  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.
