Calibration Of Car-following Models Research Articles

Extracting Vehicle Trajectories from Partially Overlapping Roadside Radar.

This work presents a methodology for extracting vehicle trajectories from six partially-overlapping roadside radars through a signalized corridor. The methodology incorporates radar calibration, transformation to the Frenet space, Kalman filtering, short-term prediction, lane-classification, trajectory association, and a covariance intersection-based approach to track fusion. The resulting dataset contains 79,000 fused radar trajectories over a 26-h period, capturing diverse driving scenarios including signalized intersections, merging behavior, and a wide range of speeds. Compared to popular trajectory datasets such as NGSIM and highD, this dataset offers extended temporal coverage, a large number of vehicles, and varied driving conditions. The filtered leader-follower pairs from the dataset provide a substantial number of trajectories suitable for car-following model calibration. The framework and dataset presented in this work has the potential to be leveraged broadly in the study of advanced traffic management systems, autonomous vehicle decision-making, and traffic research.

Traffic flow impact of mixed heterogeneous platoons on highways: an approach combining driving simulation and microscopic traffic simulation

The connected automated vehicle (CAV) platoons are expected to improve the operational performance of the transportation system. Existing platoon testing processes have used the format of mixed heterogeneous platoons (MHPs), where the leader vehicles are connected human-driven vehicles (CHDVs) and the follower vehicles are CAVs. The impact of this type of MHP on existing highway traffic flow is more complex due to the presence of human drivers, and this impact has yet to be analyzed and quantified. Therefore, this paper takes this type of MHP as the research object and conducts experiments by combining driving simulation and microscopic traffic simulation. The driving behavior of the driver of the MHP's leader vehicle is incorporated into the car-following model by means of a car-following model calibration, and an impact analysis is carried out in terms of multiple dimensions of stability, efficiency, and ecological aspects of the mixed traffic flow under different MHP market penetration rates (MPRs). The results show that MHPs weaken the oscillatory effect of mixed traffic flow and improve mixed traffic flow stability. The MPRs of MHPs are proportional to the road capacity and average speed and antipodal to the average travel time. Also, the MHPs help reduce fuel consumption and pollutant emissions (CO2, CO, NOx, HC, and PMx) during traffic operations. This study can provide theoretical support for the future large-scale application and management of MHPs.

Bi-scale car-following model calibration based on corridor-level trajectory

The precise estimation of macroscopic traffic parameters, such as travel time and fuel consumption, is essential for the optimization of traffic management systems. Despite its importance, the comprehensive acquisition of vehicle trajectory data for the calculation of these macroscopic measures presents a challenge. To bridge this gap, this study aims to calibrate car-following models capable of predicting both microscopic measures and macroscopic measures. We conduct a numerical analysis to trace the cumulative process of model prediction errors across various measurements, and our findings indicate that macroscopic measures encapsulate the accumulation of model errors. By incorporating macroscopic measures into vehicle model calibration, we can mitigate the impact of noise on microscopic data measurements. We compare three car-following model calibration methods: MiC (using microscopic measurements), MaC (using macroscopic measurements), and BiC (using both microscopic and macroscopic measurements)—utilizing real-world trajectory data. The BiC method emerges as the most successful in reconstructing vehicle trajectories and accurately estimating travel time and fuel consumption, whereas the MiC method leads to overfitting and inaccurate macro-measurement predictions. This study underscores the importance of bi-scale calibration for precise traffic and energy consumption predictions, laying the groundwork for future research aimed at enhancing traffic management strategies.

Car-following model calibration with load effect as additional optimisation objective

Calibrating a car-following model is an essential component in the traffic load analysis of bridges, since the parameter set fundamentally determines the spatiotemporal distributions of the vehicles and the magnitude of the load effects. In bridge engineering, car-following models are adapted from transportation engineering so that they do not consider load effects in the calibration process. This paper proposes a novel framework that factors vehicle motions and load effects into a multi-objective optimisation problem to calibrate car-following models. The Intelligent Driver Model (IDM) and the Gipps’ model are introduced for comparison. In the testing, three different types and spans of bridges are selected to compare the models in terms of fitness, robustness, and compactness of the solution. Within the proposed framework, the Gipps’ model proves to be superior in terms of fitness but achieves poor performance in robustness, while the IDM exhibits the opposite pattern. The solution compactness of the Gipps’ model improves with higher truck weights only in the circumstance of the load effects type with a unimodal influence line. Overall, the Gipps’ model is recommended for analysis with abundant data. Otherwise, the IDM can be adopted for a non-optimal but robust result.

