Uncertainty-Aware Multimodal Trajectory Prediction via a Single Inference from a Single Model

Data-driven trajectory prediction with weather uncertainties: A Bayesian deep learning approach

Aiming at the problems of large simplification and low accuracy of traditional trajectory prediction models, combined with the characteristics of time sequence, continuity, and interactivity of UUV trajectories, an unknown UUV trajectory prediction method based on a gated unit recursive (GRU) neural network model is proposed. The MinMaxScaler method is used to normalize the trajectory data; in order to improve the prediction accuracy, the adaptive parameter adjustment algorithm and adam algorithm are used to optimize the network structure of the established GRU-based trajectory prediction model, without human intervention for parameter adjustment. Finally, the trajectory prediction accuracy of GRU trajectory prediction model and BP trajectory prediction model are analyzed through simulation experiments. The experimental results show that the root mean square error is about 3.96m on the x-axis and 1.00m on the y-axis. The trajectory prediction model based on GRU has faster prediction speed and higher prediction accuracy for unknown UUV trajectory after bearings-only detection.

The objective of the study described in this paper was to develop an efficient uncertainty quantification framework capable of analyzing uncertainty in integrated spacecraft system models. Specifically, this paper discusses the capabilities of the developed framework and the res ults when applied to the multidisciplinary analysis of a reusable launch veh icle (RLV). This particular framework is capable of efficiently propagating mixed (inherent and epistemic) uncertainties through complex simulation codes. The Second-Order Probability Theory utilizing a stochastic response surface obta ined with Point-Collocation NonIntrusive Polynomial Chaos was used for the propagation of the mixed uncertainties. This particular methodology was applied to the RLV analysis, and the uncertainty in the output parameters of interested was obtained in terms of intervals at various probability levels. This study has also demonstrated the feasibility of the developed uncertainty quantifica tion framework for efficient propagation of mixed uncertainties in the analysis of complex aerospace systems. I. Introduction ncertainties are generally ubiquitous in the analys is and design of highly complex engineering systems. Uncertainties can arise from the lack of k nowledge in physical modeling (epistemic uncertainty), inherent variations in the systems (a leatory uncertainty), and numerical errors in the computational procedures used for analysis. It is i mportant to account for all of these uncertainties in applications such as robust and reliable design of multi-disciplinary aerospace systems. A reusable la unch vehicle (RLV) is a highly complex aerospace system, which represents a cost viable option for access t o space missions due to its reusability aspect. Since an RLV system is composed of various subsystems which must work together to serve an over-arching p urpose or mission objective/constraint, a multidisciplinary approach for the analysis and des ign of RLV systems is required. Uncertainties are generally present in the models used in each discipline of an RLV multidisciplinary analysis framework. It is important to account for all of these uncertainties for accurate and reliabl e estimates of the RLV system performance. The primary purpose of this paper will be to demonstrate an efficient approach for uncertainty quantification in the multidiscipl inary analysis of a RLV, which has a mixture of aleatory (inherent) and epistemic input uncertainties. Uncertainty quantification will be performed on various output variables of interest f or an RLV system such as the weight and vehicle crossrange. For the propagation of mixed (aleatory-epist emic) uncertainty, Second-Order Probability Theory utilizing Point-Collocation Non-Intrusive Polynomia l Chaos (NIPC) 1 will be used. 2-3 In general, the NIPC methods, which are based on the spectral representa tion of uncertainty, are computationally more effic ient than traditional Monte Carlo methods for moderate number of uncertain variables and can give highly 1 Aerospace Engineer, 4020 Long Beach Blvd, Long Beach, CA, 90807, Member AIAA

