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Trajectory Reconstruction for Travel Time Estimation
Abstract
In this article, we propose a Trajectory Reconstruction Model as an improvement to existing speed-based travel time estimation models. The proposed model utilizes point-based speed data collected by existing Intelligent Transportation Systems (ITS). Using the smoothing scheme proposed, it is possible to construct a speed surface as a function of space and time. Then, one can reconstruct the trajectory of an imaginary vehicle by allowing it to adopt the local speed determined by the speed surface wherever the vehicle travels. Therefore, the travel time of this vehicle can be readily determined from its trajectory. This article develops an analytical formulation of the model. Meanwhile, a discrete version of the formulation is also provided as a computational algorithm to facilitate real world implementation. In comparison with existing models, the proposed model accounts for continuous speed variation in both time and space. This ensures that the model preserves vehicle trajectories and provides sound estimates of travel time. Empirical studies were conducted based on comparison of the reconstructed travel time (estimated by the proposed model) against the Ground Truth travel time and the Instantaneous and Linear Model travel time. The empirical results showed that (1) the reconstructed travel time agrees well with the Ground Truth travel time; (2) the reconstructed travel time is more smooth than the Ground Truth, Instantaneous, and Linear Model travel times; (3) the Instantaneous and Linear Model travel time does not exhibit much difference from the other two when traffic condition is good (e.g., low travel time for the same stretch of road); (4) the difference is noticeable when traffic condition deteriorates; and (5) the difference reaches its peak under severe congestion. Quantitatively, the reconstructed travel time is not statistically different from the Ground Truth travel time and the corresponding mean absolute percentage error (MAPE) is 6.3%. In contrast, the Linear and Instantaneous travel time is statistically different from the Ground Truth travel time and the corresponding MAPE is 11.7% and 14.0%, respectively.
... Li [8] proposed an instantaneous model and a time slice model, which considered the variation of speed trajectory in space and the variation of speed in discrete time, respectively. Based on the instantaneous model, Cortés [9][10] proposed an improved dynamic time slice model. Van [11] proposed the linear model assuming that the speed between two adjacent nodes was a linear function of distance. ...
A travel time estimation method based on Speed-time field traversal including LSTM neural network was proposed to increase the real-time and accuracy of travel time estimation. The node departure speed of the traditional piecewise truncated quadratic speed trajectory model was optimized by the road node arrival speed, considering the impact of road conditions on travel time. The node arrival speed was modeled as time series and predicted in the short-term future by combining the LSTM neural network model to construct a spatiotemporally continuous speed trajectory, to estimate the link’s travel time. The method was tested on an actual road and gave considerably improved estimates and results compared to the original method, using LSTM neural network to predict node departure speed and the technique using node arrival speed. According to experimental results, the proposed method performs well in both smooth and crowded traffic circumstances, serving as a benchmark for precise real-time travel time estimation on urban roads.
... Accurate macroscopic traffic speeds on freeways are key inputs for many applications in traffic engineering: travel time prediction, hazard warnings, traffic control, road planning etc. (van Lint et al., 2005;Ni and Wang, 2008;Hou et al., 2007;Han et al., 2017;Chen and Chien, 2001). Often, traffic speeds are deduced from inductive loop detectors buried in the road surface measuring speeds from passing vehicle at fixed locations (Coifman and Kim, 2009). ...
This paper studies Deep Convolutional Neural Networks (DCNNs) for the accurate estimation of space–time traffic speeds given sparse data on freeways. Several aspects are highlighted which are crucial for the large-scale application of DCNNs to empirical probe data. (i) A methodology is proposed that allows to effectively train DCNNs on variable-sized space–time domains given empirical data prone to a varying penetration rate. Therefore, space–time domains are decomposed into small unified grids, which are processed separately. Second, in order to cope with varying penetration rates of available probe data, the network input is designed as two input matrices: grid-based speed data and grid occupancies. (ii) Using empirical probe data collected during 43 congestion scenarios on a freeway of 143 km length a shallow encoding–decoding CNN and a deep CNN are trained to reconstruct heterogeneous congestion types, such as moving and stationary congestion. It is demonstrated that for training only data of a single sparse data source is needed but no complete Ground Truth (GT), and still heterogeneous congestion types are reconstructed accurately. (iii) The estimation accuracy of a shallow encoding–decoding CNN and a DCNN, based on the U-net, are compared with traditional methods such as the ASM and PSM. An unseen complex congestion scenario is studied with all approaches and the estimation results are analyzed qualitatively and quantitatively. It is shown, that the DCNN outperforms the other approaches significantly.
