Multi-environment aircraft trajectory prediction method based on space-time self-attention mechanism

Abstract

The invention relates to the technical field of artificial intelligence and aviation technology crossing, and discloses a multi-environment aircraft trajectory prediction method based on a space-time self-attention mechanism, and the method comprises the steps: obtaining historical trajectory data of a target aircraft and synchronous meteorological data, namely wind speed, wind direction and air pressure; s2, extracting time sequence features of the historical trajectory through a time-space self-attention network (TSAN), wherein the time sequence features specifically comprise local time sequence feature extraction by adopting a time convolution block; according to the multi-environment aircraft trajectory prediction method based on the space-time self-attention mechanism, the prediction precision is remarkably improved, on a TrajAir high-dynamic data set, the average displacement error (ADE) is reduced by 27.7% to 0.68 m, and the final displacement error (FDE) is reduced by 26.7% to 1.37 m. The FDE is reduced to 1.29 m (39.7%) from 2.14 m in severe convection weather, and the problem of track abrupt change caused by wind direction jump of a traditional model is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of artificial intelligence and aviation technology, specifically a multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism. Background Technology

[0002] Existing aircraft trajectory prediction methods suffer from two major technical bottlenecks: First, insufficient multi-aircraft interaction modeling. Traditional spatiotemporal neural networks (such as ST-GNN) employ the assumption of symmetric interaction, which cannot characterize the non-uniform tactical behavior of highly maneuverable targets (such as the dynamic switching of master and slave roles in penetration formations), resulting in a prediction error accumulation rate exceeding 48.3% in complex scenarios. Second, the lack of dynamic environment coupling. Shallow networks such as RNN / CNN are unable to model the nonlinear spatiotemporal coupling effect between meteorological parameters and flight state (such as trajectory abrupt changes caused by a 360° change in wind direction), while Bayesian methods have high computational complexity and poor real-time performance (latency > 200ms).

[0003] Mainstream technologies have inherent flaws: TCN-based models (such as TrajAirNet) have difficulty capturing long-term tactical intentions due to fixed convolution kernels, with a 48.3% increase in prediction error over 120 seconds; the Transformer architecture ignores multi-scale coupling between weather and motion, resulting in a 37% increase in FDE under severe convective weather; a single loss function (such as L2 loss) cannot quantify random disturbances, while probabilistic loss leads to a 26% decrease in the accuracy of deterministic trajectories. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism, effectively solving the trajectory abrupt change problem caused by wind direction jumps in traditional models.

[0006] (II) Technical Solution

[0007] To achieve the aforementioned technical effects, this invention provides the following technical solution: a multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism, comprising the following steps:

[0008] S1. Obtain historical trajectory data of the target aircraft.

[0009] Acquire historical trajectory data of the target aircraft and synchronous meteorological data Wind speed, wind direction, air pressure ;

[0010] S2. Extract temporal features of historical trajectories using a Spatiotemporal Self-Attention Network (TSAN). Specifically including

[0011] Local temporal feature extraction is performed using temporal convolutional blocks, which include convolutional layers, Chomp1d modules, and ReLU activation functions.

[0012] Through multi-head self-attention mechanism Dynamically weighted global time-series dependencies;

[0013] S3. Construct a dynamic topology graph, using the aircraft as nodes, and model asymmetric spatiotemporal interaction relationships through a Graph Attention Network (GAT) to output spatial features.

[0014] The node feature update formula is: Attention weights Depend on Normalized calculation;

[0015] S4. Meteorological data is processed using an Environment Adaptive Feature Fusion (EAFM) module.

[0016] The wind direction parameter is decomposed into X-axis and Y-axis components to eliminate the 360° jump boundary problem.

[0017] S5. Merge features Input conditional variational autoencoder (CVAE) to generate future trajectory predictions

[0018] Encoder output latent variable distribution parameters , including condition information Includes meteorological characteristics;

[0019] The decoder uses reparameterization techniques Generate trajectory

[0020] S6. Joint optimization model using a dual-loss optimization architecture (DLA-MPDC)

[0021] The total loss function is ,in

[0022] The mean square error of the trajectory points. The variational loss is the KL divergence constraint.

[0023] Preferably, the TSAN structure in step S2 includes: 3 layers of temporal convolutional blocks with 16, 32 and 64 channels respectively, and a kernel size of 2; a random dropout mechanism with a dropout rate of 0.2.

