This paper introduces the Trajectory Statistical-Moment Predictability Index (TSMPI) as a lightweight, model-agnostic diagnostic and routing signal rather than a predictive component, and derives a moment-based information-theoretic lower bound on the achievable altitude-prediction error.
Abstract
Trajectory prediction is fundamental to Trajectory-Based Operations (TBO). However, prediction accuracy in Terminal Manoeuvring Area (TMA) is limited by the heterogeneous dynamics of trajectories and the lack of complexity metrics aligned with deep-learning model performance. This paper proposes a complexity-aware trajectory prediction framework comprising two integrated components. At its core is the Adaptive Dual-Stream Fusion Network (ADSF-Net), which combines a Temporal Convolutional Network branch for local kinematic features and a Bidirectional LSTM branch for global temporal intent, integrated through a Dynamic Context Gating mechanism that adaptively arbitrates between the two streams. An altitude-consistent regime-partitioning strategy then decomposes the airspace into homogeneous subspaces, coupled with a Mixture-of-Experts routing strategy that selects an appropriate expert per regime; this design reduces test-set altitude MAE by up to 41.8% relative to a single global model under a flight-level oracle, with a deployment-realistic causal estimator preserving a 28.6% reduction using only past-observed data at each prediction step. A transparent decomposition shows that the dominant share of this gain (39.2 of the 41.8 percentage points) stems from regime partitioning itself. To characterise the resulting regimes and to drive the residual gain from architecture switching, we introduce the Trajectory Statistical-Moment Predictability Index (TSMPI) as a lightweight, model-agnostic diagnostic and routing signal rather than a predictive component; it exhibits a moderate, outlier-robust correlation with per-flight prediction error (Pearson $r \approx 0.30$ , $p \lt 10^{-4}$ ) and provides a principled basis for routing decisions. We additionally derive a moment-based information-theoretic lower bound on the achievable altitude-prediction error that grounds this empirical relationship, identifying dispersion as the dominant complexity driver and clarifying why a purely moment-based signal correlates only moderately with realised error. A sensitivity analysis confirms that TSMPI is robust to weight choice under both local perturbation and uniform random sampling from the Dirichlet simplex.
High-speed maneuvering flight vehicles operating in the subsonic-to-transonic regime (250–500 m/s) pose severe challenges to defense interception systems due to their rapid and unpredictable maneuvering behaviors. Accurate short-term trajectory prediction is essential for effective terminal-phase interception guidance. This paper proposes DSGF-Net (Dual-Stream Gated Fusion Network), a hybrid deep learning architecture for 3D trajectory prediction that simultaneously exploits frequency-domain and temporal-domain information through independent parallel streams. DSGF-Net employs two Temporal Convolutional Networks (TCNs) as parallel encoders: a frequency stream processes Wavelet Packet Decomposition (WPD) features (24-dimensional, db4 wavelet, level-3 decomposition), and a temporal stream processes raw 3D coordinates. An adaptive sigmoid gating module dynamically fuses the two independently encoded streams at each time step and feature dimension, followed by an LSTM sequence learner and a single-step fully connected decoder. Experiments on a simulated dataset covering five representative maneuvering modes (cruise, dive, climb, serpentine, composite) reveal a three-level performance hierarchy. First, incorporating raw 3D coordinates alongside WPD features substantially improves clean-data accuracy over WPD-only baselines: DSGF-Net achieves ADE = 3.476 ± 0.010 m (5 random seeds) versus TCN-LSTM (WPD-only) at 3.938 ± 0.103 m (11.7% improvement). Second, a single-stream concatenation baseline (Concat-TCNLSTM) using identical inputs achieves comparable clean-data accuracy (3.333 ± 0.009 m), confirming that input information—rather than fusion mechanism—drives clean-data gains. Third, and most critically, DSGF-Net’s independently encoded dual-stream architecture enables adaptive suppression of degraded sensor inputs: under multi-sensor noise (complementary radar/GPS profiles), DSGF-Net achieves ADE = 13.91 m versus TCN-LSTM’s 21.32 m (34.9% advantage)—a substantially larger margin than on clean data—a capability structurally unavailable to concatenation-based models. With 300K parameters and a 4.96 ms inference time on an A100 GPU, DSGF-Net meets real-time terminal interception requirements (<10 ms).
