Trajectory Reconstruction Method Research Articles

Trajectory reconstruction method for spacecraft formation considering collision probability constraints

Abstract This paper introduces a trajectory reconstruction algorithm for spacecraft formation, combining collision probability and sequential convex programming algorithms. When reconstructing the trajectory of spacecraft formation, external collision avoidance constraint is added to avoid collision threats from space objects. The constraint accuracy of the external collision avoidance constraints of the BOX method and the collision probability method is analyzed. The simulation results indicate that the collision probability method has higher accuracy compared to the BOX method. It addresses the issue of inaccurate division of collision avoidance zones in the BOX method, which tends to be aggressive in the velocity direction and conservative in other directions. A reference is provided for trajectory reconstruction when formation satellites encounter non-cooperative targets.

FINet: Handwriting trajectory reconstruction of Chinese characters based on the font imitate network

Recovering online handwriting trajectory from Chinese handwritten images is still a difficult problem because of abundant strokes, complex structures and different writing styles of Chinese characters. To address this problem, this paper proposes a handwriting trajectory reconstruction method for Chinese characters called the Font Imitate Network. The Font Imitate Network integrates two networks, the spatial encoder uses HRNet to encode the spatial association information of each position on the offline image; the temporal decoder consists of a multilayer perceptron and a recurrent neural network. The stroke feature network is designed to help predict the next handwriting point by focusing on the stroke path in the form of heatmap. Experiments are conducted on the CASIA-OLHWDB1.1 with DTW, LDTW, RMSE and character recognition accuracy as the evaluation metrics. The experimental results show our FINet outperforms the state-of-the-art methods and the recognition accuracy of offline characters is improved by the handwriting reconstruction.

An approach for traffic pattern recognition integration of ship AIS data and port geospatial features

ABSTRACT Recognition of ship traffic patterns can provide insights into the rules of navigation, maneuvering, and collision avoidance for ships at sea. This is essential for ensuring safe navigation at sea and improving navigational efficiency. With the popularization of the Automatic Identification System (AIS), numerous studies utilized ship trajectories to identify maritime traffic patterns. However, the current research focuses on the spatiotemporal behavioral feature clustering of ship trajectory points or segments while lacking consideration for multiple factors that influence ship behavior, such as ship static and maritime geospatial features, resulting in insufficient precision in ship traffic pattern recognition. This study proposes a ship traffic pattern recognition method that considers multi-attribute trajectory similarity (STPMTS), which considers ship static feature, dynamic feature, port geospatial feature, as well as semantic relationships between these features. First, A ship trajectory reconstruction method based on grid compression was introduced to eliminate redundant data and enhance the efficiency of trajectory similarity measurements. Subsequently, to quantify the degree of similarity of ship trajectories, a trajectory similarity measurement method is proposed that combines ship static and dynamic information with port geospatial features. Furthermore, trajectory clustering with hierarchical methods was applied based on the trajectory similarity matrix for dividing trajectories into different clusters. The quality of the similarity measurement results was evaluated by quality criterion to recognize the optimal number of ship traffic patterns. Finally, the effectiveness of the proposed method was verified using actual port ship trajectory data from the Tianjin Port of China, ranging from September to November 2016. Compared with other methods, the proposed method exhibits significant advantages in identifying traffic patterns of ships entering and leaving the port in terms of geometric features, dynamic features, and adherence to navigation rules. This study could serve as an inspiration for a comprehensive exploration of maritime transportation knowledge from multiple perspectives.

Global Prescribed Performance Control for Strict Feedback Systems Pursuing Uncertain Target.

In this work, an online solution for reconstructing and predicting the uncertain target trajectory in real-time is proposed based on general regression neural network (GRNN). On this basis, an adaptive tracking control scheme guaranteeing prescribed performance is suggested for a class of strict-feedback systems with unknown control directions. In contrast to existing trajectory reconstruction methods, the one presented in this note does not require prior modeling of the uncertain target or offline training. Contrary to most current state-of-the-art prescribed performance control (PPC) technology, a novel time-varying scaling function and its corresponding translation function are introduced such that no strict constraints on initial conditions are needed, that is, global stability is achieved. The proposed control scheme allows the output of the system to chase the predicted value of the uncertain target, and the tracking error converges to a prescribed small set within a preassigned time, despite unmatched uncertainties and unknown control directions. The benefits of the proposed control scheme are confirmed by numerical simulations.

The Big Picture: An Improved Method for Mapping Shipping Activities

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.