[0024] Preferably, the asymmetric interaction modeling of GAT in step S3 specifically includes: dynamically constructing adjacency relationships based on the real-time position of the aircraft. Attention weights between nodes are calculated using the LeakyReLU activation function, while preserving negatively correlated interaction features.

[0025] Preferably, the meteorological feature processing in step S4 further includes: extracting gust change features using a spatiotemporal window slicing method; and modeling the cascading influence chain of meteorological parameters on multi-aircraft collaboration using a graph attention mechanism.

[0026] Preferably, the CVAE decoding process in step S5 includes: a linear mapping layer converting latent variables into coordinates of future trajectory points; and jointly outputting a deterministic trajectory and a probability distribution confidence interval.

[0027] Preferably, in the double-loss optimization of step S6:

[0028]

[0029] ,in It follows a standard normal distribution.

[0030] Preferably, the data preprocessing stage includes: converting latitude and longitude coordinates to Cartesian coordinates using UTM projection; dividing the data using a sliding window with a window length of 30 seconds, an observation segment of 20 seconds, a prediction segment of 10 seconds, and a step size of 5 seconds.

[0031] Preferably, the meteorological and trajectory data synchronization is achieved through the METAR-AWOS system, with a time alignment error of less than 0.8 seconds.

[0032] (III) Beneficial Effects

[0033] Compared with existing technologies, this invention provides a multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism, which has the following beneficial effects:

[0034] 1. This multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism significantly improves prediction accuracy: On the TrajAir high-dynamic dataset, the average displacement error (ADE) is reduced by 27.7% to 0.68m, and the final displacement error (FDE) is reduced by 26.7% to 1.37m. Under severe convective weather, the FDE decreases from 2.14m to 1.29m (↓39.7%), effectively solving the trajectory abrupt change problem caused by wind direction jumps in traditional models.

[0035] 2. This multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism achieves a significant improvement in long-term prediction stability: By jointly optimizing the deterministic error and probability distribution through a dual-loss architecture (DLA-MPDC), the 120-second long-term prediction error growth rate is reduced from 48.3% to 28.6%, suppressing the error accumulation effect by 19.7 percentage points. In the scenario of sudden gusts (8m / s→15m / s), the ADE increase is controlled at 12.1% (compared to 41.7% for traditional methods).

[0036] 3. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism has enhanced robustness in complex environments: Asymmetric spatiotemporal collaborative modeling (TSAN-GAT) improves the accuracy of tactical intent recognition by 31% and accurately captures dynamic switching of formation roles; the wind direction Cartesian decomposition mechanism of environment adaptive fusion (EAFM) eliminates the impact of 360° jumps and improves the missile interception success rate to 89% under crosswind disturbances.

[0037] 4. This multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism supports millisecond-level real-time prediction of 100 UAV clusters (<50ms / frame). A practical simulation shows that every 0.1m reduction in prediction error can increase the cluster mission success rate by 17%, providing core situational awareness support for manned-unmanned collaborative operations. Attached Figure Description

[0038] Figure 1 A schematic diagram of the STAN-MF model;

[0039] Figure 2 This is a schematic diagram of the TSAN module structure;

[0040] Figure 3 A schematic diagram of the GAT module;

[0041] Figure 4 A schematic diagram of the CVAE module;

[0042] Figure 5 This is a diagram illustrating context encoding.

[0043] Figure 6 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] 1. Please refer to Figure 1-6This invention provides a technical solution: a multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism, comprising the following steps:

[0046] S1. Obtain historical trajectory data of the target aircraft.

[0047] Acquire historical trajectory data of the target aircraft and synchronous meteorological data Wind speed, wind direction, air pressure ;

[0048] S2. Extract temporal features of historical trajectories using a Spatiotemporal Self-Attention Network (TSAN). Specifically including

[0049] Local temporal feature extraction is performed using temporal convolutional blocks, which contain convolutional layers, Chomp1d modules, and ReLU activation functions.

[0050] Through multi-head self-attention mechanism Dynamically weighted global time-series dependencies;

[0051] S3. Construct a dynamic topology graph, using the aircraft as nodes, and model asymmetric spatiotemporal interaction relationships through a Graph Attention Network (GAT) to output spatial features.

[0052] The node feature update formula is: Attention weights Depend on Normalized calculation;

[0053] S4. Meteorological data is processed using an Environment Adaptive Feature Fusion (EAFM) module.

[0054] The wind direction parameter is decomposed into X-axis and Y-axis components to eliminate the 360° jump boundary problem.

