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Vehicle trajectories deliver precious information, supporting traffic state estimation and congested traffic mitigation. However, collecting fully sampled vehicle trajectories is difficult due to unaffordable data-collection costs and maintenance costs of data collection equipment. This study aims to accurately reconstruct missing vehicle trajectories by proposing a novel approach based on sparse data collected from different types of urban roads. First, an improved map-matching algorithm combining a hidden Markov model (HMM) and a bidirectional Dijkstra algorithm is proposed to ensure the high quality of the input data for trajectory reconstruction. The matched trajectory points are then converted into a two-dimensional time-space map. Subsequently, a piecewise cubic Hermite interpolating polynomial (PCHIP) algorithm is developed to reconstruct vehicle trajectories based on a total of 371 taxi trajectories on three types of urban roads. The results demonstrate that the speed-based mean relative error (MRE) value is less than 9%, and the speed-based root mean square error (RMSE_v) value is less than 6 km/h. Furthermore, the location-based MAE is found to be less than 5.86 m, and the location-based RMSE_x value is less than 7 m. Additionally, a model comparison is conducted, and the outcomes evidence that the combined method performs better than state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

This article presents a novel pipeline for visual route recognition (VRR) in large-scale urban environments, leveraging open street view data. The proposed approach aims to identify the path of a video recorder by analyzing visual cues from continuous video frames and street landmarks, evaluated through datasets from New York and Taipei City. The pipeline begins with semantic visual geo-localization (SemVG), a semantic fused feature extraction network that filters out nonlandmark noise, generating robust visual representations. We construct a feature database from multiperspective street view images to enable efficient feature retrieval for query video frames. In addition, we introduce a spatio-temporal trajectory reconstruction method that corrects mismatches in the camera's motion path, ensuring consistency. Our contributions include the development of SemVG, a method for maintaining spatio-temporal consistency in trajectory reconstruction, and a large-scale Taipei dataset designed for VRR. This work has implications for urban surveillance, law enforcement, and smart city applications, supporting urban planning, resource management, search and rescue, and augmented reality navigation by improving localization without specialized hardware.

CCTVs and telecom base stations act as sensors, and collect massive face and phone related data. When used for person localization and trajectory characterization, they each present quite different spatiotemporal characteristics: CCTV is associated with slowly sampled face ID trajectories with spatial resolution of approximately 20 meters, while telecom readings provide fast sampled phone ID trajectories with spatial uncertainty of a few hundred meters. The face or phone trajectory can be seen as an observation of the real trajectory of a moving pedestrian. It is useful to identify the correspondence between face and phone trajectories to reconstruct the trajectory of moving persons. To this end, we propose a complementarity-oriented feature fusion mechanism (COFFM) to model and utilize the common embedding and complementarity of these two measurement modalities. Specifically, a Cycle Heterogeneous Trajectory Translation Network (CCTTN) is proposed to realize a TFE (Trajectory Feature Extractor) which captures the latent transforming relationships between the face and phone modalities. The latent features from both transforming directions are concatenated in the Feature Unifying (FU) module and fed into a binary face-phone trajectory matching discriminator (FPTPMD) to infer whether a face-phone trajectory pair corresponds to the same underlying motion trajectory. We evaluated our method on a large real-world face-phone trajectory dataset and showed promising results with the accuracy of 97.1% which exceeds the comparable similarity-based methods. The developed principle and framework generalize well to other multi-modality trajectory matching tasks.

This paper presents significant enhancements to the vertical reconstruction component of EUROCONTROL's Surveillance Analysis Support System for ATC Centres (SASS-C). We introduce four key improvements: (1) a novel segmentation algorithm for more precise flight phase identification, (2) an improved invalid height detection process using LOWESS and sliding window analysis, (3) a protection mechanism against simultaneous measurements at the Kalman filter level, and (4) an optimized approach for smooth overshoot correction during segment transitions. These advancements address limitations in the current system, particularly in trajectory segmentation accuracy and robustness against measurement anomalies. Our methodology employs both synthetic and real-world data for comprehensive evaluation, ensuring performance under controlled and operational conditions. The results demonstrate substantial improvements in segmentation precision, outlier detection, and overall trajectory reconstruction quality. The invalid detection algorithm, while incurring a slight computational cost, significantly enhances trajectory accuracy. These enhancements contribute to more reliable air traffic analysis, supporting safer and more efficient airspace management. The paper concludes by discussing potential future work, including the application of machine learning techniques and the extension of these improvements to horizontal reconstruction processes. [ABSTRACT FROM AUTHOR]

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Vehicle trajectory data are invaluable for driving behaviour and traffic flow modelling studies, especially at the microscopic level. However, existing public vehicle trajectory datasets only provide data with inherent errors and lack the corresponding ground truth. This study presents a comprehensive vehicle trajectory dataset obtained using both drone and high-precision Global Navigation Satellite System (GNSS) receiver technologies with an error of less than 5 cm. The dataset contains 70 complete trajectories with a total of 10,840 data points and an average length of 48.4 m. This includes 27 left-turn trajectories, 27 through trajectories and 16 right-turn trajectories. The trajectories collected by the centimetre-level precision GNSS receiver can be regarded as the ground truth of the trajectories extracted by the drone video. Researchers can use these two trajectory datasets to analyse driving behaviour at interactive scenarios, validate and calibrate microscopic traffic flow models, and validate trajectory reconstruction methods.