Human-centered shared steering control system design for obstacle avoidance scenarios

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.

Fast trajectory reconstruction techniques for the large acceptance magnetic spectrometer VAMOS++

The large angular and momentum acceptance magnetic spectrometer VAMOS++, at GANIL, France, is frequently used for nuclear structure and reaction dynamics studies. It provides an event-by-event identification of heavy ions produced in nuclear reactions at beam energies around the Coulomb barrier. The highly non-linear ion optics of VAMOS++ requires the use of the heavy ion trajectory reconstruction methods in the spectrometer to obtain the high-resolution definition of the measured atomic mass number. Three different trajectory reconstruction methods, developed and used for VAMOS++, are presented in this work. The performances obtained, in terms of resolution of reconstructed atomic mass number, are demonstrated and discussed using a single data-set of fission fragments detected in the spectrometer.

High-resolution reconstruction of non-motorized trajectory in shared space: A new approach integrating the social force model and particle filtering

High-resolution trajectory data from the intersection shared space (ISS) is an ideal resource for testing autonomous driving and studying microscopic traffic flow theory in urban road traffic environments. It is common to use computer vision (CV) technologies to extract trajectory data from camera recordings at the ISS. However, it is challenging to accurately extract non-motorized (NONM) trajectories due to vehicle occlusion and mutual interference, which cause trajectory noise and missing. This study proposed a novel NONM trajectory reconstruction method, which integrates the social force model with the particle filter to reduce trajectory noise. The approach was tested on trajectories extracted from two advanced CV algorithms (ie, Yolov7 and MASK RCNN), and its performance was compared with seven SOTA methods. The results show that the proposed method achieved a much better RMSE (0.6 meters) than both the baseline (unprocessed CV trajectories, the RMSE is 1.16 meters) and selected SOTA methods (the best RMSE is 0.78 meters). The contribution of the study is to enhance the classical noise reduction algorithm by introducing the driving interaction model; ablation experiments and sensitivity analysis further demonstrate the importance of the driving interaction model in reducing trajectory noise and the stability of the method. The approach also includes an LSTM-Hungarian part to make up the missing trajectory. The proposed method is expected to serve as a useful post-processing tool for current CV algorithms.

A comprehensive review on motion trajectory reconstruction for EEG-based brain-computer interface.

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.

Arbitrary Spatial Trajectory Reconstruction Based on a Single Inertial Sensor

Compared with vision, infrared rays, and ultrasonic positioning technologies, the signal acquisition of portable inertial sensors is not affected by the external environment, such as light and occlusion. Therefore, motion tracking based on inertial signals is a promising complement. However, accurate trajectory reconstruction based on inertial sensors is a great challenge due to the intrinsic and measurement errors, especially the drift error that exacerbates the accumulative error in trajectory calculation. To address this challenge, we propose a new trajectory reconstruction method, Geometric Dynamic Segmental Reconstruction (GDSR), where we treat the movement trajectory as a combination of basic trajectories. To this end, we design a temporal and spatial interaction segmentation approach to decompose the trajectory into basic segments by combining the dynamic feature of IMU signals with the spatial morphological feature of motion. Accordingly, we design a geometrical model library with undetermined parameters to match these segments. For precise parameter prediction, we propose an extra-supervised learning method that integrates different prediction tasks into one framework, which can not only expand training samples but also enable different subtasks to compete with each other, thus improving the parameter prediction accuracy of each subtask, thereby accurately approximating the trajectory segments. To quantify the trajectory reconstruction accuracy, we propose the Fréchet Spline Sliding Error (FSSE) and Length Error Ratio (LER) to evaluate curve similarity. The range of FSSE is [0, 2], where 0 means that the two curves have the same shape. The range of LER is [1, +∞], where 1 means that the two curves have the same length. We test different IMUs in two experimental scenarios and one public available data set. In all the three tests, the FSSE of the GDSR method is less than 0.09, and the LER is less than 1.31, which is significantly better than all the comparison methods.

Unsupervised vessel trajectory reconstruction

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 Χ={x1,x2,...,xN}, the goal is to track trajectories by clustering the AIS points with predicted positions using the information from the true trajectories Χ. 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.

Destin2: Integrative and cross-modality analysis of single-cell chromatin accessibility data.