Examining traffic flow in complex motorway corridors requires fine-grained empirical observation of the flow, including both longitudinal and lateral maneuvers of vehicles. Various approaches for estimating the traffic situation along motorway networks have been proposed. Although they accurately capture longitudinal behavior, methods to observe lateral maneuvers are far less numerous. Considering that many of the traffic flow phenomena are rooted in the lateral maneuvers of drivers, the limited knowledge about where and when lateral maneuvers are concentrated leads to incomplete insight and insufficient interpretation of critical phenomena such as breakdown, capacity drop, and queue spillback. In this paper, the authors propose a matching algorithm based on individual vehicle data from dual inductive loop detectors to approximate the full set of trajectories along a turbulent motorway corridor. The validation of the results on simulated PTV-VISSIM data portrays an accuracy rate of around 77 percent. The authors demonstrate how the results of the proposed algorithm can add insights into lane change patterns in a busy weaving section yielding a better understanding of traffic flow breakdown conditions. The approximated traffic state information has several potential uses in traffic estate estimation, policy analysis, bottlenecks management, microsimulation software calibration, and safety analysis.
While lane-changing movements are performed on the entire motorway network for various reasons, such as overtaking, their intensity is substantially greater near complex segments, such as weaving areas. Aside from mandatory lane changes, some drivers also conduct lateral maneuvers for cooperation or anticipation near network nodes. Unlike longitudinal driver behavior (car-following models), lateral driver behavior (lane-changing movements) has received fewer research efforts. The scarcity of suitable data resources to analyze these behaviors and movements might be a crucial cause for this research gap. This paper presents a four-step approach for reconstructing and correcting lateral bias in trajectories collected by a commercial traffic information application running on everyday smartphones. The resulting lateral position is accurate enough to allow for identification of the driving lane, and thus, the lane changes. The algorithm's core is built on a data fusion method using trajectory and loop detector data. The evaluation and validation of the proposed algorithm using drones and closed-circuit television (CCTV) data demonstrate that the core of the algorithm can correctly match more than 94% of trajectory and loop detector data. Between each pair of successive detector stations, the lateral position error has been significantly corrected and reduced to less than half the width of a standard lane of motorway networks. As a result, more than 90% of processed trajectory sample points are in the correct lane. The algorithm requires just two calibration parameters, so it is relatively simple to apply to other test networks.
Vehicle trajectory data derived from automatic vehicle location (AVL) and automatic vehicle identification (AVI) systems provide critical support for intelligent transportation systems. However, the field-obtained vehicle trajectories are usually incomplete due to sensor malfunction or communication issues. To recover the incomplete data, the existing reconstruction methods have to impose strong assumptions on driver route choice behaviors (network level) and/or traffic dynamics (link level). With the tremendous data available, leveraging data-driven approaches to address the vehicle trajectory reconstruction problem with minimal assumptions is promising. This paper proposes a general dynamic sequential learning framework to reconstruct vehicle trajectory points for both AVL and AVI data. First, an Isolation Forest based ensemble learning model is developed to extract trajectory sequences attributed to different trips in an entire trip chain of a vehicle. Second, the dynamic recurrent neural network (dynamic RNN) is tailored to learn the underlying patterns from the complete AVL and AVI trajectories, respectively. Third, a sequential prediction scheme is customized to reconstruct AVL and AVI trajectories based on the trained networks. To validate the proposed method, two experiments are conducted. One is a simulation experiment with AVL data gathered from a well-calibrated simulation model. The other is a field experiment with AVI data collected from a real-world automatic license plate recognition (ALPR) system. The results show that the proposed method achieves superior performance for both AVL and AVI data compared with the traditional methods. The impacts of different sampling rates and traffic conditions on the model performance are also discussed.
