Modelling the lateral dimension of vehicles movement: a stochastic differential approach with applications

Abstract

A stochastic lateral movement model is proposed to address the limitations of current traffic models, which fail to capture the stochastic nature of the lateral component in vehicle movement during lane keeping and lane changing. This model incorporates a lateral noise component and a lateral movement component, with parameters that have clear physical interpretations including noise intensity, driver’s sensitivity to lateral deviation, and sensitivity to noise. The model successfully describes the real-world distribution and standard deviation of lateral displacement, achieves over 70% accuracy in distinguishing between human driven vehicles and autonomous vehicles, derives the lane changing duration distribution consistent with experimental observation, and shows that the sensitivity to lateral deviation is about 7 times higher in lane changing compared to lane keeping.

KEYWORDS:

• Lateral movement
• microscopic behaviour
• stochastic differential equation
• Fokker-Planck

Acknowledgements

Project supported by the ‘Pioneer’ and ‘Leading Goose’ R&D Program of Zhejiang (2023C01240); National Natural Science Foundation of China (No. 52272314, 52131202); The ministry of education in china project of humanities and social science (21YJCZH116); and Zhejiang province public welfare scientific research project (LGF22E080007).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The highD dataset can be accessed via https://www.highd-dataset.com.

highD dataset contains detailed trajectories of each vehicle covered by the drone. In highD dataset, the lane keeping data is extracted as follows. The raw data contain the land ID. The moment when the vehicle traverses the lane mark can be identified immediately. Then we delete the trajectory 10 s before and after the lane mark traversing moment. The results are given in Figure 1-d.

2 Note that in the equation, the derivatives are taken with respect to time t. In reality, when the vehicle speed is zero, the lateral noise and displacement both don’t change. Thus alternatively, we can interpret the equation as the derivatives with respect to longitudinal coordinate, x. In this way, the equations are reasonable.

3 https://catalog.data.gov/dataset/next-generation-simulation-ngsim-vehicle-trajectories-and-supporting-data; https://www.highd-dataset.com/

4 https://www.highd-dataset.com/

5 https://github.com/QHS2020/LateralDynamicsMetrica/blob/master/inbook/sde_lateral_2round_git.ipynb

6 https://data.jrc.ec.europa.eu/dataset/9702c950-c80f-4d2f-982f-44d06ea0009f

Additional information

Funding

This work was supported by the “Pioneer" and "Leading Goose" R&D Program of Zhejiang (2023C01240); National Natural Science Foundation of China (No. 52272314, 52131202); The ministry of education in China project of humanities and social science (21YJCZH116); and Zhejiang province public welfare scientific research project (LGF22E080007).