Sparse Trajectory Research Articles

Incorporating Kinematic Wave Theory Into a Deep Learning Method for High-Resolution Traffic Speed Estimation

We propose a kinematic wave-based Deep Convolutional Neural Network (Deep CNN) to estimate high-resolution traffic speed fields from sparse probe vehicle trajectories. We introduce two key approaches that allow us to incorporate kinematic wave theory principles to improve the robustness of existing learning-based estimation methods. First, we propose an anisotropic traffic kernel for the Deep CNN. The anisotropic kernel explicitly accounts for space-time correlations in macroscopic traffic and effectively reduces the number of trainable parameters in the Deep CNN model. Second, we propose to use simulated data for training the Deep CNN. Using a targeted simulated data for training provides an implicit way to impose desirable traffic physical features on the learning model. In the experiments, we highlight the benefits of using anisotropic kernels and evaluate the transferability of the trained model to real-world traffic using the Next Generation Simulation (NGSIM) and the German Highway Drone (HighD) datasets. The results demonstrate that anisotropic kernels significantly reduce model complexity and model over-fitting, and improve the physical correctness of the estimated speed fields. We find that model complexity scales linearly with problem size for anisotropic kernels compared to quadratic scaling for isotropic kernels. Furthermore, evaluation on real-world datasets shows acceptable performance, which establishes that simulation-based training is a viable surrogate to learning from real-world data. Finally, a comparison with standard estimation techniques shows the superior estimation accuracy of the proposed method.

A Path-Clustering Driving Travel-Route Excavation

The refueling trajectory of self-driving tourists is sparse, and it is difficult to restore the real travel route. A sparse trajectory clustering algorithm is proposed based on semantic representation to mine popular self-driving travel routes. Different from the traditional trajectory clustering algorithm based on trajectory point matching, the semantic relationship between different trajectory points is researched in this algorithm, and the low-dimensional vector representation of the trajectory is learned. First, the neural network language model is used to learn the distributed vector representation of the fueling station; then, the average of all the station vectors in each trajectory is taken as the vector representation of the trajectory. Finally, the classic k-means algorithm is used to cluster the trajectory vectors. The final visualization results show that the proposed algorithm effectively mines two popular self-driving travel routes.

Detecting Lagrangian coherent structures from sparse and noisy trajectory data

Many complex flows such as those arising from the collective motion of ocean plastics in geophysics or motile cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian coherent structures (LCSs) of hyperbolic and elliptic nature in such datasets. Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion over a finite amount of time, are computed through a regularized least-squares approximation of the flow map gradient. Elliptic LCSs, which identify regions of coherent motion such as vortices and jets, are extracted using DBSCAN – a popular data clustering algorithm – combined with a systematic parameter selection strategy. We deploy these methods on various benchmark analytical flows and real-life experimental datasets ranging from oceanography to biology and show that they yield accurate results, despite sparse and noisy data. We also provide a lightweight computational implementation of these techniques as a user-friendly and straightforward Python code.

Traffic Volume Estimation for both Undersaturated and Oversaturated Signalized Intersections With Stopbar Location Estimation Using Trajectory Data

We proposed an estimator for traffic volumes at signalized intersections using only sparse trajectory data. Each pair of observed trajectories defined a statistical event, from which traffic volume was inferred. The interaction between trajectory stop distances, arrival speeds, and signal plan defined different classes of statistical events, with distinct likelihood expressions. Contrary to recent approaches found in the literature, our method addressed oversaturation and residual queues. We also proposed a method to estimate stopbar location, crucial to properly estimating stop distances and queue lengths. Arrivals were assumed to follow a negative exponential distribution., and the method was compatible with any kind of control. The signal plan was assumed to be known, but an estimated signal plan could also be used. The estimation was formulated as a maximum marginal likelihood problem. We showed the problem to be globally concave and, thus, optimally solvable by standard gradient-based methods. The estimator was first validated by an event-based Lighthill–Whitham–Richards simulation, suppressing any measurement errors from trajectories and uncertainty from driver behavior. The estimator was found to consistently show bias below 10% in low-penetration-rate situations, when the [Formula: see text] ratio was medium to high. Finally, the estimator was tested at a real-world intersection set by the authors in Beijing, China, which obtained a bias of similar of magnitude.

