In wireless localization systems, location information with respect to anchors will be exposed to untrusted target or third party inevitably leading to location privacy leakage. Differential privacy based techniques can provide theoretical guarantee to privacy preservation, while such privacy preservation will degrade localization accuracy. We note that the quantitative relationship between localization accuracy and privacy level is still unclear. In this paper, we derive the Cramér-Rao lower bound (CRLB) about the target location when the anchors take a privacy preservation mechanism satisfying geo-indistinguishability, which is an application of differential privacy on Euclidean metric. The closed-form relationship between the target localization accuracy and the anchors’ location privacy level is provided respectively for range-only and bearing-only localization. Numerical results in further verify our theoretical results.

中文翻译：

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无线定位系统中定位精度与位置隐私等级的定量关系

在无线定位系统中，锚点的位置信息会暴露给不可信的目标或第三方，不可避免地导致位置隐私泄露。基于差分隐私的技术可以为隐私保护提供理论保障，但这种隐私保护会降低定位精度。我们注意到定位精度和隐私级别之间的定量关系仍不清楚。在本文中，我们推导出了当锚点采用满足地理不可区分性的隐私保护机制时关于目标位置的 Cramér-Rao 下界（CRLB），这是差分隐私在欧几里德度量上的应用。目标定位精度和锚点位置隐私级别之间的封闭关系分别为仅范围和仅轴承定位提供。数值结果进一步验证了我们的理论结果。