Trajectory Prediction Research Articles

Evaluation of Trajectory and Destination Prediction Models: A Systematic Classification and Analysis of Methodologies and Recent Results

Predicting trajectories and destinations is of considerable relevance in the context of urban mobility, as it can be useful for suggesting detours, avoiding congestion, and optimizing people's commutes. Therefore, this research performs a classification and analysis of trajectory and destination prediction models in articles published from 2017 to 2023. These models were mapped considering: authors; the existence of more than one geographic scenario; the type of forecast; the use of semantic and contextual data; and description of the algorithms. The result consists of discussions of representative works, based on classification, with grouping of techniques. Furthermore, there is a focus on works that used contextual and/or semantic data, from which another framework was developed, specifying the titles of the articles, and whether the methodology involved the use of points or areas of interest, and a reference to how they were generated. This focus expands the previous framework, specifying the differences of a portion of published studies.

A Novel Trajectory Prediction Method Based on CNN, BiLSTM, and Multi-Head Attention Mechanism

A four-dimensional (4D) trajectory is a multi-dimensional time series that embodies rich spatiotemporal features. However, its high complexity and inherent uncertainty pose significant challenges for accurate prediction. In this paper, we present a novel 4D trajectory prediction model that integrates convolutional neural networks (CNNs), bidirectional long short-term memory networks (BiLSTMs), and multi-head attention mechanisms. This model effectively addresses the characteristics of aircraft flight trajectories and the difficulties associated with simultaneously extracting spatiotemporal features using existing prediction methods. Specifically, we leverage the local feature extraction capabilities of CNNs to extract key spatial and temporal features from the original trajectory data, such as geometric shape information and dynamic change patterns. The BiLSTM network is employed to consider both forward and backward temporal orders in the trajectory data, allowing for a more comprehensive capture of long-term dependencies. Furthermore, we introduce a multi-head attention mechanism that enhances the model’s ability to accurately identify key information in the trajectory data while minimizing the interference of redundant information. We validated our approach through experiments conducted on a real ADS-B trajectory dataset. The experimental results demonstrate that the proposed method significantly outperforms comparative approaches in terms of trajectory estimation accuracy.

Probabilistic model for high-level intention estimation and trajectory prediction in urban environments

To enable successful automated driving, precise behavior prediction of surrounding vehicles is indispensable in urban traffic scenarios. Furthermore, given that a vehicle’s behavior is influenced by the movements of other road users, it becomes crucial to estimate their intentions to anticipate precise future motion. However, the elevated complexity resulting from interdependencies among traffic participants and the uncertainty arising from the object recognition errors present additional challenges. Despite extensive research on inferring intentions, many studies have concentrated on estimating intentions from interactions, resulting in a lack of practicality in urban traffic environments due to low computational efficiency and low robustness against recognition failure of strongly interacting road users. In this paper, we introduce a practical stochastic model for intention estimation and trajectory prediction of surrounding vehicles in automated driving under urban traffic environments. The trajectory is forecasted based on hierarchically computed and probabilistically estimated intentions, which represent an interpretation of vehicle behavior, utilizing only the kinematic state of the focal vehicle and HD maps to ensure real-time performance and enhance robustness. The evaluated results demonstrate that the proposed model surpasses straightforward methods in terms of accuracy while maintaining computational efficiency and exhibits robustness against the recognition failure of traffic participants which strongly influence the focal vehicle.

Iterative Trajectory Prediction Model Based on Interactive Agent

Iterative Trajectory Prediction Model Based on Interactive Agent

Neural relational and dynamics inference for complex systems

Many complex processes in the real world can be viewed as complex systems and their evolution is governed by underlying nonlinear dynamics. However, one can only access the trajectories of the system without knowing the underlying system structure and dynamics in most cases. To address this challenge, this paper proposes a model called Neural Relational and Dynamics Inference (NRDI) that combines graph neural networks (GNNs) and ordinary differential equation systems (ODEs) to handle both continuous-time dynamics prediction and network topology inference for complex systems. Our model contains two modules: (1) the network inference module, which infers system structure from input system trajectories using GNNs, and (2) the dynamics learning module, which employs GNNs to fit the differential equation system for predicting future trajectories. We tested NRDI’s performance on system trajectory prediction and graph reconstruction separately. Experimental results show that the proposed NRDI outperforms many baseline models on continuous-time complex network dynamics prediction, and can explicitly infer network structures with high accuracy.