Abnormal-trajectory detection can be used to detect fraudulent behavior of taxi drivers transporting passengers. Aiming at the problem that existing methods do not fully consider abnormal fragments of trajectories, this paper proposes an abnormal-trajectory detection method based on sub-trajectory classification and outlier-factor acquisition, which effectively detects abnormal sub-trajectories and further detects abnormal trajectories. First, each trajectory is reconstructed using the turning angles and is divided into multiple sub-trajectories according to the turning angle threshold and trajectory point original acceleration. The sub-trajectories are then classified according to the extracted directional features. Finally, the multivariate distances between angular adjacent segments are calculated to obtain the outlier factor, and abnormal sub-trajectories are detected. The sum of the lengths of the abnormal sub-trajectories is used to calculate the outlier score and identify abnormal trajectories. Based on experimental results using real trajectory datasets, it has been found that the proposed method performs better at detecting abnormal trajectories than other similar methods. [ABSTRACT FROM AUTHOR]

ObjectiveIn order to improve the accuracy and efficiency of ship trajectory anomaly detection, and solve the problems of traditional anomaly detection methods such as limited feature characterization ability, insufficient compensation accuracy, gradient disappearance and overfitting, an unsupervised ship trajectory anomaly detection method based on the Transformer_LSTM codec module is proposed.MethodBased on the encoder decoder architecture, the Transformer_LSTM module replaces the traditional neural network to achieve track feature extraction and track reconstruction. By embedding the transformer into the recursive mechanism of LSTM, combined with the cyclic unit and attention mechanism, self-attention and cross-attention can be used to calculate the state vector of the cyclic unit and effectively construct the long sequence model. By minimizing the difference between the reconstructed output and original input, the model learns the characteristics and motion mode of the general trajectory, and trajectories with a reconstruction error greater than the abnormal threshold are judged as abnormal trajectories. ResultsAIS data collected in January 2021 is adopted. The results show that the accuracy, precesion and recall rate of the model are significantly improved compared with those of LOF, DBSCAN, VAE, LSTM, etc. The F1 score is improved by 8.11% compared with that of the VAE_LSTM model.ConclusionThe anomaly detection performance of the proposed method is significantly superior to the traditional algorithm in various indexes, and the model can be effectively and reliably applied to the trajectory anomaly detection of ships at sea.

Currently the state-of-the-art monocular 3D object detectors use machine learning to estimate the 6DOF pose and shape of vehicles. This requires large amounts of precisely annotated 3D data for the training process and significant computing power for inference. Alternatively, there exist methods, which attempt to reconstruct target vehicle shapes and scales using projective geometry and classically detected feature points such as SURF and ORB. These methods use specific camera motion or geometrical constraints which cannot always be assumed. The resulting model is an unstructured point cloud which contains no semantic information, making its utility inconvenient in a distributed perception system. In this study, the applicability of semantic keypoints for vehicle shape and trajectory estimation is explored. A novel method is presented, which is capable reconstructing the semantic shape and trajectory of the target vehicle from a sequence of images with state-of-the art accuracy. The resulting semantic vertex model is then used for monocular, single frame 6DOF pose estimation with high accuracy. Building on this, a cooperative perception framework is also introduced. The algorithm is tested in both in-vehicle and infrastructure mounted mono-camera sensor setups. In addition to achieving state of the art depth accuracy in vehicle trajectory reconstruction on the Argoverse dataset, our method outperforms the state of the art shape-aware deep learning method in pose estimation in a cooperative perception scenario both in simulation and in real-world experiments.

Airborne Wide angle staring Synthetic Aperture Radar (WasSAR) is a novel SAR imaging technique that enables multiangle and long-time staring imaging of an observation region. The combination of WasSAR and Ground Moving Target Indication (GMTI) facilitates the long-time tracking of moving targets in key areas, thereby obtaining dynamic sensing information. Herein, we initially constructed a moving target echo model for airborne multi-channel WasSAR, followed by an analysis of the characteristics of a moving target during WasSAR imaging. Further, group phase shift calibration and modified A2DC methods are proposed to mitigate the influence of platform attitude errors and channel imbalances. In accordance with this, an extended airborne multi-channel WasSAR ground moving target detection and tracking method is proposed, which achieves accurate detection and tracking of targets moving on complex roads. Finally, a trajectory reconstruction method for moving targets in airborne multi-channel WasSAR-GMTI is presented, demonstrating accurate trajectory reconstruction for targets on complex roads. Moreover, a flight experiment using our independently developed airborne multi-channel WasSAR-GMTI system, along with the associated real data processing results, is presented. These results confirm the validity and practicability of airborne WasSAR-GMTI for moving target dynamic surveillance and serve as a foundation for future research.

This paper presents significant enhancements to the vertical reconstruction component of EUROCONTROL’s Surveillance Analysis Support System for ATC Centres (SASS-C). We introduce four key improvements: (1) a novel segmentation algorithm for more precise flight phase identification, (2) an improved invalid height detection process using LOWESS and sliding window analysis, (3) a protection mechanism against simultaneous measurements at the Kalman filter level, and (4) an optimized approach for smooth overshoot correction during segment transitions. These advancements address limitations in the current system, particularly in trajectory segmentation accuracy and robustness against measurement anomalies. Our methodology employs both synthetic and real-world data for comprehensive evaluation, ensuring performance under controlled and operational conditions. The results demonstrate substantial improvements in segmentation precision, outlier detection, and overall trajectory reconstruction quality. The invalid detection algorithm, while incurring a slight computational cost, significantly enhances trajectory accuracy. These enhancements contribute to more reliable air traffic analysis, supporting safer and more efficient airspace management. The paper concludes by discussing potential future work, including the application of machine learning techniques and the extension of these improvements to horizontal reconstruction processes.

