## 2 Related Work
### Trajectory Prediction Methods and Uncertainty Modeling  
Aircraft trajectory prediction methodologies have evolved from physics-based models to data-driven approaches. Physics-based models use aircraft performance parameters and atmospheric conditions to model motion using differential equations. Although interpretable, these methods often require detailed knowledge about aircraft that is unavailable to diverse general aviation fleets [3]. Statistical approaches provide computational efficiency, but may struggle with generalization beyond observed patterns.  
Hybrid methods that combine physics-based and statistical techniques have emerged to leverage their complementary strengths. [PERSON] and [PERSON] [17] employed machine learning to estimate aircraft parameters for physics-based models. Despite their promise, these approaches often rely on simplifications that limit their applicability to complex operating conditions of general aviation [4].  
Deep learning has significantly advanced trajectory prediction capabilities. Recurrent neural networks, particularly LSTMs [8, 18], have demonstrated success in capturing temporal dependencies on flight paths. Attention mechanisms [13] adapted from natural language processing enhance the focus of models on relevant sequence features [19]. Hybrid architectures combining CNNs with recurrent networks effectively capture spatial and temporal patterns in flight data.  
The success of deep learning in trajectory prediction extends beyond aviation to other transportation domains, providing valuable insights for our approach. In pedestrian trajectory prediction, Social LSTM [20] pioneered the use of pooling mechanisms to model human-human interactions in crowded spaces, demonstrating how spatial relationships can be effectively captured through neural architectures. Building on this, Social GAN [21] introduced adversarial training for generating socially acceptable trajectories, highlighting the importance of modeling multimodal trajectory distributions. For autonomous vehicle applications, Trajectron++ [12] advanced the field by incorporating semantic maps and agent dynamics into a unified probabilistic framework, achieving state-of-the-art performance in complex traffic scenarios. Similarly, PiP [22] demonstrated how planning information can be integrated into trajectory prediction, improving long-term prediction accuracy. More recently, DenseTNT [23] showed that predicting a dense set of goal candidates before trajectory generation significantly improves prediction quality. These cross-domainadvances inform our approach to aviation trajectory prediction, particularly in handling uncertainty quantification and incorporating environmental context.  
To address inherent uncertainties in aircraft operations, probabilistic approaches have gained prominence. Gaussian processes model trajectory uncertainty with confidence intervals [24], while Bayesian methods handle multimodal trajectory distributions [25]. Ensemble techniques combine multiple models to improve resilience to environmental variability [26]. More recently, deep probabilistic models enable learning complex uncertainty distributions directly from data [12], although their application to general aviation remains limited [9].