A pattern recognition algorithm for assessing trajectory completeness

Vehicular trajectories are widely used for car-following (CF) model calibration and validation, as they embody characteristics of individual driving behaviour (each trajectory reflects an individual driver). Previous studies have highlighted that the trajectories should contain all the major vehicular interactions (driving regimes) between the leader and the follower for reliable CF model calibration and validation. Based on Dynamic Time Warping and Bottom-Up algorithms, this paper develops a pattern recognition algorithm for vehicle trajectories (PRAVT) to objectively, accurately, and automatically differentiate different driving regimes in a trajectory and then select the most complete trajectories (i.e. trajectories containing a maximum number of regimes). PRAVT is rigorously tested using synthetic data and then applied to the NGSIM data. We have observed that the NGSIM data are dominated by the trajectories which contain only three regimes, namely acceleration, deceleration, and following, 77% of the trajectories lack the standstill regime, and no trajectory in the NGSIM data is complete. These findings’ impact on how to properly utilize NGSIM data can be profound. Given the extensive use of the NGSIM data in the traffic flow community, this paper also provides insights about the types of regimes contained in each trajectory of the NGSIM data.     

Second-order models and traffic data from mobile sensors

Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the standpoint of capturing higher-order traffic quantities such as acceleration/deceleration, emission and fuel consumption rates, it is desirable to examine the impact on the estimation accuracy of sampling frequency on vehicle position. Of the two issues raised above, the latter is rarely studied in the literature. This paper addresses the impact of both sampling frequency and penetration rate on mobile sensing of highway traffic. To capture inhomogeneous driving conditions and deviation of traffic from the equilibrium state, we employ the second-order phase transition model (PTM). Several data fusion schemes that incorporate vehicle trajectory data into the PTM are proposed. And, a case study of the NGSIM dataset is presented which shows the estimation results of various Eulerian and Lagrangian traffic quantities. The findings show that while first-order traffic quantities can be accurately estimated even with a low sampling frequency, higher-order traffic quantities, such as acceleration, deviation, and emission rate, tend to be misinterpreted due to insufficiently sampled vehicle locations. We also show that a correction factor approach has the potential to reduce the sensing error arising from low sampling frequency and penetration rate, making the estimation of higher-order quantities more robust against insufficient data coverage of the highway traffic.     

A new methodology for vehicle trajectory reconstruction based on wavelet analysis

Vehicle trajectories with high spatial and temporal resolution are known as the most ideal source of data for developing innovative microscopic traffic models. Aside from the method applied for collecting the vehicle trajectories, such data are more or less error-infected. The ever-increasing noise amplitude during the process of deriving the data (such as speed and acceleration) required for developing models, might change or even hide the structure of data and lead to useful information being overlooked. This highlights the importance of presenting the efficient methods which are adequate to remove noise and enhance the quality of vehicle trajectory data. Accordingly, in this paper a simple two-step technique based on wavelet analysis has been recommended for filtering errors and reconstructing trajectory data. Primarily, by using wavelet transform a special treatment was employed to identify and modify the outliers. Next, the noise in trajectory data was eliminated by applying the wavelet-based filter. The results of applying the proposed method to the synthetic noise-infected trajectory and the NGSIM dataset reveal how appropriate its performance is compared with other methodologies in terms of quantitative criteria.     

A generic data assimilation framework for vehicle trajectory reconstruction on signalized urban arterials using particle filters

With trajectory data, a complete microscopic and macroscopic picture of traffic flow operations can be obtained. However, trajectory data are difficult to observe over large spatiotemporal regions—particularly in urban contexts—due to practical, technical and financial constraints. The next best thing is to estimate plausible trajectories from whatever data are available. This paper presents a generic data assimilation framework to reconstruct such plausible trajectories on signalized urban arterials using microscopic traffic flow models and data from loops (individual vehicle passages and thus vehicle counts); traffic control data; and (sparse) travel time measurements from whatever source available. The key problem we address is that loops suffer from miss- and over-counts, which result in unbounded errors in vehicle accumulations, rendering trajectory reconstruction highly problematic. Our framework solves this problem in two ways. First, we correct the systematic error in vehicle accumulation by fusing the counts with sparsely available travel times. Second, the proposed framework uses particle filtering and an innovative hierarchical resampling scheme, which effectively integrates over the remaining error distribution, resulting in plausible trajectories. The proposed data assimilation framework is tested and validated using simulated data. Experiments and an extensive sensitivity analysis show that the proposed method is robust to errors both in the model and in the measurements, and provides good estimations for vehicle accumulation and vehicle trajectories with moderate sensor quality. The framework does not impose restrictions on the type of microscopic models used and can be naturally extended to include and estimate additional trajectory attributes such as destination and path, given data are available for assimilation.     

