Trajectory prediction for flying objects is critical in domains ranging from sports analytics to aerospace. However, traditional methods struggle with complex physical modeling, computational inefficiencies, and high hardware demands, often neglecting critical trajectory events like landing points. This paper introduces a novel, hardware-efficient trajectory prediction framework that integrates environmental priors with a Dual-Transformer-Cascaded (DTC) architecture. We demonstrate this approach by predicting the landing points of tennis balls in real-world outdoor courts. Using a single industrial camera and YOLO-based detection, we extract high-speed flight coordinates. These coordinates, fused with structural environmental priors (e.g., court boundaries), form a comprehensive dataset fed into our proposed DTC model. A first-level Transformer classifies the trajectory, while a second-level Transformer synthesizes these features to precisely predict the landing point. Extensive ablation and comparative experiments demonstrate that integrating environmental priors within the DTC architecture significantly outperforms existing trajectory prediction frameworks
Figures & tables
The type of trajectory
Prediction model
Flying ball trajectory
RNN [ 13 ] ; LSTM [ 11 , 12 ] , [ 32 ]
Vehicle trajectory
Markov [ 24 ] ; LSTM [ 28 ] ;
Transformer [ 35 ]
Ship trajectory
GRU [ 29 ] , [ 38 ] ; LSTM [ 30 ]
TABLE I: Summary of data-driven trajectory prediction
Fig. 1: (a) The schematic overview of the trajectory data acquisition system. (b) Schematic diagram of the experimental scene.
Fig. 2: Flowchart of dataset construction.
Fig. 3: Overview of the trajectory prediction model - PIDTC.
Fig. 4: (a) Structure of the trajectory classification module. (b) Structure of the landing point prediction module.
Parameter
Classification
Prediction
Epoch
500
1000
Batch-size
10
10
Learning rate
0.0001
0.0001
Embedding number
128
500
dmodel
64
512
Dropout rate
0.1
0.1
TABLE II: Parameters for training
Fig. 5: The loss during training and testing processes. (a) The BCE loss of classification module. (b) The MSE loss of prediction module.
Fig. 6: The loss of ablation models versus training epochs. (a) The BCE loss. (b) The MSE loss.
CMN
CMP
Accuracy
52.86%
85.71%
Precision
52.85%
81.40%
Recall
100%
94.59%
TABLE III: Classification performance comparison of ablation models
PMN
PMP
PMC
MSE
1183.39
690.16
372.39
RMSE
34.40
26.27
19.30
Bias (pixel)
23.06
18.02
13.35
PhyBias (cm)
29.58
23.16
17.07
TABLE IV: Prediction performance comparison of ablation models
Fig. 7: The training loss across different models versus training epochs: (a) MSE, (b) RMSE, (c) Bias.
MSE
RMSE
Bias (pixel)
PhyBias (cm)
RNN [ 13 ]
1064.99
32.63
26.71
34.16
GRU [ 38 ]
3417.77
58.46
49.24
63.98
LSTM [ 11 ]
866.72
29.44
23.96
30.55
Transformer [ 35 ]
1170.42
34.21
22.48
27.74
PIDTC
372.39
19.30
13.35
17.07
TABLE V: Prediction Performance Comparison ACROSS DIFFERENT MODELS
20% Nt
40% Nt
60% Nt
80% Nt
MSE
499.41
547.52
542.15
372.39
RMSE
22.35
23.40
23.28
19.30
Bias (pixel)
15.65
17.10
16.22
13.35
PhyBias (cm)
19.98
21.57
20.65
17.07
TABLE VI: Prediction performance comparison for different training set sizes
Accurate trajectory prediction can improve General Aviation safety in non-towered terminal airspace, where high traffic density increases accident risk. We present ASCENT, a lightweight transformer-based model for multi-modal 3D aircraft trajectory forecasting, which integrates domain-aware 3D coordinate normalization and parameterized predictions. ASCENT employs a transformer-based motion encoder and a query-based decoder, enabling the generation of diverse maneuver hypotheses with low latency. Experiments on the TrajAir and TartanAviation datasets demonstrate that our model outperforms prior baselines, as the encoder effectively captures motion dynamics and the decoder aligns with structured aircraft traffic patterns. Furthermore, ablation studies confirm the contributions of the decoder design, coordinate-frame modeling, and parameterized outputs. These results establish ASCENT as an effective approach for real-time aircraft trajectory prediction in non-towered terminal airspace.
Alexander Prutsch, David Schinagl, Horst Possegger
Institute of Visual Computing, Graz University of Technology, Austria
Advanced automation is a key technology for enhancing the safety of ground operations amidst the increasing density of commercial air traffic. While motion forecasting is a well-studied task in autonomous driving, its application to airport surface movements remains underexplored. To enable efficient and accurate prediction in this domain, we propose DESCENT, a transformer-based architecture designed to handle heterogeneous dynamics and strict topological constraints. Our approach features a Potential Reachable Set (PRS) context sampling mechanism that adaptively collects airfield environment context across diverse operational phases. Combined with a detection transformer-based decoder, DESCENT generates accurate trajectory forecasts. Extensive evaluations on the Amelia-10 benchmark demonstrate significant performance improvements over state-of-the-art baselines. These gains are especially pronounced in safety-critical scenarios, where our domain-aware sampling provides critical long-horizon context necessary for safe navigation.
Alexander Prutsch, David Schinagl, Horst Possegger
Institute of Visual Computing, Graz University of Technology, Austria
Autonomous aerial vehicles operating in shared airspace must predict the future positions of non-cooperative obstacles to plan evasive maneuvers before a collision becomes unavoidable. Unlike cooperative systems that share intent, non-cooperative obstacles such as birds, uncontrolled drones, or debris exhibit multi-modal motion that deterministic predictors cannot adequately represent. Existing methods either rely on recurrent encoders that propagate temporal information sequentially, limiting their ability to capture long-range kinematic precursors of maneuver initiation, or produce point forecasts that provide no distributional information to downstream planners. This paper presents AeroCast, a probabilistic trajectory prediction framework that combines a Transformer encoder with a Mixture Density Network output head to predict per-timestep Gaussian mixture distributions over future three-dimensional displacements. A translation-invariant consecutive displacement encoding and a calibration-oriented training objective address the input design and mode-degeneracy challenges specific to mixture-based aerial trajectory prediction. On a hybrid real-and-synthetic quadrotor corpus spanning nine motion categories, AeroCast reduces Average Displacement Error and Final Displacement Error by approximately 50% relative to the baselines over a five-second horizon, and achieves the lowest negative log-likelihood and Continuous Ranked Probability Score among all compared methods. Ablation analysis identifies velocity input and model capacity as the primary contributors to prediction quality, and positional encoding as essential for long-horizon trajectory coherence. AeroCast inference completes in 0.1ms per sample, compatible with real-time onboard deployment at 100Hz.
Syed Izzat Ullah, Jose Baca
Department of Engineering, Texas A&M University–Corpus Christi, Corpus Christi, TX 78412 USA