We propose Destin2, a novel statistical and computational method for cross-modality dimension reduction, clustering, and trajectory reconstruction for single-cell ATAC-seq data. The framework integrates cellular-level epigenomic profiles from peak accessibility, motif deviation score, and pseudo-gene activity and learns a shared manifold using the multimodal input, followed by clustering and/or trajectory inference. We apply Destin2 to real scATAC-seq datasets with both discretized cell types and transient cell states and carry out benchmarking studies against existing methods based on unimodal analyses. Using cell-type labels transferred with high confidence from unmatched single-cell RNA sequencing data, we adopt four performance assessment metrics and demonstrate how Destin2 corroborates and improves upon existing methods. Using single-cell RNA and ATAC multiomic data, we further exemplify how Destin2's cross-modality integrative analyses preserve true cell-cell similarities using the matched cell pairs as ground truths. Destin2 is compiled as a freely available R package available at https://github.com/yuchaojiang/Destin2.

Recognizing and Recovering Ball Motion Based on Low-Frame-Rate Monocular Camera

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.

Adaptive physics-informed trajectory reconstruction exploiting driver behavior and car dynamics

As more and more trajectory data become available, their analysis creates unprecedented opportunities for traffic flow investigations. However, observed physical quantities like speed or acceleration are often measured having unrealistic values. Furthermore, observation devices have different hardware and software specifications leading to heterogeneity in noise levels and limiting the efficiency of trajectory reconstruction methods. Typical strategies prune, smooth, or locally modify vehicle trajectories to infer physically plausible quantities. The filtering strength is usually heuristic. Once the physical quantities reach plausible values, additional improvement is impossible without ground truth data. This paper proposes an adaptive physics-informed trajectory reconstruction framework that iteratively detects the optimal filtering magnitude, minimizing local acceleration variance under stable conditions and ensuring compatibility with feasible vehicle acceleration dynamics and common driver behavior characteristics. Assessment is performed using both synthetic and real-world data. Results show a significant reduction in the speed error and invariability of the framework to different data acquisition devices. The last contribution enables the objective comparison between drivers with different sensing equipment.

Non-stationary crash risk modelling of powered two-wheelers using extreme value analysis of surrogate crash events

Evaluating the impact of evasive actions such as braking and steering on the crash risk assessment of vehicles is a scarce endeavor due to the lack of relevant data. This study uses Extreme Value Theory to investigate and model the effect of evasive actions on the sideswipe crash risk of powered two-wheelers (PTWs) moving on multilane rural highways. The crash risk was projected from the observed sideswipe conflicts that were quantified using a surrogate safety indicator called anticipated collision time (ACT). The vehicle trajectory data extracted from traffic videos, collected using an unmanned aerial vehicle, was used as the input for the analysis. The data was denoised using a state-of-the-art trajectory reconstruction method called recursively ensembled low pass filtering. Once the conflicts were identified from the trajectory data, the crash risk models were developed considering five covariates: maximum deceleration rate, maximum yaw rate, and the times spent in decelerating, accelerating, and steering during a sideswipe conflict. These covariates were used to capture the non-stationarity in the traffic conflict extremes. The best performing non-stationary model was selected by comparing the negative log-likelihood values with the stationary-one. The findings suggest that the PTWs experience significant sideswipe crash risk on four-lane (crash risk 0.09%) and six-lane (crash risk 0.17%) highways. The sideswipe crash risk of PTWs increases with the increase in the intensity of braking and steering actions measured in terms of maximum deceleration and yaw rates. Further, this study emphasizes that incorporating the effects of evasive actions in the crash risk estimation and developing non-stationary models could significantly improve the precision of crash frequency estimates. Based on the findings it can be concluded that for the safety improvement of PTWs on multilane highways, lane-restriction should be imposed which can increase the safety margin during sideswipe conflicts.

Vehicle trajectory reconstruction for intersections: an integrated wavelet transform and Savitzky-Golay filter approach

Reconstructing vehicle trajectories is an essential step in obtaining high-precision vehicle trajectory data owing to observation errors. Although considerable efforts have been made to reconstruct trajectories on road segments, it is still challenging to reconstruct two-dimensional vehicle trajectories at intersections. In this study, a three-step vehicle trajectory reconstruction method for intersections was proposed to correct abnormal velocities and direction angles in raw trajectories. First, outliers were identified by wavelet transform. They were then filtered out and interpolated using Gaussian kernel-based locally weighted linear regression. Finally, the trajectories were smoothed using a Savitzky-Golay filter. The proposed method was validated using empirical trajectory data collected at 15 intersections in Shanghai, China. The results demonstrate that the proposed trajectory reconstruction method performs well in terms of trajectory rationality and consistency. The mean outlier rate and root mean square error of the reconstructed trajectories are 3% and 0.821 m, respectively.

