Traffic State Estimation Research Articles

ShieldTSE: A Privacy-Enhanced Split Federated Learning Framework for Traffic State Estimation in IoV

<i>ShieldTSE</i>: A Privacy-Enhanced Split Federated Learning Framework for Traffic State Estimation in IoV

Self-adaptive equation embedded neural networks for traffic flow state estimation with sparse data

The data-driven approach in intelligent traffic systems has achieved successive breakthroughs, thanks to the ever-increasing volume of traffic data. Nonetheless, in practical scenarios, the collected data often contain some issues, e.g., missing values, significantly impacting the accuracy and efficiency of the algorithms. To enhance the precision of traffic estimation utilizing the sparse data, we have developed a physics-informed neural network (PINN) based algorithm in the line with the traffic flow theory and deep learning principles. In contrast to the conventional PINNs, our approach uniquely incorporates a self-adaptive macro model for mixed flow into the network's architecture, serving as an embedded source of physics information. With this algorithm, we can capture the dynamic behavior of an entire traffic flow including its spatiotemporal evolution with sparse traffic data such as initial and boundary value information. To realize the model's adaptability, we have revised the macro model by inverting its parameters and incorporating a data-driven nonlinear element, which simplifies the intricate macro model structure. The network's effectiveness has been validated through the experiments conducted on a mixed traffic flow system experiencing local agglomeration and real-world data, demonstrating its capability for precise traffic simulation, efficient traffic flow prediction, and interpretability. Our study offers a novel insight for data-driven traffic flow state estimation.

Multi-level traffic-responsive tilt camera surveillance through predictive correlated online learning

In urban traffic management, the primary challenge of dynamically and efficiently monitoring traffic conditions is compounded by the insufficient utilization of thousands of surveillance cameras along the intelligent transportation system. This paper introduces the multi-level Traffic-responsive Tilt Camera surveillance system (TTC-X), a novel framework designed for dynamic and efficient monitoring and management of traffic in urban networks. By leveraging widely deployed pan–tilt-cameras (PTCs), TTC-X overcomes the limitations of a fixed field of view in traditional surveillance systems by providing mobilized and 360-degree coverage. The innovation of TTC-X lies in the integration of advanced machine learning modules, including a detector–predictor–controller structure, with a novel Predictive Correlated Online Learning (PiCOL) methodology and the Spatial–Temporal Graph Predictor (STGP) for real-time traffic estimation and PTC control. The TTC-X is tested and evaluated under three experimental scenarios (e.g., maximum traffic flow capture, dynamic route planning, traffic state estimation) based on a simulation environment calibrated using real-world traffic data in Brooklyn, New York. The experimental results showed that TTC-X captured over 60% total number of vehicles at the network level, dynamically adjusted its route recommendation in reaction to unexpected full-lane closure events, and reconstructed link-level traffic states with best MAE less than 1.25 vehicle/hour. Demonstrating scalability, cost-efficiency, and adaptability, TTC-X emerges as a powerful solution for urban traffic management in both cyber–physical and real-world environments.

A data-driven optimization-based approach for freeway traffic state estimation based on heterogeneous sensor data fusion

Accurate estimation of freeway traffic states is crucial for designing effective traffic management and operational strategies. The integration of various sensor data, such as data from the Electronic Toll Collection (ETC) system and traffic detectors, can significantly enhance the granularity and coverage of traffic state estimation. This study introduces a data-driven optimization-based approach for estimating freeway traffic states, leveraging the fusion of ETC data with detector data. This methodology capitalizes on the broad coverage provided by ETC data and the fine granularity offered by detector data. The probabilistic interdependence between the traffic state of a segment and its upstream and downstream counterparts is captured from real-world traffic state data. Two optimization models, based on the maximum likelihood and maximin likelihood principles, are developed to accurately depict the distribution patterns of freeway traffic states. To address the computational challenges of large-scale scenarios, the study proposes both a decomposition algorithm and a heuristic algorithm. A case study utilizing real-world data from the G92 freeway in Zhejiang, China, is conducted. The findings indicate that the two optimization models exhibit commendable accuracy, with mean absolute percentage errors of 0.9% and 2.3% during peak hours, and 0.9% and 1.4% during off-peak hours, respectively.

Traffic state estimation incorporating heterogeneous vehicle composition: A high-dimensional fuzzy model

Traffic state estimation incorporating heterogeneous vehicle composition: A high-dimensional fuzzy model

Adaptive observer design for coupled ODE–hyperbolic PDE systems with application to traffic flow estimation

This paper studies the state estimation problem for a class of coupled linear ODE–hyperbolic PDE systems with unknown in-domain parameters. Based on the swapping transformation and the least squares parameter estimation method, a Luenberger-type adaptive boundary observer is designed to estimate the ODE–PDE states under the unknown parameters. The exponential convergence conditions w.r.t. the observer feedback gains are given by employing the Lyapunov technique. Finally, an application to traffic state estimation of the Aw–Rascle–Zhang (ARZ) model involving the unknown relaxation time and the boundary input speed deviation is provided to validate the theoretical result.

