Traffic State Estimation with Anisotropic Gaussian Processes from Vehicle Trajectories

Accurately monitoring road traffic state and speed 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 propagation of traffic waves in traffic flow data. This method can be applied to impute traffic state data from fixed sensors or probe vehicles. 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. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. Results show that our method outperforms state-of-the-art methods in terms of estimation accuracy, efficiency, and robustness.