To minimize the human–machine conflict in the shared steering control system and protect the driving intention of the driver, a human-centered shared steering control system is proposed in obstacle avoidance scenarios. First, a framework is proposed based on the parallel shared steering control system framework, which includes the trajectory reconstruction, driver model, authority allocation model, autonomous controller, and vehicle. And mathematical model of the sub-modules in the shared steering control system is constructed. Then, the trajectory reconstruction method considering the driving intention of the driver is designed. A trigger mechanism with human–machine conflict as input is designed for trajectory reconstruction. More specifically, to protect the driving intention of the driver, the steering input of the driver is used as the constraint to reconstruct the trajectory. Finally, the effectiveness of the proposed method is verified by simulation. The simulation results show that the proposed method can effectively reduce human–machine conflict while the driving intention of the driver is protected. However, the trajectory tracking performance and lateral stability of the vehicle may be may sacrificed within a limited extent. [ABSTRACT FROM AUTHOR]

Density maps support a bird's eye view of vessel traffic, through providing an overview of vessel behavior, either at a regional or global scale in a given timeframe. However, any inaccuracies in the underlying data, due to sensor noise or other factors, evidently lead to erroneous interpretations and misleading visualizations. In this work, we propose a novel algorithmic framework for generating highly accurate density maps of shipping activities, from incomplete data collected by the Automatic Identification System (AIS). The complete framework involves a number of computational steps for (1) cleaning and filtering AIS data, (2) improving the quality of the input dataset (through trajectory reconstruction and satellite image analysis) and (3) computing and visualizing the subsequent vessel traffic as density maps. The framework describes an end-to-end implementation pipeline for a real world system, capable of addressing several of the underlying issues of AIS datasets. Real-world data are used to demonstrate the effectiveness of our framework. These experiments show that our trajectory reconstruction method results in significant improvements up to 15% and 26% for temporal gaps of 3–6 and 6–24 h, respectively, in comparison to the baseline methodology. Additionally, a use case in European waters highlights our capability of detecting "dark vessels", i.e., vessel positions not present in the AIS data. [ABSTRACT FROM AUTHOR]

This paper discusses the use of networks of Inertial Measurement Units (IMUs) for the reconstruction of trajectories from sensor data. Logistics is a natural application domain to verify the quality of the handling of goods. This is a mass application and the economics of logistics impose that the IMUs to be used must be low-cost and use basic computational devices. The approach in this paper converts a strategy from the literature, used in the multi-target following problem, to reach a consensus in a network of IMUs. This paper presents results on how to achieve the consensus in trajectory reconstruction, along with covariance intersection data fusion of the information obtained by all the nodes in the network. [ABSTRACT FROM AUTHOR]

Trajectory estimation is essential for obtaining a complete picture of traffic flow with limited and continuously detected traffic data, which are helpful in evaluating transportation performance and developing precise control measures. Most existing models assume the first-in-first-out principle, which generally is violated by the overtaking action in microscopic simulations and observations. This study focused on improving the accuracy of trajectory reconstruction by incorporating probes and fixed sensor data in multilane facilities. Accordingly, we developed a staircase vehicle order–changing model to describe the overtaking behaviors of vehicles. A field-test data set containing Global Positioning System (GPS) trajectories and automatic vehicle identification (AVI) observations was collected from some probe position units and fixed vehicle-identification cameras. Empirical studies demonstrated that the estimated error of the proposed algorithm was approximately 7%, which was approximately 22% and 12.5% less than that of two benchmark models. These results verified the superiority of our proposed algorithm and confirmed the importance of considering the overtaking behavior of vehicles in trajectory reconstruction. [ABSTRACT FROM AUTHOR]

AIS (Automatic Identification System) is a telecommunication system created to enable ships to transmit information regarding their trajectories (such as their position, speed, course, etc.) to other ships and shore stations. With the use of AIS, collisions between ships can be avoided. Unfortunately, AIS suffers from some technical issues that lead to part of the transmitted data being damaged (incorrect or missing). This paper contains a review of machine learning based methods of reconstructing this damaged AIS data as well as examples of inspiration from other telecommunication systems for dealing with this kind of a problem. Finally, after analysing frameworks available in the relevant literature, a novel algorithm for AIS data reconstruction is briefly presented. [ABSTRACT FROM AUTHOR]

Copyright of Geography & Geographic Information Science is the property of Geography & Geo-Information Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Brain computer interface (BCI) is a system that directly uses brain neural activities to communicate with the outside world. Recently, the decoding of the human upper limb based on electroencephalogram (EEG) signals has become an important research branch of BCI. Even though existing research models are capable of decoding upper limb trajectories, the performance needs to be improved to make them more practical for real-world applications. This study is attempt to reconstruct the continuous and nonlinear multi-directional upper limb trajectory based on Chinese sign language. Here, to reconstruct the upper limb motion trajectory effectively, we propose a novel Motion Trajectory Reconstruction Transformer (MTRT) neural network that utilizes the geometric information of human joint points and EEG neural activity signals to decode the upper limb trajectory. Specifically, we use human upper limb bone geometry properties as reconstruction constraints to obtain more accurate trajectory information of the human upper limbs. Furthermore, we propose a MTRT neural network based on this constraint, which uses the shoulder, elbow, and wrist joint point information and EEG signals of brain neural activity during upper limb movement to train its parameters. To validate the model, we collected the synchronization information of EEG signals and upper limb motion joint points of 20 subjects. The experimental results show that the reconstruction model can accurately reconstruct the motion trajectory of the shoulder, elbow, and wrist of the upper limb, achieving superior performance than the compared methods. This research is very meaningful to decode the limb motion parameters for BCI, and it is inspiring for the motion decoding of other limbs and other joints.

