Privacy in Location-Based Services (LBS) has become a paramount concern with the ubiquity of mobile devices and the increasing integration of location data into various applications. In this paper, we present several novel contributions aimed at advancing the understanding and management of privacy leakage in LBS. Our contributions provides a more comprehensive framework for analyzing privacy concerns across different facets of location-based interactions. Specifically, we introduce $(\epsilon, \delta)$-location privacy, $(\epsilon, \delta, \theta)$-trajectory privacy, and $(\epsilon, \delta, \theta)$-POI privacy, which offer refined mechanisms for quantifying privacy risks associated with location, trajectory, and points of interest when continuously interacting with LBS. Furthermore, we establish fundamental connections between these privacy notions, facilitating a holistic approach to privacy preservation in LBS. Additionally, we present a lower bound analysis to evaluate the utility of the proposed privacy-preserving mechanisms, offering insights into the trade-offs between privacy protection and data utility. Finally, we instantiate our framework with the Plannar Isotopic Mechanism to demonstrate its practical applicability while ensuring optimal utility and quantifying privacy leakages across various dimensions. The conducted evaluations provide a comprehensive insight into the efficacy of our framework in capturing privacy loss on location, trajectory, and Points of Interest (POI) while facilitating quantification of the ensured accuracy.

翻译：随着移动设备的普及以及位置数据在各类应用中日益深入的整合，基于位置服务（LBS）中的隐私问题已成为一项关键考量。本文提出若干创新性贡献，旨在推进对LBS隐私泄露的理解与管理。我们的贡献构建了一个更全面的框架，用于分析基于位置交互中不同层面的隐私问题。具体而言，我们引入了$(\epsilon, \delta)$-位置隐私、$(\epsilon, \delta, \theta)$-轨迹隐私以及$(\epsilon, \delta, \theta)$-兴趣点隐私，这些概念为在持续与LBS交互时量化与位置、轨迹及兴趣点相关的隐私风险提供了精细化机制。此外，我们建立了这些隐私概念之间的基本联系，促进了LBS隐私保护中的整体性方法。同时，我们通过下界分析评估所提隐私保护机制的效用，深入揭示了隐私保护与数据效用之间的权衡关系。最后，我们以平面各向同性机制实例化所提框架，在确保最优效用的同时，展示了其在多维度量化隐私泄露方面的实际应用性。所进行的评估全面揭示了本框架在捕获位置、轨迹及兴趣点（POI）隐私损失方面的有效性，并支持对所保证精度的量化分析。