A deep learning method for the trajectory reconstruction of cosmic rays with the DAMPE mission

A deep learning method for the particle trajectory reconstruction with the DAMPE experiment is presented. The developed algorithms constitute the first fully machine-learned track reconstruction pipeline for space astroparticle missions. Significant performance improvements over the standard hand-engineered algorithms are demonstrated. Thanks to the better accuracy, the developed algorithms facilitate the identification of the particle absolute charge with the tracker in the entire energy range, opening a door to the measurements of cosmic-ray proton and helium spectra at extreme energies, towards the PeV scale, hardly achievable with the standard track reconstruction methods. In addition, the developed approach demonstrates an unprecedented accuracy in the particle direction reconstruction with the calorimeter at high deposited energies, above several hundred GeV for hadronic showers and above a few tens of GeV for electromagnetic showers.

Rockfall trajectory reconstruction: a flexible method utilizing video footage and high-resolution terrain models

Abstract. Many examples of rockfall simulation software provide great flexibility to the user at the expense of a hardly achievable parameter unification. With sensitive site-dependent parameters that are hardly generalizable from the literature and case studies, the user must properly calibrate simulations for the desired site by performing back-calculation analyses. Thus, rockfall trajectory reconstruction methods are needed. For that purpose, a computer-assisted videogrammetric 3D trajectory reconstruction method (CAVR) built on earlier approaches is proposed. Rockfall impacts are visually identified and timed from video footage and are manually transposed on detailed high-resolution 3D terrain models that act as the spatial reference. This shift in reference removes the dependency on steady and precisely positioned cameras, ensuring that the CAVR method can be used for reconstructing trajectories from witnessed previous records with nonoptimal video footage. For validation, the method is applied to reconstruct some trajectories from a rockfall experiment performed by the WSL Institute for Snow and Avalanche Research SLF. The results are compared to previous ones from the SLF and share many similarities. Indeed, the translational energies, bounce heights, rotational energies, and impact positions against a flexible barrier compare well with those from the SLF. The comparison shows that the presented cost-effective and flexible CAVR method can reproduce proper 3D rockfall trajectories from experiments or real rockfall events.

Trajectory reconstruction for mixed traffic flow with regular, connected, and connected automated vehicles on freeway

AbstractVehicular trajectory data collected by connected automated vehicles (CAVs) is minimal due to the low penetration rates (PRs) of CAVs, and fail to capture the characteristics of traffic flow. This study proposes a fully sampled trajectory reconstruction method for mixed traffic flow with regular vehicles (RVs), connected vehicles (CVs), and CAVs based on car‐following behaviour. Firstly, considering the minimum safety distance constraints between vehicles, an optimization model for minimizing the impact on the acceleration of the known vehicles is developed to obtain the number of inserted RVs. Secondly, the speed of the inserted RVs is estimated based on the traffic flow model. Then, an optimization model is proposed to determine the position of each inserted RV. Finally, numerical simulation is designed to investigate the influence of traffic density and PRs of CAVs and CVs. Results show that the proposed method can better reconstruct the vehicle trajectory on the freeway under the different traffic densities in a congested state. The MAPE of the number and position of inserted RVs is less than 10.7% and 0.37%, respectively. In addition, the proposed method performs well even if the PRs of CAVs and CVs are extremely low.

Approximate method for helical particle trajectory reconstruction in high energy physics experiments

High energy physics experiments, in particular experiments at the LHC, require the reconstruction of charged particle trajectories. Methods of reconstructing such trajectories have been known for decades, yet the applications at High Luminosity LHC require this reconstruction to be fast enough to be suitable for online event filtering. A particle traversing the detector volume leaves signals in active detector elements from which the trajectory is reconstructed. If the detector is submerged in a uniform magnetic field that trajectory is approximately helical. Since a collision event results in the production of many particles, especially at high luminosities, the first phase of trajectory reconstruction is the formation of candidate trajectories composed of a small subset of detector measurements that are then subject of resource intensive precise track parameters estimation. In this paper, we suggest a new approach that could be used to perform this classification. The proposed procedure utilizes the z coordinate in the longitudinal direction in addition to the x, y coordinates in the plane perpendicular to the direction of the magnetic field. The suggested algorithm works equally well for helical trajectories with different proximities to the beamline which is beneficial when searching for products of particles with longer lifetimes.