Yizhi Wang, Xu Zhou, Han Wu et al.· Electronics· 0 citations
Experiments on ERA5 data show that AMBHFN outperforms eight retrained baselines over the 0–23 h forecast horizon, with an average error reduction of more than 12%.
Vessel trajectory prediction is a key basis for port traffic monitoring, collision-risk identification and navigation decision support. However, AIS data are often affected by irregular sampling, noise and complex manoeuvring behaviours in port waters, making it difficult for models to simultaneously capture global navigation trends and local motion variations. To address this issue, this study proposes a Transformer-based trajectory prediction model enhanced by multi-scale temporal motion encoding, termed MTME-Transformer. The model introduces temporal convolutional branches with different kernel sizes into the Transformer encoder to capture motion patterns over short, medium and wider temporal receptive fields, and is evaluated under a unified data preprocessing, resampling and multi-step autoregressive prediction framework. Experimental results show that, under a 2-min sampling interval and a 30-min prediction horizon, MTME outperforms the Transformer and RNN-based comparison models across multiple evaluation metrics. Ablation experiments further indicate that larger kernel scales are more important for trajectory extrapolation. These results suggest that multi-scale local motion modelling can stably improve the accuracy of AIS-based vessel trajectory prediction.
Qi Xu, Hua-Sheng Nong, Tianwei Ma et al.· International Conference on...· 0 citations
Deep learning-based vessel trajectory prediction using Automatic Identification System (AIS) has become a hot topic in the fields of maritime traffic monitoring, situational awareness, and navigational decision support. However, most previous studies have focused primarily on end-to-end model training using trajectory data from a single water area, which limits the resulting models’ ability to generalize to regions with different traffic patterns. To address this issue, this study proposes a method that constructs traffic context from historical AIS records at multiple geographic resolutions using H3, a hexagonal hierarchical spatial indexing system, and integrates this context with a Transformer-based trajectory predictor. A reliability-aware selector determines the contribution of the context to the final prediction, conditioning this decision on the vessel’s motion state and the retrieved historical patterns. Experiments on AIS data from three distinct water areas demonstrated that H3-indexed context improved cross-water prediction accuracy without requiring model retraining on the target area. These findings demonstrate that H3-indexed context, structured at multiple geographic resolutions and integrated through a selective mechanism, serves as transferable spatial context for vessel trajectory prediction.
We present a training-free method for multi-modal trajectory prediction that achieves comparable accuracy to a 57M-parameter transformer while requiring no GPU and zero learned parameters. The method builds a transition table of historical state-to-next-position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces trajectories covering distinct plausible routes, while beam search finds the highest-likelihood path. On the TrAISformer benchmark (Danish Maritime AIS), our method achieves competitive accuracy at full data availability and dramatically outperforms the transformer in data-scarce regimes---remaining stable down to 10% of training data where TrAISformer degrades catastrophically. This enables deployment in new geographic regions from an order of magnitude less historical data, and with no GPU training.
Michael Fore, Akshay Jain, J. Downes et al.· 0 citations
Long-term ship trajectory prediction is a fundamental capability for maritime safety and autonomous navigation. While recent Transformer-based architectures have improved forecasting horizons, they predominantly rely on historical kinematic states, treating vessel motion as an isolated system. In reality, maritime navigation is profoundly modulated by extrinsic factors like weather and constrained by static vessel characteristics. Existing multimodal approaches fundamentally model the joint distribution over states and contexts, treating environmental variables as peer features rather than encoding the directional physical dependence of vessel dynamics on environmental conditions. In this work, we propose the Conditional Informer, a novel encoder-decoder architecture that formulates trajectory prediction as a conditional generation task. We employ a dedicated Conditional Attention mechanism where the vessel state explicitly queries environmental contexts through cross-attention, encoding the physical prior that weather modulates - but is not generated by - vessel dynamics. Furthermore, to address the intermittency of real-world data, we introduce a Modality Masking training strategy to prevent catastrophic degradation during sensor fallback. Extensive experiments on AIS and ERA5 data demonstrate that our approach outperforms kinematic and concatenation-based baselines by 15.4% in prediction accuracy when context is available. Crucially, Modality Masking prevents shortcut learning, reducing fallback error by nearly an order of magnitude compared to unconstrained models.
Yuansheng Guan, C. Squires, Timothy Hu et al.· 0 citations