Sequence Of Trajectories Research Articles

Outlier Detection of Crowdsourcing Trajectory Data Based on Spatial and Temporal Characterization

As an emerging type of spatio-temporal big data based on positioning technology and navigation devices, vehicle-based crowdsourcing data has become a valuable trajectory data resource. However, crowdsourcing trajectory data has been collected by non-professionals and with multiple measurement terminals, resulting in certain errors in data collection. In these cases, to minimize the impact of outliers and obtain relatively accurate trajectory data, it is crucial to detect and clean outliers. This paper proposes an efficient crowdsourcing trajectory outlier detection (CTOD) method that detects outliers from the trajectory sequence data in both spatial view and temporal view. Specifically, we first use the adaptive spatial clustering algorithm based on the Delaunay triangulation (ASCDT) algorithm to remove the location offset points in the trajectory sequence. After that, based on the most basic attributes of the trajectory points, a 6-dimensional movement feature vector is constructed for each point as an input. The feature-rich trajectory sequence data is reconstructed using the proposed temporal convolutional network autoencoder (TCN-AE), and the Squeeze-and-Excitation (SE) channel attention mechanism is introduced. Finally, the effectiveness of the CTOD method is experimentally verified.

Multi-Agent Trajectory Prediction With Spatio-Temporal Sequence Fusion

Accurate trajectory prediction of surrounding agents is an important issue for building up an intelligent transportation system. Frequent interactions among agents have a major impact on their movement patterns. Current research mainly relies on agents’ spatial structure associated with the last frame of the observation to model social interactions, while paying less attention to structure information from previous moments. In addition, existing methods merely consider temporal features of a single trajectory sequence, while neglecting temporal dependencies across multiple trajectories. In this work, we endeavor to capture comprehensively social interactions among agents with the proposed Spatio-Temporal Sequence Fusion Network (STSF-Net). Specifically, we construct a spatio-temporal sequence that encodes contextual information taking explicitly spatial distributions of agents during movement into account while capturing socially temporal dependencies across multiple trajectory sequences. Besides, a social recurrent mechanism is introduced to explicitly capture temporal correlations between interactions by concerning spatial structure at each time-step. Finally, our model is evaluated on datasets covering pedestrian, vehicle, and heterogeneous multi-agent trajectories. Experimental evidence manifests that our method achieves excellent performance.

Locally unipotent invariant measures and limit distribution of a sequence of polynomial trajectories on homogeneous spaces

Let $ G $ be a Lie group, and let $ \Gamma $ be a lattice in $ G $. We introduce the notion of locally unipotent invariant measures on $ G/\Gamma $. We then prove that under some conditions, the limit measure supported on the image of polynomial trajectories on $ G/\Gamma $ is locally unipotent invariant, thus give a partial answer to an equidistribution problem for higher dimensional polynomial trajectories on homogeneous spaces, which was raised by Shah in [15].The proof relies on Ratner's measure classification theorem, a linearization technique for polynomial trajectories near singular sets, and a twisting technique of Shah.

Behavioral fractal method associated with GPS tracking to spatial activity sequences of grazing cattle

Global positioning and geographic information systems are essential for studying foraging animal behavior. This study aims to implement a fractal self-similarity and chaos game computational efficient methodology to determine the behavior-associated fractal using GPS data of activity sequences in spatial ranges of livestock movement trajectories in interaction with habitat factors. Six cows were randomly selected with an average weight of 480 kg, maintained under the same conditions, and a GPS-equipped collar was installed, programmed at intervals of 1 min and an average of 9 h daylight. Roughly 192810 registries and an average of 32135 signals per cow from trajectory tracking in spatial activity sequencing were used as a variable of interest in the fractal characterization methodology. Spatial patterns were evaluated using the Morán’s spatial autocorrelation indices, cluster, and non-parametric statistics, evaluating deterministic spatial patterns of preferential activities associated to spatial ranges of less than 7.1 m (resting 42 %, grazing 38 %). GPS information was refined through spatial ranges and changes in activities under resting, eating, traveling, and complementary schemes associated to the fractal displacement behavior of grazing cattle. This information was processed and mapped using fractal self-similarity rules in the Sierpinski triangle to determine the typical fractal of spatial activities per animal in the habitat. The particular fractal record of each bovine as a function of trajectory sequences was mapped for binary image matrices, registering a good classification (83 %) of the animals by breed and climatological cycle, using information from the sequencing of spatial activities associated to the preferred behavior in the habitat.