An Online Time-Optimal Trajectory Planning Method for Constrained Multi-Axis Trajectory With Guaranteed Feasibility

Online time-optimal trajectory planning exists in a wide range of applications such as computer numerical control (CNC) manufacturing, robotics and autonomous vehicles. Generally, the methods to generate such time-parameterized trajectory can be categorized as offline methods and online methods. Offline methods tend to generate time-optimal trajectory while it is computationally prohibitive for high frequency real-time applications. Current online methods are computationally efficient but either deal with the sparse waypoint trajectories or sacrifice the time optimality a lot. This letter innovatively proposed a time-optimal switching trajectory index coordination (TOS-TIC) strategy to solve the online time-optimal planning problem for continuous multi-axis trajectories. The proposed method is able to generate time-optimal trajectory for continuous geometric paths while considering high order kinematic constraints. The time-optimality of the trajectory planned by TOS-TIC is nearly the same as the offline planned optimal results. Meanwhile, the proposed method is computationally efficient for online applications. The proposed TOS-TIC planning strategy is an universal approach and firstly able to solve the online time-optimal trajectory planning problem for constrained continuous multi-axis trajectories, which has excellent application prospect in modern automatic industry and intelligent robots/vehicles.

Real-time time-optimal continuous multi-axis trajectory planning using the trajectory index coordination method

Real-time time-optimal trajectory planning exists in a wide range of applications such as computer numerical control (CNC) manufacturing, robotics and autonomous vehicles. Generally, the methods to generate time-optimal trajectory can be categorized as non-real-time methods and real-time methods. Non-real-time methods such as direct optimization method tend to generate time-optimal trajectory through nonlinear or linear programming while it is computationally prohibitive for high frequency real-time applications. Current real-time methods are computationally efficient but either deal with the sparse waypoint trajectories or sacrifice the time optimality a lot. This paper innovatively proposed a time-optimal switching trajectory index coordination (TOS-TIC) framework to solve the real-time time-optimal planning problem for continuous multi-axis trajectories. The proposed method is able to generate time-optimal trajectory for continuous geometric paths while considering the axial velocity and acceleration constraints. The time-optimality of the trajectory planned by TOS-TIC is nearly the same as the offline planned optimal results. Meanwhile, the proposed method is computationally efficient for even 5kHz real-time applications. The main idea of TOS-TIC is coordinating several one-axis time-optimal switching controls to generate a modified control that decreases the state deviation from the desired trajectory. Several comparative experiments are carried out on an industrial biaxial linear motor stage. And the experimental results consistently verify that the proposed TOS-TIC real-time planner generates faster trajectory compared with the real-time lookahead method. In addition, the trajectory running time and final tracking error of the proposed method are nearly the same as the offline direct optimization method.

Knowledge Graph-Based Enhanced Transformer for Metro Individual Travel Destination Prediction

Accurate and timely destination prediction of subway passengers is of great significance in improving urban residents’ travel efficiency, alleviating urban traffic pressure, and recommending the proper location-based service. Although some individual travel destination prediction methods have been proposed, the prediction performance is poor due to the large difference in travel locations of different individuals, the difficulty of evaluating the individual travel intention, the sparsity of individual travel trajectory data, and other problems. To solve these problems, this paper proposes a knowledge graph-based enhanced Transformer method (KG-Trans) for the metro individual travel destination prediction task (MITD-Pre), which contains three main modules: (1) the knowledge graph (KG) module constructs a multilayer individual travel KG from top to bottom, which accurately describes the travel individuals and their travel intentions. By analyzing the association relationship between nodes in the KG, the relationship between travel individuals can be naturally established. The learned similar travel regularity can solve the problem of sparse travel trajectories of some individuals. (2) The enhanced Transformer module extracts the dynamic and hierarchical features from the long-term sequential travel trajectory data. (3) The classifier module introduces the cross-entropy loss to constrain the uniqueness of the predicted subway travel station. The experimental results show that the proposed method obtains a higher destination prediction accuracy than the previous individual travel destination prediction methods.

