Flight trajectory prediction method fusing space perception and time-frequency conversion

Abstract

The invention provides a flight path prediction method fusing space perception and time-frequency conversion, and relates to the technical field of computers and air traffic management. The method comprises the following steps: firstly, constructing a flight path data set, preprocessing a complete flight path in the flight path data set to obtain a flight path sequence, and generating a training sample; a flight path prediction model is constructed for flight path prediction; the method comprises the following steps: firstly, carrying out feature dimension expansion on a flight path sequence by a flight path prediction model to obtain flight path high-dimensional feature representation; and learning a spatial structure dependency relationship and a time dependency relationship in the flight path sequence high-dimensional feature representation to generate a final flight path prediction result. And finally, constructing a loss function of the flight path prediction model based on the idea of supervised learning, and training the constructed flight path prediction model to obtain a trained flight path prediction model. According to the method, the prediction accuracy is improved while the model complexity is reduced.

Description

Technical Field

[0001] The present invention relates to the fields of computers and air traffic management, and particularly relates to a flight trajectory prediction method integrating spatial perception and time-frequency conversion. Background Art

[0002] With the continuous growth of global air transportation demand, the air transportation system faces increasingly complex airspace management and traffic flow problems. As a key technology in air traffic management, flight trajectory prediction can effectively improve the safety and operation efficiency of air traffic. Especially in short-term prediction, it is of great significance for flight scheduling, airspace optimization, and conflict warning. Accurate flight trajectory prediction can not only understand the future position of the aircraft in advance, but also provide decision-making support for flight scheduling and air traffic control, thus effectively reducing air traffic congestion and safety risks.

[0003] Existing flight trajectory prediction methods can be roughly divided into two categories: traditional methods based on physical models and deep learning methods based on data-driven. Traditional physical models, such as state space models and aerodynamic models, conduct trajectory prediction by considering the motion characteristics of the aircraft and the influence of the external environment. However, these methods generally have the drawback of being unable to accurately capture complex environmental factors and dynamic changes. Especially in the case of complex airspace traffic or large changes in environmental factors, the prediction error will rapidly accumulate over time, resulting in insufficient accuracy. With the development of big data technology, data-driven flight trajectory prediction methods have gradually attracted attention. These methods extract implicit spatio-temporal patterns from historical flight trajectory data and combine machine learning and deep learning algorithms for prediction. Deep learning models, such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and convolutional neural networks (CNNs), have achieved remarkable success in modeling time series data and can better capture the time-dependent relationships in flight trajectories. However, existing deep learning methods mainly focus on time-domain modeling and often ignore the spatial dependence relationships in flight trajectory data. Especially when dealing with flight trajectory data, multiple features of the aircraft (such as longitude, latitude, and altitude) have spatial dependence at the same time point, and existing models fail to effectively capture the interaction between these spatial features, resulting in unsatisfactory prediction results.

[0004] In addition, although deep learning models have strong capabilities in processing time series data, they still face some challenges. Traditional time-domain modeling methods usually cannot comprehensively reveal the complex time dependencies in flight trajectory data. Especially in long-term prediction tasks, the modeling of time-dependent relationships is vulnerable to the limitations of time-domain modeling. Some existing frequency-domain analysis methods, such as the multi-layer perceptron model based on Fourier transform, have achieved good results in the field of time series prediction. However, there are often problems of wasted feature information when learning the spatial structure dependencies of flight trajectory data. Especially for flight trajectory data with fewer feature dimensions, this waste of spatial structure information is more significant.