PB-Trajectron: Physics bounded neural network for generalized trajectory prediction

Vehicle trajectory prediction is a critical technology in autonomous driving systems, as the quality of prediction directly affects downstream path planning and vehicle control. Although recent studies have shown that models combining kinematic rules with data-driven methods exhibit better interpretability in trajectory prediction, these models often adopt fixed constraint strengths, limiting their generalization ability in diverse traffic scenarios. This fixed constraint strength design restricts the model’s adaptability to different traffic environments.To address this issue, we propose PB-Trajectron, a dynamic integration mechanism that enhances the model’s prediction performance and generalization capability. PB-Trajectron is a dynamic integration mechanism that combines vehicle kinematic rules with deep learning prediction models for generalized vehicle trajectory prediction. The model integrates physics-based motion models and Deep Neural Networks (DNNs) to provide reasonable physical explanations for predicting vehicle trajectories at different speeds. First, we establish two vehicle kinematic constraints applicable to different prediction scenarios, enabling the agent to switch between these constraints based on the causal relationships between vehicle motion states to avoid generating non-physical trajectory results. Second, we propose a kinematic constraint decision framework based on velocity thresholds, which demonstrates adaptive adjustment, allowing the agent to switch tasks according to real-time state conditions and adaptively adjust the contribution of different physical constraints based on actual vehicle speeds. Finally, we investigate the advantages of PB-Trajectron in Out-of-Domain(OOD) generalization.Cross-scenario experiments on the nuScenes dataset show that, compared to previous methods, PB-Trajectron reduces the final displacement error by 7.69% when the prediction step length is 4. Furthermore, out-of-domain generalization tests on the INTERACTION dataset demonstrate that PB-Trajectron achieves a 12.23% reduction in average prediction error on datasets from different countries and scenarios compared to previous methods. The proposed mechanism can better adapt to complex and diverse traffic scenarios, laying the foundation for explainable and robust autonomous driving systems.

Modeling longitudinal skewed functional data.

This paper introduces a model for longitudinal functional data analysis that accounts for pointwise skewness. The proposed procedure decouples the marginal pointwise variation from the complex longitudinal and functional dependence using copula methodology. Pointwise variation is described through parametric distribution functions that capture varying skewness and change smoothly both in time and over the functional argument. Joint dependence is quantified through a Gaussian copula with a low-rank approximation-based covariance. The introduced class of models provides a unifying platform for both pointwise quantile estimation and prediction of complete trajectories at new times. We investigate the methods numerically in simulations and discuss their application to a diffusion tensor imaging study of multiple sclerosis patients. This approach is implemented in the R package sLFDA that is publicly available on GitHub.

Multimodal vehicle trajectory prediction and integrated threat assessment algorithm based on adaptive driving intention

As autonomous driving and connected communication technologies advance swiftly, vehicle trajectory prediction has become increasingly significant. The motion of a vehicle is contingent not only on its historical trajectory but is also subject to the influence of surrounding vehicles, thereby exhibiting intricate social and temporal interdependencies. Furthermore, the inherent randomness and uncertainty in driver behavior render vehicle trajectory prediction inherently multimodal, a factor that is frequently neglected in current research. Against this backdrop, a multimodal vehicle trajectory prediction (MTP) model based on an encoder-decoder architecture is proposed to hierarchically extract historical features of vehicles. The model consists of five key components: temporal feature encoder module, spatial interaction module, spatial-temporal dependence module, driving intention fusion module and multimodal trajectory output module. Experiments on the NGSIM dataset show that the predictive performance of the model has been improved to varying degrees, especially at 3–5 s, where the improvement is more significant. Compared with state-of-the-art models, the Root Mean Square Error (RMSE) error at 5 s time horizon is 3.38 m on NGSIM dataset, which represents a 25 % improvement. To measure the safety of predicted trajectories, we propose a comprehensive threat assessment model that combines collision time (TTC), headway (TH) and time to lateral collision (TLC) metrics based on safe distance theory. This model not only evaluates the longitudinal collision threat in the following state, but also evaluates the lateral collision threat during driving maneuvers in multi lane scenarios, thereby comprehensively improving the safety of vehicle driving. This research also offers new perspectives and insights for the development of autonomous driving.