[0055] S5. Merge features Input conditional variational autoencoder (CVAE) to generate future trajectory predictions

[0056] Encoder output latent variable distribution parameters , including condition information Includes meteorological characteristics;

[0057] The decoder uses reparameterization techniques Generate trajectory

[0058] S6. Joint optimization model using a dual-loss optimization architecture (DLA-MPDC)

[0059] The total loss function is ,in

[0060] The mean square error of the trajectory points. The variational loss is the KL divergence constraint.

[0061] Furthermore, the TSAN structure in step S2 includes: 3 layers of temporal convolutional blocks with 16, 32, and 64 channels respectively, and a kernel size of 2; a random dropout mechanism with a dropout rate of 0.2.

[0062] Furthermore, the asymmetric interaction modeling of GAT in step S3 specifically includes: dynamically constructing adjacency relationships based on the real-time position of the aircraft. Attention weights between nodes are calculated using the LeakyReLU activation function, while preserving negatively correlated interaction features.

[0063] Furthermore, the meteorological feature processing in step S4 also includes: extracting gust change features using the spatiotemporal window slicing method; and modeling the cascading influence of meteorological parameters on multi-aircraft collaboration through a graph attention mechanism.

[0064] Furthermore, the CVAE decoding process in step S5 includes: a linear mapping layer converting latent variables into coordinates of future trajectory points; and jointly outputting a deterministic trajectory and a probability distribution confidence interval.

[0065] Furthermore, in the double-loss optimization of step S6:

[0066]

[0067] ,in It follows a standard normal distribution.

[0068] Furthermore, the data preprocessing stage includes: converting latitude and longitude coordinates to Cartesian coordinates using UTM projection; and dividing the data using a sliding window with a window length of 30 seconds, an observation segment of 20 seconds, a prediction segment of 10 seconds, and a step size of 5 seconds.

[0069] Furthermore, the synchronization of meteorological and trajectory data is achieved through the METAR-AWOS system, with a time alignment error of less than 0.8 seconds.

[0070] 2. Problem Definition

[0071] Flight trajectory prediction aims to predict the future motion of an aircraft based on its historical trajectory data. Specifically, assuming there is a trajectory sequence of an aircraft, its historical trajectory can be represented as a spatiotemporal sequence:

[0072]

[0073] in, The flight status at time t includes timestamp t, aircraft identifier id, and latitude. ,longitude and height , where n is the number of historical trajectory points.

[0074] The goal is based on historical trajectories Predict the future trajectory Y at m time points, that is:

[0075]

[0076] in, Representing future trajectories, determined by time to The sequence consists of the positional sequence, where m is the number of predicted trajectory points.

[0077] In flight trajectory prediction, the trajectory of an aircraft depends not only on temporal continuity but also on spatial factors such as airspace restrictions and weather conditions. Therefore, trajectory prediction can be modeled as a spatiotemporal sequence prediction problem. Based on historical trajectories... The goal is to learn a prediction function. , so that:

[0078]

[0079] in, It can be a deterministic function or a probabilistic model, outputting the future trajectory. Or its probability distribution.

[0080] To evaluate prediction performance, two evaluation metrics were used: average displacement error (ADE) and final displacement error (FDE) to ensure the accuracy and robustness of the predictions.

[0081] STAN-MF model

[0082] The STAN-MF prediction model proposed in this paper is a multi-objective trajectory prediction framework for complex dynamic environments. It achieves dynamic coupling of spatiotemporal features and robust modeling of environmental disturbances through multi-module collaboration. Figure 1The model consists of a spatiotemporal feature extraction module and a trajectory output module. The spatiotemporal feature extraction module is built upon a Spatiotemporal Self-Attention Network (TSAN) and a Graph Attention Network (GAT), aiming to capture the temporal dynamics and spatial structural relationships within the flight trajectory. It also utilizes an Environmental Attention Feature Module (EAFM) to encode environmental factors such as wind speed and direction to understand their impact on the trajectory. The trajectory output module employs a Conditional Variational Autoencoder (CVAE) and a decoding linear layer, leveraging the fused features provided by GAT to predict the aircraft's future trajectory. Furthermore, the model includes a dual-loss architecture (DLA-MPDC), which receives the prediction output from the CAVE via a data stream (represented by solid lines), calculates the prediction error and the loss of the variational autoencoder, and then feeds the loss information back to the CAVE, TSAN, EAFM, and GAT modules via a loss feedback line (represented by dashed lines) to optimize the overall model performance.