Aircraft trajectory prediction is a challenging problem in air traffic control, especially for conflict detection. Traditional trajectory predictors require a variety of inputs such as flight-plans, aircraft performance models, meteorological forecasts, etc. Many of these data are subjected to environmental uncertainties. Further, limited information about such inputs, especially the lack of aircraft tactical intent, makes trajectory prediction a challenging task. In this work, we propose a deep learning model that performs trajectory prediction by modeling and incorporating aircraft tactical intent. The proposed model adopts the encoder-decoder architecture and makes use of the convolutional layer as well as Gated Recurrent Units (GRUs). The proposed model does not require explicit information about aircraft performance and wind data. Results demonstrate that the provision of enriched aircraft intent, together with appropriate model design, could improve the prediction error up to 30% at a prediction horizon of 10 minutes (from 4.9 nautical miles to 3.4 nautical miles). The model also guarantees the mean error growth rate with increasing look-ahead time to be lower than 0.2 nautical miles per minute. In addition, the model offers a very low variance in the prediction, which satisfies the variance-standard specified by EUROCONTROL (EU Organization for Safety and Navigation of Air Traffic) for trajectory predictors. The proposed model also outperforms the state-of-the-art trajectory prediction model, where the Root Mean Square Error (RMSE) is reduced from 0.0203 to 0.0018 for latitude prediction, and from 0.0482 to 0.0021 for longitude prediction in a single prediction step of 15 seconds look-ahead. We showed that the pre-trained model on ADS-B data maintains its high performance, in terms of cross-track and along-track errors, when being validated in the Bluesky Air Traffic Simulator. The proposed model would significantly improve the performance of conflict detection systems where such trajectory prediction models are needed.

High-performance trajectory prediction is at the core of strategic airspace capacity and safety enhancement. Current state-of-the-art trajectory prediction models are based on a three-dimensional point-mass model, using often predefined settings from existing databases rather than real-time information available onboard the aircraft to determine aircraft dynamics. As a result trajectory prediction performance is limited by the accuracy of these settings. This paper addresses this limitation and proposes a high-performance four-dimensional trajectory prediction model for civil aircraft. The model includes a new flight-control system and an enhanced flight-script. The latter incorporates new taxonomy and content enabling better definition of aircraft intent. The performance of the trajectory prediction model is assessed using data acquired during a real flight trial, and shown to be significantly better than the current models. It has the potential to meet the required navigation performance for departure, en-route and non-precision-approach phases of flight.

Trajectory prediction is one of the key technologies of the autonomous driving system. The accurate and efficient prediction can assist the autonomous driving system in making correct decisions and ensuring driving safety. This paper summarizes the research on trajectory prediction for autonomous vehicles based on deep learning. First, trajectory prediction models’ input representation and output types are analyzed. Then, deep learning-based trajectory prediction methods are reviewed with their advantages and limitations. Finally, future research directions are proposed to address the shortcomings of existing methods in terms of multi-agent interaction modeling and generalization capability.

Recent deep learning methods for vessel trajectory prediction are able to learn complex maritime patterns from historical automatic identification system (AIS) data and accurately predict sequences of future vessel positions with a prediction horizon of several hours. However, in maritime surveillance applications, reliably quantifying the prediction uncertainty can be as important as obtaining high accuracy. This article extends deep learning frameworks for trajectory prediction tasks by exploring how recurrent encoder–decoder neural networks can be tasked not only to predict but also to yield a corresponding prediction uncertainty via Bayesian modeling of aleatoric and epistemic uncertainties. We compare the prediction performance of two different models based on labeled or unlabeled input data to highlight how uncertainty quantification and accuracy can be improved by using, if available, additional information on the intention of the ship (e.g., its planned destination).

