Traffic Parameters Estimation With Partial Vehicle Trajectories by the Iterative Partial Backpropagation Maximum Likelihood Estimation (IPB-MLE) Framework

This study proposes a novel framework for traffic parameters estimation at signalized intersections with partial vehicle trajectory data, namely the Iterative Partial Backpropagation Maximum Likelihood Estimation (IPB-MLE) framework. The framework utilizes analytical approximations of the Poisson distribution, which enables the joint likelihood of the observed trajectories to be continuous and differentiable, hence providing better convergence results. The traffic parameters, including the Poisson parameter for the number of incoming vehicles, the free pace mean and variance, and the residual queue length, are optimized by maximizing the joint likelihood using a gradient-based algorithm with the Adam optimizer. The Iterative Backpropagation (IB) approach utilized in this framework allows for flexibility in the problem formulation. As shown in the experiments, the IPB-MLE framework yields good accuracies and robustness in satisfactory computational times. Empirical experiments further show that at least two trajectories are needed for guaranteed convergence, which implies that data volume is also a critical criterion (apart from penetration rate) for accuracy. Estimations take on average 10 to 20 seconds, respectively, for unsaturated and saturated cycles at a 20% penetration rate, and the framework has a linear computational complexity with respect to the number of variables and data points, making it suitable for online or real-time estimation. Moreover, the IPB-MLE framework can be easily extended to more complex situations by incorporating simulation models or neural networks to approximate the travel time distributions. These features of the IPB-MLE framework offer it great potential for more complex and realistic situations.