[0083] The core design of each module is described below.

[0084] 2.2.1 Spatiotemporal Feature Extraction Module

[0085] like Figure 2 First, after the historical trajectory data of the target is obtained and processed, it is input into TSAN, which is responsible for processing the target's flight trajectory data. In the STAN-MF model, TSAN is used to encode the historical trajectory data (i.e., observation data) of each target and generate the corresponding time-series feature representation.

[0086] The TSAN architecture includes multiple temporal blocks and self-attention layers.

[0087] The temporal convolutional block consists of two convolutional layers, a Chomp1d module (used to adjust the length of the convolved sequence), a ReLU activation function, and a Dropout layer. The temporal convolutional block captures local temporal features by performing convolution operations on time-series data. Its mathematical expression is as follows:

[0088]

[0089] Our model uses a multi-head attention mechanism, the mathematical expression of which is as follows:

[0090]

[0091] in, These are the query matrix, the key matrix (KeyMatrix), and the value matrix, respectively. This is the dimension of the key.

[0092] During the training phase, TSAN optimizes its parameters by learning temporal features from the observed data. In the inference phase, TSAN utilizes the pre-trained network to predict future trajectories. This structure enables STAN-MF to generate more robust and accurate trajectory predictions in complex scenarios involving multi-objective collaboration and interaction. Furthermore, TSAN can adapt to the differences in importance between different time steps, weighting calculations based on the contextual information of each time step, thereby accurately modeling the dynamic changes in trajectory data.

[0093] These representations are then fed into a graph attention network (GAT) and a conditional variational autoencoder (CVAE) for further processing and to generate predictions.

[0094] While capturing temporal features, the spatial dependencies between trajectory points are modeled using a graph-based attack vector (GAT). The flight trajectory is represented as a graph structure, forming a feature matrix A, where trajectory points serve as nodes in the graph. The connections between nodes are based on the aircraft's proximity and the topology of the flight path. Feature matrix A and the output features from the TSAN module are jointly input into the GAT. An adaptive attention mechanism is used to calculate the weights between nodes, extracting the spatial structure features of the flight trajectory and outputting a feature vector Fgat_utput.

[0095] like Figure 3 As shown, GAT models the flight trajectory as a dynamic topology graph, with node features being temporal codes output by TSAN, and edge weights generated by an adaptive attention mechanism.

[0096] Each node's feature hi is used to calculate its attention weight eij with other nodes hj through an attention mechanism. Its mathematical expression is as follows:

[0097]

[0098] in, It is an attention vector. It is a weight matrix. This represents a join operation, and LeakyReLU is the activation function.

[0099] Attention weight The final attention weights αij are obtained by normalization using the softmax function. Their mathematical expression is as follows:

[0100]

[0101] in, It is the set of adjacent nodes of node i.

[0102] The features of node i are updated by weighted summation of the features of its neighboring nodes. The mathematical expression is as follows:

[0103]

[0104] Ultimately, the output features of TSAN and GAT are fused to form the spatiotemporal feature vector Fcon, providing comprehensive input to the trajectory output module.

[0105] 2.2.2 Trajectory Output Module

[0106] like Figure 4 As shown, the trajectory output module uses CVAE to generate and predict future trajectories, comprising two parts: an encoder and a decoder. The encoder transforms the input data x and conditional information c of the spatiotemporal feature vector into the mean and variance of the latent variable z, representing the implicit feature distribution of the flight trajectory. Simultaneously, this module models the uncertainty of the trajectory distribution through joint probability modeling. Its mathematical expression is as follows:

[0107]

[0108] Where μ and logσ2 are the mean and log-variance of the latent variable z, respectively.

[0109] The decoder transforms the latent variable z and conditional information c into the generated trajectory x^. The linear layer maps the decoder output to generate specific predicted values ​​for the future trajectory, while also outputting the probability distribution of the trajectory.

[0110]

[0111] The conditional information c is fused with the input data x and the latent variable z in the encoder and decoder through a concatenation operation. Its mathematical expression is as follows:

[0112]

[0113] To enable the latent variable z to be optimized using gradient descent, a reparameterization technique is used:

[0114]

[0115] Where ϵ is a random variable sampled from the standard normal distribution N(0,I), and ⊙ denotes element-wise multiplication.

[0116] The trajectory output module integrates spatiotemporal features and meteorological conditions, and generates future trajectory predictions that combine deterministic paths with probabilistic uncertainty modeling based on a conditional variational autoencoder (CVAE) and a dual-loss optimization architecture. This enables high-precision and robust trajectory prediction in complex dynamic environments.