A dynamic lane-changing trajectory planning model for automated vehicles

This paper focuses on the lane-changing trajectory planning (LTP) process in the automatic driving technologies. Existing studies on the LTP algorithms are primarily the static planning method in which the states of the surrounding vehicles of a lane-changing vehicle are assumed to keep unchanged in the whole lane-changing process. However, in real-world traffic, the velocities of the surrounding vehicles change dynamically, and the lane-changing vehicle needs to adjust its velocity and positions correspondingly in real-time to maintain safety. To address such limitations, the dynamic lane-changing trajectory planning (DLTP) model is proposed in the limited literature. This paper proposes a novel DLTP model consisting of the lane-changing starting-point determination module, trajectory decision module and trajectory generation module. The model adopts a time-independent polynomial trajectory curve to avoid the unrealistic assumptions on lane-changing velocities and accelerations in the existing DLTP model. Moreover, a rollover-avoidance algorithm and a collision-avoidance algorithm containing a reaction time are presented to guarantee the lane-changing safety of automated vehicles, even in an emergent braking situation. The field lane-changing data from NGSIM data are used to construct a real traffic environment for lane-changing vehicles and verify the effectiveness of the proposed model, and CarSim is applied to investigate the traceability of the planned lane-changing trajectories using the proposed model. The results indicate that an automated vehicle can complete the lane-changing process smoothly, efficiently and safely following the trajectory planned by the proposed model, and the planned velocity and trajectory can be well-tracked by automated vehicles.     

A probabilistic stationary speed–density relation based on Newell’s simplified car-following model

Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow–density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic forecasting applications, probabilistic extensions of macroscopic relations are widely used. However, how to obtain such relations, in a manner that results in physically reasonable behavior has not been addressed. This paper presents the derivation of probabilistic macroscopic traffic flow relations from Newell’s simplified car-following model. The probabilistic nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow. The physical features of the model are verified analytically and shown to produce behavior which is consistent with well-established traffic flow principles. An empirical investigation is carried out using trajectory data from the New Generation SIMulation (NGSIM) program and the model’s ability to reproduce real-world traffic data is validated.     

Method for investigating intradriver heterogeneity using vehicle trajectory data: A Dynamic Time Warping approach

After first extending Newell’s car-following model to incorporate time-dependent parameters, this paper describes the Dynamic Time Warping (DTW) algorithm and its application for calibrating this microscopic simulation model by synthesizing driver trajectory data. Using the unique capabilities of the DTW algorithm, this paper attempts to examine driver heterogeneity in car-following behavior, as well as the driver’s heterogeneous situation-dependent behavior within a trip, based on the calibrated time-varying response times and critical jam spacing. The standard DTW algorithm is enhanced to address a number of estimation challenges in this specific application, and a numerical experiment is presented with vehicle trajectory data extracted from the Next Generation Simulation (NGSIM) project for demonstration purposes. The DTW algorithm is shown to be a reasonable method for processing large vehicle trajectory datasets, but requires significant data reduction to produce reasonable results when working with high resolution vehicle trajectory data. Additionally, singularities present an interesting match solution set to potentially help identify changing driver behavior; however, they must be avoided to reduce analysis complexity.     

Estimating traffic volumes for signalized intersections using connected vehicle data

