Longitudinal geospatial frequency estimation under adaptive local differentially private model

Abstract

The collection of geospatial data under Local Differential Privacy (LDP) enables valuable spatial analytics without compromising user privacy. However, existing LDP mechanisms rely on static spatial discretizations, such as uniform grids or fixed-depth quadtrees, that are ill-suited to the dynamic and non-uniform nature of real-world mobility data. These limitations are further amplified in longitudinal settings, where users report their locations repeatedly over time. In this work, we propose ALOQ (Adaptive Longitudinal Quadtree), a novel data collection model for continuous, privacy-preserving location frequency estimation under LDP. ALOQ introduces a dynamic quadtree-based spatial representation that evolves in response to noisy user density distributions, improving estimation accuracy while preserving strong privacy guarantees. The model includes a Quadtree Adaptation Window (QAW) to detect significant temporal changes, a similarity-aware privacy budget allocation mechanism, and a bounded refinement strategy that ensures the cumulative privacy loss remains under control. We provide a theoretical analysis of ALOQ’s privacy guarantees and evaluate its performance on both synthetic and real-world datasets. Our results show that ALOQ consistently outperforms state-of-the-art LDP baselines in terms of utility and budget efficiency, particularly in scenarios with skewed spatial distributions and evolving mobility patterns.