Vessel Trajectory Prediction at Inner Harbor Based on Deep Learning Using AIS Data

This study aims to improve vessel trajectory prediction in the inner harbor of Busan Port using Automatic Identification System (AIS) data and deep-learning techniques. The research addresses the challenge of irregular AIS data intervals through linear interpolation and focuses on enhancing the accuracy of predictions in complex port environments. Recurrent neural network (RNN), Long Short-Term Memory (LSTM), Bidirectional LSTM, Gated Recurrent Unit (GRU), and Bidirectional GRU models were developed, with LSTM delivering the highest performance. The primary scientific question of this study is how to reliably predict vessel trajectories under varying conditions in inner harbors. The results demonstrate that the proposed method not only improves the precision of predictions but also identifies critical areas where Vessel Traffic Service Operators (VTSOs) can better manage vessel movements. These findings contribute to safer and more efficient vessel traffic management in ports with high traffic density and complex navigational challenges.

Counterfactual-based two-stage trajectory prediction framework for autonomous vehicle navigation systems

Abstract Accurate prediction of a vehicle’s trajectory is essential for autonomous driving and robotic operations in a complex, dynamic environment. However, current methods that rely on historical and environmental cues to predict future trajectories make the inner distance between testing and training environments often overlooked. To address this issue, we propose a counterfactual analysis method specifically designed for vehicle trajectory prediction. We begin by constructing a causal graph that includes historical trajectories, future trajectories, and environmental interactions. This graph captures the causal relationships between these elements. Our approach directly intervenes on the trajectory itself, effectively cutting off the inference from the environment to the trajectory. By doing so, we mitigate the negative impact of environmental bias. Furthermore, by comparing observed and intervened trajectory clues, we highlight the influence of environmental distance. Our goal is to improve the accuracy of trajectory prediction. Our counterfactual analysis module integrates seamlessly into various baseline prediction models. Experimental data demonstrates that our method outperforms others on publicly available Argoverse2 motion forecasting benchmarks.

A dual-level graph attention network and transformer for enhanced trajectory prediction under road network constraints

Predicting vehicle future trajectories enables various Location-Based Services (LBS), including traffic flow monitoring, vehicle route planning, etc. Vehicles are constrained to predefined road networks. Their traveling behaviors are influenced by both their own attributes and road network characteristics hidden in other vehicles’ travel histories. Most of the existing methods fail to sufficiently leverage such collaborative trajectory data under road network constraints. This paper proposes a novel model, called HGT-RN (Hierarchical Graph Attention Network and Transformer Networks for Enhanced Trajectory Prediction under Road Network Constraints), which exploits all vehicles’ trajectories and integrates road network constraints. Specifically, HGT-RN creates a dual-level Graph Attention Network (GAT) based on global traffic flow and local individual trajectory graph to learn trajectory embeddings: (i) Weighted-directional global traffic flow graph and Weighted-Directional GAT to learn the global-level trajectory embedding by aggregating the neighbors’ embeddings based on the spatial transitional relationships among road intersections over all vehicles’ trajectories, considering the preference of current trajectory; and (ii) Local individual trajectory graph attention network to learn the local-level trajectory embedding by modeling the transitions within the current trajectory at each intersection. When incorporating the trajectory embeddings into a transformer model for future trajectory prediction, a road network topology-aware loss function is designed to improve accuracy. Extensive experiments conducted on three city-scale real-world taxi trajectory datasets demonstrate that HGT-RN significantly outperforms existing baseline models. The code is available at https://github.com/zjy9826/HGT-RN.

