The Effects of Motion on Distributed Detection in Mobile Ad Hoc Sensor Networks

We consider a set of mobile wireless sensors that collect observations about a brief, localized event. As they continue to move about, one of them processes its observations, decides that an event of interest occurred, and wants to determine if other sensors confirm its results. This sensor assumes the role of a Cluster Head (CH) and requests that all other sensors that collected observations at that time/location reply to it with their decisions. The motion of the sensors since the observation time determines how many wireless hops their decision must cross to reach the CH. We analyze the effect of this motion in the 1D case by modeling each sensor's motion as a Correlated Random Walk (CRW). We also account for measurement errors and communication or processing errors in each wireless hop. Quantities, such as the error probability of the final decision at the CH and the minimum energy required to collect the local decisions from all relevant sensors, can then be directly calculated as functions of time and the parameters of the CRW, the measurement noise and the channel noise. These results allow rapid characterization of the time-dependence of distributed detection algorithms that are executed in mobile sensor networks.