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.

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