Effect of autonomous vehicles on car-following behavior of human drivers: Analysis based on structural equation models

Road traffic will experience a transition towards a mixed traffic flow, consisting of both autonomous vehicles (AVs) and human-driving vehicles (HVs), scenarios where HV drivers follow AVs will inevitably arise. This necessitates a comprehensive and in-depth exploration of driver behavior in such contexts, particularly focusing on the changes in their following behavior. To investigate the factors that influence the following behavior of HV drivers when following AVs in a human-machine mixed driving environment. Specifically, this study examines the impact of four variables on following intentions and following distance: driver’s understanding of AV performance, safety trust, tolerance for slow driving, and the driver’s perception of traffic flow conditions. To this end, a model framework is constructed that captures the relationships among these factors. A total of 376 valid samples were obtained through a survey. After verifying the internal consistency and reliability of the data, a structural equation model was utilized to conduct path analysis and mediation effect analysis to examine the relationships among the influencing factors. The results indicate that safety trust has a significant positive impact on following intentions, while traffic environmental perception has a significant negative impact. Safety trust has a significant negative impact on following distance, while tolerance for slow driving has a significant positive impact. Environmental perception and understanding of vehicle performance only indirectly influence following distance through their effects on safety trust and tolerance for slow driving. Among all factors, safety trust has the greatest impact on both following intentions and following distance. The results of this study can serve as a foundation for analyzing vehicle interactive behavior in human-machine mixed driving environments and as a basis for parameter calibration of car-following models.

Mamdani vs. Takagi-Sugeno Fuzzy Inference Systems in the Calibration of Continuous-Time Car-Following Models.

The transition to intelligent transportation systems (ITSs) is necessary to improve traffic flow in urban areas and reduce traffic congestion. Traffic modeling simplifies the understanding of the traffic paradigm and helps researchers to estimate traffic behavior and identify appropriate solutions for traffic control. One of the most used traffic models is the car-following model, which aims to control the movement of a vehicle based on the behavior of the vehicle ahead while ensuring collision avoidance. Differences between the simulated and observed model are present because the modeling process is affected by uncertainties. Furthermore, the measurement of traffic parameters also introduces uncertainties through measurement errors. To ensure that a simulation model fully replicates the observed model, it is necessary to have a calibration process that applies the appropriate compensation values to the simulation model parameters to reduce the differences compared to the observed model parameters. Fuzzy inference techniques proved their ability to solve uncertainties in continuous-time models. This article aims to provide a comparative analysis of the application of Mamdani and Takagi-Sugeno fuzzy inference systems (FISs) in the calibration of a continuous-time car-following model by proposing a methodology that allows for parallel data processing and the determination of the simulated model output resulting from the application of both fuzzy techniques. Evaluation of their impact on the follower vehicle considers the running distance and the dynamic safety distance based on the observed behavior of the leader vehicle. In this way, the identification of the appropriate compensation values to be applied to the input of the simulated model has a great impact on the development of autonomous driving solutions, where the real-time processing of sensor data has a crucial impact on establishing the car-following strategy while ensuring collision avoidance. This research performs a simulation experiment in Simulink (MATLAB R2023a, Natick, MA, USA: The MathWorks Inc.) and considers traffic data collected by inductive loops as parameters of the observed model. To emphasize the role of Mamdani and Takagi-Sugeno FISs, a noise injection is applied to the model parameters with the help of a band-limited white-noise Simulink block to simulate sensor measurement errors and errors introduced by the simulation process. A discussion based on performance evaluation follows the simulation experiment, and even though both techniques can be successfully applied in the calibration of the car-following models, the Takagi-Sugeno FIS provides more accurate compensation values, which leads to a closer behavior to the observed model.

