Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processes

TL;DR

We address the problem of estimating traffic state from sparse observations by proposing a Gaussian process framework with a rotated anisotropic kernel that captures directional congestion propagation. The approach combines variational sparse GP for scalability and a multi-output GP to jointly estimate speeds across lanes, delivering uncertainty quantification for imputed states. Key contributions include the rotated kernel with a propagation-angle parameter $α$, a scalable inference scheme, and demonstrated robustness across NGSIM, HighD, and bottleneck simulations at low CV penetration, outperforming baselines like ASM and STH-LRTC. The method offers practical value for traffic management under mixed CV/HV environments and sparse detector coverage, with public code available for replication.

Abstract

Accurately monitoring road traffic state is crucial for various applications, including travel time prediction, traffic control, and traffic safety. However, the lack of sensors often results in incomplete traffic state data, making it challenging to obtain reliable information for decision-making. This paper proposes a novel method for imputing traffic state data using Gaussian processes (GP) to address this issue. We propose a kernel rotation re-parametrization scheme that transforms a standard isotropic GP kernel into an anisotropic kernel, which can better model the congestion propagation in traffic flow data. The model parameters can be estimated by statistical inference using data from sparse probe vehicles or loop detectors. Moreover, the rotated GP method provides statistical uncertainty quantification for the imputed traffic state, making it more reliable. We also extend our approach to a multi-output GP, which allows for simultaneously estimating the traffic state for multiple lanes. We evaluate our method using real-world traffic data from the Next Generation simulation (NGSIM) and HighD programs, along with simulated data representing a traffic bottleneck scenario. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation (TSE) scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. We also test the traffic state estimation when traffic flow information is obtained from loop detectors. The results demonstrate the adaptability of our TSE method across different CV penetration rates and types of detectors, achieving state-of-the-art accuracy in scenarios with sparse observation rates.

Figures (7)

• Figure 1: Illustration of the rotated coordinates.
• Figure 2: A TSE experiment on the NGSIM dataset with 5% CVs penetration rate. The observed trajectories are superimposed on the TSE results. (a) The traffic speed of the full dataset. (b) The traffic speed of observed trajectories. (c) The traffic speed estimated by the ASM method. (d) The traffic speed estimated by the STH-LRTC method. (e) The traffic speed estimated by the GP with ARD Matérn$\frac{5}{2}$ kernel. (f) The traffic speed estimated by the GP with the proposed rotated Matérn$\frac{5}{2}$ kernel.
• Figure 3: When observing 5% trajectories, the RMSE error of ASM when using different congestion propagation speed in the NGSIM dataset.
• Figure 4: An TSE experiment on the NGSIM dataset with observation at three detectors.
• Figure 5: A TSE experiment on a simulated bottleneck. Locations of trajectories and detectors are shown in white lines. (a) The traffic speed of full simulated data. (b) The traffic speed of observed trajectories. (c) The traffic speed estimated by the ASM method. (d) The traffic speed estimated by the STH-LRTC method. (e) The traffic speed estimated by the GP with ARD Matérn$\frac{5}{2}$ kernel. (f) The traffic speed estimated by the GP with the proposed rotated Matérn$\frac{5}{2}$ kernel.