[0005] Therefore, how to simultaneously process spatio-temporal dependencies in flight trajectory prediction and make full use of the advantages of frequency-domain analysis is an important challenge in the current technology. The existing methods in this regard are still not deeply studied, and new technologies need to be further developed to improve the accuracy and stability of flight trajectory prediction. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a flight trajectory prediction method for fusing spatial perception and time-frequency conversion in view of the above-mentioned deficiencies of the existing technology. By combining spatial perception learning and time-frequency conversion, the spatio-temporal dependencies in flight trajectory data are accurately modeled to solve the problems of insufficient accuracy of the prediction results of existing flight trajectory prediction methods and excessive differences in prediction effects among prediction attributes. This method uses deep learning and time-frequency domain conversion technologies to model the spatio-temporal dependence relationships in flight trajectory data, improve the prediction accuracy, and is widely applied to scenarios such as flight trajectory prediction, flight scheduling, and air conflict detection in air traffic management.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is: A flight trajectory prediction method for fusing spatial perception and time-frequency conversion, comprising:

[0008] Construct a flight trajectory dataset; the flight trajectory dataset includes several complete flight trajectories in the form of Automatic Dependent Surveillance - Broadcast (ADS - B), and each trajectory consists of several discrete trajectory points;

[0009] Preprocess the complete flight trajectories in the flight trajectory dataset to obtain a flight trajectory sequence, generate training samples for deep learning model training from the flight trajectory sequence, and obtain a preprocessed flight trajectory dataset;

[0010] Divide the preprocessed flight trajectory dataset into a training set, a validation set, and a test set according to a set ratio;

[0011] Construct a flight trajectory prediction model; the flight trajectory prediction model expands the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory; learn the spatial structure dependence and temporal dependence in the high-dimensional feature representation of the flight trajectory sequence to generate the final flight trajectory prediction result;

[0012] According to the flight trajectory data in the training set, construct the loss function of the flight trajectory prediction model based on the idea of supervised learning, and train the constructed flight trajectory prediction model to obtain the trained flight trajectory prediction model;

[0013] Use the flight trajectories in the validation set to verify the trained flight trajectory prediction model to obtain the final flight trajectory prediction model;

[0014] Input the flight trajectory sequence for which the prediction result is to be generated into the final flight trajectory prediction model to automatically generate the flight trajectory prediction result.

[0015] Furthermore, the flight trajectory prediction model includes a trajectory characterization module, a spatial perception learner, a frequency-time learner, and a prediction mapping module;

[0016] The trajectory characterization module uses a representation learning method to expand the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory carrying more semantic information;

[0017] The spatial perception learner learns the spatial structure dependence in the high-dimensional feature representation of the flight trajectory sequence; the frequency-time learner performs time-frequency conversion on the output result of the spatial perception learner to learn the temporal dependence in the high-dimensional feature representation of the flight trajectory sequence;

[0018] The prediction mapping module performs mapping prediction on the output result of the frequency-time learner through a two-layer feedforward neural network to generate the final flight trajectory prediction result.

[0019] Furthermore, the spatial perception learner uses a feature decoupling module and a channel feature recalibration module to learn the spatial structure dependence in the high-dimensional feature representation of the flight trajectory sequence;

[0020] The input of the feature decoupling module is the high-dimensional representation of the flight trajectory output by the trajectory characterization module. The feature decoupling module separates features in the feature dimension of the trajectory characterization, and performs feature decoupling operations on the trajectory sequence within each feature's characterization slice to enhance the model's learning ability for different features and reduce the mutual interference between features;

[0021] The channel feature recalibration module dynamically selects relatively important semantic features in the high-dimensional representations of trajectory features with different scales and different abstraction levels, further captures the per-channel spatial dependencies in the flight trajectory data, and enhances the spatial interaction ability of the trajectory representation.

[0022] Furthermore, the frequency-time learner includes a domain transformation module, a frequency-domain learning module, and a domain inverse transformation module;

[0023] The input of the domain transformation module is the output result of the spatial perception learner, and it transforms the real-time domain representation of the flight trajectory into a complex representation in the frequency domain through Fourier transform;

[0024] The frequency-domain learning module performs frequency-domain learning on the real part and the imaginary part of the domain transformation result of the domain transformation module through two frequency-domain multi-layer perceptrons respectively, and stacks the learned real part and imaginary part to output a frequency-domain signal;

[0025] The domain inverse transformation module performs an inverse Fourier transform on the stacked frequency-domain signal to restore it to a time-domain signal.

