On the Existence of an MVU Estimator for Target Localization with Censored, Noise Free Binary Detectors

TL;DR

This paper investigates the existence and properties of minimum variance unbiased estimators for target localization using censored binary sensors, revealing conditions for their existence and proposing practical alternatives.

Contribution

It proves the non-existence of MVU estimators when detection radius is unknown and introduces a sub-optimal estimator with near-MVU performance.

Findings

MVU estimator exists only when detection radius is known

Center of mass of the feasible region is the MVU when radius is known

Proposed sub-optimal estimator performs close to MVU in simulations

Abstract

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 not known 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. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. 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.