The ability to accurately predict flight time of arrival in real time during a flight is critical to the efficiency and reliability of aviation system operations. This paper proposes a data-light and trajectory-based machine learning approach for the online prediction of estimated time of arrival at terminal airspace boundary (ETA_TAB) and estimated landing time (ELDT), while a flight is airborne. Rather than requiring a large volume of data on aircraft aerodynamics, en-route weather, and traffic, this approach uses only flight trajectory information on latitude, longitude, and speed. The approach consists of four modules: (a) reconstructing the sequence of trajectory points from the raw trajectory that has been flown, and identifying its best-matched historical trajectory which bears the most similarity; (b) predicting the remaining trajectory, based on what has been flown and the best-matched historical trajectory; this is achieved by developing a long short-term memory (LSTM) network trajectory prediction model; (c) predicting the ground speed of the flight along its predicted trajectory, iteratively using the current position and previous speed information; to this end, a gradient boosting machine (GBM) speed prediction model is developed; and (d) predicting ETA_TAB using trajectory and speed prediction from (b) and (c), and using ETA_TAB to further predict ELDT. Since LSTM and GBM models can be trained offline, online computation efforts are kept at a minimum. We apply this approach to real-world flights in the US. Based on our findings, the proposed approach yields better prediction performance than multiple alternative methods. The proposed approach is easy to implement, fast to perform, and effective in prediction, thus presenting an appeal to potential users, especially those interested in flight ETA prediction in real time but having limited data access. [ABSTRACT FROM AUTHOR]

Brain computer interface (BCI) is a system that directly uses brain neural activities to communicate with the outside world. Recently, the decoding of the human upper limb based on electroencephalogram (EEG) signals has become an important research branch of BCI. Even though existing research models are capable of decoding upper limb trajectories, the performance needs to be improved to make them more practical for real-world applications. This study is attempt to reconstruct the continuous and nonlinear multi-directional upper limb trajectory based on Chinese sign language. Here, to reconstruct the upper limb motion trajectory effectively, we propose a novel Motion Trajectory Reconstruction Transformer (MTRT) neural network that utilizes the geometric information of human joint points and EEG neural activity signals to decode the upper limb trajectory. Specifically, we use human upper limb bone geometry properties as reconstruction constraints to obtain more accurate trajectory information of the human upper limbs. Furthermore, we propose a MTRT neural network based on this constraint, which uses the shoulder, elbow, and wrist joint point information and EEG signals of brain neural activity during upper limb movement to train its parameters. To validate the model, we collected the synchronization information of EEG signals and upper limb motion joint points of 20 subjects. The experimental results show that the reconstruction model can accurately reconstruct the motion trajectory of the shoulder, elbow, and wrist of the upper limb, achieving superior performance than the compared methods. This research is very meaningful to decode the limb motion parameters for BCI, and it is inspiring for the motion decoding of other limbs and other joints. [ABSTRACT FROM AUTHOR]

The advance in neuroscience and computer technology over the past decades have made brain-computer interface (BCI) a most promising area of neurorehabilitation and neurophysiology research. Limb motion decoding has gradually become a hot topic in the field of BCI. Decoding neural activity related to limb movement trajectory is considered to be of great help to the development of assistive and rehabilitation strategies for motor-impaired users. Although a variety of decoding methods have been proposed for limb trajectory reconstruction, there does not yet exist a review that covers the performance evaluation of these decoding methods. To alleviate this vacancy, in this paper, we evaluate EEG-based limb trajectory decoding methods regarding their advantages and disadvantages from a variety of perspectives. Specifically, we first introduce the differences in motor execution and motor imagery in limb trajectory reconstruction with different spaces (2D and 3D). Then, we discuss the limb motion trajectory reconstruction methods including experiment paradigm, EEG pre-processing, feature extraction and selection, decoding methods, and result evaluation. Finally, we expound on the open problem and future outlooks. [ABSTRACT FROM AUTHOR]

We study the Hamilton-Jacobi (HJ) approach for a two-person zero-sum differential game with state constraints and where controls of the two players are coupled within the dynamics, the state constraints and the cost functions. It is known for such problems that the value function may be discontinuous and its characterization by means of an HJ equation requires some controllability assumptions involving the dynamics and the set of state constraints. In this work, we characterize this value function through an auxiliary differential game free of state constraints. Furthermore, we establish a link between the optimal strategies of the constrained problem and those of the auxiliary problem and we present a general approach allowing to construct approximated optimal feedbacks to the constrained differential game for both players. Finally, an aircraft landing problem in the presence of wind disturbances is given as an illustrative numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we aim to reconstruct meteoroid trajectories using a forward scatter radio system transmitting a continuous wave (CW) with no modulation. To do so, we use the meteor echoes recorded at the receivers of the BRAMS (Belgian RAdio Meteor Stations) network. This system consists, at the time of writing, of a dedicated transmitter and 44 receiving stations located in and nearby Belgium, all synchronized using GPS clocks. Our approach processes the meteor echoes at the BRAMS receivers and uses the time delays as inputs to a nonlinear optimization solver. We compare the quality of our reconstructions with and without interferometric data to the trajectories given by the optical CAMS (Cameras for Allsky Meteor Surveillance) network in Benelux. We show that the general CW forward scatter trajectory reconstruction problem can be solved, but we highlight its strong ill‐conditioning. With interferometry, this high sensitivity to the inputs is alleviated and the reconstructed trajectories are in good agreement with optical ones, displaying an uncertainty smaller than 10% on the velocity and 2° on the inclination for most cases. To increase accuracy, the trajectory reconstruction with time delays only should be complemented by information about the signal phase. The use of at least one interferometer makes the problem much easier to solve and greatly improves the accuracy of the retrieved velocities and inclinations. Increasing the number of receiving stations also enhances the quality of the reconstructions. Plain Language Summary: This paper presents a method for tracking the path and speed of meteoroids using radio observations. A simple continuous wave signal is reflected by the electrons created when the meteoroid enters the upper atmosphere and creates ionization. The reflected signal, called a meteor echo, is recorded at various locations not co‐located with the transmitter. The time delays between several echoes is used to retrieve the meteoroid trajectory and speed. In this work, we apply this method using data from Belgian RAdio Meteor Stations (BRAMS), a Belgian network of 44 receiving stations. The results are compared to accurate observations from Cameras for Allsky Meteor Surveillance, an optical network of cameras surveying the sky for meteors. Our method perfectly works with no measurement errors but small uncertainties on the time delays may significantly impact the accuracy of the reconstruction. Using a large amount of receivers and/or a radio interferometer greatly improves the results. This project is the first to tackle the meteoroid trajectory reconstruction using this type of radio system (with no range information and many receivers at different locations). This novel method is essential to fully exploit the capabilities of BRAMS for future applications such as determination of fluxes or sounding of the upper atmosphere (e.g., wind speed measurements). Key Points: Meteoroid trajectory and speed determined with a continuous wave forward scatter radio set‐upTrajectory reconstruction solver is validated against simulated data but the problem is ill‐conditionedInterferometry required for an accuracy of <10% on the velocity and <2° on the inclination for most trajectories [ABSTRACT FROM AUTHOR]