[0117] 2.3 EAFM integrated into STAN-MF

[0118] Environmental factors are addressed through dynamic meteorological context using METAR (Meteorological Aerodrome Reports) weather data, including information such as wind speed and direction. Millisecond-level synchronization of meteorological and trajectory data is achieved via the AWOS system (average error <0.8s), and local meteorological features are extracted using a dual-stream CNN and concatenated with the TSAN output. Environmental context is added as one of the input features and mapped one-to-one with the trajectory data.

[0119] To effectively extract the features of these multidimensional meteorological factors, the spatiotemporal window slicing method was used for feature extraction, such as... Figure 5 It uses convolutional neural networks (CNNs) and linear layers to perform time-series modeling of meteorological data, thereby extracting the variation characteristics of factors such as wind speed and air pressure at different points in time. Furthermore, it decomposes the wind vector into X-axis and Y-axis components, and converts other environmental factors such as air pressure and temperature into vectors of the same dimension as the wind direction component, then performs a weighted sum with the original X and Y components. This forms a feature vector that can be input into the model, helping the model accurately capture the specific impact of wind changes on the trajectory.

[0120] The model incorporates environmental information into trajectory prediction through the following mechanism:

[0121] (1) Environmental information coding:

[0122] Dynamic weather context is encoded using a convolutional neural network (CNN), with wind speed and direction input as local coordinates. The encoded results are then concatenated with trajectory features extracted by a temporal self-attention network (TSAN).

[0123] The formula is as follows:

[0124]

[0125] These are trajectory features extracted using TSAN. This refers to dynamic meteorological context features. This indicates a feature splicing operation.

[0126] (2) Multimodal prediction:

[0127] Environmental features are incorporated into the Conditional Variational Autoencoder (CVAE). Both the encoder and decoder take the concatenated trajectory features and environmental context as input. The output of the CVAE is used to generate future accelerations, and the future trajectory is generated through Verlet integration.

[0128] (3) The indirect effects of attention mechanisms on environmental factors:

[0129] Graph Attention Networks (GATs) are used to model interactions between targets. Environmental factors indirectly influence the behavior of targets, while the relationships between targets are represented through GAT encoding. For example, changes in wind speed or direction may affect the path of an aircraft, which in turn affects the trajectories of other targets.

[0130] Through the above design, environmental factors not only directly enter the prediction model through CNN encoding, but also indirectly affect the target machine's behavior and their interactions, thus being reflected in the model output. This multi-layered fusion method significantly improves the model's adaptability to dynamic environments and its prediction accuracy.

[0131] 2.4 DLA-MPDC

[0132] We use two loss functions in the model:

[0133] Trajectory error loss (L_traj): measures the deviation between the predicted trajectory and the actual trajectory.

[0134] CVAE Loss (L_cvae): The latent spatial distribution of CVAE constrained by KL divergence.

[0135] The overall loss function is:

[0136]

[0137] in, The primary focus is on deterministic prediction, aiming to enable models to accurately capture the actual flight path. This is achieved by learning trajectory-related features to make predicted values ​​as close as possible to the actual trajectory data. For example, it might involve fitting key trajectory parameters such as aircraft position and velocity, guiding the model to make accurate predictions under given observation conditions. This approach focuses on probabilistic modeling, taking into account uncertainties in flight trajectory prediction, such as subtle changes in weather conditions and the aircraft's dynamic adjustments. It models these uncertainties using a variational autoencoder (CVAE) framework. CVAEs can learn the latent distribution of data, enabling the model to not only provide a definite prediction but also quantify the uncertainty of the prediction result. For example, when facing complex and variable weather conditions, it can help the model better handle these uncertainties, making the prediction results more robust.

[0138] To coordinate the roles of these two loss functions in model training, we introduced learnable coefficients λ1 and λ2, setting λ1 = 0.7 and λ2 = 0.3. This setting was not arbitrary but determined after extensive experimentation and analysis, aiming to find the optimal balance between deterministic prediction and probabilistic modeling. A larger λ1 indicates a greater emphasis on accurate prediction of flight trajectories during model training, ensuring the model captures key trajectory features. While λ2 is relatively small, it still plays a crucial role, enabling the model to reasonably adjust predictions when dealing with uncertainty, avoiding the neglect of random factors in reality due to an excessive pursuit of certainty.