[0026] Furthermore, the trajectory representation module performs a matrix multiplication operation on the input flight trajectory sequence data X t and a learnable weight vector where d is the embedding dimension; to obtain an implicit representation carrying more semantic information as the input of the spatial perception learner, where N and L are the number of features and the number of trajectory points of the flight trajectory sequence respectively.

[0027] Furthermore, the feature decoupling module of the spatial perception learner aims at the nth feature channel of the implicit representation G output by the trajectory representation module The feature decoupling process is as follows:

[0028] Query = G (n) ·W Q

[0029] Key = G (n) ·W K

[0030] Value = G (n) ·W V

[0031]

[0032] Weigh = Softmax(Score)

[0033] U (n) = Weigh·Value

[0034] Among them, are three query, key, and value matrices corresponding to the feature channel G (n) , and Score is the attention score in the attention mechanism, which is calculated by Query and Key; h is the dimension of the hidden layer in the fully connected layer, and U is the feature decoupling result of the nth feature channel; (n) The decoupling results of all feature channels form the output U of the feature decoupling module through the Concat operation.

[0035] Specifically, the channel feature recalibration module of the spatial perception learner targets the d'-th feature channel of the output U of the feature decoupling module

[0036] where d' is a variable that takes any integer value in the closed interval [1, 128]. The channel feature recalibration process is as follows: Compress U in the spatial dimension N×L to generate a statistic

[0037] where the d'-th element z of z is calculated as follows: (d′) The statistic z is the output of F

[0038]

[0039] and is interpreted as a set of local descriptors whose statistical information can express the spatial features of the entire trajectory representation; Fc compres s is a functional operation that performs global average pooling on the two-dimensional training samples of N×L, that is, calculates the arithmetic mean of these N×L elements, and uses this one value to represent the information on the entire N×L feature slice; ompres s To fully utilize the information aggregated after the F

[0040] (·) operation, a gating mechanism is adopted and an activation operation is performed to fully capture the dependencies between channels, that is, to capture the spatial relationships in the flight trajectory, and the activated value representation s of z is obtained; compres s The final output of the channel feature recalibration module is obtained by using the activated value s

[0041] to rescale U (d′) to obtain the feature recalibration result of the d'-th feature channel, as shown in the following formula: (d′) H

[0042] H (d′) = F scale (U (d′) , s (d′) ) = s (d′) U (d′)

[0043] Among them, H (d′) represents the feature recalibration result of the d'-th feature channel; several two-dimensional feature slices are synthesized to obtain the final three-dimensional representation of the trajectory feature F scale (U (d′) , s (d′) ) represents the activation value s (d′) and the feature map for per-channel multiplication; the F scale (·) operation maps a specific input z to a set of channel weights.

[0044] Furthermore, the domain conversion module of the frequency-time learner converts the time-domain input H into a frequency-domain representation

[0045]

[0046] where v is the time-domain integration variable, f is the frequency-domain component, and j is the imaginary unit, defined as the square root of -1; is the real part of is the imaginary part of

[0047] Furthermore, the frequency-domain learning module of the frequency-time learner for the complex input given the complex weight matrix and the complex bias the frequency-domain multi-layer perceptron of the frequency-domain learning module is expressed as:

[0048]

[0049] where is the final output of the frequency-domain multi-layer perceptron, l represents the l-th layer of the frequency-domain multi-layer perceptron, σ represents the ReLU activation function, is the 0-th layer of the frequency-domain multi-layer perceptron;

[0050] Since and are both complex numbers, according to the complex multiplication rule, the frequency-domain multi-layer perceptron is further expanded to:

[0051]

[0052] where and

[0053] The domain inverse conversion module of the frequency-time learner uses the following inverse conversion formula to convert the frequency-domain signal back to the time domain:

[0054]

[0055] Among them, f is the integration variable.

[0056] Furthermore, the prediction mapping module uses the spatial and temporal dependencies learned by the frequency-time learner to predict the flight trajectory for the next τ time stamps through a two-layer feedforward network. This two-layer feedforward network only performs one-step forward propagation, as shown in the following formula:

[0057]

[0058] Among them, is the output of the frequency-time learner, σ is the Leaky ReLU activation function, and are weight matrices, and are bias terms, d h is the dimension size of the hidden layer of the two-layer feedforward network.