AIS (Automatic Identification System) is a telecommunication system created to enable ships to transmit information regarding their trajectories (such as their position, speed, course, etc.) to other ships and shore stations. With the use of AIS, collisions between ships can be avoided. Unfortunately, AIS suffers from some technical issues that lead to part of the transmitted data being damaged (incorrect or missing). This paper contains a review of machine learning based methods of reconstructing this damaged AIS data as well as examples of inspiration from other telecommunication systems for dealing with this kind of a problem. Finally, after analysing frameworks available in the relevant literature, a novel algorithm for AIS data reconstruction is briefly presented.

The advances in positioning techniques have generated massive trajectory data that represent the mobility of objects, e.g., pedestrians and mobile phones. It is important to integrate information from various modalities for subject tracking or trajectory prediction. Our work attempts to match a face with a corresponding mobile phone based on the heterogeneous trajectories. We propose a framework which associates face trajectories with their corresponding mobile phone trajectories using elaborate and explainable features. Our solution includes two stages: an initial selection of phone trajectories for a given face trajectory and a subsequent identification of which phone trajectory provides an exact match to the given face trajectory. In the first stage, we propose a Multi-Granularity SpatioTemporal Window Searching (MGSTWS) algorithm to select candidate mobile phones that are spatiotemporally close to a given face. In the second stage, we first build an affinity function to score face–phone trajectory point pairs selected by MGSTWS, and construct a feature set for building a face–phone trajectory matching determinator which determines whether a phone trajectory matches a given face trajectory. Our well-designed features guarantee high model simplicity and interpretability. Among the feature set, BGST intelligently leverages disassociation between a face and a mobile phone even if there exists some co-occurence for a non-matching face–phone pair. Based on the feature set, we represent the face–phone matching task as a binary classification problem and train various models, among which LightGBM achieves the best performance with 92.6% accuracy, 96.9% precision, 88.5% recall, and 92.5% F1. Our framework is acceptable in most application scenarios and may benefit some downstream tasks. The preselection-refining architecture of our framework guarantees the applicability and efficiency of the face–phone trajectory pair matching frame. [ABSTRACT FROM AUTHOR]

In maritime operations, instances occur where vessels flee after colliding with buoys. Automatic Identification System (AIS) data collected from these buoys play a vital role in identifying the responsible party and determining liability. However, data from buoys can be lost in rough sea conditions and equipment failure, which makes it difficult to identify accidents where ships collide with buoys. To address this issue, this study proposes a model that combines Long Short-Term Memory Network (LSTM) with Multiple Attention mechanisms to reconstruct buoy trajectories with high precision. In this paper, the buoy trajectory reconstruction test is carried out using Qingdao Harbour Buoy 304 a case study, and the validation results show that the mean squared error (MSE) of this model is 12.15. In addition, the LSTM-Attention model shows a significant improvement in all the metrics compared with other models: compared with the Random sampling model, the mean absolute error (MAE) is improved by 75.15%, and the root mean squared error (RMSE) by 71.02%; MSE by 77.31%, MAE by 36.70%, and RMSE by 52.36% compared to the Cubic spline model; and MSE by 49.92%, MAE by 27.35%, and RMSE by 29.52% compared to the Hermite model. These results show that the LSTM-Attention model significantly improves the accuracy and reliability of trajectory reconstruction. • A novel LSTM-Attention model for reconstructing buoy trajectories is presented. • The model greatly improves the accuracy, and its MSE, MAE and RMSE are better than those of traditional methods. • A case study of buoy 304 in Qingdao harbour demonstrates the effectiveness of the model in a maritime environment. [ABSTRACT FROM AUTHOR]

• A Physics-Informed Neural Network (PINN)-based framework is proposed to address the trajectory stitching problem. • This framework incorporates the advantages of the physics model-based and learning-based methods. • This framework has demonstrated fairly good extrapolation ability, making it suitable for diverse traffic dynamics and ensuring robust performance across varying scenarios. • The dataset processed by the proposed framework, named the High-granularity Highway Simulation (HIGH-SIM) dataset, has been published online for public use. High-accuracy long-coverage vehicle trajectory data can benefit the investigations of various traffic phenomena. However, existing datasets frequently contain broken trajectories due to sensing limitations, which impedes a thorough understanding of traffic. To address this issue, this paper proposes a Physics-Informed Neural Network (PINN)-based method for stitching broken trajectories. The proposed PINN-based method enhances traditional neural networks by integrating physics priors, including vehicle kinematics and boundary conditions, aiming to provide information beyond training domain and regularization, thus increasing method accuracy and extrapolation ability for cross-dynamics scenarios (e.g., extrapolating from low-speed training data to reconstruct high-speed trajectories). Two publicly available vehicle trajectory datasets, NGSIM and HighSIM, were adopted to validate the proposed PINN-based method, and four biased training scenarios were designed to assess the PINN-based method's extrapolation ability. Results indicate that the PINN-based method demonstrated superior performance regarding trajectory stitching accuracy and consistency compared to benchmark models. The dataset processed using our proposed PINN-based method has been made publicly available online to support the traffic research community. Additionally, this PINN-based approach can be applied to a broader range of scenarios that include physics-based priors. [ABSTRACT FROM AUTHOR]