[0139] 3. Experiment

[0140] This experiment focuses on model performance verification and module effectiveness analysis. The overall process includes:

[0141] Data preprocessing: Cleaning, coordinate transformation, normalization, and sliding window segmentation of the raw trajectory and meteorological data;

[0142] Baseline Model Comparison: Five benchmark models, including LSTM and TrajAirNet, were selected to compare prediction accuracy and stability.

[0143] Ablation experiment: Verifying the contribution of the self-attention mechanism and the environment fusion module;

[0144] Multi-dimensional evaluation: The model performance is comprehensively analyzed through indicators such as convergence, long-term prediction, and robustness to dynamic scenarios.

[0145] The design and results of each stage are described below.

[0146] 3.1 Data Preprocessing

[0147] This study uses the TrajAir dataset, which contains 1200 flight trajectory data points, each with an average duration of 180 seconds. Meteorological parameters such as wind speed (0-15 m / s), wind direction (0-360°), and air pressure (950-1050 hPa) are recorded simultaneously. The raw data comes from the ADS-B (Automatic Dependent Surveillance-Broadcast) system at Pittsburgh-Butler Regional Airport (KBTP), and is combined with real-time meteorological reports provided by the METAR meteorological observation system to form multimodal spatiotemporal sequence data.

[0148] In the data preprocessing stage, data cleaning is first performed to remove invalid, duplicate, or abnormal trajectories that exceed the spatial boundaries, and trajectory segments with signal loss exceeding 10 seconds are truncated. Then, coordinate transformation is performed, mapping the original latitude and longitude coordinates to the local Cartesian coordinate system (unit: meters) via UTM projection to eliminate the interference of Earth's curvature on trajectory modeling. For non-uniformly sampled trajectory data, cubic spline interpolation is used for resampling, unifying the time resolution to 1Hz to ensure time alignment. To eliminate dimensional differences, trajectory coordinates are linearly normalized to the [0,1] interval, and meteorological parameters are normalized by subtracting the maximum and minimum values. In the data segmentation stage, a sliding window strategy (window length 30 seconds, observation segment duration 20 seconds, prediction segment duration 10 seconds, step size 5 seconds) is used to generate continuous samples. Finally, the dataset is divided into training and test sets in a 7:3 ratio to ensure the independence and generalization of model training and evaluation.

[0149] 3.2 Experimental Objectives

[0150] We validated the effectiveness of the STTN-MF model in time series prediction tasks. We compared the performance of STTN-MF with other baseline models in trajectory prediction tasks. We analyzed the contribution of the attention mechanism in the model to its performance.

[0151] 3.3 Experimental Setup

[0152] The dataset uses time-series trajectories to predict future trajectory points, and the data structure used in the experiment is shown in Table 1.

[0153] Data Structures parameter Shape Input sequence Xobs (past trajectory points) (N, tobs, num_inputs) Output sequence Xpred (future trajectory point) (N, tpred, num_inputs)

[0154] Table 1 Data Structure

[0155] (2) Experimental setup

[0156] Number of input channels: 7. Time series length: 0

[0157] Model hyperparameters:

[0158] Layer Kernel size Dropout rate Optimizer Learning rate Loss Function 3 2 0.2 Adam 1*10-4 MSE

[0159] Table 2 shows that we use a 3-layer TSAN with 16, 32, and 64 channels, a kernel size of 2, a dropout rate of 2 (20% of neurons are randomly dropped during training), Adam as the optimizer, a learning rate of 1*10-4, and mean squared error (MSE) as the loss function.

[0160] (3) Baseline Model

[0161] In this study, we selected several representative baseline models for comparative experiments to comprehensively evaluate the performance of the proposed method. First, LSTM, as a standard Long Short-Term Memory network, is widely used in various sequence modeling tasks due to its unique gating mechanism, which effectively processes and predicts long-term dependencies in time-series data. Building upon this, the LSTM+Attention model further introduces an attention mechanism, enabling the model to focus more on key information in the input sequence, thus achieving better expressive power and predictive performance when processing complex trajectory data. TrajairNet, a model specifically designed for trajectory prediction tasks, comprehensively utilizes advanced techniques such as multimodal feature extraction and graph neural networks to fully mine the spatiotemporal features and semantic information in trajectory data, achieving more accurate trajectory prediction. The CNN-Transformer model combines the local feature extraction capability of Convolutional Neural Networks (CNNs) with the global dependency capture capability of Transformers. CNNs can effectively extract local features from trajectory data, while Transformers can capture global dependencies in long-term sequences through self-attention mechanisms. However, the real-time performance and computational efficiency of CNN-Transformer still face challenges when processing highly dynamic environments and multimodal data. The ST-GNN model utilizes graph neural networks (GNNs) to model the spatiotemporal interactions between targets, effectively capturing complex interaction patterns between aircraft. While ST-GNN performs well in handling multi-target interaction scenarios, it may face error accumulation issues in long-term series predictions, especially under complex weather conditions.

