Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline—which we name the V-spline—that incorporates position and velocity information and a penalty term that controls acceleration. We introduce an adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is proposed, and, in simulation studies, the V-spline shows superior performance to existing methods. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle.

中文翻译：

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轨迹重建的自适应平滑样条

轨迹重建是推断连续观测之间的运动物体路径的过程。在本文中，我们提出了一个平滑样条线（我们称为V样条线），该样条线包含位置和速度信息以及控制加速度的惩罚项。我们介绍了一种自适应V样条，旨在控制不规则采样的观测值和噪声速度测量的影响。提出了一种用于估计V样条参数的交叉验证方案，并且在仿真研究中，V样条显示了优于现有方法的性能。最后，给出了在两个维度上将V样条应用于车辆轨迹重构的应用，其中允许惩罚项进一步取决于车辆的已知操作特性。