Car-Following Behavior of Human-Driven Vehicles in Mixed-Flow Traffic: A Driving Simulator Study

Connected and autonomous vehicles (CAVs) and human-driven vehicles (HDVs) will inevitably coexist on roads in the future, creating mixed-flow traffic. The heterogeneous car-following (CF) behavior of HDVs can degrade the control performance of CAVs and introduce inefficiencies in CAV operations. To address these challenges, it is necessary to comprehend HDV CF behavior in mixed-flow traffic. This driving simulator-based study investigates HDV CF behavior in mixed-flow traffic under three different CAV control settings (string-stable, string-unstable, and HDV-like). The effects of traffic congestion level and demographic characteristics on CF behavior are also considered. Statistical analysis and CF model calibration, based on trajectory data collected from 72 participants in driving simulator experiments, are performed to examine the impacts of these factors on string stability, traffic efficiency, and safety. Then, online parameter estimation is conducted to illustrate the time-varying desired time headway, and sensitivity to spacing and speed variations (i.e., CF behavior evolution). Additionally, analysis of post-experiment interview results and eye-tracking data show that the string-stable CAV control setting is preferred by most HDV drivers, but can trigger driver distraction. The results also provide insights for CF behavior prediction and the optimal mixed platoon formation to enhance CAV benefits for traffic flow.

Car-Following Model Calibration Based on Driving Simulator Data to Study Driver Characteristics and to Investigate Model Validity in Extreme Traffic Situations

In this paper we use traffic data from a driving simulator study to calibrate four different car-following models. We also present two applications for which the calibration results can be used. The first application relied on the advantage that driving simulator data also contain information on driver characteristics, for example, age, gender, or the self-assessment of driver behavior. By calibrating the models for each driver individually, the resulting model parameters could be used to analyze the influence of driver characteristics on driver behavior. The analysis revealed that certain characteristics, for example, self-identification as an aggressive driver, were reflected in the model parameters. The second application was based on the capability to simulate dangerous situations that require extreme driving behavior, which is often not included in datasets from real traffic and cannot be provoked in field studies. The model validity in these situations was analyzed by comparing the prediction errors of normal and extreme driving behavior. The results showed that all four car-following models underestimated the deceleration in an emergency braking scenario in which the drivers were momentarily shocked. The driving simulator study was validated by comparing the calibration results with those obtained from real trajectory data. We concluded that driving simulator data were suitable for the two proposed applications, although the validity of driving simulator studies must always be regarded.

Parameterized Derivative-free Optimization Approach for Car-following Model Calibration

Parameterized Derivative-free Optimization Approach for Car-following Model Calibration

Hybrid Solution Combining Kalman Filtering with Takagi-Sugeno Fuzzy Inference System for Online Car-Following Model Calibration.

Nowadays, the intelligent transportation concept has become one of the most important research fields. All of us depend on mobility, even when we talk about people, provide services, or move goods. Researchers have tried to create and test different transportation models that can optimize traffic flow through road networks and, implicitly, reduce travel times. To validate these new models, the necessity of having a calibration process defined has emerged. Calibration is mandatory in the modeling process because it ensures the achievement of a model closer to the real system. The purpose of this paper is to propose a new multidisciplinary approach combining microscopic traffic modeling theory with intelligent control systems concepts like fuzzy inference in the traffic model calibration. The chosen Takagi–Sugeno fuzzy inference system proves its adaptive capacity for real-time systems. This concept will be applied to the specific microscopic car-following model parameters in combination with a Kalman filter. The results will demonstrate how the microscopic traffic model parameters can adapt based on real data to prove the model validity.

Calibration of car-following model for Indian traffic conditions

In order to implement transport polices effectively and efficiently on the ground, it is prudent to evaluate such policies using high accurate techniques such as microscopic traffic simulation models. Car-following model is regarded as vital in representing individual vehicle behaviour and highly influences the accuracy of the simulation model predictions. Though, there are number of car-following models available especially for developed countries where the traffic conditions are highly homogeneous in nature. Adopting these car-following models for Indian traffic conditions would result inaccurate estimations and unrealistic evaluation of transport policies due to the existence of highly heterogeneous traffic conditions, different driver behaviour, no lane discipline etc. on the Indian roads. In view of this, an attempt has been made in this paper to develop car-following model for Indian traffic conditions. Accordingly, data of latitude, longitude positions and speed has been collected precisely for each one tenth of second time interval on both urban corridor and non-urban corridor using VBOX equipments which are fitted in both leader and following vehicles. To develop car-following models for Indian traffic conditions, the formulations of standard car-following models namely General Motors (GM) Model and Hidas Model have been considered and accordingly modified car-following models have been developed by calibrating the parameters using the collected data on both urban and non-urban corridors. By comparing the RMSE and MAE values from estimated and observed data, it can be inferred that the developed car-following models are able to estimate the following vehicle accelerations with fair amount of accuracy.