Trajectory Estimation From Sparse Cellular Network Data Based on the Historical Vehicular Data

By coupling data-mining techniques with historical cellular and vehicular data, it is possible to find a certain spatiotemporal logic in the observed data. The primary motivation for combining multiple data sources derives from the fact that origin-destination matrices, extracted from cellular data sets, represent only the route's start and end-point without the information about the complete trajectory. This paper proposes a method to estimate sparse cellular data trajectories by reconstructing possible paths from the historical vehicular data. The possible routes are generated by solving the shortest-path problems for given origin-destination pair. A spatiotemporal similarity value is computed to evaluate the paths relative to the ground-truth origin-destination pair. In the end, the path with the highest similarity value is selected. Three criteria for the computation of the spatiotemporal similarity are used: length-based, modified length-based and time-based. The results show the application of proposed methods on the collected historical data, with average percentage similarity ranging from 39.85% to 56.11% (depending on the transport mode and criteria used) with modified-length criteria producing the best results - in some cases producing a trajectory with 98% similarity to the actual cellular trajectory.

Braids in the heart: global measures of mixing for cardiovascular flows

The flow patterns in the heart, in health and disease, have been of great interest for several years. Modern fluid dynamics analyses elucidate how underlying inefficient energetic or mixing characteristics of these flow patterns correlate with adverse effects. Unfortunately, translation of such modern analyses to the clinical stage remains a challenge. In this experimental work, we propose and demonstrate that braids of random and sparse particle trajectories provide an intuitive, global and practical description of cardiovascular flows. Moreover, we expose the flow pattern in an experimental healthy left ventricle model as a highly effective blood mixer at the topological level. Flow topologies that deviate from this pattern are accompanied by a reduction in energetic efficiency, as shown through comparisons with diseased flow models. These results suggest an ideal clinical approach to patient follow-up and the evaluation of the performance of medical devices.

Inferring Daily Itinerary for Drivers Based on Sparse and Incomplete Trajectory Data

Inferring Daily Itinerary for Drivers Based on Sparse and Incomplete Trajectory Data

Automatic interpolation algorithm for NURBS trajectory of shoe sole spraying based on 7-DOF robot

PurposeThe purpose of this paper is to propose an automatic interpolation algorithm for robot spraying trajectories based on cubic Non-Uniform Rational B-Splines (NURBS) curves, to solve the problem of sparse and incomplete trajectory points of the head and heel of the shoe sole when extracting robot motion trajectories using structured-light 3D cameras and to ensure the robot joints move smoothly, so as to achieve a good effect of automatic spraying of the shoe sole with a 7-degree-of-freedom (DOF) robot.Design/methodology/approachFirstly, the original shoe sole edge trajectory position points acquired by the 3D camera are fitted with NURBS curves. Then, the velocity constraint at the local maximum of the trajectory curvature is used as the reference for curve segmentation and S-shaped acceleration and deceleration planning. Immediately, real-time interpolation is performed in the time domain to obtain the position and orientation of each point of the robot motion trajectory. Finally, the inverse kinematics of the anthropomorphic motion of the 7-DOF robot arm is used to obtain the joint motion trajectory.FindingsThe simulation and experiment prove that the shoe sole spraying trajectory is complete, the spraying effect is good and the robot joint movement is smooth, which show that the algorithm is feasible.Originality/valueThis study is of good practical value for improving the quality of automated shoe sole spraying, and it has wide applicability for different shoe sole shapes.

A functional proportional hazard cure rate model for interval-censored data.

