Smoothing and Imputation of Longitudinal Vehicle Trajectory Data

The purpose of this study is to develop a methodology for processing vehicle trajectory data which are presented as a series of discrete positions of vehicles recorded over consecutive time intervals. The framework combines vehicle trajectory smoothing and imputation, ensuring that speeds and higher-order derivatives of positions are consistently defined as symplectic differences in positions, while adhering to physically meaningful bounds determined by traffic laws, drivers' behaviors, and vehicle characteristics.