Calibration of Car-Following Models Using a Dual Genetic Algorithm with Central Composite Design

Calibration of Car-Following Models Using a Dual Genetic Algorithm with Central Composite Design

Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method

Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem and compares different algorithms for its solution. The optimization consists of an arbitrary car following model, posed as either an ordinary or delay differential equation, being calibrated to an arbitrary source of trajectory data that may include lane changes. Typically, the calibration problem is solved using gradient free optimization. In this work, the gradient of the optimization problem is derived analytically using the adjoint method. The computational cost of the adjoint method does not scale with the number of model parameters, which makes it more efficient than evaluating the gradient numerically using finite differences. Numerical results are presented that show that quasi-Newton algorithms using the adjoint method are significantly faster than a genetic algorithm and also achieve slightly better accuracy of the calibrated model.

Is more always better? The impact of vehicular trajectory completeness on car-following model calibration and validation

This paper investigates the impact of vehicular trajectory completeness on car-following (CF) model calibration and validation. Synthetic data with different levels of trajectory completeness, i.e., different number of driving regimes, generated from carefully designed numerical experiments are mainly used to calibrate and validate the Intelligent Driver Model (IDM) and the Newell's CF model. Model calibration results suggest that some driving regimes in a trajectory impact calibration errors and the particular regime and its exact impact are model-specific, e.g., the presence of the standstill and the absence of the cruising regimes impacts IDM and Newell's CF model calibration errors, respectively. However, level of trajectory completeness has no impact. The acceleration behaviour of IDM drivers in different driving regimes is determined by more than one parameter, i.e., a one-to-one mapping between the parameters and the driving regimes do not exist. On the contrary, for Newell's CF model, there exists a one-to-one mapping between the cruising regime and the desired speed. Furthermore, level of trajectory completeness impacts IDM and Newell's CF model validation. More specifically, the average calibrated parameters obtained from more complete trajectories performs better in validation and leads to smaller validation errors. These findings can have a profound impact on how future research on CF model calibration and validation using trajectories should be planned and implemented.

Calibration of Gipps’ car‐following model for trucks and the impacts on fuel consumption estimation

Calibration of car-following models plays an important role not only in traffic simulation but also in the estimation of traffic-related energy consumption. However, the majority of calibration studies only focus on errors on position or speed, whereas these models are used to evaluate environmental parameters associated with road traffic (e.g. pollutant emissions, energy consumption). Then, this study focuses on the ability of Gipps' car-following model calibrated on trajectory parameters to estimate properly the fuel consumption of a heavy vehicle. First, the shape of one of the most used Goodness-of-Fit function, Theil's inequality coefficient, is investigated. It will be demonstrated that optimal domains are flat and large, and so many combinations of parameters could accurately reproduce the vehicle trajectory. Then, the authors found that Gipps model, calibrated via a multi-objective particle swarm optimisation is relevant to simulate the trajectory of a heavy vehicle, but fuel consumption estimation resulting of these trajectories exhibits large discrepancies. To solve this issue, it is proposed to add the fuel consumption estimation directly in the calibration process as a further dimension. The results show an improvement in the value of energy consumption estimation without increasing too much the error on the trajectory.

基于交叉熵算法的跟驰模型标定

基于交叉熵算法的跟驰模型标定

A global optimization algorithm for trajectory data based car-following model calibration