Multi-Scale Fusion Localization Based on Magnetic Trajectory Sequence

Magnetic fingerprint has a multitude of advantages in the application of indoor positioning, but as a weak magnetic field, the dynamic range of the data is limited, which exerts direct influence on the positioning accuracy. Aiming at resolving the problem wherein the indoor magnetic positioning results tremendously rest with the magnetic characteristics, this paper puts forward a method based on deep learning to fuse the temporal and spatial characteristics of magnetic fingerprints, to fully explore the magnetic characteristics and to obtain stable and trustworthy positioning results. First and foremost, the trajectory of the acquisition area is extracted by adopting the ameliorated random waypoint model, and the simulation of pedestrian trajectory is completed. Then, the magnetic sequence is obtained by mapping the magnetic data. Aside from that, considering the scale characteristics of the sequence, a scale transformation unit is designed to obtain multi-scale features. At length, the neural network self-attention mechanism is adopted to fuse multiple features and output the positioning results. By probing into the positioning results of dissimilar indoor scenes, this method can adapt to diverse scenes. The average positioning error in a corridor, open area and complex area reaches 0.65 m, 0.93 m and 1.38 m respectively. The addition of multi-scale features has certain reference value for ameliorating the positioning performance.

Aircraft Trajectory Prediction Based on Bayesian Optimised Temporal Convolutional Network–Bidirectional Gated Recurrent Unit Hybrid Neural Network

Efficient and accurate flight trajectory prediction is a key technology for promoting intelligent and informative air traffic management and improving the operational capabilities and predictability of air traffic. To address the problems in extracting hidden information from historical trajectory information, the approach must accurately select high-dimensional features related to the prediction target and overcome the short-term memory of the time series. Herein, we present a novel trajectory prediction model based on a dual-self-attentive (DSA)-temporal convolutional network (TCN)-bidirectional gated recurrent unit (BiGRU) neural network. In this model, the TCN provides highly stable training, high parallelism, and a flexible perceptual domain. The self-attentive mechanism of the TCN structure can focus on features that contribute the most to the output. After the TCN, the BiGRU network combined with the self-attentive mechanism is used to further bidirectionally mine the connections between the features and outputs of the trajectory sequence, and a Bayesian algorithm is used to optimise the hyperparameters of the model for optimal performance. A comparison and validation based on current well-known neural network models (i.e., CNN, TCN, GRU, and their variants) shows that the DSA-TCN-BiGRU model based on Bayesian hyperparameter optimisation has the best performance. Therefore, the improved predictive model is applicable and valuable, providing a basis for future decision trajectory-based operations.

Structural Transformer Improves Speed-Accuracy Trade-Off in Interactive Trajectory Prediction of Multiple Surrounding Vehicles

Fast and accurate long-term trajectory prediction of surrounding vehicles (SVs) is critical to autonomous driving systems. In high-density traffic flows, strongly correlated vehicle behaviors require considering the interactions among multiple SVs when predicting their future trajectories. However, existing interactive prediction methods, most based on Long Short-Term Memory (LSTM), are suffering from slow prediction because they analyze SVs one by one and analyze trajectory sequence node by node. This paper presents a fast interactive trajectory prediction method called Structural Transformer which learns both spatial and temporal dependencies among multiple SVs in parallel. Specifically, our model first removes the internal states and loops of LSTM and replaces with a weighted self-reference mapping to realize parallel computation. Then, it embeds the relative spatial information of multiple SVs into trajectory states and reorganizes the self-reference mapping with neighbor-only interaction masks to achieve interactive prediction. Results on the NGSIM dataset show satisfyingly speed and accuracy performance on long-term trajectory prediction of multiple SVs. The longitudinal and lateral errors are reduced to 2.67m and 0.25m over 5s time horizon. The computational time of each step is only 12ms on a 2080ti GPU, which is over 4 times faster than the Structural LSTM.