Recently connected vehicle (CV) technology has received significant attention thanks to active pilot deployments supported by the US Department of Transportation (USDOT). At signalized intersections, CVs may serve as mobile sensors, providing opportunities of reducing dependencies on conventional vehicle detectors for signal operation. However, most of the existing studies mainly focus on scenarios that penetration rates of CVs reach certain level, e.g., 25%, which may not be feasible in the near future. How to utilize data from a small number of CVs to improve traffic signal operation remains an open question. In this work, we develop an approach to estimate traffic volume, a key input to many signal optimization algorithms, using GPS trajectory data from CV or navigation devices under low market penetration rates. To estimate traffic volumes, we model vehicle arrivals at signalized intersections as a time-dependent Poisson process, which can account for signal coordination. The estimation problem is formulated as a maximum likelihood problem given multiple observed trajectories from CVs approaching to the intersection. An expectation maximization (EM) procedure is derived to solve the estimation problem. Two case studies were conducted to validate our estimation algorithm. One uses the CV data from the Safety Pilot Model Deployment (SPMD) project, in which around 2800 CVs were deployed in the City of Ann Arbor, MI. The other uses vehicle trajectory data from users of a commercial navigation service in China. Mean absolute percentage error (MAPE) of the estimation is found to be 9–12%, based on benchmark data manually collected and data from loop detectors. Considering the existing scale of CV deployments, the proposed approach could be of significant help to traffic management agencies for evaluating and operating traffic signals, paving the way of using CVs for detector-free signal operation in the future.     

Spatial and temporal characterization of travel patterns in a traffic network using vehicle trajectories

This paper presents a trajectory clustering method to discover spatial and temporal travel patterns in a traffic network. The study focuses on identifying spatially distinct traffic flow groups using trajectory clustering and investigating temporal traffic patterns of each spatial group. The main contribution of this paper is the development of a systematic framework for clustering and classifying vehicle trajectory data, which does not require a pre-processing step known as map-matching and directly applies to trajectory data without requiring the information on the underlying road network. The framework consists of four steps: similarity measurement, trajectory clustering, generation of cluster representative subsequences, and trajectory classification. First, we propose the use of the Longest Common Subsequence (LCS) between two vehicle trajectories as their similarity measure, assuming that the extent to which vehicles’ routes overlap indicates the level of closeness and relatedness as well as potential interactions between these vehicles. We then extend a density-based clustering algorithm, DBSCAN, to incorporate the LCS-based distance in our trajectory clustering problem. The output of the proposed clustering approach is a few spatially distinct traffic stream clusters, which together provide an informative and succinct representation of major network traffic streams. Next, we introduce the notion of Cluster Representative Subsequence (CRS), which reflects dense road segments shared by trajectories belonging to a given traffic stream cluster, and present the procedure of generating a set of CRSs by merging the pairwise LCSs via hierarchical agglomerative clustering. The CRSs are then used in the trajectory classification step to measure the similarity between a new trajectory and a cluster. The proposed framework is demonstrated using actual vehicle trajectory data collected from New York City, USA. A simple experiment was performed to illustrate the use of the proposed spatial traffic stream clustering in application areas such as network-level traffic flow pattern analysis and travel time reliability analysis.     

Calibration of nonlinear car-following laws for traffic oscillation prediction

Frequency-domain analysis has been successfully used to (i) predict the amplification of traffic oscillations along a platoon of vehicles with nonlinear car-following laws and (ii) measure traffic oscillation properties (e.g., periodicity, magnitude) from field data. This paper proposes a new method to calibrate nonlinear car-following laws based on real-world vehicle trajectories, such that oscillation prediction (based on the calibrated car-following laws) and measurement from the same data can be compared and validated. This calibration method, for the first time, takes into account not only the driver’s car-following behavior but also the vehicle trajectory’s time-domain (e.g., location, speed) and frequency-domain properties (e.g., peak oscillation amplitude). We use Newell’s car-following model (1961) as an example and calibrate its parameters based on a penalty-based maximum likelihood estimation procedure. A series of experiments using Next Generation Simulation (NGSIM) data are conducted to illustrate the applicability and performance of the proposed approach. Results show that the calibrated car-following models are able to simultaneously reproduce observed driver behavior, time-domain trajectories, and oscillation propagation along the platoon with reasonable accuracy.     

A copula-based approach for estimating the travel time reliability of urban arterial

Estimating the travel time reliability (TTR) of urban arterial is critical for real-time and reliable route guidance and provides theoretical bases and technical support for sophisticated traffic management and control. The state-of-art procedures for arterial TTR estimation usually assume that path travel time follows a certain distribution, with less consideration about segment correlations. However, the conventional approach is usually unrealistic because an important feature of urban arterial is the dependent structure of travel times on continuous segments. In this study, a copula-based approach that incorporates the stochastic characteristics of segments travel time is proposed to model arterial travel time distribution (TTD), which serves as a basis for TTR quantification. First, segments correlation is empirically analyzed and different types of copula models are examined. Then, fitting marginal distributions for segment TTD is conducted by parametric and non-parametric regression analysis, respectively. Based on the estimated parameters of the models, the best-fitting copula is determined in terms of the goodness-of-fit tests. Last, the model is examined at two study sites with AVI data and NGSIM trajectory data, respectively. The results of path TTD estimation demonstrate the advantage of the proposed copula-based approach, compared with the convolution model without capturing segments correlation and the empirical distribution fitting methods. Furthermore, when considering the segments correlation effect, it was found that the estimated path TTR is more accurate than that by the convolution model.     