A trajectory is a sequence of observations in time and space, for examples, the path formed by maritime vessels, orbital debris, or aircraft. It is important to track and reconstruct vessel trajectories using the Automated Identification System (AIS) data in real-world applications for maritime navigation safety. In this project, we use the National Science Foundation (NSF)'s Algorithms for Threat Detection program (ATD) 2019 Challenge AIS data to develop novel trajectory reconstruction method. Given a sequence of N unlabeled timestamped observations X = {x1,x2,…,xN}, the goal is to track trajectories by clustering the AIS points with predicted positions using the information from the true trajectories X. It is a natural way to connect the observed point xî with the closest point that is estimated by using the location, time, speed, and angle information from a set of the points under consideration xi ∀ i ∈ {1, 2, …, N}. The introduced method is an unsupervised clustering-based method that does not train a supervised model which may incur a significant computational cost, so it leads to a real-time, reliable, and accurate trajectory reconstruction method. Our experimental results show that the proposed method successfully clusters vessel trajectories.

The recent advancement in single-cell RNA sequencing technologies enables the understanding of dynamic cellular processes at the single-cell level. Using trajectory inference methods, pseudotimes can be estimated based on reconstructed single-cell trajectories which can be further used to gain biological knowledge. Existing methods for modeling cell trajectories, such as minimal spanning tree or k-nearest neighbor graph, often lead to locally optimal solutions. In this paper, we propose a penalized likelihood-based framework and introduce a stochastic tree search (STS) algorithm aiming at the global solution in a large and non-convex tree space. Both simulated and real data experiments show that our approach is more accurate and robust than other existing methods in terms of cell ordering and pseudotime estimation. [ABSTRACT FROM AUTHOR]

The fingerprinting-based positioning has great potential for indoor location estimation where GPS signals are mostly blocked. However, fingerprinting-based methods need a calibration step for establishing a fingerprint map. The site survey process should be performed to record fingerprints which is a labor-intensive task essentially in large buildings. In this paper, we address the pedestrian trajectory reconstruction problem for fingerprint map creation. Where the goal is to predict and refine users' trajectories obtained from smartphone sensor measurements. Our proposed spatial–temporal matching mechanism consists of three stages. First, the initial trajectory is calculated using the PDR algorithm. Then, landmarks error is eliminated using the proposed forward/backward error correction (FEC/BEC) algorithm. Afterward, the proposed dynamic time warping-based path-matching (DTW-PM) method applies to handle map-related errors. The evaluation results show positioning accuracy improves up to 53.69%. Finally, a traditional KNN algorithm is performed to evaluate the positioning efficiency over generated radio map, which validates the quality of the obtained radio map. [ABSTRACT FROM AUTHOR]

Reconstructing sphere motion is an essential part of indoor screen-based ball sports. Current sphere recognition techniques require expensive high-precision equipment and complex field deployment, which limits the application of these techniques. This paper proposes a novel method for recognizing and recovering sphere motion based on a low-frame-rate monocular camera. The method captures ball motion streaks in input images, reconstructs trajectories in space, and then estimates ball speed. We evaluated the effectiveness of the streak detection method and obtained an F1-score of 0.97. We also compared the performance of the proposed trajectory reconstruction method with existing methods, and the proposed method outperformed the compared techniques. [ABSTRACT FROM AUTHOR]

In shooting incident reconstructions, forensic examiners usually deal with scenes involving short-range trajectories, typically ≤30 m. In situations such as this, a linear trajectory reconstruction model is appropriate. However, a forensic expert can also be asked to estimate a shooter's position by reconstructing a long-range trajectory where the bullet's path becomes arced as a result of gravity and the greater time in flight. In this study, the point mass model (PMM) was used, because it is accessible and considered sufficiently accurate. A computer program using PMM can perform long-range trajectory reconstructions starting from an impact point. The reconstruction results in an area where the shot is expected to be fired from, not a single location. This is caused by varying the input parameters of the PMM. The aim of this study is to assess the accuracy of the method and discuss the influence of the most relevant parameters. The model has been validated by comparing its performance with 20 handgun bullet trajectories that were determined using Doppler radar measurements over long ranges, i.e. from 500 m to 1800 m. Comparison between the area calculated using the model and the actual shooter position demonstrates the limits of these reconstructions, particularly at high incident angles. The differences between the reconstructed deflections and the deflections measured by the tracking radar are rather large. This phenomenon is caused by either measurement errors in the cross wind as a function of height or inaccuracy of the radar's deflection measurements., (© 2025 American Academy of Forensic Sciences.)

Determining the trajectories of all vehicles on freeways is a challenging yet critical topic as trajectories reflect the characteristics of traffic flow and serve as a good basis for traffic management and control. With the advances of mobile sensing technology, connected and automated vehicles (CAVs) as a new source of probe car can provide high-resolution sampled trajectory data. Furthermore, as CAVs sense the surrounding traffic situation, they can offer information to understand the vehicle motions around them. Utilizing the data from CAVs thus supports the trajectory reconstruction of fully-sampled traffic flow and enables sophisticated evaluation of traffic states. This study develops a CAV detection data-based trajectory reconstruction method for freeway traffic. First, the intelligent driver model (IDM) is used to judge the motion of undetected human-driven vehicles (HV) between trajectories. The undetected vehicles will be inserted in traffic flow with the position and speed estimated by a modified IDM model. Subsequently, the complete trajectories of the inserted HVs will be reconstructed by IDM. Last, the validity of the method is verified by both simulation and empirical experiments. The results demonstrate the proposed method enables sufficient reconstruction of vehicle trajectories under different traffic densities and penetration rates of CAVs. [ABSTRACT FROM AUTHOR]

