A Signaling Problem Arising in Decentralized Detection.
MICHIGAN UNIV ANN ARBOR COMMUNICATIONS AND SIGNAL PROCESSING LAB
Pagination or Media Count:
An unknown object, called H, moves across two detectors, called D sub 1 and D sub 2, which take noisy measurements of the object. Based on these measurements D sub 1 and D sub 2 must collectively decide which of the two possible values, 0 or 1, H actually takes. H first travels across the field of view of D sub 1 which starts taking measurements at time 0. At some time tau sub 1 which must occur before an a priori fixed time T, D sub 1 must summarize its information into a single bit u sub 1 is an element of 0,1 and instantaneously and accurately transmit it to D sub 2. Upon receiving U sub 1 is an element of 0,1, D sub 2 starts taking its own observation. At some subsequent time tau sub 2 or tau sub 1, D sub 2 declares that H is u sub 2. The detectors must select their decision rules to minimize a cost due to their observations and the terminal cost associated with D sub 2s decision U sub 2. The problem faced by each detector is separately analyzed. Detector D sub 2s problem is a standard optimal stopping problem, whereas detector D sub 1s problem is related to the optimal real-time encoding of Markov processes. It is shown that the detectors optimal decision rules are characterized by thresholds.
- Operations Research