[0059] The beneficial effects of adopting the above technical solutions are as follows: A flight trajectory prediction method for integrating spatial perception and time-frequency conversion provided by the present invention can not only effectively capture the spatial feature dependencies in the flight trajectory, but also enhance the modeling ability of time dependence through the time-frequency domain conversion method, thereby significantly improving the prediction accuracy and robustness, and meeting the requirements of modern aviation systems for high-precision flight trajectory prediction. It solves the problems of low prediction accuracy of existing models and prediction differences for different prediction attributes, and improves the prediction accuracy while reducing the model complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Schematic diagram of the flight trajectory prediction model SATF provided by an embodiment of the present invention;

[0061] Figure 2 Schematic diagram of constructing a dataset by a sliding window provided by an embodiment of the present invention;

[0062] Figure 3 Schematic diagram of the structure of the feature decoupling module provided by an embodiment of the present invention;

[0063] Figure 4 Schematic diagram of the structure of the channel feature recalibration module provided by an embodiment of the present invention;

[0064] Figure 5 Schematic diagram of the structure of a one-layer frequency domain perceptron provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0065] The following will further describe in detail the specific implementation manners of the present invention in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0066] In this embodiment, a flight trajectory prediction method that fuses spatial perception and time-frequency conversion is as Figure 1 shown, and specifically includes the following steps:

[0067] Step 1: Construct a flight trajectory dataset; the flight trajectory dataset includes several complete flight trajectories in the form of Automatic Dependent Surveillance - Broadcast (ADS - B), and each trajectory consists of several discrete trajectory points;

[0068] In this embodiment, the original flight trajectory data in the form of ADS - B from Variflight is collected to construct a flight trajectory dataset to verify the method of the present invention. The flight trajectory dataset covers flight trajectory data for approximately 30 days from October 1st to October 31st, 2024. The time interval between every two adjacent trajectory points is 15 seconds, with a total of 20,576 trajectory points. In this embodiment, 6 key attributes including time, longitude, latitude, altitude, speed, and heading angle are extracted from the original flight trajectory data to construct an experimental dataset and perform predictions.

[0069] Step 2: Preprocess the complete flight trajectories in the flight trajectory dataset to obtain a flight trajectory sequence, and generate training samples for deep learning model training from the flight trajectory sequence to obtain a preprocessed flight trajectory dataset;

[0070] In this embodiment, in order to improve data quality, the complete flight trajectories in the flight trajectory dataset are preprocessed, including operations such as data checking and data cleaning, to obtain a flight trajectory sequence. At the same time, in order to construct a dataset form that the model can process, the sliding window method is used to generate training samples for deep learning model training from the preprocessed flight trajectory sequence, specifically a sub - trajectory segment in a flight trajectory, as Figure 2 shown. For trajectory prediction based on L historical trajectory points, the size of the sliding window is set to L + τ, where τ is the prediction step. Each sample contains L + τ consecutive trajectory points, where the first L points represent the historical trajectory sequence (i.e., the model input), and the last τ points represent the trajectory points to be predicted (i.e., the model output).

[0071] Step 3: Divide the preprocessed flight trajectory dataset into a training set, a validation set, and a test set according to a set ratio;

[0072] In this embodiment, in order to evaluate the model performance, the preprocessed flight trajectory dataset is divided into a training set, a validation set, and a test set according to a ratio of 8:1:1, and the division results are shown in Table 1.