A Deep Generative Model for Trajectory Modeling and Utilization

Modern location-based systems have stimulated explosive growth of urban trajectory data and promoted many real-world applications, e.g. , trajectory prediction. However, heavy big data processing overhead and privacy concerns hinder trajectory acquisition and utilization. Inspired by regular trajectory distribution on transportation road networks, we propose to model trajectory data privately with a deep generative model and leverage the model to generate representative trajectories for downstream tasks or directly support these tasks ( e.g. , popularity ranking), rather than acquiring and processing the original big trajectory data. Nevertheless, it is rather challenging to model high-dimensional trajectories with time-varying yet skewed distribution. To address this problem, we model and generate trajectory sequence with judiciously encoded spatio-temporal features over skewed distribution by leveraging an important factor neglected by the literature - the underlying road properties ( e.g. , road types and directions), which are closely related to trajectory distribution. Specifically, we decompose trajectory into map-matched road sequence with temporal information and embed them to encode spatio-temporal features. Then, we enhance trajectory representation by encoding inherent route planning patterns from the underlying road properties. Later, we encode spatial correlations among edges and daily and weekly temporal periodicity information. Next, we employ a meta-learning module to generate trajectory sequence step by step by learning generalized trajectory distribution patterns from skewed trajectory data based on the well-encoded trajectory prefix. Last but not least, we preserve trajectory privacy by learning the model differential privately with clipping gradients. Experiments on real-world datasets show that our method significantly outperforms existing methods.

A Context Awareness Hierarchical Attention Network for Next POI Recommendation in IoT Environment

The rapid increase in the number of sensors in the Internet of things (IoT) environment has resulted in the continuous generation of massive and rich data in Location-Based Social Networks (LBSN). In LBSN, the next point-of-interest (POI) recommendation has become an important task, which provides the best POI recommendation according to the user’s recent check-in sequences. However, all existing methods for the next POI recommendation only focus on modeling the correlation between POIs based on users’ check-in sequences but ignore the significant fact that the next POI recommendation is a time-subtle recommendation task. In view of the fact that the attention mechanism does not comprehensively consider the influence of the user’s trajectory sequences, time information, social relations and geographic information of Point-of-Interest (POI) in the next POI recommendation field, a Context Geographical-Temporal-Social Awareness Hierarchical Attention Network (CGTS-HAN) model is proposed. The model extracts context information from the user’s trajectory sequences and designs a Geographical-Temporal-Social attention network and a common attention network for learning dynamic user preferences. In particular, a bidirectional LSTM model is used to capture the temporal influence between POIs in a user’s check-in trajectory. Moreover, In the context interaction layer, a feedforward neural network is introduced to capture the interaction between users and context information, which can connect multiple context factors with users. Then an embedded layer is added after the interaction layer, and three types of vectors are established for each POI to represent its sign-in trend so as to solve the heterogeneity problem between context factors. Finally reconstructs the objective function and learns model parameters through a negative sampling algorithm. The experimental results on Foursquare and Yelp real datasets show that the AUC, precision and recall of CGTS-HAN are better than the comparison models, which proves the effectiveness and superiority of CGTS-HAN.

NExG: Provable and Guided State-Space Exploration of Neural Network Control Systems Using Sensitivity Approximation

We propose a new technique for performing state-space exploration of closed-loop control systems with neural network feedback controllers. Our approach involves approximating the sensitivity of the trajectories of the closed-loop dynamics. Using such an approximator and the system simulator, we present a guided state-space exploration method that can generate trajectories visiting the neighborhood of a target state at a specified time. We present a theoretical framework which establishes that our method will produce a sequence of trajectories that will reach a suitable neighborhood of the target state. We provide a thorough evaluation of our approach on various systems with neural network feedback controllers of different configurations. We outperform earlier state-space exploration techniques and achieve significant improvement in both the quality (explainability) and performance (convergence rate). Finally, we adopt our algorithm for the falsification of a class of temporal logic specification, assess its performance, and show its potential in supplementing existing falsification algorithms.

