Optimal distributed estimation in mobile ad hoc sensor networks

Consider a set of mobile wireless sensors that are embedded in devices that might, for example, be carried by pedestrians or vehicles that move about a city. A subset of these sensors may observe a localized event that occurs when they are all at approximately the same time/location. As they continue to move, the first one to take action based on its observations assumes the role of a Cluster-Head (CH) and floods the ad-hoc network with a request that all other sensors that collected observations of that event send in estimates related to some aspect of it.A BLUE estimator is used to fuse the individual estimates received by the CH. To ensure that these local estimates are unbiased, even if they are based on noisy observations and are relayed over multiple noisy wireless channels, we employ dithered quantization and channel compensation. We then determine the optimal number of bits for each sensor to transmit to minimize the energy the network uses to produce a BLUE with a specified MSE. The motion of each sensor determines how many hops its transmitted data traverses to reach the CH and thus how many bits it should transmit to the CH. We model this motion in the 1D case as a Correlated Random Walk (CRW). This allows us to precisely determine transient behavior, even with geographical restrictions and preferred directions of motion. We can then determine the energy, as a function of time, required to collect the estimates from all relevant sensors for the MSE of the final estimate to achieve a threshold. We demonstrate the capability of this approach by determining the minimum energy required to produce the estimate from a set of sensors that starts walking at one traffic light, spreads out in space, and then gathers together at the next traffic light.