The 4D trajectory is a multi-dimensional time series with plentiful spatial-temporal features and has a high degree of complexity and uncertainty. Aiming at these features of aircraft flight trajectory and the problem that it is difficult for existing trajectory prediction methods to extract spatial-temporal features from the trajectory data at the same time, we propose a novel 4D trajectory prediction hybrid architecture based on deep learning, which combined Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). An 1D convolution is used to extract the spatial dimension feature of the trajectory, and LSTM is used to mine the temporal dimension feature of the trajectory. Hence the high-precision prediction of the 4D trajectory is realized based on the sufficient fusion of the above features. We use real Automatic Dependent Surveillance -Broadcast (ADS-B) historical trajectory data for experiments and compare the proposed method with a single LSTM model and BP model on the same data set. The experimental results show that the trajectory prediction accuracy of the CNN-LSTM hybrid model is superior to a single model. The prediction error is reduced by an average of 21.62% compared to the LSTM model and by an average of 52.45% compared to the BP model. It provides a certain reference for the trajectory prediction research and Air Traffic Management decision-making.

This article introduces a novel model for low-quality pedestrian trajectory prediction, the social nonstationary transformers (NSTransformers), that merges the strengths of NSTransformers and spatiotemporal graph transformer (STAR). The model can capture social interaction cues among pedestrians and integrate features across spatial and temporal dimensions to enhance the precision and resilience of trajectory predictions. We also propose an enhanced loss function that combines diversity loss with logarithmic root mean squared error (log-RMSE) to guarantee the reasonableness and diversity of the generated trajectories. This design adapts well to complex pedestrian interaction scenarios, thereby improving the reliability and accuracy of trajectory prediction. Furthermore, we integrate a generative adversarial network (GAN) to model the randomness inherent in pedestrian trajectories. Compared to the conventional standard Gaussian distribution, our GAN approach better simulates the intricate distribution found in pedestrian trajectories, enhancing the trajectory prediction's diversity and robustness. Experimental results reveal that our model outperforms several state-of-the-art methods. This research opens the avenue for future exploration in low-quality pedestrian trajectory prediction.

The long-term prediction of hypersonic glide vehicle (HGV) trajectory based on radar tracking data still faces challenges. Existing approaches are hard to provide satisfactory performances in long-term HGV trajectory prediction tasks due to insufficient long-range dependency extraction ability and cumulative errors. To address the above issues, a trajectory prediction model physics-informed Transformer (PIT) is proposed in this work. The top$\tau$-mean attention mechanism and the generative decoder are designed in this model to extract the trajectories' long-range dependency and reduce the cumulative errors. Furthermore, the physical knowledge is applied at both the input and output ends of the model, which further improves the model's prediction accuracy even in the case of missing a small amount of radar tracking data. A simulated HGV trajectory dataset is established based on the dynamic equations for the PIT trajectory prediction model. The experimental results show that the PIT performs better than other state-of-the-art deep neural network models. The additional experiments on a small-scale dataset and datasets with missing tracking data further verify the excellent performance and robustness of the PIT in these cases.

Accurate trajectory prediction of vehicles is essential for reliable autonomous driving. To maintain consistent performance as a vehicle driving around different cities, it is crucial to adapt to changing traffic circumstances and achieve lifelong trajectory prediction model. To realize it, catastrophic forgetting is a main problem to be addressed. In this paper, a divergence measurement method based on conditional Kullback-Leibler divergence is proposed first to evaluate spatiotemporal dependency difference among varied driving circumstances. Then based on generative replay, a novel lifelong vehicle trajectory prediction framework is developed. The framework consists of a conditional generation model and a vehicle trajectory prediction model. The conditional generation model is a generative adversarial network conditioned on position configuration of vehicles. After learning and merging trajectory distribution of vehicles across different cities, the generation model replays trajectories with prior samplings as inputs, which alleviates catastrophic forgetting. The vehicle trajectory prediction model is trained by the replayed trajectories and achieves consistent prediction performance on visited cities. A lifelong experiment setup is established on four open datasets including five tasks. Spatiotemporal dependency divergence is calculated for different tasks. Even though these divergence, the proposed framework exhibits lifelong learning ability and achieves consistent performance on all tasks.

