On the existence of an MVU estimator for target localization with censored, noise-free binary detectors

The problem of target localization with censored, noise-free binary detectors is considered. In this setting only the detecting sensors report their locations to the fusion center. It is proven that if the radius of detection is unknown to the fusion center, a minimum variance unbiased (MVU) estimator does not exist. Also it is shown that when the radius is known the center of mass of the possible target region is the MVU estimator among estimators that are invariant under Euclidean motion. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. Moreover, for the case when the radius of detection is unknown a sub-optimum estimator is proposed that performs close to the Clairvoyant estimator. Furthermore, minimal sufficient statistics have been provided, both when the detection radius is known and when it is not. Simulations confirmed that the derived MVU estimator outperforms several heuristic location estimators.