Existing survival models involving functional covariates typically rely on the Cox proportional hazards structure and the assumption of right censorship. Motivated by the aim of predicting the time of conversion to Alzheimer's disease from sparse biomarker trajectories in patients with mild cognitive impairment, we propose a functional mixture cure rate model with both functional and scalar covariates for interval censoring and sparsely sampled functional data. To estimate the nonparametric coefficient function that depicts the effect of the shape of the trajectories on the survival outcome and cure probability, we utilize the functional principal component analysis to extract the functional features from the sparsely and irregularly sampled trajectories. To obtain parameter estimates from the mixture cure rate model with interval censoring, we apply the expectation-maximization algorithm based on Poisson data augmentation. The estimation accuracy of our method is assessed via a simulation study and we apply our model on Alzheimer's disease Neuroimaging Initiative data set.

Map-Matching Using Hidden Markov Model and Path Choice Preferences under Sparse Trajectory

In the field of map matching, algorithms using topological relationships of road networks along with other data are normally suitable for high frequency trajectory data. However, for low frequency trajectory data, the above methods may cause problems of low matching accuracy. In addition, most past studies only use information from the road network and trajectory, without considering the traveler’s path choice preferences. In order to address the above-mentioned issue, we propose a new map matching method that combines the widely used Hidden Markov Model (HMM) with the path choice preference of decision makers. When calculating transition probability in the HMM, in addition to shortest paths and road network topology relationships, the choice preferences of travelers are also taken into account. The proposed algorithm is tested using sparse and noisy trajectory data with four different sampling intervals, while compared the results with the two underlying algorithms. The results show that our algorithm can improve the matching accuracy, especially for higher frequency locating trajectory. Importantly, the method takes into account the route choice preferences while correcting deviating trajectory points to the corresponding road segments, making the assumptions more reasonable. The case-study is in the city of Beijing, China.

Estimation of Path Travel Time Distributions in Stochastic Time-Varying Networks with Correlations

Transportation research has increasingly focused on the modeling of travel time uncertainty in transportation networks. From a user’s perspective, the performance of the network is experienced at the level of a path, and, as such, knowledge of variability of travel times along paths contemplated by the user is necessary. This paper focuses on developing approaches for the estimation of path travel time distributions in stochastic time-varying networks so as to capture generalized correlations between link travel times. Specifically, the goal is to develop methods to estimate path travel time distributions for any path in the networks by synthesizing available trajectory data from various portions of the path, and this paper addresses that problem in a two-fold manner. Firstly, a Monte Carlo simulation (MCS)-based approach is presented for the convolution of time-varying random variables with general correlation structures and distribution shapes. Secondly, a combinatorial data-mining approach is developed, which aims to utilize sparse trajectory data for the estimation of path travel time distributions by implicitly capturing the complex correlation structure in the network travel times. Numerical results indicate that the MCS approach allowing for time-dependence and a time-varying correlation structure outperforms other approaches, and that its performance is robust with respect to different path travel time distributions. Additionally, using the path segmentations from the segment search approach with a MCS approach with time-dependence also produces accurate and robust estimates of the path travel time distributions with the added benefit of shorter computation times.

Self-supervised human mobility learning for next location prediction and trajectory classification

Massive digital mobility data are accumulated nowadays due to the proliferation of location-based service (LBS), which provides the opportunity of learning knowledge from human traces that can benefit a range of business and management applications, such as location recommendation, anomaly trajectory detection, crime discrimination, and epidemic tracing. However, human mobility data is usually sporadically updated since people may not frequently access mobile apps or publish the geo-tagged contents. Consequently, distilling meaningful supervised signals from sparse and noisy human mobility is the main challenge of existing models. This work presents a Self-supervised Mobility Learning (SML) framework to encode human mobility semantics and facilitate the downstream location-based tasks. SML is designed for modeling sparse and noisy human mobility trajectories, focusing on leveraging rich spatio-temporal contexts and augmented traces to improve the trajectory representations. It provides a principled way to characterize the inherent movement correlations while tackling the implicit feedback and weak supervision problems in existing model-based approaches. Besides, contrastive instance discrimination is first introduced for spatio-temporal data training by explicitly distinguishing the real user check-ins from the negative samples that tend to be wrongly predicted. Extensive experiments on two practical applications, i.e., location prediction and trajectory classification, demonstrate that our method can significantly improve the location-based services over the state-of-the-art baselines.

