Optimal Distributed Detection in Clustered Wireless Sensor Networks: The Weighted Median

− In a clustered, multi-hop sensor network, a large number of inexpensive, geographically-distributed sensor nodes each use their observations of the environment to make local hard (0/1) decisions about whether an event has occurred. Each node then transmits its local decision over one or more wireless hops to the clusterhead. When all local decisions have been gathered by the clusterhead, it fuses them into a final hard decision about the event. Two sources of error affect the clusterhead’s final decision: (i) local decision errors made by the sensor nodes because of noisy measurements or unreliable sensors, and (ii) bit errors affecting each hop on the wireless communication channel. Previous work assumed error-free communication or a single-hop cluster. We show that if both of these sources of error are considered, then the optimal data fusion algorithm at the clusterhead is a weighted median. The optimal weights are shown to be functions of the bit error probability of the channel and the ring from which the local decision originated. We determine: the error probability of this optimal fusion algorithm; the effect of adding more nodes or rings to the cluster; and the tradeoff between energy consumed in the network and the decision error probability. This paper thus provides tools to add the effect of measurement and communication errors to other tradeoffs in the design of clustered sensor networks.