[0073] Table 1 Division of Flight Trajectory Dataset

[0074] Number of trajectory points Usage PartI 16460 Training set PartII 2058 Test set PartIII 2058 Validation set

[0075] Step 4: Construct a flight trajectory prediction model; the flight trajectory prediction model expands the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory; learn the spatial structure dependence and temporal dependence in the high-dimensional feature representation of the flight trajectory sequence to generate the final flight trajectory prediction result;

[0076] The flight trajectory prediction model includes a trajectory characterization module, a spatial perception learner, a frequency-time learner, and a prediction mapping module;

[0077] The trajectory characterization module uses a representation learning method to expand the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory carrying more semantic information;

[0078] The spatial perception learner uses a Feature Decoupling (FD) module and a Channelwise Feature Recalibration (CFR) module to learn the spatial structure dependence in the high-dimensional feature representation of the flight trajectory sequence; the input of the feature decoupling module is the high-dimensional representation of the flight trajectory output by the trajectory characterization module. The feature decoupling module performs feature separation in the feature dimension of the trajectory characterization, and performs feature decoupling operations on the flight trajectory sequence within each feature's representation slice to enhance the model's learning ability for different features and reduce the mutual interference between features;

[0079] The specific process of the feature decoupling module performing feature separation in the feature dimension of the trajectory characterization is as follows: Imagine the information contained in each flight trajectory training sample in the dataset as a two-dimensional matrix. The number of rows of the matrix is L, that is, L historical trajectory points; the number of columns is N, that is, the number of features in the flight trajectory data used in this embodiment, which is 5, specifically including: longitude, latitude, altitude, speed, and heading angle.

[0080] After constructing the training set through a sliding window in this way, the obtained training samples are only two-dimensional with a dimension of N×L. In the trajectory characterization module, this N×L sample will be increased by one dimension to become N×L×1, and then multiplied by a learnable vector (dimension 1×d), and the dimension becomes (N×L×1)×(1×d) = N×L×d. This "feature dimension of the trajectory characterization" is actually the N dimension, and the meaning of N is the number of features, which is 5. After "feature separation", N×L×d becomes N two-dimensional slices of L×d. Then, based on these N two-dimensional slices, the following feature decoupling operations are performed.

[0081] The channel feature recalibration module dynamically selects relatively important semantic features in the high-dimensional representations of trajectory features with different scales and different abstraction levels, further captures the per-channel level spatial dependencies in the flight trajectory data, and enhances the spatial interaction ability of the trajectory representation;

[0082] The frequency-time learner is used to learn the temporal dependencies in the high-dimensional feature representation of the flight trajectory sequence;

[0083] The frequency-time learner includes a domain transformation module, a frequency domain learning module, and a domain inverse transformation module;

[0084] The input of the domain transformation module is the output result of the spatial perception learner, and it transforms the real number representation in the time domain of the flight trajectory to the complex number representation in the frequency domain through Fourier transform;

[0085] The frequency domain learning module performs frequency domain learning on the real part and the imaginary part of the domain transformation result of the domain transformation module respectively through two frequency domain multi-layer perceptrons, and stacks the learned real part and imaginary part to output a frequency domain signal; the frequency domain multi-layer perceptron contains trainable built-in parameters, and the built-in parameters are randomly initialized according to the set dimension and continuously optimized during the model training process;

[0086] The domain inverse transformation module performs inverse Fourier transform on the stacked frequency domain signal to restore it to a time domain signal;

[0087] The prediction mapping module maps and predicts the time domain signal output by the inverse transformation module through a two-layer feedforward neural network to generate the final flight trajectory prediction result.

[0088] In this embodiment, for the training sample data generated by the sliding window Apply a trajectory representation module to enhance the learning effect of the flight trajectory prediction model. X is a general representative notation, representing each training sample, that is, L trajectory points containing N features. Specifically, inspired by word embedding, in order to obtain a more expressive hidden layer representation G t , the input data X is multiplied by a learnable weight vector through matrix multiplication. The meaning of d is the embedding dimension in the trajectory representation module, that is, the original two-dimensional trajectory segment N×L is upsampled to three dimensions, and the dimension of this third dimension is d. In this embodiment, d = 128. An implicit representation carrying more semantic information is obtained as the input of the spatial perception learner.

[0089] As Figure 3 shown, for the nth feature channel of the implicit representation G The feature decoupling process is as follows:

[0090] Query = G (n) ·W Q

[0091] Key = G (n) ·W K

[0092] Value = G (n) ·W V

[0093]

[0094] Weigh = Softmax(Score)

[0095] U (n) = Weigh·Value

[0096] Among them, are three query, key, and value matrices corresponding to the feature channel G (n) ; W is a trainable parameter matrix, Score is the attention score in the attention mechanism, calculated from Query and Key; h is the dimension of the hidden layer in the fully connected layer, is the feature decoupling result of the nth feature channel. The decoupling results of all feature channels form the output U of the feature decoupling module through the Concat operation.

