On Differential Privacy and Traffic State Estimation Problem for Connected Vehicles

TL;DR

This paper addresses traffic state estimation in highway networks with junctions, integrating differential privacy mechanisms with sensor data, and compares various estimation algorithms using a nonlinear traffic model.

Contribution

It introduces a differentially private traffic data mechanism and evaluates multiple state estimation methods for highway traffic with privacy considerations.

Findings

Gaussian noise effectively ensures differential privacy.

Moving Horizon Estimation outperforms Kalman Filter variants in accuracy.

The approach maintains privacy without significantly compromising estimation quality.

Abstract

This letter focuses on the problem of traffic state estimation for highway networks with junctions in the form of on- and off-ramps while maintaining differential privacy of traffic data. Two types of sensors are considered, fixed sensors such as inductive loop detectors and connected vehicles which provide traffic density and speed data. The celebrated nonlinear second-order Aw-Rascle- Zhang (ARZ) model is utilized to model the traffic dynamics. The model is formulated as a nonlinear state-space difference equation. Sensitivity relations are derived for the given data which are then used to formulate a differentially private mechanism which adds a Gaussian noise to the data to make it differentially private. A Moving Horizon Estimation (MHE) approach is implemented for traffic state estimation using a linearized ARZ model. MHE is compared with Kalman Filter variants namely Extended Kalman Filter, Ensemble Kalman Filter and Unscented Kalman Filter. Several research and engineering questions are formulated and analysis is performed to find corresponding answers.