Integrating Multisourced Sensor Data for Enhanced Traffic State Estimation

Integrating Multisourced Sensor Data for Enhanced Traffic State Estimation

Traffic state estimation from vehicle trajectories with anisotropic Gaussian processes

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 observations.

Data poisoning attacks on traffic state estimation and prediction

Data has become ubiquitous nowadays in transportation, including vehicular data and infrastructure-generated data. The growing reliance on data poses potential cybersecurity issues to transportation systems, among which the so-called “data poisoning” attacks by adversaries are becoming increasingly critical. Such attacks aim to compromise a system’s performance by adding systematic and malicious noises, perturbations, or deviations to the dataset used by the system. Formal investigations of data poisoning attacks are essential for understanding the attacks and developing effective defense methods. This study develops a general data poisoning attack model for traffic state estimation and prediction (TSEP) that is a basic application in transportation. We first formulate data poisoning attacks as a general sensitivity analysis of parameterized optimization problems over parameter changes (i.e., data perturbations) and study the Lipschitz continuity property of the solution with the presence of general (equality and inequality) constraints. Then, we develop attack models that fit a broader spectrum of learning applications (such as TSEP) by extending existing models that only focus on learning problems with no or equality constraints (widely used in the cybersecurity field). Since the solution of such general problems is often continuous but not differentiable with data changes, we apply the generalized implicit function theorem to compute the semi-derivatives that express how the TSEP solution responds to data perturbations. The semi-derivatives enable us to evaluate TSEP models’ vulnerability (at each data point) and solve the proposed attack model. We demonstrate the generality and effectiveness of the proposed method on two TSEP models using mobile sensing data.

Real-time freeway traffic state estimation for inhomogeneous traffic flow

This paper addresses model-based approach considering online model parameters estimation to estimate the real-time freeway traffic state for inhomogeneous traffic flow. Its effectiveness is demonstrated through macroscopic simulation and the influence of detector configuration on the estimation performance is investigated. The results indicate that when a freeway is inhomogeneity, additional detectors need to be placed at the boundary of traffic flow inhomogeneity to achieve better estimation performance. Finally, it is confirmed that considering traffic flow inhomogeneity can achieve better estimation performance using real expressway data from Shanghai.

Modified Model Predictive Control for Coordinated Signals along an Arterial under Relaxing Assumptions

This paper proposes modified model predictive control (MMPC) for coordinated signals, aiming to enhance a model’s fidelity to the realistic traffic environment by relaxing typical assumptions. We focus on the arterial, where every intersection is equipped with a dual-ring-barrier signal controller that complies with the standards of the National Electric Manufacturers Association. MMPC employs the store-and-forward model to describe traffic flow, thereby transforming the signal control problem into a model-based rolling-horizon optimization problem, in which the prediction horizon is composed of several future sample intervals, commonly equal to the cycle length. A radar detector is used to collect vehicle data upstream of the stop line at every sampling instant. The optimization problem is solved to minimize the number of vehicles within the prediction horizon, and the next timing plan is determined based on the optimization results. Constraints are added and modified in order to incorporate the typical relaxed assumptions in the optimization process. For this purpose, MMPC introduces a transition-free ring-barrier structure, vehicle distribution ratio, and percent arrival before the end of green. Simulation results indicate that coordination can be maintained by MMPC without the need for transitions, and the estimation of current and future traffic states can be improved with the assistance of modified constraints. Compared with benchmark techniques, MMPC offers superior vehicle progression for coordinated movement and significant improvements in delays, number of stops, and total travel time from a system-wide perspective, with an acceptable small increase in runtime.

Real-Time Unmanned Aerial Vehicle-Based Traffic State Estimation for Multi-Regional Traffic Networks

Traffic state estimation is a challenging task because of the collection of sparse and noisy measurements from fixed points in the traffic network. Induction loops, as they are non-intrusive, can observe any area of the traffic network on demand and provide accurate traffic density and speed measurements. Our main contribution is the development of an optimization framework where small parts of the traffic network are monitored by Unmanned Aerial Vehicles (UAVs) and accurate estimates of traffic density and mean speeds for every region in the traffic network are returned in real-time. Assuming regional-based traffic dynamics, a cyclical UAV flight path is defined for each region. One UAV is assigned to each flight path and monitors a small area of the region below. The UAV-based traffic measurements are expressed as moving averages to smooth out fluctuations in traffic density and mean speed. A moving horizon optimization problem is formulated, which minimizes the estimation and process errors over a moving time window. The problem is non-convex and challenging to solve, because of the presence of nonlinear traffic dynamics. By considering free-flow conditions, the optimization problem is recast to a quadratic program that returns density estimations for each region of the traffic network in real-time. Simulation results compare our UAV framework to an alternative, where the whole traffic network is monitored by UAVs. Both frameworks obtain similar results, despite the alternative framework using more UAVs than our framework.

