Calibrating Adaptive Smoothing Methods for Freeway Traffic Reconstruction

TL;DR

This work addresses freeway traffic reconstruction by calibrating the Adaptive Smoothing Method (ASM) through end-to-end kernel optimization using ground-truth data from the I-24 MOTION testbed. It introduces a parameterized, anisotropic-kernel framework with a nonlinear adaptive blend between congested and free-flow reconstructions, and solves for the calibration by minimizing the weighted RMSE against ground truth in a PyTorch implementation that uses FFT-based convolutions for efficiency. The paper provides a reproducible, open-source benchmark including cross-lane and cross-day evaluations, offering detailed metrics (WRMSE, RMSE, Wasserstein distance, IoU) and practical deployment insights across multiple corridors. The results show calibrated ASM better aligns with observed speeds, while also highlighting inherent non-convexity and data-quality issues, informing future extensions such as non-stationary kernels and more nuanced wave modeling for real-time freeway operation support.

Abstract

The adaptive smoothing method (ASM) is a widely used approach for traffic state reconstruction. This article presents a Python implementation of ASM, featuring end-to-end calibration using real-world ground truth data. The calibration is formulated as a parameterized kernel optimization problem. The model is calibrated using data from a full-state observation testbed, with input from a sparse radar sensor network. The implementation is developed in PyTorch, enabling integration with various deep learning methods. We evaluate the results in terms of speed distribution, spatio-temporal error distribution, and spatial error to provide benchmark metrics for the traffic reconstruction problem. We further demonstrate the usability of the calibrated method across multiple freeways. Finally, we discuss the challenges of reproducibility in general traffic model calibration and the limitations of ASM. This article is reproducible and can serve as a benchmark for various freeway operation tasks.

Figures (24)

• Figure 1: Preprocessed sparse speed matrix
• Figure 2: Simple filled speed matrix
• Figure 3: Ground truth speed matrix
• Figure 5: Parameter evolution over epochs for the lane 1 calibration task ($\tau$, $\delta$, $c_\text{cong}$, $c_\text{free}$, $V_\text{thr}$, and $\Delta V$ from top to bottom). The starting point is the initial guess suggested by treiber2011reconstructing, with the red dot indicating the best parameter values achieved during the calibration process.
• Figure 6: The loss function over the calibration epochs for the lane 1 calibration task, with the red dot indicating the best result achieved during the process.