On the Definition and Existence of an MVU Estimator for Target Location Estimation

TL;DR

This paper investigates the existence of minimum variance unbiased (MVU) estimators for target location in one-dimensional space using binary detectors, revealing conditions under which MVU estimators exist or do not.

Contribution

It establishes the conditions for the existence of MVU estimators in censored and non-censored target localization scenarios, including the impact of known or unknown detection radius.

Findings

MVU estimator exists when detection radius is known and deployment region is large.

In censored case, MVU estimator exists even if detection radius is unknown.

In non-censored case, MVU estimator does not exist if detection radius is unknown.

Abstract

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.