area of decentralized sequential detection, we first consider the case in which each sensor performs a sequential test on its observations and arrives at a local decision about the true hypothesis; subsequently, the local decisions of all of the sensors are used for a common purpose. Here we assume that decision errors at the sensors are penalized through a common cost function and that each time step taken by the detectors as a team is assigned a positive cost. We show that optimal sensor decision functions can be found in the class of generalized sequential probability ratio tests with monotonically convergent thresholds. We present a technique for obtaining optimal thresholds. We also consider the case in which each sensor sends a sequence of summary messages to a fusion center in which a sequential test is carried out to determine the true hypothesis. Here we assume that decision errors at the fusion center are penalized through a cost function and that each time step taken to arrive at the final decision costs a positive amount. We show that the problem is tractable when the information structure in the system is quasiclassical. In particular, we show that an optimal fusion center policy has a simple structure resembling a sequential probability ratio test and that a stationary set of monotone likelihood ratio tests is optimal at the sensors. Finally, we compute the optimal decision functions for some representative examples. In the area of robust decentralized detection, we consider the case in which the sensor distributions are assumed to belong to known uncertainty classes. We show for a broad class of such decentralized detection problems that a set of least favorable distributions exists for minimax robust testing between the hypotheses. We thus establish that minimax robust tests are obtained as solutions to simple decentralized detection problems in which the sensor distributions are specified to be the least favorable distributions. iv ACKNOWLEDGEMENTS First and foremost, I would like to thank my advisors, Professor T. Ba¸sar and Professor H. V. Poor, for their guidance and support throughout my graduate work at the University of Illinois. I would also like to thank the other members of my thesis committee, Professors B. Hajek, S. Meyn and K. Jenkins, for many helpful and stimulating discussions. Thanks are also …