Publishing trajectories with differential privacy guarantees

The pervasiveness of location-acquisition technologies has made it possible to collect the movement data of individuals or vehicles. However, it has to be carefully managed to ensure that there is no privacy breach. In this paper, we investigate the problem of publishing trajectory data under the differential privacy model. A straightforward solution is to add noise to a trajectory - this can be done either by adding noise to each coordinate of the position, to each position of the trajectory, or to the whole trajectory. However, such naive approaches result in trajectories with zigzag shapes and many crossings, making the published trajectories of little practical use. We introduce a mechanism called SDD (Sampling Distance and Direction), which is ε-differentially private. SDD samples a suitable direction and distance at each position to publish the next possible position. Numerical experiments conducted on real ship trajectories demonstrate that our proposed mechanism can deliver ship trajectories that are of good practical utility.