# Distributed Detection

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## Abstract

Connexions module: m11233 1 Distributed Detection ∗ Don Johnson This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License 1.0 † So far, we have derived a detector's computational structure for a given problem from the likelihood ratio. In some cases, we need to structure the detector to meet real-world constraints of how we make observations and where decisions must be made. One particular structure that has received much attention is the distributed structure shown in Figure 1. Figure 1: The generic distributed detection has sensors gathering observations, making decisions µn , and sending them to the fusion center that makes the final decision. Here, observations that reflect the same model are made at several locations, what we call sensors. Let the number of sensors be N and let each sensor's observation be of the form Mi : rn = si + nn, n ∈ {0, . . . , N − 1} with the noise at each sensor statistically independent of the others. Each sensor makes a decision about its local observations and sends these hard decisions to "headquarters," the fusion center, which assimilates all the decisions and makes a final decision as to which model applies best. This decision structure is optimal: examples can be easily found where a smaller probability of error would result if each sensor sent its likelihood ratio rather than its decision. We want to understand the consequences and design of this simpler but suboptimal structure. Let µn ∈ {0, 1}, n ∈ {1, . . . , N} denote each sensor's decision (however it is made) as to which model described its observations best. The fusion center makes its decision based on the likelihood ratio formed from ∗ Version 1.5: Aug 22, 2003 11:14 am -0500 † http://creativecommons.org/licenses/by/1.0 http://cnx.org/content/m11233/1.5/ Connexions module: m11233 2 the sensor decision variables. Because each sensor's observations and their decision processes are statisticall

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