[0097] As shown, for the d'-th feature channel of U

[0098] where d' is a variable that can take any integer value in the closed interval [1, 128], the channel feature recalibration process is as follows: Figure 4 Compress U in the spatial dimensions N×L to generate a statistic

[0099] where the d'-th element z of z is calculated as follows: (d′)

[0100]

[0101]

[0101] The statistic z is the output of F compres s and can be interpreted as a set of local descriptors whose statistical information can express the spatial characteristics of the entire trajectory representation. F compres s is a functional operation that performs global average pooling on the two-dimensional training samples of N×L, that is, calculates the arithmetic mean of these N×L elements and uses this single value to represent the information on the entire N×L feature slice.

[0102] To make full use of the information obtained in Fcompres s (·) The information aggregated after the operation is then activated to fully capture the dependencies between channels, that is, to more fully and deeply capture the deep spatial relationships in the flight trajectory. To limit model complexity and promote generalization, in this embodiment, a bottleneck is constructed to parameterize the gating mechanism, that is, two fully connected layers are used to implement a simple gating mechanism. These two fully connected layers consist of two layers. The first layer is a dimensionality reduction layer with a dimensionality reduction ratio r, and the second layer is a dimensionality increase layer that restores the dimensionality after reduction to the original dimension d = 128. Therefore, in this embodiment, a simple gating mechanism is selected and the Sigmoid activation function is used to capture the dependencies between channels, and the activation value representation s of z is obtained:

[0103] s = F activate (z, W) = σ(g(z, W)) = δ(W2σ(W1z))

[0104] where F activate is a functional operation that assigns importance to the d'-th result of z in the previous step, and this process is achieved through a fully connected layer. W is the overall summary of the parameters in this process, specifically W1 and W2. δ and σ represent the Sigmoid and ReLU activation functions respectively, r is the dimensionality reduction ratio.

[0105] The final output of the channel feature recalibration module is obtained by using the activation value s (d′) to rescale U (d′) to obtain the feature recalibration result of the d'-th feature channel:

[0106] H (d′) = F scale (U (d′) , s (d′) ) = s (d′) U (d′)

[0107] where H (d′) represents the feature recalibration result of the d'-th feature channel; several two-dimensional feature slices are synthesized to obtain the final three-dimensional representation of the trajectory feature represents the scalar s (d′) and the feature map for per-channel multiplication. F scale (·) operation maps a specific input z to a set of channel weights.

[0108] The domain conversion module converts the time-domain input H into a frequency-domain representation

[0109]

[0110] where \(v\) is the time-domain integration variable, \(f\) is the frequency-domain component, and \(j\) is the imaginary unit, defined as the square root of -1; is the real part of is the imaginary part of Then, the frequency-domain representation is equivalently written as:

[0111] For example Figure 5 as shown, formally, for a complex input given a complex weight matrix and a complex bias the frequency-domain multi-layer perceptron of the frequency-domain learning module can be expressed as:

[0112]

[0113] where is the final output of the frequency-domain multi-layer perceptron, \(l\) represents the \(l\)-th layer of the frequency-domain multi-layer perceptron, \(\sigma\) represents the ReLU activation function, is the 0-th layer of the frequency-domain multi-layer perceptron. Since and are both complex numbers, according to the complex multiplication rule, the frequency-domain multi-layer perceptron is further expanded to:

[0114]

[0115] where and

[0116] According to this formula, the multi-layer perceptron is implemented in the frequency domain by separately calculating the real and imaginary parts of the frequency components, and then combining them to form a complex number to obtain the final result.

[0117] In the flight trajectory prediction model SATF, only the domain transformation is performed on the time dimension. Once the frequency-domain learning is completed, the domain inverse transformation module can use the following inverse transformation formula to transform the frequency-domain signal back to the time domain:

[0118]

[0119] where \(f\) is the integration variable.

