With the popularization of different kinds of smart terminals and the development of autonomous driving technology, more and more services based on spatio-temporal data have emerged in our lives, such as online taxi services, traffic flow prediction, and tracking virus propagation. However, the privacy concerns of spatio-temporal data greatly limit the use of them. To address this issue, differential privacy method based on spatio-temporal data has been proposed. In differential privacy, a good aggregation query can highly improve the data utility. But the mainstream aggregation query methods are based on area partitioning, which is difficult to generate trajectory with high utility for they are hard to take time and constraints into account. Motivated by this, we propose an aggregation query based on the relationships between trajectories, so it can greatly improve the data utility as compared to the existing methods. The trajectory synthesis task can be regarded as an optimization problem of finding trajectories that match the relationships between trajectories. We adopt gradient descent to find new trajectories that meet the conditions, and during the gradient descent, we can easily take the constraints into account by adding penalty terms which area partitioning based query is hard to achieve. We carry out extensive experiments to validate that the trajectories generated by our method have higher utility and the theoretic analysis shows that our method is safe and reliable.

翻译：随着各类智能终端的普及和自动驾驶技术的发展，基于时空数据的服务逐渐融入日常生活，例如在线约车服务、交通流预测以及病毒传播追踪等。然而，时空数据的隐私问题极大地限制了其应用。针对这一问题，研究者提出了基于时空数据的差分隐私方法。在差分隐私中，良好的聚合查询能够显著提升数据效用。但主流聚合查询方法基于区域划分，难以兼顾时间维度与约束条件，因此难以生成高可用性的轨迹。受此启发，我们提出了一种基于轨迹间关系的聚合查询方法，相较于现有方法能大幅提升数据效用。轨迹合成任务可被视为寻找与轨迹间关系相匹配的轨迹优化问题。我们采用梯度下降法寻找满足条件的新轨迹，并在梯度下降过程中通过添加惩罚项轻松纳入约束条件——这是基于区域划分的查询难以实现的。通过大量实验验证，本方法生成的轨迹具有更高的可用性，且理论分析证明该方法安全可靠。