On the Definition and Existence of a Minimum Variance Unbiased Estimator for Target Localization

Abstract

The problem of target localization with ideal, binary detectors is considered in one-dimensional space for both the censored and noncensored scenarios. In the censored setting, the problem is equivalent to estimating the center of a uniform distribution, and does not admit a minimum-variance unbiasedestimator (MVUE). However, it is proven that if the detection range is known and the sensor deployment region is large, both censored and noncensored cases will have an MVUE within the class of functions that are invariant to Euclidean motion. In addition, it is shown that when the detection range is unknown, for the censored case one can still form an MVUE whereas in the noncensored case, an MVUE does not exist. Numerical tests support the theoretical findings of this letter.