How to calibrate the parameters of car-following models based on observed traffic data is a vital problem in traffic simulation. Usually, the core of calibration is cast into an optimization problem, in which the decision variables are car-following model parameters and the objective function usually characterizes the difference between empirical vehicle movements and their simulated correspondences. Since the objective function is usually nonlinear and non-convex, various greedy or stochastic algorithms had been proposed during the last two decades. However, the performance of these algorithms remains to be further examined. In this paper, we revisit this important problem with a special focus on the geometric feature of the objective function. First, we prove that, from a global perspective, most existing objective functions are Lipschitz continuous. Second, we show that, from a local perspective, many of these objective functions are relatively flat around the global optimal solution. Based on these two features, we propose a new global optimization algorithm that integrates global direct search and local gradient search to find the optimal solution in an efficient manner. We compare this new algorithm with several existing algorithms, including Nelder–Mead (NM) algorithm, sequential quadratic programming (SQP) algorithm, genetic algorithm (GA), and simultaneous perturbation stochastic approximation (SPSA) algorithm, on NGSIM trajectory datasets. Results demonstrate that the proposed algorithm has a fast convergence speed and a high probability of finding the global optimal solution. Moreover, it has only two major configuration parameters that can be easily determined in practice.

Calibration of Car-Following Models Considering the Impacts of Warning Messages from Tablet/Smartphone Application

The phenomenon of car-following is special in traffic operations. Traditional car-following models can well describe the reactions of the movements between two concessive vehicles in the same lane within a certain distance. With the invention of connected vehicle technologies, more and more advisory messages are in development and applied in our daily lives, some of which are related to the measures and warnings of speed and headway distance between the two concessive vehicles. Such warnings may change the conventional car-following mechanisms. This paper intends to consider the possible impacts of in-vehicle warning messages to improve the traditional car-following models, including the General Motor (GM) Model and the Linear (Helly) Model, by calibrating model parameters using field data from an arterial road in Houston, Texas, U.S.A. The safety messages were provided by a tablet/smartphone application. One exponent was applied to the GM model, while another one applied to the Linear (Helly) model, both were on the stimuli term “difference in velocity between two concessive vehicles”. The calibration and validation were separately conducted for deceleration and acceleration conditions. Results showed that, the parameters of the traditional GM model failed to be properly calibrated with the interference of in-vehicle safety messages, and the parameters calibrated from the traditional Linear (Helly) Model with no in-vehicle messages could not be directly used in the case with such messages. However, both updated models can be well calibrated even if those messages were provided. The entire research process, as well as the calibrated models and parameters could be a reference in the on-going connected vehicle program and micro/macroscopic traffic simulations.

Improving the Efficacy of Car-Following Models With a New Stochastic Parameter Estimation and Calibration Method

Microscopic roadway traffic simulators, which attempt to mimic real-world driver behaviors, are based on car-following models and have been widely used as a cost-effective tool for intelligent transportation system (ITS) evaluation. In addition to evaluation, ITSs can benefit from accurate car-following models that can provide current estimations and future predictions of various traffic situations to support real-time traffic management. The accuracy and reliability of these applications are greatly dependent on the appropriate calibration of car-following models. In this paper, the authors developed a process to apply a stochastic calibration method with appropriate regularization to estimate the distribution of parameters for car-following models. The calibration method is based on the Markov chain Monte Carlo simulation that uses the Bayesian estimation theory. An intelligent driver model and Helly's car-following model were utilized to evaluate this method. The Bayesian approach provided better results in terms of the cost function than the deterministic optimization algorithm. With the Bayesian approach, the mean square error per vehicle is decreased with the increased number of vehicles. Analysis also revealed that the Bayesian approach predicted drivers' speed and acceleration/deceleration profiles more closely to the real-world data compared with the deterministic approach evaluated in this paper. Positive validation outcomes suggest potential efficacy of the calibration approach presented in this paper for future applications.

A general framework for calibrating and comparing car-following models

Recent research has shown that there exists large heterogeneity in car-following behaviour such that different car-following models best describe different drivers' behaviour. A literature review reveals that current approaches to calibrate and compare different models for one driver do not take the complexity of the models into account or are only able to compare a specific set of models. This contribution applies Bayesian techniques to the calibration of car-following models. The Bayesian framework promotes models that fit the data well but punishes models with a high complexity, resulting in a measure called the evidence. This evidence quantifies how probable each model is to be the model that best describes the car-following behaviour of a single driver. It can be computed for any car-following model. When considered over multiple drivers, the evidences can be used to describe the heterogeneity of the driving population. In an experiment seven different car-following models are calibrated and compared using a data set that was collected with a helicopter. The results indicate that multi-leader models better describe the car-following models even if their higher complexity is accounted for, and that for the description of microscopic driving behaviour the reaction time is essential; models without a reaction time perform significantly worse.