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Reconstruction of Highway Vehicle Paths Using a Two-Stage Model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Weifeng Yin & Junyong Zhai & Yongbo Yu, 2025. "Reconstruction of Highway Vehicle Paths Using a Two-Stage Model," Mathematics, MDPI, vol. 13(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:618-:d:1590688
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    References listed on IDEAS

    as
    1. Bo Xu & Xiaodong Ji & Zhengrong Cheng, 2025. "A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph," Mathematics, MDPI, vol. 13(1), pages 1-18, January.
    2. Vladimir A. Kulyukin, 2023. "On the Computability of Primitive Recursive Functions by Feedforward Artificial Neural Networks," Mathematics, MDPI, vol. 11(20), pages 1-16, October.
    3. Wang, Yinpu & An, Chengchuan & Ou, Jishun & Lu, Zhenbo & Xia, Jingxin, 2022. "A general dynamic sequential learning framework for vehicle trajectory reconstruction using automatic vehicle location or identification data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    4. Irina Deeva & Anna Bubnova & Anna V. Kalyuzhnaya, 2023. "Advanced Approach for Distributions Parameters Learning in Bayesian Networks with Gaussian Mixture Models and Discriminative Models," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
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