A Formalism for Scalable Maritime Traffic Monitoring and Explainable Anomaly Detection and Resolution at Vessel Traffic Services

Abstract Vessel traffic service (VTS) centres around the globe monitor and manage the ship traffic in their areas of responsibility and respond to arising unsafe or inefficient situations. Decision support tools (DST) help vessel traffic service operators (VTSO) to enhance their situational awareness and decision-making process, thus to recognise and assess dangerous situations. However, current DST have unsophisticated features and require manual configuration by the operator. Firstly, triggers for alerts are mostly based on the creation of geographical polygons for spatial-dependent assignment of rules, thresholds, ranges and limits for specific features. Secondly, calculations for the detection of safety-critical situations rely on measurements based on the closest point of approach (CPA) without taking contextual information into account. Thirdly, trajectory predictions are performed considering a constant velocity model (CVM) which does not depict reality. Due to these and other peculiarities, current DST are prone to false alerts. This results into a high workload where unsafe situations may be overlooked. In this paper, we propose a hierarchical formalism as foundation for an anomaly detection and resolution which generates less false alerts. The formalism consists of three hierarchical layers which represent, objects, measurements and situations. The formalism ensures adaptability and extensibility to various VTS areas and traffic patterns. Moreover, due to the given structure, the presented formalism is easily implementable, adaptable and scalable taking the currently available technological capabilities at VTS centres into account. We demonstrate the feasibility of this formalism by implementing a proof-of-concept and assessing it with realistic scenarios. Our implementation utilizes a rule-based system as central framework and it is configured through statistical methods, e.g. machine learning. Given this hybrid approach, the implementation provides reasonable and explainable results. This enables comprehensibility and verifiability by authorities and operators which is crucial for acceptance.

위험 시나리오에 대한 트랜스포머 네트워크 기반 자율주행차량의 충돌 및 궤적 예측 알고리즘 개발

위험 시나리오에 대한 트랜스포머 네트워크 기반 자율주행차량의 충돌 및 궤적 예측 알고리즘 개발

Approaches to Early Parkinson's Disease Subtyping.

Parkinson's disease (PD) unfolds with pathological processes and neurodegeneration well before the emergence of noticeable motor symptoms, providing a window for early identification. The extended prodromal phase allows the use of risk stratification measures and prodromal markers to pinpoint individuals likely to develop PD. Importantly, a growing body of evidence emphasizes the heterogeneity within prodromal and clinically diagnosed PD. The disease likely comprises distinct subtypes exhibiting diverse clinical manifestations, pathophysiological mechanisms, and patterns of α-synuclein progression in the central and peripheral nervous systems. There is a pressing need to refine the definition and early identification of these prodromal subtypes. This requires a comprehensive strategy that integrates genetic, pathological, imaging, and multi-omics markers, alongside careful observation of subtle motor and non-motor symptoms. Such multi-dimensional classification of early PD subtypes will improve our understanding of underlying disease pathophysiology, improve predictions of clinical endpoints, progression trajectory and medication response, contribute to drug discovery and personalized medicine by identifying subtype-specific disease mechanisms, and facilitate drug trials by reducing confounding effects of heterogeneity. Here we explore different subtyping methodologies in prodromal and clinical PD, focusing on clinical, imaging, genetic and molecular subtyping approaches. We also emphasize the need for refined, theoretical a priori disease models. These will be prerequisite to understanding the biological underpinnings of biological subtypes, which have been defined by large scale data-driven approaches and multi-omics fingerprints.

A POV-Based Highway Vehicle Trajectory Dataset and Prediction Architecture

A POV-Based Highway Vehicle Trajectory Dataset and Prediction Architecture

Growing evolutional deep echo state network

Deep echo state network (Deep ESN) is a powerful method for time-series prediction, but developing the optimal structure of Deep ESN remains challenging. A novel generative framework, growing evolutional Deep ESN (GE Deep ESN) is proposed, where networks are generated through alternating growth and evolution. A model compression method is implemented during the evolution phase to optimize the inner structure of the reservoirs, and to automatically determine reservoir size. A simple termination criterion of growth is introduced to determine network depth. The feasibility and superiority of GE Deep ESN were validated experimentally with two benchmark prediction tasks. For real-time trajectory prediction in photoelectric tracking systems, an iterative learning model based on GE Deep ESN is proposed, the real time prediction result showed that network evolution enhances the model’s suitability for this task, and improves prediction precision.

