Reconstruction of Highway Vehicle Paths Using a Two-Stage Model

Weifeng Yin, Junyong Zhai () and Yongbo Yu
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Weifeng Yin: School of Automation, Southeast University, Nanjing 210096, China
Junyong Zhai: School of Automation, Southeast University, Nanjing 210096, China
Yongbo Yu: Jiangsu Communications Holding Digital Transportation Research Institute Co., Ltd., Nanjing 210019, China

Mathematics, 2025, vol. 13, issue 4, 1-20

Abstract: The accurate reconstruction of vehicle paths is essential for effective highway toll management. To address the challenge of multiple possible paths due to missing trajectory data, this study proposes a novel two-stage model for vehicle path reconstruction. In the first stage, a Gaussian Mixture Model (GMM) is integrated into a path choice model to estimate the mean and standard deviation of travel times for each road segment, utilizing an improved Expectation Maximization (EM) algorithm. In the second stage, based on the estimated time parameters, path choice prior probabilities and observed data are combined using maximum likelihood estimation to infer the most probable paths among candidate routes. The results indicate that the improved EM algorithm achieved convergence in 17 iterations compared to 41 iterations for the traditional EM algorithm. The two-stage model outperforms the Shortest Path and Bidirectional Long Short-Term Memory models in path reconstruction, particularly with a high number of missing trajectory points. Additionally, when the number of candidate paths K = 4 , the path reconstruction performance is optimal. These results demonstrate the effectiveness of the proposed method in handling sparse and incomplete trajectory data, offering robust and accurate vehicle path estimations that enhance traffic management and toll calculation precision.

Keywords: vehicle path reconstruction; Gaussian mixture models; path choice model; expectation maximization algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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