Recognition and Prediction of Surgical Gestures and Trajectories Using Transformer Models in Robot-Assisted Surgery.

Surgical activity recognition and prediction can help provide important context in many Robot-Assisted Surgery (RAS) applications, for example, surgical progress monitoring and estimation, surgical skill evaluation, and shared control strategies during teleoperation. Transformer models were first developed for Natural Language Processing (NLP) to model word sequences and soon the method gained popularity for general sequence modeling tasks. In this paper, we propose the novel use of a Transformer model for three tasks: gesture recognition, gesture prediction, and trajectory prediction during RAS. We modify the original Transformer architecture to be able to generate the current gesture sequence, future gesture sequence, and future trajectory sequence estimations using only the current kinematic data of the surgical robot end-effectors. We evaluate our proposed models on the JHU-ISI Gesture and Skill Assessment Working Set (JIGSAWS) and use Leave-One-User-Out (LOUO) cross validation to ensure generalizability of our results. Our models achieve up to 89.3% gesture recognition accuracy, 84.6% gesture prediction accuracy (1 second ahead) and 2.71mm trajectory prediction error (1 second ahead). Our models are comparable to and able to outperform state-of-the-art methods while using only the kinematic data channel. This approach can enabling near-real time surgical activity recognition and prediction.

Design of 3-D trajectory sequences for multiple asteroid flyby missions

Prospecting is a necessary pre-requisite of future asteroid mining ventures. It is generally assumed that inspection for the purpose of identifying the asteroid composition can be effectively accomplished from a distance through remote sensing. To be carried out in a timely and economically viable way, prospecting is best performed by devising trajectories such that a single spacecraft manages to fly by as many asteroid as possible, yet seeking to minimize a cost function that we assume to be coincident with propellant consumption. In this paper, we present a method to identify trajectory sequences to multiple asteroids. We restrict our analysis to Near-Earth Asteroids (NEAs), i.e.,, those with perihelion at less than 1.3 AU from the Sun, focusing on Apollo class NEAs only. The volume of space where encounter seeking takes place is a torus-shaped 3-D region in the proximity of the ecliptic. Under the assumption of using impulsive maneuvers to connect ballistic coast arcs, we show that a deterministic building blocks approach is successful in finding a significant number of multi-flyby mission profiles with the desired characteristics. Using this scheme, it is possible to envisage realistic asteroid prospecting missions using a single launch to deploy a number of small spacecraft, with tens—or possibly hundreds—of asteroids visited in a few years.

A general dynamic sequential learning framework for vehicle trajectory reconstruction using automatic vehicle location or identification data

Vehicle trajectory data derived from automatic vehicle location (AVL) and automatic vehicle identification (AVI) systems provide critical support for intelligent transportation systems. However, the field-obtained vehicle trajectories are usually incomplete due to sensor malfunction or communication issues. To recover the incomplete data, the existing reconstruction methods have to impose strong assumptions on driver route choice behaviors (network level) and/or traffic dynamics (link level). With the tremendous data available, leveraging data-driven approaches to address the vehicle trajectory reconstruction problem with minimal assumptions is promising. This paper proposes a general dynamic sequential learning framework to reconstruct vehicle trajectory points for both AVL and AVI data. First, an Isolation Forest based ensemble learning model is developed to extract trajectory sequences attributed to different trips in an entire trip chain of a vehicle. Second, the dynamic recurrent neural network (dynamic RNN) is tailored to learn the underlying patterns from the complete AVL and AVI trajectories, respectively. Third, a sequential prediction scheme is customized to reconstruct AVL and AVI trajectories based on the trained networks. To validate the proposed method, two experiments are conducted. One is a simulation experiment with AVL data gathered from a well-calibrated simulation model. The other is a field experiment with AVI data collected from a real-world automatic license plate recognition (ALPR) system. The results show that the proposed method achieves superior performance for both AVL and AVI data compared with the traditional methods. The impacts of different sampling rates and traffic conditions on the model performance are also discussed.