Vehicle Speed and Position Estimation considering Microscopic Heterogeneous Car-Following Characteristics in Connected Vehicle Environments

This paper proposes a method for estimating the speed and position of unsampled vehicles using sampled data from connected automated vehicles (CAVs). The determination of vehicle speed and position on the road is a challenging and crucial task, as they can effectively reflect traffic flow characteristics and contribute to traffic state estimation and intersection signal timing optimization. Connected automated vehicles have the capability to upload their own trajectory data while also capturing trajectory data of surrounding vehicles through onboard sensors. Therefore, this paper proposes a novel approach to estimate the speed and position of unsampled vehicles. Firstly, using real vehicle trajectory data, the correlation between the velocity of following vehicles and the velocity of leading vehicles under different densities is analyzed, leading to the development of a velocity estimation model incorporating a speed correction factor. Secondly, the correlation between time headway, the rate of change of following vehicle acceleration, and traffic density is examined. To address the issue of heterogeneous behavior in vehicle following described by the Intelligent Driver Model (IDM), a real-time optimization model for estimating vehicle position by optimizing IDM parameters is proposed. The velocity estimation model and the position estimation model are summarized as two nonlinear optimization problems. Finally, the proposed method is validated using actual vehicle trajectory data. Experimental results demonstrate that when the number of connected automated vehicles (CAVs) is 2, the proposed method reduces the average absolute error by 30.73% and the standard deviation of the average absolute error by 42.8% compared to a linear model-based speed estimation method under different density conditions. Compared to a method that estimates vehicle position by calibrating desired gaps, the proposed method reduces the average absolute error by 38.2% and the standard deviation of the average absolute error by 41.7% under different density conditions. Furthermore, the proposed method exhibits good practicality under different CAV penetration rates.

Urban Road Traffic Spatiotemporal State Estimation Based on Multivariate Phase Space–LSTM Prediction

The road traffic state is usually analyzed from a temporal and macroscopic perspective; however, traffic flow parameters, such as density and spacing, can explain the evolution of traffic states from the microscopic perspective and the spatial distribution of vehicles in lanes. In this paper, we attempt to take both temporal and spatial characteristics into consideration simultaneously, and a parameter is defined as the traffic spatiotemporal state of urban road sections to represent the operational status of road traffic, using advanced prediction techniques to estimate its short-term trends. An estimation method is constructed for the traffic spatiotemporal state considering travel times, speeds, and queuing situations from temporal and spatial perspectives. Then, based on Takens’ theorem and the single variable phase space, the phase space of multiple traffic parameters is reconstructed and the chaotic characteristics are analyzed. Next, an LSTM prediction model is constructed based on the phase space reconstruction of multiple variables, and the traffic parameters are predicted by empirical analysis. The results show the proposed estimation method has a significantly improved accuracy. Finally, combined with RFID data, the traffic spatiotemporal state of the case section is calculated, which provides a theoretical basis and practical reference for road traffic state evaluations.

MVCV-Traffic: multiview road traffic state estimation via cross-view learning

Fine-grained urban traffic data are often incomplete owing to limitations in sensor technology and economic cost. However, data-driven traffic analysis methods in intelligent transportation systems (ITSs) heavily rely on the quality of input data. Thus, accurately estimating missing traffic observations is an essential data engineering task in ITSs. The complexity of underlying node-wise correlation structures and various missing scenarios presents a significant challenge in achieving high-precision estimation. This study proposes a novel multiview neural network termed MVCV-Traffic, equipped with a cross-view learning mechanism, to improve traffic estimation. The contributions of this model can be summarized into two parts: multiview learning and cross-view fusing. For multiview learning, several specialized neural networks are adopted to fit diverse correlation structures from different views. For cross-view fusing, a new information fusion strategy merges multiview messages at both feature and output levels to enhance the learning of joint correlations. Experiments on two real-world datasets demonstrate that the proposed model significantly outperforms existing traffic speed estimation methods for different types and rates of missing data.