Obtaining sufficient trajectory data of human-driven vehicles (HDVs) is critical for effective control of connected automated vehicles (CAVs) in mixed traffic of HDVs and CAVs. However, due to limited sensing and communication capabilities, only a fraction of HDVs’ trajectories are often observed. This paper proposes a completion method to recovery all HDVs’ trajectories in a mixed platoon based on partial observations. The trajectory completion problem is formulated as an optimization problem, aiming to minimize the error between observed and completed trajectories with car-following constraints defined by Newell’s simplified car-following model. The method also allows various model parameters of different drivers, which is known as the inter-driver heterogeneity, to reduce the completion error. Validation using empirical trajectory data shows that the proposed method greatly lowers the completion error than other typical trajectory completion methods under sparse observation (6s/sample).
Microscopic emission models estimate second-by-second emissions and fuel consumption for individual vehicles based on vehicle trajectories. A vehicle trajectory describes how the position, speed and acceleration of a vehicle evolves over time. In practice, collecting a complete trajectory data set on a road stretch is not always feasible due to economic and privacy constraints. Therefore, several researchers suggest approaches for generating Virtual Vehicle Trajectories (VVT) given some partially observed traffic data. However, the traditional VVT generation approaches, being originally developed for travel time estimations, usually consider a simplified description of vehicle kinematics, hindering their applicability in emission modelling. In this paper, we suggest a novel approach for generating VVT, which facilitates their use in emission modelling. We empirically evaluate our method by comparing it to the traditional approaches. The results are promising, showing that, under certain experimental settings, our method can enhance the accuracy of emission estimations.
Statistics from a corridor along Interstate 5 in Los Angeles show that average travel time and travel-time variability are meaningful measures of freeway performance. Variability of travel time is an important measure of service quality for travelers. Travel time can be used to quantify the effect of incidents, and incident information can help reduce travel-time uncertainty. Predictability of travel time is a measure of the benefits of intelligent transportation systems. These measures differ from those defined in the Highway Capacity Manual and other aggregate measures of delay.
This study develops a dynamic bus arrival time prediction model using the data collected by the automatic vehicle location and automatic passenger counter systems. It is based on the Kalman filter algorithm with a two-dimensional state variable in which the prediction error in the most recent observation is used to optimize the arrival time estimate for each downstream stop. The impact of schedule recovery is considered as a control factor in the model to reflect the driver’s schedule recovery behavior. The algorithm performs well when tested with a set of automatic vehicle location-automatic passenger counter data collected from a real-world bus route. The algorithm does not require intensive computation or an excessive data preprocessing effort. It is a promising approach for real-time bus arrival time prediction in practice.
A travel time prediction algorithm scalable to large freeway networks with many nodes with arbitrary travel routes is proposed. Instead of constructing separate predictors for individual routes, it first predicts the whole future space–time field of travel times and then traverses the required subsection of the predicted travel time field to compute the travel time estimate for the requested route. Compared with the traditional approach that offers the same flexibility, the proposed method substantially reduces storage and computation time requirements at the relatively small computational cost at the time of actual prediction. It is first established that travel times computed by traversing travel time fields are compatible with more direct measurements of travel times from a vehicle reidentification technique based on electronic toll collection tags. This provides a conceptual justification of the proposed approach. When applied to the loop data from an 8.7-mi section of the I-80 freeway, the proposed approach with a time-varying coefficient (TVC) linear regression model as the component predictor not only improves the baseline historical travel time predictor substantially, with a 40% to 60% reduction in the prediction error, but also improves the traditional whole-route predictor based on the same TVC regression model by 6% to 9%. The result suggests that the proposed algorithm not only achieves the scalability but also improves prediction accuracy, both of which are critical for successful deployment of the advanced traveler information system for large freeway networks.
