Traffic State Estimation for Connected Vehicles using the Second-Order Aw-Rascle-Zhang Traffic Model

TL;DR

This work advances traffic state estimation by formulating a nonlinear second-order ARZ model that includes ramp junctions and a coupled nonlinear measurement model for heterogeneous sensors. It demonstrates a linearized Moving Horizon Estimation (MHE) approach that handles state constraints and outperforms KF variants in speed estimation, especially when leveraging connected-vehicle data. Through VISSIM-based simulations, the study shows moving CV data improves estimation accuracy, with performance improvements contingent on sensor placement, data quality, and change frequencies. The findings highlight the practical value of integrating CV data for real-time TSE and point to future work in real-world validation, sensor-coverage optimization, and comparisons with first-order models under non-equilibrium conditions.

Abstract

This paper addresses the problem of traffic state estimation (TSE) in the presence of heterogeneous sensors which include both fixed and moving sensors. Traditional fixed sensors are expensive and cannot be installed throughout the highway. Moving sensors such as Connected Vehicles (CVs) offer a relatively cheap alternative to measure traffic states across the network. Moving forward it is thus important to develop such models that effectively use the data from CVs. One such model is the nonlinear second-order Aw-Rascle-Zhang (ARZ) model which is a realistic traffic model, reliable for TSE and control. A state-space formulation is presented for the ARZ model considering junctions in the formulation which is important to model real highways with ramps. A Moving Horizon Estimation (MHE) implementation is presented for TSE using a linearized ARZ model. Various state-estimation methods used for TSE in the literature along with the presented approach are compared with regard to accuracy and computational tractability with the help of a numerical study using the VISSIM traffic simulation software. The impact of various strategies for querying CV data on the estimation performance is also considered. Several research questions are posed and addressed with a thorough analysis of the results.

Figures (15)

• Figure 1: Heterogenous sensors on the highway: fixed sensors represented by dashed lines across the highway and CVs represented by the solid black rectangles.
• Figure 2: Schematic diagram of the highway considered in this study.
• Figure 3: Configurations for fixed sensor placement on the mainline segments. Black boxes depict segments with sensors and white boxes depict otherwise. Arrows indicate the direction of traffic. The ramp segments containing an additional 3 sensors are not presented in this figure. The top and bottom rows present the configuration with a total of 5 and 12 sensors in the system, respectively.
• Figure 4: $\mathrm{RMSE}_{\rho}$ [top left], $\mathrm{RMSE}_{v}$ [top right], $\mathrm{SMAPE}_{\rho}$ [bottom left], and $\mathrm{SMAPE}_{v}$ [bottom right] with different numbers of fixed sensors.
• Figure 5: Plots of simulated and estimated trajectories for densities [left] (a, c, e, g) and speeds [right] (b, d, f, h) in the presence of 4 additional fixed sensors. Rows of figures correspond to the unmeasured Segments 2, 4, 6, and 8 respectively.