Vehicle trajectory reconstruction is an indispensable step before using the observed trajectory data for analysis. A recurrent challenge of the existing smoothing/filtering-based methods is the design of the smoothing parameters to avoid over-smoothing while ensuring realistic vehicle dynamics, but they often fall short in two-dimensional (2D) vehicle movements with coupled longitudinal and lateral vehicle motion. To tackle this challenge, we propose a novel approach to reconstruct vehicle trajectories based on constrained optimal control. The proposed approach outputs 2D trajectories to minimize the errors of the reconstructed trajectory with respect to the measured trajectory while respecting the vehicle dynamics and motion constraints. Bounded curvature and acceleration are used as the control variables that resemble human driver behaviour, and plausible ranges of the 2D motion variables are set as the state constraints of the optimal control problem. The proposed model is validated using both the pNEUMA trajectory dataset and a new high-precision trajectory dataset. Results show that the average Euclidean distance between the reconstructed and measured trajectory points is 0.040 m and the vehicle motion variables are all strictly within the permitted range.

车辆轨迹重建是利用观测轨迹数据进行分析之前必不可少的步骤。现有基于平滑/过滤的方法经常面临的挑战是平滑参数的设计，以避免过度平滑，同时确保真实的车辆动力学，但它们在车辆纵向和横向耦合的二维（2D）车辆运动中往往达不到要求。运动。为了应对这一挑战，我们提出了一种基于约束最优控制重建车辆轨迹的新方法。所提出的方法输出 2D 轨迹，以最小化重建轨迹相对于测量轨迹的误差，同时尊重车辆动力学和运动约束。有界曲率和加速度被用作类似于人类驾驶员行为的控制变量，并且二维运动变量的合理范围被设置为最优控制问题的状态约束。使用 pNEUMA 轨迹数据集和新的高精度轨迹数据集对所提出的模型进行了验证。结果表明，重构轨迹点与实测轨迹点之间的平均欧氏距离为0.040 m，车辆运动变量均严格在允许范围内。