Route Restoration Method for Sparse Taxi GPS trajectory based on Bayesian Network

Route Restoration Method for Sparse Taxi GPS trajectory based on Bayesian Network

Quasi-objective coherent structure diagnostics from single trajectories

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate objective (i.e., observer-independent) coherence diagnostics in frames satisfying a certain condition. This condition requires the trajectory accelerations to dominate the angular acceleration induced by the spatial mean vorticity. We illustrate on examples how quasi-objective coherence diagnostics highlight elliptic and hyperbolic Lagrangian coherent structures even from very sparse trajectory data.

Enhancing trajectory prediction using sparse outputs: application to team sports

Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly challenging to train a deep learning model for player trajectory prediction which outperforms linear extrapolation on average distance between predicted and true future trajectories. We propose and test a novel method for improving training by predicting a sparse trajectory and interpolating using constant acceleration, which improves performance for several models. This interpolation can also be used on models that aren't trained with sparse outputs, and we find that this consistently improves performance for all tested models. Additionally, we find that the accuracy of predicted trajectories for a subset of players can be improved by conditioning on the full trajectories of the other players, and that this is further improved when combined with sparse predictions. We also propose a novel architecture using graph networks and multi-head attention (GraN-MA) which achieves better performance than other tested state-of-the-art models on our dataset and is trivially adapted for both sparse trajectories and full-trajectory conditioned trajectory prediction.

Cycle-Based Queue Length Estimation for Signalized Intersections Using Sparse Vehicle Trajectory Data

Intersection queue length estimation using high-resolution probe vehicle trajectory data has received increasing attentions in recent years. Existing methods for cycle-based queue length estimation still face the challenge of low and/or unstable estimation accuracies under the condition of sparse vehicle trajectory data, i.e., there is no greater than one vehicle trajectory per cycle on average. To address this challenge, this study proposed a novel approach for cycle-based queue length estimation by fusing real-time and historical probe vehicle trajectory data, through a statistical parameter estimation method, i.e., maximum likelihood estimation (MLE). With known signal timing information, firstly, the historical probe trajectory data are used to acquire the arrival flow rate distribution over the entire study period. Then, a likelihood function of queue length is derived by fully exploiting real-time traffic flow information provided by the queued and non-queued probe vehicles. Finally, the MLE method is adopted to estimate the cycle-based queue lengths with the maximum probability. The proposed approach is verified using both simulation and empirical data. Results indicate that precise estimation for cycle-based queue lengths can be realized based on sparse vehicle trajectory data, while showing superiority to a representative existing method. The proposed method is basically an offline method, but it can also work in an online manner if provided a priori arrival distribution either acquired from historical probe vehicle trajectory data or a theoretical assumption.

Vehicle Trajectory Reconstruction on Urban Traffic Network Using Automatic License Plate Recognition Data

Vehicle trajectory data are critical to urban active traffic management and simulation applications. Automatic license plate recognition (ALPR) data can provide partial vehicle trajectory information by matching the detected vehicle license plates through time series. However, the trajectory extracted from ALPR data tend to be sparse and incomplete due to technical and financial constraints. This paper deals with the problem of sparse trajectory reconstruction based on ALPR data. Firstly, the multiple travel activities of the vehicle are divided based on the reasonable travel time threshold, and the incomplete vehicle trajectory is identified. Then, candidate trajectories are generated by an improved K-shortest-path (KSP) algorithm based on space-time prism theory. Finally, the auto-encoder model is utilized to select the candidate trajectory with optimal decision indicators, which realizes the vehicle trajectory reconstruction. The proposed method was implemented on a realistic urban traffic network in Ningbo, China. The verification results show that the proposed method has a comprehensive accuracy of 85% and good robustness. From the comparison with the baseline algorithm, it can be seen that the proposed method still has high accuracy in low ALPR coverage rate, and there exists a minimum required ALPR coverage rate (50% in the test network) for reconstructing trajectories accurately.