[0120] In fact, the spectrum can be represented as a combined superposition of cosine and sine waves with different frequencies and amplitudes in H. This spectrum representation can reveal the hidden periodic characteristics and frequency distribution in the signal. Therefore, by studying the spectrum, the significant frequency components in the time series can be identified more clearly, providing strong support for further analyzing and predicting the trajectory. In the following part, in this embodiment, the time-domain input H will be converted into a frequency-domain representation using DomainConversion Use DomainInversion to represent the frequency-domain signal Converted back to the time domain to simplify the expression.

[0121] The frequency-time learner aims to learn the time patterns in the frequency domain. It is constructed based on the frequency-domain multi-layer perceptron performed on each feature channel and shares weights among N channels. Specifically, it takes the output As the input, for the nth channel Apply the frequency-time learner in the following way:

[0122]

[0123] where is the spectrum representation corresponding to H (n) , and DomainConversion() and DomainInversio() represent the domain conversion operations performed in the time dimension; is the complex weight matrix, where is the complex bias, i represents the imaginary part; r represents the real part, where is the output of the frequency-domain multi-layer perceptron FreMLPs and is converted back to the time domain K through DomainInversio() (n) .

[0124] Finally, integrating and superimposing all N feature channels, the frequency-time learner outputs

[0125] The prediction mapping module uses the spatial and temporal dependencies learned by the frequency-time learner to predict the flight trajectory for the next τ time stamps through a two-layer feed-forward network (FFN) This two-layer feed-forward network only performs one-step forward propagation, thus avoiding error accumulation, as shown in the following formula:

[0126]

[0127] where is the output of the frequency-time learner, and σ is the Leaky ReLU activation function, and is the weight matrix, and is the bias term, d h is the dimension size of the hidden layer of the two-layer feedforward network.

[0128] Step 5: According to the flight trajectory data in the training set, construct the loss function of the flight trajectory prediction model based on the idea of supervised learning, and use the gradient descent algorithm to train the constructed flight trajectory prediction model to obtain the trained flight trajectory prediction model;

[0129] In this embodiment, the mean squared error (MSE) loss is used as the loss function:

[0130]

[0131] where N t represents the total number of samples in the test set, Y l,k is the true value of the l-th attribute (longitude, latitude, altitude) of the k-th sample, is the corresponding predicted value.

[0132] Step 6: Use the flight trajectory data in the validation set to verify the trained flight trajectory prediction model, and tune the parameters of the flight trajectory prediction model according to the evaluation metrics, and retrain the flight trajectory prediction model until the verification effect on the test set meets the requirements, and obtain the final flight trajectory prediction model;

[0133] In this embodiment, the root mean squared error (RMSE), mean absolute error (MAE), and mean relative error (MRE) are used as the evaluation metrics:

[0134]

[0135] Step 7: Input the flight trajectory sequence for which the prediction result is to be generated into the final flight trajectory prediction model to automatically generate the flight trajectory prediction result.

[0136] In this embodiment, the flight trajectory prediction model is built using the PyTorch framework. The specific model parameter settings are shown in Table 2, and the experimental environment is shown in Table 3.

[0137] Table 2 Model Hyperparameter Settings

[0138] Hyperparameter Value Description N 5 Number of features used in the trajectory dataset L 64 Review window size d 128 Embedding dimension of the trajectory characterization module Batch size 32 Batch size Learning rate 0.001 Learning rate r 2 Dimensionality reduction ratio size in the channel feature recalibration module h 256 Hidden layer size in the feature decoupling module <![CDATA[d h > 256 Hidden layer size in the mapping prediction module

[0139] Table 3 Experimental Environment Configuration

[0140] Name Configuration CPU Intel(R)Xeon(R)Silver 4210R CPU@2.40GHz GPU model NVIDIA GeForce RTX 3090 Ti Memory 128G GPU video memory 24G Operating system CentOS Linux(3.10.0)7(Core) Deep learning framework PyTorch

[0141] In this embodiment, to verify the performance of the model of the present invention in the flight trajectory prediction task, 4 mainstream FTP models and 1 time series prediction model FreTS (the SOTA model in the field of time series prediction) are selected as the baseline models for comparison. And with the important model parameters set the same, the experimental results of the model of the present invention are compared with the experimental results of the following mainstream models on the flight trajectory dataset constructed in step 1. The comparison results are shown in Table 4.