As exploitation of low and medium airspace for air traffic management (ATM) is gaining more attention, aerial vehicles’ security issues pose a major challenge to the air–ground-integrated vehicle networks (AGIVNs). Traditional surveillance technology lacks the capacity to support the intensive ATM of the future. Therefore, an advanced automatic-dependent surveillance-broadcast (ADS-B) technique is applied to track and monitor aerial vehicles in a more effective manner. In this article, we propose a grouping-based conflict detection algorithm based on the preprocessed ADS-B data set, and analyze the experimental results and visualize the detected conflicts. Then, in order to further improve flight safety and conflict detection, the trajectories of the aerial vehicles are predicted based on machine learning-based algorithms. The results are fed into the conflict detection algorithm to execute conflict prediction. It was shown that the trajectory prediction model using long short-term memory (LSTM) can achieve better prediction performance, especially when predicting the long-term trajectory of aerial vehicles. The conflict detection results based on the trajectory prediction methods show that the proposed scheme can make it possible to detect whether there would be conflicts within seconds.

Trajectory prediction is a challenging problem in autonomous driving, due to changes in scene structure and multimodal distributions of future trajectories. This study proposes a novel trajectory prediction model (LGINet). The central innovation of LGINet is the Context-Aware Graph Attention (CAGA) layer, which achieves a balance between handling scene complexity and the ability to capture information, improving prediction performance. Unlike conventional attention mechanisms, CAGA uses Sparsemax to focus on key neighbors, reducing noise and enhancing computational efficiency. The multi-head attention mechanism enhances the ability of the model to capture interactions across both local and long-distance spatial scales. Experiments with the nuScenes dataset show that the proposed LGINet model outperforms existing prediction methods. Specifically, the MinADE 5 value of LGINet is 1.23, the MR 5,2 value is 0.49, and the MinFDE 5 value is 2.39, demonstrating its effectiveness in generating diverse and accurate future trajectories for autonomous driving applications. Qualitative comparisons confirm that LGINet generates diverse trajectories aligned with scene structures and agent motion, highlighting its potential for autonomous driving.

In the field of trajectory prediction, when new scene data is continuously introduced, the system may forget the historical trajectory information that has been learned before, leading to the phenomenon of decreasing the prediction accuracy of previous scenes, which is called catastrophic forgetting. The Multi-Memo Net framework proposed in this paper is an instance-based approach that stores typical trajectories through a memory bank thereby establishing a direct link between the current and historical scenes. During training, self-encoders and decoders are used to efficiently memorize the feature expressions of past trajectories and future intentions; during prediction, the controller finds similar scenes that have occurred in history in the memory bank based on the past trajectories and contextual information for trajectory prediction, and ultimately obtains a multimodal trajectory prediction through K-means clustering, and while predicting, the model can keep updating the content of the memory bank to learn, thus iteratively optimizing the model prediction performance. Thus, the model prediction performance is iteratively optimized. Compared with baseline models such as Kalman filter and Memory Augmented Networks for Multiple Trajectory Prediction (MANTRA) model, the method in this paper has significant improvement in Average Displacement Error (ADE) and Final Displacement Error (FDE) metrics.

Predicting a vehicle's trajectory is an essential ability for autonomous vehicles navigating through complex urban traffic scenes. Bird's-eye-view roadmap information provides valuable information for making trajectory predictions, and while state-of-the-art models extract this information via image convolution, auxiliary loss functions can augment patterns inferred from deep learning by further encoding common knowledge of social and legal driving behaviors. Since human driving behavior is inherently multimodal, models which allow for multimodal output tend to outperform single-prediction models on standard metrics. We propose a loss function which enhances such models by enforcing expected driving rules on all predicted modes. Our contribution to trajectory prediction is twofold; we propose a new metric which addresses failure cases of the off-road rate metric by penalizing trajectories that oppose the ascribed heading (flow direction) of a driving lane, and we show this metric to be differentiable and therefore suitable as an auxiliary loss function. We then use this auxiliary loss to extend the the standard multiple trajectory prediction (MTP) and MultiPath models, achieving improved results on the nuScenes prediction benchmark by predicting trajectories which better conform to the lane-following rules of the road.