In this paper, a case study is carried out in Hong Kong for demonstration of the Transport Information System (TIS) prototype. A traffic flow simulator (TFS) is presented to forecast the short-term travel times that can be served as a predicted travel time database for the TIS in Hong Kong. In the TFS, a stochastic deviation coefficient is incorporated to simulate the minute-by-minute fluctuation of traffic flows within the peak hour period. The purposes of the case study are: 1) to show the applicability of the TFS for larger-scale road network; and 2) to illustrate the short-term forecasting of path travel times in practice. The results of the case study show that the TFS can be applied to real network effectively. The predicted travel times are compared with the observed travel times on the selected paths for an OD pair. The results show that the observed path travel times fall in the 90% confidence interval of the predicted path travel times.
With the advent of route guidance systems (RGS), the prediction of short-term link travel times has become increasingly important. For RGS to be successful, the calculated routes should be based on not only historical and real-time link travel time information but also anticipatory link travel time information. An examination is conducted on how real-time information gathered as part of intelligent transportation systems can be used to predict link travel times for one through five time periods (of 5 minutes' duration). The methodology developed consists of two steps. First, the historical link travel times are classified based on an unsupervised clustering technique. Second, an individual or modular artificial neural network (ANN) is calibrated for each class, and each modular ANN is then used to predict link travel times. Actual link travel times from Houston, Texas, collected as part of the automatic vehicle identification system of the Houston Transtar system were used as a test bed. It was found that the modular ANN outperformed a conventional singular ANN. The results of the best modular ANN were compared with existing link travel time techniques, including a Kalman filtering model, an exponential smoothing model, a historical profile, and a real-time profile, and it was found that the modular ANN gave the best overall results.
A methodology was developed to find appropriate travel times for highway links using data from point detectors that could be at various points within the link or could even be outside the link. The travel times were found using a definition that the appropriate value is the one experienced by a virtual vehicle reaching the midpoint of the link at the mid-point of the time step. A simple iterative scheme was proposed to find the travel time profiles. The accuracy of the scheme depends on whether aggregated detector data or individual vehicle spot speeds are used. Comparison of estimated travel times with actual experienced travel times of all vehicles in a microscopic simulation showed the technique to give very good results, comparable with having a high number of probe vehicles reporting travel times.
One objective of the Department of Transport (DoT) in the Netherlands is to provide better information to road users about the traffic situation on Dutch freeways. The idea was put forward to use existing historical freeway inductive loop data to predict a customized pretrip travel time for road users. To investigate the feasibility and usefulness of that idea, DoT launched the AIDA project. A prototype database was constructed; it contained almost 2 years of travel time data for all Dutch freeway road sections with inductive loops. A statistical algorithm was designed to compute the average travel time for any freeway journey on any future date and time. An Internet trial application was built to test the database and algorithm. Accuracy of the travel time predictions was evaluated with independent loop data. The usefulness for road users was investigated with an online survey. Results show a good match between the predicted and actual travel times. Only in 10% of analyzed cases did the actual travel time exceed the predicted travel time by more than 5 min. Of 161 respondents, 50% indicated that they found the information useful. Furthermore, 22% indicated that they would consider a different departure time on the basis of AIDA information. Thus the project has shown convincingly that the AIDA concept is not only feasible but also useful to road users. Presently DoT is looking into the uses of the concept for road users and possibly also for traffic operators.
Advanced traveler information systems (ATIS) are one component of intelligent transportation systems (ITS), and a major component of ATIS is travel time information. Automatic vehicle location (AVL) systems, which are a part of ITS, have been adopted by many transit agencies to track their vehicles and to predict travel time in real time. Because of the complexity involved, there is no universally adopted approach for this latter application, and research is needed in this area. The objectives of the research in this paper are to develop a model to predict bus arrival time using AVL data and apply the model for real-time applications. The test bed was a bus route located in Houston, Texas, and the travel time prediction model considered schedule adherence, traffic congestion, and dwell times. A historical data-based model, regression models, and artificial neural network (ANN) models were used to predict bus arrival time. It was found that ANN models outperformed both the historical data-based model and the regression model in terms of prediction accuracy. It was also found that the ANN models can be used for real-time applications.