Accurately monitoring road traffic state and speed is crucial for various applications, including travel time prediction, traffic control, and traffic safety. However, the lack of sensors often results in incomplete traffic state data, making it challenging to obtain reliable information for decision-making. This paper proposes a novel method for imputing traffic state data using Gaussian processes (GP) to address this issue. We propose a kernel rotation re-parametrization scheme that transforms a standard isotropic GP kernel into an anisotropic kernel, which can better model the propagation of traffic waves in traffic flow data. This method can be applied to impute traffic state data from fixed sensors or probe vehicles. Moreover, the rotated GP method provides statistical uncertainty quantification for the imputed traffic state, making it more reliable. We also extend our approach to a multi-output GP, which allows for simultaneously estimating the traffic state for multiple lanes. We evaluate our method using real-world traffic data from the Next Generation simulation (NGSIM) and HighD programs. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. Results show that our method outperforms state-of-the-art methods in terms of estimation accuracy, efficiency, and robustness.

翻译：准确监测道路交通状态与速度对于行程时间预测、交通控制及交通安全等应用至关重要。然而，传感器不足常导致交通状态数据不完整，难以获取可靠信息以支持决策。本文提出一种基于高斯过程的交通状态数据填补新方法以解决此问题。我们设计了一种核旋转重参数化方案，可将标准各向同性高斯过程核转换为各向异性核，从而更好地建模交通流数据中的交通波传播特性。该方法适用于固定传感器或探测车数据的交通状态填补。此外，旋转高斯过程方法可为填补的交通状态提供统计不确定性量化，提升其可靠性。我们还将该方法扩展至多输出高斯过程，可同时估计多车道的交通状态。利用下一代仿真（NGSIM）和HighD项目的真实交通数据评估方法性能。考虑当前及未来网联车与人类驾驶车混合交通场景，我们基于5%至50%可用轨迹数据开展交通状态估计实验，模拟混合交通环境下不同网联车渗透率。结果表明，本方法在估计精度、效率及鲁棒性方面均优于现有最优方法。