Multi-Scale Learnable Gabor Transform for Pedestrian Trajectory Prediction From Different Perspectives

Multi-Scale Learnable Gabor Transform for Pedestrian Trajectory Prediction From Different Perspectives

Development of an algorithm for proton dose calculation in magnetic fields.

The advantages of proton therapy can be further enhanced with online magnetic resonance imaging (MRI) guidance. One of the challenges in the realization of MRI-guided proton therapy (MRPT) is accurately calculating the radiation dose in the presence of magnetic fields. This study aims to develop an efficient and accurate proton dose calculation algorithm adapted to the presence of magnetic fields. An analytical-numerical radiation dose calculation algorithm, Proton and Ion Dose Engine (PRIDE), was developed. The algorithm combines the pencil beam algorithm (PBA) with a novel iterative voxel-based ray-tracing algorithm. The new ray-tracing method uses fewer assumptions and ensures broader applicability for proton beam trajectory prediction in magnetic fields, and has been compared to Wolf's method and Schellhammer's method. The accuracy of PRIDE algorithm was validated on three phantoms and two practical plans (one single-field water plan and one prostate tumor plan) in different magnetic field strengths up to 3.0 T. The validation was performed by comparing the results against the Monte Carlo (MC) simulations, using the global gamma index criteria of 2%/2mm and 3%/3mm with a 10% threshold. PRIDE showed good agreement with MC in homogeneous and slab heterogeneous phantom, achieving gamma passing rates (%GPs) above 99% for 2%/2mm criteria when magnetic field strength is not greater than 1.5 T. Although the agreement decreased for scenarios involving high proton energy (240 MeV) and strong magnetic field (3.0 T), the 2%/2mm %GPs still remained above 98%. In lateral heterogeneous phantom, the accuracy of PRIDE decreased due to the PBA's limitation. For the two practical plans in different magnetic fields, %GPs exceeded 98% and 99% for 2%/2mm and 3%/3mm criteria, respectively. PRIDE can perform efficient and accurate proton dose calculation in magnetic fields up to 3.0 T, and is expected to work as a useful tool for proton dose calculation in MRPT.

STdi4DMPC: Distributed Model Predictive Control for Connected and Automated Truck Platoon With Mixed Traffic Flow Based on Spatiotemporal Trajectory Prediction

STdi4DMPC: Distributed Model Predictive Control for Connected and Automated Truck Platoon With Mixed Traffic Flow Based on Spatiotemporal Trajectory Prediction

Lithium-ion battery future degradation trajectory early description amid data-driven end-of-life point and knee point co-prediction

This study develops a novel lithium-ion battery future degradation trajectory early description method amid data-driven end-of-life (EOL) point and knee point (KP) co-prediction. Inspired by the concept of KP, the proposed method firstly employs two-stage curve fitting to offline locate KP with minimization total absolute error between the original trajectory and fitted secants as object. Secondly, from partial multi-step fast-charging curves lying in high state-of-charge (SOC) level with only approximately 0.09 SOC interval, our method mines three new aging-dependent features for EOL and knee cycle co-prediction via two optimized Gaussian process regression models. Afterwards, considering the highly linear characteristics of slow degradation stage, knee capacity is further calculated by the linear function fitted via early capacity degradation sequence. Finally, with early capacity degradation sequence, predicted KP and predicted EOL point, the developed method adopts piece-wise cubic Hermite interpolating polynomial to directly generate future degradation trajectory. The verification results using a 140-cell aging dataset demonstrate that the proposed method is powerful for future degradation trajectory early prediction with high accuracy and extremely low real-time computational cost, where most root-mean-square-error and mean-absolute-percentage-error of trajectory prediction results are below 0.03 Ah and 3%, respectively. Our work, for the first time, reveals the possibility of feature extraction from partial multi-step fast-charging curves, and also provides a low-complexity universal framework for accurate future degradation trajectory early prediction.