Trajectory Planning for Narrow Environments That Require Changes of Driving Directions

In the area of mobile robotics, trajectory planning is the task to find a sequence of primitive trajectories that connect two configurations, whereas non-holonomic constraints, obstacles and driving costs have to be considered. In this paper, we present an approach that is able to handle situations that require changes of driving directions. In such situations, optimal trajectory sequences contain costly turning maneuvers – sometimes not even on the direct path between start and target. These situations are difficult for most optimization approaches as the robot partly has to drive paths with higher cost values that seem to be disadvantageous. We discuss the problem in depth and provide a solution that is based on maneuvers, partial backdriving and free-place discovery. We applied the approach on top of our Viterbi-based trajectory planner.

Optimization Calculation Method and Mathematical Modeling of Big Data Chaotic Model Based on Improved Genetic Algorithm

In order to find a chaotic trajectory sequence with strong global optimization ability to help the genetic selection of direction after the reversal of chemotaxis, an improved genetic algorithm based on chaos optimization is proposed by combining the characteristics of chaotic motion with the improved genetic algorithm. The optimal coverage problem in sensor networks can carry out fine optimization search on local areas. The results show that the overall trend of fitness and optimization efficiency is relatively stable. The optimization efficiency will be gradually improved with the continuous progress of time and genetics, and the error analysis will be reduced. This will greatly improve the impact of various adverse factors in the optimization process. In addition, the change rate of fitness is basically kept at a high change rate, which also reflects that the basic framework of the model is very excellent, and the whole algorithm structure and data processing are improved by 54%. The improved genetic algorithm proposed in this paper is used to adjust and optimize the controller parameters. When the uncertain parameters change greatly, the control system still has good control quality and strong robustness.

Simultaneous Localization and Mapping for Pedestrians Using Radio Frequency Signals

Among various sensor measurements that are obtained through smartphones, the received signal strength indicator (RSSI) of a radio frequency (RF) signal is widely used to estimate a user’s location. In this study, we propose a novel RF-based simultaneous localization and mapping (SLAM) technology for robust map construction. Typically, building an indoor map using the SLAM requires accurate loop closure detection. However, it is generally difficult to accurately estimate the loop closure using RSSI owing to the large variance of RF RSSI in indoor environments. To address this, we utilize the user trajectory and RSSI sequence to identify the correct loop closure. The RSSI sequence accumulated in consecutive poses generates a unique signal pattern. Therefore, it is possible to accurately estimate the revisiting of a pedestrian to a specific position. To evaluate the performance of the proposed method, we performed a field test in a laboratory building. Moreover, SLAM was performed using only 25% of the received RF measurements to validate that the proposed method can perform accurate SLAM despite a poor RF infrastructure environment. The obtained experimental results verify that a mean error of less than 3 m can be achieved in various test scenarios.

Brain white matter correlates of learning ankle tracking using a wearable device: importance of the superior longitudinal fasciculus II

BackgroundWearable devices have been found effective in training ankle control in patients with neurological diseases. However, the neural mechanisms associated with using wearable devices for ankle training remain largely unexplored. This study aimed to investigate the ankle tracking performance and brain white matter changes associated with ankle tracking learning using a wearable-device system and the behavior–brain structure relationships in middle-aged and older adults.MethodsTwenty-six middle-aged and older adults (48–75 years) participated in this study. Participants underwent 5-day ankle tracking learning with their non-dominant foot using a custom-built ankle tracking system equipped with a wearable sensor and a sensor-computer interface for real-time visual feedback and data acquisition. Repeated and random sequences of target tracking trajectories were both used for learning and testing. Ankle tracking performance, calculated as the root-mean-squared-error (RMSE) between the target and actual ankle trajectories, and brain diffusion spectrum MR images were acquired at baseline and retention tests. The general fractional anisotropy (GFA) values of eight brain white matter tracts of interest were calculated to indicate their integrity. Two-way (Sex × Time) mixed repeated measures ANOVA procedures were used to investigate Sex and Time effects on RMSE and GFA. Correlations between changes in RMSE and those in GFA were analyzed, controlling for age and sex.ResultsAfter learning, both male and female participants reduced the RMSE of tracking repeated and random sequences (both p < 0.001). Among the eight fiber tracts, the right superior longitudinal fasciculus II (R SLF II) was the only one which showed both increased GFA (p = 0.039) after learning and predictive power of reductions in RMSE for random sequence tracking with its changes in GFA [β = 0.514, R2 change = 0.259, p = 0.008].ConclusionsOur findings implied that interactive tracking movement learning using wearable sensors may place high demands on the attention, sensory feedback integration, and sensorimotor transformation functions of the brain. Therefore, the SLF II, which is known to perform these brain functions, showed corresponding neural plasticity after such learning, and its plasticity also predicted the behavioral gains. The SLF II appears to be a very important anatomical neural correlate involved in such learning paradigms.

