Quantitative Relationship Between Localization Accuracy and Location Privacy Level in Wireless Localization System

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.