Universal decentralized estimation in a bandwidth constrained sensor network

Consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval [-U,U]. Each sensor collects one noise-corrupted sample, performs a local estimation, and transmits a message to the fusion center, while the latter combines the received messages to produce a final estimate. This correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one-bit message. Such a binary message constraint is well motivated by the bandwidth limitation of the communication links, fusion center, and by the limited power budget of local sensors. In the absence of bandwidth constraint and assuming the noises are bounded to the interval [-U,U], additive, independent, but otherwise unknown, the classical estimation theory suggests that a total of O(U²/epsi²) sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error (MSE). It is shown in this correspondence that the same remains true even with the binary message constraint. Furthermore, the optimal decentralized estimation scheme suggests allocating 1/2 of the sensors to estimate the first bit of the unknown parameter, 1/4 of the sensors to estimate the second bit, and so on