Physics-informed deep learning for traffic state estimation based on the traffic flow model and computational graph method

Traffic state estimation (TSE) is a critical task for intelligent transportation systems. However, it is extremely challenging because the traffic data quality is often affected by the installation position of devices, data collection frequency, interference during the transmission process, etc., thus causing the problem of data sparsity or data missing. To address the issue of traffic state estimation under the scenario of data sparsity, we propose a TSE model that combines the computational graph with physics-informed deep learning (PIDL) methods. Firstly, we apply the computational graph method to determine the parameters of the traffic fundamental diagram. These parameters are embedded into the computational graph framework, and their values are determined through the forward propagation of variables and the backward propagation of errors. Next, we employ the PIDL method to realize TSE (taking the LWR model based on the Greenshields fundamental diagram as an example). The PIDL leverages the advantages of data-driven and model-driven approaches to achieve accurate traffic state estimation. Case studies are conducted using the NGSIM dataset under two sparse data scenarios: loop detectors and probe vehicles. Experimental results demonstrate that PIDL can accurately reconstruct the traffic state of the entire road segment based on partially observed data. Furthermore, compared to pure deep learning methods and other baseline models, PIDL performs better in situations with sparse data, thereby proving the feasibility of integrating domain knowledge with deep learning frameworks. This paper fully acknowledges the issue of data sparsity in TSE and effectively addresses it by applying the PIDL method to achieve precise TSE, which holds significant implications for the control and management of real traffic flow.

GA-KELM: Genetic-Algorithm-Improved Kernel Extreme Learning Machine for Traffic Flow Forecasting

A prompt and precise estimation of traffic conditions on the scale of a few minutes by analyzing past data is crucial for establishing an effective intelligent traffic management system. Nevertheless, because of the irregularity and nonlinear features of traffic flow data, developing a prediction model with excellent robustness poses a significant obstacle. Therefore, we propose genetic-search-algorithm-improved kernel extreme learning machine, termed GA-KELM, to unleash the potential of improved prediction accuracy and generalization performance. By substituting the inner product with a kernel function, the accuracy of short-term traffic flow forecasting using extreme learning machines is enhanced. The genetic algorithm evades manual traversal of all possible parameters in searching for the optimal solution. The prediction performance of GA-KELM is evaluated on eleven benchmark datasets and compared with several state-of-the-art models. There are four benchmark datasets from the A1, A2, A4, and A8 highways near the ring road of Amsterdam, and the others are D1, D2, D3, D4, D5, D6, and P, close to Heathrow airport on the M25 expressway. On A1, A2, A4, and A8, the RMSEs of the GA-KELM model are 284.67 vehs/h, 193.83 vehs/h, 220.89 vehs/h, and 163.02 vehs/h, respectively, while the MAPEs of the GA-KELM model are 11.67%, 9.83%, 11.31%, and 12.59%, respectively. The results illustrate that the GA-KELM model is obviously superior to state-of-the-art models.

Effects of loop detector position on the macroscopic fundamental diagram

Loop detectors are probably the widest-used technology for traffic state estimation. Previous research has shown that loop detector positions within the link significantly affect the estimation of the macroscopic fundamental diagram (MFD) of a given network. This paper examines the biases produced by the positioning of loop detectors on the MFD, using both analytical and simulation methods, as well as empirical data from UTD19. We confirm earlier results that a uniform distribution of loop detector positions reduces the bias. We discovered that: (i) subsets of the MFD determined by the loop detector position can help estimate whether the loop detector MFD will have a bias; (ii) non-uniform distribution of loop detectors is more likely to cause a discrepancy in the position subsets of the MFD, particularly if detectors in the network are positioned more downstream with a greater variation; and (iii) a lower ratio of link length to green signal time increases the possibility of bias in loop detector MFD, while the impact of the aggregation interval was found to be negligible. This research opens the possibility for the bias of MFD induced by the loop detector data to be corrected by only using itself.

Physics-informed neural networks for integrated traffic state and queue profile estimation: A differentiable programming approach on layered computational graphs

This paper presents an integrated framework for physics-informed joint traffic state and queue profile estimation (JSQE) on freeway corridors, utilizing heterogeneous data sources. The integrated modeling framework aims to maximize the benefits of information from physics-informed analytical traffic flow models and field observations while leveraging joint estimation spaces. Potential inconsistencies between different modeling components must be acknowledged and carefully managed to ensure model feasibility. To minimize such inconsistencies, a nonlinear programming model is formulated for the JSQE problem, taking into account traffic flow models and observations from both corridor and local segment levels. At the corridor level, a fluid queue approximation is employed to model queuing dynamics. Assuming polynomial arrival and departure rates, critical system variables such as time-dependent delay, travel time, and queue length are analytically derived. To preserve the differentiability of traffic state variables, continuous space–time distribution functions are introduced to model traffic flow variables and partial differential equations. A computational graph is constructed to represent the nonlinear programming model in a layered structure, which is then solved using a forward–backward method. Comprehensive numerical experiments based on real-world and hypothetical datasets are designed to demonstrate the effectiveness of the proposed framework.

Physics-Informed Deep Learning for Traffic State Estimation: A Survey and the Outlook

For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNNs), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how the physics is encoded into DNNs and how the physics and data components are represented. In this paper, we offer an overview of a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset.