Accurate travel time estimation is essential for navigation and itinerary planning. While existing research employs probabilistic modeling to assess travel time uncertainty and account for correlations between multiple trips, modeling the temporal variability of multi-trip travel time distributions remains a significant challenge. Capturing the evolution of joint distributions requires large, well-organized datasets; however, real-world trip data are often temporally sparse and spatially unevenly distributed. To address this issue, we propose SPTTE, a spatiotemporal probabilistic framework that models the evolving joint distribution of multi-trip travel times by formulating the estimation task as a spatiotemporal stochastic process regression problem with fragmented observations. SPTTE incorporates an RNN-based temporal Gaussian process parameterization to regularize sparse observations and capture temporal dependencies. Additionally, it employs a prior-based heterogeneity smoothing strategy to correct unreliable learning caused by unevenly distributed trips, effectively modeling temporal variability under sparse and uneven data distributions. Evaluations on real-world datasets demonstrate that SPTTE outperforms state-of-the-art deterministic and probabilistic methods by over 10.13%. Ablation studies and visualizations further confirm the effectiveness of the model components.

本研究解决了多次旅行时间分布的时变建模难题，提出了SPTTE框架，将估计任务公式化为时空随机过程回归，以应对稀疏观察带来的挑战。SPTTE利用RNN基础的时间高斯过程参数化，显著提升了在稀疏和不均匀数据分布下的旅行时间估计准确性，超过现有方法10.13%。

SPTTE：一种时空概率框架用于旅行时间估计