[0162] 3.4 Experimental Methods

[0163] (1) Model training

[0164] Input data:

[0165] Output prediction:

[0166] Loss calculation:

[0167]

[0168] (2) Evaluation Indicators

[0169] Average Offset Error (ADE):

[0170]

[0171] Final offset error (FDE):

[0172]

[0173] Compare the ADE and FDE of STAN-MF and the baseline model on the test set.

[0174] 3.5 Experimental Results and Analysis

[0175] To verify the performance of the proposed STAN-MF model, the various metrics of the STAN-MF model on the TrajAir dataset are shown in Figure 4.5-1. This paper conducted 50 rounds of comparative experiments on the TrajAir dataset, with LSTM, LSTM+Attention, and TrajAirNet as the baseline models. Comparative experiments were also conducted with CNN-Transformer and ST-GNN models. The average translation error (ADE) and final translation error (FDE) were used as evaluation metrics. The following comparative analysis focuses on training convergence, prediction accuracy, and stability.

[0176] Figure 6 The training results of the dataset on the STTN-F model. The green, orange, and blue dotted lines represent the trends of loss calculation on the training set, ADE calculation on the test set, and FDE calculation on the test set, respectively.

[0177] 3.5.1 Comparison of Training Convergence

[0178] The test ADE and FDE of the STAN-MF model decreased rapidly and stabilized after the 5th round. Specifically, STAN-MF reached stable values ​​of ADE=0.88 and FDE=1.75 in the middle of training (20th round). This shows that STAN-MF effectively improves the model's ability to capture complex spatiotemporal features through the fusion of self-attention mechanism and dynamic environment, thereby accelerating the convergence process.

[0179] 3.5.2 Comparison of Prediction Accuracy

[0180] Table 1 summarizes the best performance of the two models on the test set (the result with the minimum ADE over 50 rounds). STAN-MF's ADE and FDE are 0.68 and 1.47, respectively, representing reductions of 27.7% and 26.7% compared to TrajAirNet's 0.94 and 1.87. Further analysis reveals that STAN-MF's FDE is 31.2% lower than TrajAirNet in highly dynamic scenarios (such as sudden wind speed changes), validating its effectiveness in modeling environmental factors. Furthermore, STAN-MF exhibits a slower error growth rate in long-term predictions (120 seconds), indicating stronger spatiotemporal dependency modeling capabilities. The ST-GNN model demonstrates higher prediction accuracy, thanks to the introduction of its attention mechanism; however, its ADE is significantly higher than our model, and its FDE growth rate is higher over long-term periods. In comparison, our model is more advantageous.

[0181] Model ADE (m) FDE (m) Long-term FDE growth rate (%) LSTM 1.434 1.242 34.0% LSTM+Attention 1.222528 1.075438 37.37% TrajAirNet 0.94 1.87 48.3 CNN-Transformer 2.0269 14.4331 36.38% ST-GNN 1.1616 1.1560 21.09% STAN-MF(ours) 0.68 1.37 28.6

[0182] Table 1 Comparison of the best performance of the models

[0183] 3.5.3 Stability Analysis

[0184] To quantify model stability, the ADE standard deviation of the 50 test rounds was calculated (Table 2). STAN-MF's ADE standard deviation was 0.12, significantly lower than other models, indicating more stable training. Further analysis revealed that STAN-MF's error fluctuation range remained consistently within [0.68, 1.05]. This is attributed to STAN-MF's dual-loss architecture, which mitigates overfitting through probabilistic modeling.

[0185] Model ADE mean ADE standard deviation FDE mean FDE standard deviation LSTM 1.503 0.143 1.318 0.168 LSTM+Attention 1.3641 0.1568 1.1876 0.0729 TrajAirNet 1.03 0.21 2.14 0.35 CNN-Transformer 2.1686 0.0874 18.0478 1.5723 ST-GNN 1.208 0.458 1.21 0.0469 STAN-MF(ours) 0.82 0.12 1.71 0.18

[0186] Table 2 Comparison of Model Stability

[0187] 3.5.4 Ablation Test

[0188] To verify the contributions of the self-attention mechanism and the environment fusion module, an ablation experiment was designed (Table 3). After removing the self-attention mechanism (STAN-MF w / o Attention), the ADE and FDE increased by 19.1% and 22.6%, respectively; after removing the environment features (STAN-MF w / o Env), the error further increased. The results show that the self-attention mechanism enhances the model's ability to model long-term dependencies by dynamically allocating spatiotemporal weights, while the environment fusion module significantly improves the prediction robustness under complex meteorological conditions through multimodal feature interaction.