The implementation of autonomous driving is inseparable from developing intelligent driving decision-making models, which are facing high scene complexity, poor decision-making coupling, and the inability to guarantee decision-making safety. This paper starts with the priority and logic of lane change and car-following decision-making, considering driving efficiency, safety, and comfort, then constructs a double-layer decision-making model. This paper uses two deep reinforcement learning algorithms for the upper and lower layers to process large-scale mixed state space and ensure the composite action output of lane-changing decisions and car-following decisions. In the upper layer model, we use the D3QN algorithm to distinguish the potential value of the environment and the value of selecting lane-changing actions when making lane-changing decisions. Different from the traditional mechanisms that only use negative rewards, the lane changing benefit function and dangerous action shielding mechanism are used to eliminate collisions. DDPG algorithm is adopted in the lower layer model to process car-following decisions and output continuous vehicle speed control. Besides, coupled training is taken for the two algorithms to improve the coordination of the double-layer model. This paper selected mixed standard driving cycle conditions to build a highly complex training environment and used NGSIM data to reconstruct scenes to test our model. Simulations in SUMO are presented that the double-layer model can increase the driving speed of the original data by 23.99%, which has higher effectiveness than other models. [ABSTRACT FROM AUTHOR]

Traffic parameter characteristics in congested road networks are explored based on traffic flow theory, and observed variables are transformed to a uniform format. The Gaussian mixture model is used to reconstruct route trajectories based on data regarding travel routes containing only the origin and destination information. Using a bi-level optimization framework, a Bayesian traffic demand estimation model was built using route trajectory reconstruction in congested networks. Numerical examples demonstrate that traffic demand estimation errors, without considering a congested network, are within ±12; whereas estimation demands considering traffic congestion are close to the real values. Using the Gaussian mixture model's technology of trajectory reconstruction, the mean of the traffic demand root mean square error can be stabilized to approximately 1.3. Traffic demand estimation accuracy decreases with an increase in observed data usage, and the designed iterative algorithm can predict convergence with 0.06 accuracy. The evolution rules of urban traffic demands and road flows in congested networks are uncovered, and a theoretical basis for alleviating urban traffic congestion is provided to determine traffic management and control strategies. [ABSTRACT FROM AUTHOR]

Single-cell responses are shaped by the geometry of signalling kinetic trajectories carved in a multidimensional space spanned by signalling protein abundances. It is, however, challenging to assay a large number (more than 3) of signalling species in live-cell imaging, which makes it difficult to probe single-cell signalling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 to more than 40) of signalling species but are unable to track single cells. Thus, cytometry experiments provide detailed time-stamped snapshots of single-cell signalling kinetics. Is it possible to use the time-stamped cytometry data to reconstruct single-cell signalling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signalling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signalling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations, live-cell imaging measurements, and, synthetic flow cytometry datasets. The application of invariants and slow variables to reconstruct trajectories provides a radically different way to track objects using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.

The ability to accurately predict flight time of arrival in real time during a flight is critical to the efficiency and reliability of aviation system operations. This paper proposes a data-light and trajectory-based machine learning approach for the online prediction of estimated time of arrival at terminal airspace boundary (ETA_TAB) and estimated landing time (ELDT), while a flight is airborne. Rather than requiring a large volume of data on aircraft aerodynamics, en-route weather, and traffic, this approach uses only flight trajectory information on latitude, longitude, and speed. The approach consists of four modules: (a) reconstructing the sequence of trajectory points from the raw trajectory that has been flown, and identifying its best-matched historical trajectory which bears the most similarity; (b) predicting the remaining trajectory, based on what has been flown and the best-matched historical trajectory; this is achieved by developing a long short-term memory (LSTM) network trajectory prediction model; (c) predicting the ground speed of the flight along its predicted trajectory, iteratively using the current position and previous speed information; to this end, a gradient boosting machine (GBM) speed prediction model is developed; and (d) predicting ETA_TAB using trajectory and speed prediction from (b) and (c), and using ETA_TAB to further predict ELDT. Since LSTM and GBM models can be trained offline, online computation efforts are kept at a minimum. We apply this approach to real-world flights in the US. Based on our findings, the proposed approach yields better prediction performance than multiple alternative methods. The proposed approach is easy to implement, fast to perform, and effective in prediction, thus presenting an appeal to potential users, especially those interested in flight ETA prediction in real time but having limited data access.

This paper presents a deep auto-encoder model and a phased framework approach to predict the next 12 h of vessel trajectories using 1 to 3 h of Automatic Identification System data as input. The strategy involves fusing spatiotemporal features from AIS messages with probabilistic features engineered from historical AIS data to reduce forecasting uncertainty. The probabilistic features have an F1-Score of approximately 85% and 75% for the vessel route and destination prediction, respectively. Under such circumstances, we achieved an R2 Score of over 98% with different layer structures and varying feature combinations; the high R2 Score is a natural outcome of the well-defined shipping lanes in the study region. However, our proposal stands out among competing approaches as it demonstrates the capability of complex decision-making during turnings and route selection. Furthermore, we have shown that our model achieves more accurate forecasting with average and median errors of 11km and 6km, respectively, a 25% improvement from the current state-of-the-art approaches. The resulting model from this proposal is deployed as part of a broader Decision Support System to safeguard whales by preventing the risk of vessel-whale collisions under the smartWhales initiative and acting on the Gulf of St. Lawrence in Atlantic Canada. [Display omitted] • Probabilistic feature augmentation for deriving trajectory route and destination. • Conditional probability model for spatial feature distillation from AIS data streams. • Feature fusion and augmentation for problem shifting into trajectory reconstruction. • AutoEncoder designed for faster trajectory reconstruction with fewer parameters. • Module of a Decision Support System that avoids vessel-whale collisions in Canada. [ABSTRACT FROM AUTHOR]

