The problem of target localization with ideal binary detectors is considered in one dimensional space. The problem is investigated in both a censored and non-censored scheme. In the censored setting, the problem is equivalent to estimating the center of a uniform distribution by knowing samples of data. It does not admit an MVU estimator according to the previous results of Lehmann-Sheffe. However, it is proven that if the radius of detection is known and sensor deployment region is very large, both censored and non-censored cases will have an MVU estimator among the functions that are invariant to Euclidean motion. In addition, it is shown that when the radius of detection is not known, the censored case still has an MVU estimator whereas in the non-censored case, an MVU estimator does not exist, even under the assumption that the estimators are invariant to Euclidean motion.