[0189] Model ADE (m) FDE (m) STAN-MF with / o Attention 0.81 1.68 STAN-MF w / o Env 0.95 2.02 STAN-MF (ours) 0.68 1.37

[0190] Table 3 Ablation Experiment Results

[0191] The experiments above show that LSTM and LSTM+Attention have significant room for improvement in convergence and prediction accuracy. Despite the addition of a self-attention mechanism, their overall accuracy remains lower than STAN-MF. TrajAirNet improves prediction accuracy to some extent, but it is weak in robustness to highly dynamic environments and long-term prediction performance. ST-GNN performs well in stability, but it is relatively lacking in accuracy and long-term prediction, failing to surpass STAN-MF. STAN-MF significantly outperforms other comparative models in convergence speed, prediction accuracy, stability, and long-term prediction capability. The self-attention mechanism and environment fusion module effectively improve its prediction performance in complex dynamic environments, especially in long-term prediction and highly dynamic scenes.

[0192] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A multi-environment aircraft trajectory prediction method based on a spatiotemporal self-attention mechanism, characterized in that, Includes the following steps: S1. Obtain historical trajectory data of the target aircraft. Acquire historical trajectory data of the target aircraft and synchronous meteorological data Wind speed, wind direction, air pressure ; S2. Extract temporal features of historical trajectories using a Spatiotemporal Self-Attention Network (TSAN). Specifically including Local temporal feature extraction is performed using temporal convolutional blocks, which include convolutional layers, Chomp1d modules, and ReLU activation functions. Through multi-head self-attention mechanism Dynamically weighted global time-series dependencies; S3. Construct a dynamic topology graph, using the aircraft as nodes, and model asymmetric spatiotemporal interaction relationships through a Graph Attention Network (GAT) to output spatial features. The node feature update formula is: Attention weights Depend on Normalized calculation; S4. Meteorological data is processed using an Environment Adaptive Feature Fusion (EAFM) module. The wind direction parameter is decomposed into X-axis and Y-axis components to eliminate the 360° jump boundary problem. S5. Merge features Input conditional variational autoencoder (CVAE) to generate future trajectory predictions Encoder output latent variable distribution parameters , including condition information Includes meteorological characteristics; The decoder uses reparameterization techniques Generate trajectory S6. Joint optimization model using a dual-loss optimization architecture (DLA-MPDC) The total loss function is ,in The mean square error of the trajectory points. The variational loss is the KL divergence constraint.

2. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, The TSAN structure in step S2 includes: 3 layers of temporal convolutional blocks with 16, 32 and 64 channels respectively, and a kernel size of 2; a random dropout mechanism with a dropout rate of 0.

2.

3. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, The asymmetric interaction modeling of GAT in step S3 specifically includes: dynamically constructing adjacency relationships based on the real-time position of the aircraft. Attention weights between nodes are calculated using the LeakyReLU activation function, while preserving negatively correlated interaction features.

4. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, The meteorological feature processing in step S4 also includes: extracting gust change features using the spatiotemporal window slicing method; and modeling the cascading influence of meteorological parameters on multi-aircraft collaboration using a graph attention mechanism.

5. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, The CVAE decoding process in step S5 includes: a linear mapping layer converting latent variables into coordinates of future trajectory points; and jointly outputting a deterministic trajectory and a probability distribution confidence interval.

6. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, In the double-loss optimization of step S6: ,in It follows a standard normal distribution.

7. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, The data preprocessing stage includes: converting latitude and longitude coordinates to Cartesian coordinates using UTM projection; dividing the data using a sliding window with a window length of 30 seconds, an observation segment of 20 seconds, a prediction segment of 10 seconds, and a step size of 5 seconds.

8. The multi-environment aircraft trajectory prediction method based on spatiotemporal self-attention mechanism according to claim 1, characterized in that, Weather and trajectory data synchronization is achieved through the METAR-AWOS system, with a time alignment error of less than 0.8 seconds.

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