Efficient and Robust Freeway Traffic Speed Estimation under Oblique Grid using Vehicle Trajectory Data

TL;DR

This study proposes an efficient and robust low-rank model for precise spatiotemporal traffic speed state estimation (TSE) using low-penetration vehicle trajectory data and achieves up to a 12% improvement in Root Mean Squared Error in the TSE scenarios and an 18% improvement in RMSE in the robust TSE scenarios.

Abstract

Accurately estimating spatiotemporal traffic states on freeways is a significant challenge due to limited sensor deployment and potential data corruption. In this study, we propose an efficient and robust low-rank model for precise spatiotemporal traffic speed state estimation (TSE) using lowpenetration vehicle trajectory data. Leveraging traffic wave priors, an oblique grid-based matrix is first designed to transform the inherent dependencies of spatiotemporal traffic states into the algebraic low-rankness of a matrix. Then, with the enhanced traffic state low-rankness in the oblique matrix, a low-rank matrix completion method is tailored to explicitly capture spatiotemporal traffic propagation characteristics and precisely reconstruct traffic states. In addition, an anomaly-tolerant module based on a sparse matrix is developed to accommodate corrupted data input and thereby improve the TSE model robustness. Notably, driven by the understanding of traffic waves, the computational complexity of the proposed efficient method is only correlated with the problem size itself, not with dataset size and hyperparameter selection prevalent in existing studies. Extensive experiments demonstrate the effectiveness, robustness, and efficiency of the proposed model. The performance of the proposed method achieves up to a 12% improvement in Root Mean Squared Error (RMSE) in the TSE scenarios and an 18% improvement in RMSE in the robust TSE scenarios, and it runs more than 20 times faster than the state-of-the-art (SOTA) methods.

Figures (8)

• Figure 1: Visualization of constructing a traffic state matrix (TSM). Traffic states exhibit high correlations along the direction of backward traffic waves. Conventional rectangular grid-based modeling in (a) is less desirable to effectively capture such correlations, as it simply vertically and horizontally divides the spatiotemporal region (e.g., cells A and B). In this study, we adopted the oblique grid-based modeling in (b), strategically positioning traffic state observations along the traffic wave direction into the same matrix column (e.g., cells C and D). This approach adeptly transforms the correlation of traffic states into the algebraic low-rankness of the matrix, therefore ensuring a low-rank representation method to proficiently capture the spatiotemporal correlations inherent in traffic states.
• Figure 2: Illustration of the proposed method. An oblique grid-based traffic state matrix is constructed (subsection \ref{['subsec: matrix construction']}) using incomplete and corrupted traffic state observations, and then a low-rank and sparse matrix completion model (subsection \ref{['subsec: TSE tailored LRR model']}) is applied to recover the complete low-rank spatiotemporal traffic state and to simultaneously detect potential sparse corrupted/anomaly data.
• Figure 3: Illustration of constructing an oblique grid-based traffic state matrix.
• Figure 4: A TSE experiment on the NGSIM dataset: (a) The ground truth traffic speed; (b) The observed traffic speed from 5$\%$ randomly selected vehicle trajectories; (c) The estimation result by LSMC; (d) The estimation result by LWR-CG; (e) The estimation result by ASM; (f) The estimation result by PSM; (g) The estimation results by STH-LRTC; (h) The estimation results by the proposed TW-LSMC.
• Figure 5: Comparison between rectangular and oblique grid-based methods (Zoom In).