Phase transition model of non-stationary traffic flow: Definition,properties and solution method

We consider the problem of modeling traffic phenomena at a macroscopic level. Increasing availability of streaming probe data allowing the observation of non-stationary traffic motivates the development of models capable of leveraging this information. We propose a phase transition model of non-stationary traffic in conservation form, capable of propagating joint measurements from fixed and mobile sensors, to model complex traffic phenomena such as hysteresis and phantom jams, and to account for forward propagation of information in congested traffic. The model is shown to reduce to the Lighthill–Whitham–Richards model within each traffic phase for the case of stationary states, and to have a physical mesoscopic interpretation in terms of drivers’ behavior. A corresponding discrete formulation appropriate for practical implementation is shown to provide accurate numerical solution to the proposed model. The performance of the model introduced is assessed on benchmark cases and on experimental vehicle trajectories from the NGSIM datasets.     

Prediction of aircraft performances based on data collected by air traffic control centers

Accurate prediction of aircraft position is becoming more and more important for the future of air traffic. Currently, the lack of information about flights prevents us to fulfill future demands for the needed accuracy in 4D trajectory prediction. Until we get the necessary information from aircraft and until new more accurate methods are implemented and used, we propose an alternative method for predicting aircraft performances using machine learning from historical data about past flights collected in a multidimensional database. In that way, we can improve existing applications by providing them better inputs for their trajectory calculations. Our method uses flight plan data to predict performance values, which are suited individually for each flight. The results show that based on recorded past aircraft performances and related flight data we can effectively predict performances for future flights based on how similar flights behaved in the past.     

Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns

This paper shows that the behavior of driver models, either individually or entangled in stochastic traffic simulation, is affected by the accuracy of empirical vehicle trajectories. To this aim, a “traffic-informed” methodology is proposed to restore physical and platoon integrity of trajectories in a finite time–space domain, and it is applied to one NGSIM I80 dataset. However, as the actual trajectories are unknown, it is not possible to verify directly whether the reconstructed trajectories are really “nearer” to the actual unknowns than the original measurements. Therefore, a simulation-based validation framework is proposed, that is also able to verify indirectly the efficacy of the reconstruction methodology. The framework exploits the main feature of NGSIM-like data that is the concurrent view of individual driving behaviors and emerging macroscopic traffic patterns. It allows showing that, at the scale of individual models, the accuracy of trajectories affects the distribution and the correlation structure of lane-changing model parameters (i.e. drivers heterogeneity), while it has very little impact on car-following calibration. At the scale of traffic simulation, when models interact in trace-driven simulation of the I80 scenario (multi-lane heterogeneous traffic), their ability to reproduce the observed macroscopic congested patterns is sensibly higher when model parameters from reconstructed trajectories are applied. These results are mainly due to lane changing, and are also the sought indirect validation of the proposed data reconstruction methodology.     

Aircraft initial mass estimation using Bayesian inference method

Aircraft mass is a crucial piece of information for studies on aircraft performance, trajectory prediction, and many other topics of aircraft traffic management. However, It is a common challenge for researchers, as well as air traffic control, to access this proprietary information. Previously, several studies have proposed methods to estimate aircraft weight based on specific parts of the flight. Due to inaccurate input data or biased assumptions, this often leads to less confident or inaccurate estimations. In this paper, combined with a fuel-flow model, different aircraft initial masses are computed independently using the total energy model and reference model at first. It then adopts a Bayesian approach that uses a prior probability of aircraft mass based on empirical knowledge and computed aircraft initial masses to produce the maximum a posteriori estimation. Variation in results caused by dependent factors such as prior, thrust and wind are also studied. The method is validated using 50 test flights of a Cessna Citation II aircraft, for which measurements of the true mass were available. The validation results show a mean absolute error of 4.3% of the actual aircraft mass.     