Inference of detailed vehicle trajectories is crucial for applications such as traffic flow modeling, energy consumption estimation, and traffic flow optimization. Static sensors can provide only aggregated information, posing challenges in reconstructing individual vehicle trajectories. Shockwave theory is used to reproduce oscillations that occur between sensors. However, as the emerging of connected vehicles grows, probe data offers significant opportunities for more precise trajectory reconstruction. Existing methods rely on Eulerian observations (e.g., data from static sensors) and Lagrangian observations (e.g., data from connected vehicles) incorporating shockwave theory and car-following modeling. Despite these advancements, a prevalent issue lies in the static assignment of shockwave speed, which may not be able to reflect the traffic oscillations in a short time period caused by varying response times and vehicle dynamics. Moreover, driver dynamics while reconstructing the trajectories are ignored. In response, this paper proposes a novel framework that integrates Eulerian and Lagrangian observations for trajectory reconstruction on freeways. The approach introduces a calibration algorithm for time-varying shockwave speed. The shockwave speed calibrated by the CV is then utilized for trajectory reconstruction of other non-connected vehicles based on shockwave theory. Additionally, vehicle and driver dynamics are introduced to optimize the trajectory and estimate energy consumption by applying a vehicle movement model. The proposed method is evaluated using real-world datasets, demonstrating superior performance in terms of trajectory accuracy, reproducing traffic oscillations, and estimating energy consumption. • Integrate Lagrangian and Eulerian observations to reconstruct trajectories. • Calibrate time-varying short-term shockwave speeds using the two types of data. • Reconstruct trajectories for non-connected vehicles based on shockwave theory. • Optimize trajectories by adding driver dynamics for better energy estimation. • Evaluation on real-world datasets shows excellent performances from several aspects. [ABSTRACT FROM AUTHOR]

The Automatic Identification System (AIS) enhances maritime safety and environmental monitoring by providing crucial ship trajectory data. However, this data is often compromised by missing or abnormal values due to signal blockage, transmission errors, and equipment failures, jeopardizing safety and the accuracy of environmental analyses. Addressing these challenges, we propose a novel Customized Tensor-Based Maritime Trajectory Reconstruction (CTMTR) framework that leverages the self-similarity of ship trajectories to reformulate trajectory reconstruction as a matrix rank minimization issue. The CTMTR framework consists of three steps: data preprocessing, trajectory matrix construction, and trajectory reconstruction. We conducted simulation experiments using a dataset comprising vessel trajectories from the east coast of Dover in the United States in 2022. To validate its effectiveness, the CTMTR is compared with four advanced methods (LRMC, LRTC-TNN, TRPCA, and TNN-DCT) under diverse missing and anomalous scenarios. The results substantiate that the performance of CTMTR outperforms other approaches, especially in anomalous cases. Our method outperforms existing methods by an order of magnitude under random missing combined with anomaly scenarios. The CTMTR framework thus has the potential to advance maritime trajectory reconstruction methodologies, providing a solid foundation for future innovations in maritime data analysis and navigation safety technologies. • Introduced a novel CTMTR framework for ship trajectory reconstruction. • Addressed missing and abnormal AIS data issues effectively. • Utilized ship trajectory self-similarity for data reconstruction. • Outperformed existing methods in handling missing and anomalous scenarios. [ABSTRACT FROM AUTHOR]

A greater variety of technologies are being applied in sports and health with the advancement of technology, but most optoelectronic systems have strict environmental restrictions and are usually costly. To visualize and perform quantitative analysis on the football kick, we introduce a 3D motion analysis system based on a six-axis inertial measurement unit (IMU) to reconstruct the motion trajectory, in the meantime analyzing the velocity and the highest point of the foot during the backswing. We build a signal processing system in MATLAB and standardize the experimental process, allowing users to reconstruct the foot trajectory and obtain information about the motion within a short time. This paper presents a system that directly analyzes the instep kicking motion rather than recognizing different motions or obtaining biomechanical parameters. For the instep kicking motion of path length around 3.63 m, the root mean square error (RMSE) is about 0.07 m. The RMSE of the foot velocity is 0.034 m/s, which is around 0.45% of the maximum velocity. For the maximum velocity of the foot and the highest point of the backswing, the error is approximately 4% and 2.8%, respectively. With less complex hardware, our experimental results achieve excellent velocity accuracy. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar ground moving target indication (SAR-GMTI) is an attractive mode for radar system to obtain high-resolution regional images and detection of moving targets simultaneously. Moreover, the 360° observation capability of circular SAR (CSAR) makes it possible for moving target trajectory reconstruction. In order to address the problem that slow-moving targets, which are buried in strong stationary ground clutter, are difficult to be detected, a framework of multichannel SAR-GMTI is presented in this article. For ground moving target detection in the presence of stationary clutter, the proposed method first adopts clutter suppression interferometry and relaxation-based cyclic algorithm to suppress clutterand retrieve parameters (e.g., radial velocity and Doppler information). Then, to further reduce the false alarm rate, multiple moving target tracking algorithm is performed in range–Doppler domain. Finally, the moving target trajectory is reconstructed by using the proposed two-stage parameter estimation method based on Doppler characteristic and CSAR geometry, and the mathematical analysis of this method is performed. The proposed method is robust and insensitive to the signal-to-noise ratio. It does not rely on priori road information, so it has wide applicability, especially in military application. In addition, the framework is performed in echo domain and independent of imaging processing. The experimental results on simulated data are presented to evaluate the estimation accuracy of the proposed method, and the real data processing results are provided to demonstrate the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]