BMAM: complete the missing POI in the incomplete trajectory via mask and bidirectional attention model

Studies on the checked-in point-of-interests have become an important means to learn user’s behavior. Nevertheless, users do not sign in to all visited locations. There are unobserved check-in locations in the generated POI trajectory. Such the trajectory is called an incomplete trajectory, and unobserved point is called missing point. However, incomplete trajectory has a negative impact on downstream tasks such as personalized recommendation system, criminal identification and next location prediction. It is a challenge to use the forward sequence and backward sequence information of the missing point to complete the missing POI. Therefore, we propose a bidirectional model based on mask and attention mechanism (BMAM) to solve the problem of missing POI completion in user’s incomplete trajectory. The context information of trajectory checked in by user can be mined to connect the missing POI with the forward sequence and backward sequence information. Therefore, the model learns the order dependence between each location according to the user trajectory sequence and obtain the user’s dynamic preference to identify the missing POI in the sequence. Besides, the attention mechanism is used to improve the user's representation feature, that is, the preference for POI categories. The experimental results demonstrate that our BMAM outperforms the state-of-the-art models for completion on missing POI of user’s incomplete sequence.

Secure Data Publishing of Private Trajectory in Edge Computing of IoT

Secure data publishing of private trajectory is a typical application scene in the Internet of Things (IoT). Protecting users’ privacy while publishing data has always been a long-term challenge. In recent years, the mainstream method is to combine the Markov model and differential privacy (DP) mechanism to build a private trajectory generation model and publishes the generated synthetic trajectory data instead of the original data. However, Markov cannot effectively model the long-term trajectory data spatio-temporal correlation, and the DP noise results in the low availability of the synthetic data. To protect users’ privacy and improve the availability of synthetic trajectory data, we propose a trajectory generation model with differential privacy and deep learning (DTG). In DTG, we design a private hierarchical adaptive grid method. It divides the geospatial region into several subregions according to the density of positions to realize the discretization of coordinates of the trajectory data. Second, GRU is used to capture the temporal features of the trajectory sequence for good availability, and we generate synthetic trajectory data by predicting the next position. Third, we adopt the optimizer perturbation method in gradient descent to protect the privacy of model parameters. Finally, we experimentally compare DTG with the state-of-the-art approaches in trajectory generation on actual trajectory data T-Drive, Portotaxi, and Swedishtaxi. The result demonstrates that DTG has a better performance in generating synthetic trajectories under four error metrics.

Research on real-time reachability evaluation for reentry vehicles based on fuzzy learning

Abstract Accurate and rapid prediction of reentry trajectory and landing point is the basis to ensure the reentry vehicle recovery and rescue, but it has high requirements for the continuity and stability of real-time monitoring and positioning data and the fidelity of the reentry prediction model. In order to solve the above contradiction, based on the theory of relative entropy and closeness in fuzzy learning, research on real-time evaluation of reentry reachability is presented in this article. With the Monte Carlo analysis data during the design and evaluation of the reentry vehicle control system, the reentry trajectory feature information base is designed. With the matching identification decision strategy between the identified trajectory and trajectory feature base, the reachability of the reentry vehicle, reachable trajectory, and landing point can be predicted. The simulation results show that by reasonably selecting the time window and using the evaluation method designed in this article, making statistics of the trajectory sequence number and frequency identified based on relative entropy and closeness method, the reachability evaluation results can be given stably, which is suitable for the real-time task evaluation of TT&amp;C system.