Study on the framework of hybrid collision warning system using loop detectors and vehicle information

Safety warning systems generally operate based on information from sensors attached to individual vehicles. Various types of data used for collision risk calculation can be categorized into two types, microscopic or macroscopic, depending on how the sensors collect the information of traffic state. Most collision warning systems use only either of these types of data, but they all have limitations imposed by the data, such as requirement of high installation cost and high market penetration rate of devices. In order to overcome these limits, we propose a collision warning system that utilizes the integrated information of macroscopic data and microscopic data, from loop detectors and smartphones respectively. The proposed system is evaluated by simulating a real vehicle trip based on the NGSIM data. We compare the results against collision warning systems based on macroscopic data from infrastructure and microscopic data from Vehicle-to-Vehicle information. The analysis of three systems shows two findings that (a) ICWS (Infrastructure-based Collision Warning System) is inadequate for immediate collision warning system and (b) VCWS (V2V communication based Collision Warning System) and HCWS (Hybrid Collision Warning System) produce collision warning at very similar timing, even with different behavior of individual drivers. Advantages of HCWS are that it can be directly applied to existing system with small additional cost, because data of loop detector are already available to be used in Korea and smartphones are widely spread. Also, the computation power distributed to each individual smartphone greatly increases the efficiency of the system by distributing the computation resources and load.     

Sight distance analysis of highways using GIS tools

Analyzing the distance visible to a driver on the highway is important for traffic safety, especially in maneuvers such as emergency stops, when passing another vehicle or when vehicles cross at intersections. This analysis is necessary not only in the design phase of highways, but also when they are in service. For its use in this last phase, a procedure supported by a Geographic Information System (GIS) has been implemented that determines the highway distances visible to the driver. The use of a GIS allows the sight distance analysis to be integrated with other analyses related to traffic safety, such as crash and design consistency analyses. In this way, more complete analyses could be made and costs shared. Additionally, with the procedure proposed it is possible to use data regarding the trajectory of a vehicle obtained on a highway with a Global Positioning System (GPS) device. This application is very useful when highway design data are not available. The procedure developed and its application in a case study are presented in this article.     

A car-following model considering asymmetric driving behavior based on long short-term memory neural networks

Asymmetric driving behavior is a critical characteristic of human driving behaviors and has a significant impact on traffic flow. In consideration of the asymmetric driving behavior, this paper proposes a long short-term memory (LSTM) neural networks (NN) based car-following (CF) model to capture realistic traffic flow characteristics by incorporating the driving memory. The NGSIM data are used to calibrate and validate the proposed CF model. Meanwhile, three characteristics closely related to the asymmetric driving behavior are investigated: hysteresis, discrete driving, and intensity difference. The simulation results show the good performance of the proposed CF model on reproducing realistic traffic flow features. Moreover, to further demonstrate the superiority of the proposed CF model, two other CF models including recurrent neural network based CF model and asymmetric full velocity difference model, are compared with LSTM-NN model. The results reveal that LSTM-NN model can capture the asymmetric driving behavior well and outperforms other models.     

Studying the benefits of carpooling in an urban area using automatic vehicle identification data

Carpooling has been considered a solution for alleviating traffic congestion and reducing air pollution in cities. However, the quantification of the benefits of large-scale carpooling in urban areas remains a challenge due to insufficient travel trajectory data. In this study, a trajectory reconstruction method is proposed to capture vehicle trajectories based on citywide license plate recognition (LPR) data. Then, the prospects of large-scale carpooling in an urban area under two scenarios, namely, all vehicle travel demands under real-time carpooling condition and commuter vehicle travel demands under long-term carpooling condition, are evaluated by solving an integer programming model based on an updated longest common subsequence (LCS) algorithm. A maximum weight non-bipartite matching algorithm is introduced to find the optimal solution for the proposed model. Finally, road network trip volume reduction and travel speed improvement are estimated to measure the traffic benefits attributed to carpooling. This study is applied to a dataset that contains millions of LPR data recorded in Langfang, China for 1 week. Results demonstrate that under the real-time carpooling condition, the total trip volumes for different carpooling comfort levels decrease by 32–49%, and the peak-hour travel speeds on most road segments increase by 5–40%. The long-term carpooling relationship among commuter vehicles can reduce commuter trips by an average of 30% and 24% in the morning and evening peak hours, respectively, during workdays. This study shows the application potential and promotes the development of this vehicle travel mode.