[0142] Vanilla LSTM (basic LSTM): This is a prediction model based on the recurrent neural network (RNN), which uses the long short-term memory (LSTM) network to model the trajectory points. This model uses input and output embedding layers and a fully connected network to achieve feature projection.

[0143] TCN (temporal convolutional network): This is a sequence modeling architecture, and its causal convolution mechanism can more effectively model time information. The application of the temporal convolutional network in flight trajectory prediction (FTP) has recently been studied, and this embodiment also verifies its performance on the flight trajectory dataset of this embodiment.

[0144] CNN-LSTM: This is an improved model based on the basic LSTM. On the basis of the LSTM, a convolutional neural network (CNN) is applied to extract spatial information, and further combined with the LSTM network to achieve the flight trajectory prediction task.

[0145] Transformer: Referring to other works in the fields of computer vision (CV), time series forecasting (TSF), and natural language processing (NLP), the Transformer architecture is also selected as the baseline model for implementing the flight trajectory prediction task.

[0146] FreTS: This is a model in the field of time series prediction, and it has achieved SOTA prediction results in multiple different types of time series datasets. The flight trajectory prediction model SATF is improved on the basis of FreTS to be more suitable for flight trajectory prediction. Therefore, FreTS is also selected as the baseline model for comparison.

[0147] These models cover the current mainstream deep learning architectures and the most competitive prediction models in the field of time series prediction, providing a comprehensive comparison scheme for this flight trajectory prediction model to evaluate the performance of different deep learning models in the flight trajectory prediction task.

[0148] Table 4 Comparison of prediction results between the method of the present invention and the baseline methods

[0149]

[0150]

[0151] Table 4 shows the comparison of the prediction accuracy between the flight trajectory prediction model SATF and 5 baseline models on the test set under three evaluation metrics. The best results are highlighted in bold. As can be seen from Table 4, SATF is almost superior to all baseline models in terms of RMSE, MAE, and MRE in longitude-latitude-altitude (LLA). Overall, the SATF method proposed in the present invention has better prediction accuracy than other baseline models, demonstrating its performance advantages and also proving the effectiveness of spatial perception and time-frequency conversion in the FTP task. Quantitative analysis shows that compared with the Transformer model with better performance in the time domain, LLA is reduced by 32.4%, 73.3%, and 75.8% on average in RMSE, and by 46%, 76.5%, and 78.3% on average in MAE. In addition, compared with the SOTA model FreTS in the field of time series prediction, LLA is reduced by 42.9%, 49.9%, and 33.2% on average in RMSE, and by 40.3%, 52.9%, and 37.2% on average in MAE. The present invention attributes the success to the fact that SATF explicitly models and captures the potential spatial relationships and time dependencies, thus effectively capturing the spatio-temporal dependencies in flight trajectory data. From the above analysis, it can be concluded that SATF has achieved the best prediction performance in 6 short-term prediction tasks.

[0152] Looking at the experimental results of all prediction durations, the SATF proposed in the present invention combines the advantages of frequency domain analysis. At the same time, in order to fully extract the trajectory spatial structure information with fewer feature numbers, a spatial perception learner is specially designed to make up for the defects of FreTS. In short, the proposed SATF flight trajectory prediction method has achieved the best prediction effect, proving the superiority of the spatial perception module for learning the spatial structure dependence of trajectories.

[0153] To further prove the effectiveness of the technical modules proposed in the present invention, this embodiment also conducts ablation experiments on short-term and long-term flight trajectory predictions by removing the corresponding modules in SATF. The experimental results are shown in Table 5. In the ablation experiments, three variables are mainly considered, and models with the following configurations are considered:

[0154] (1) A1: The feature decoupling module is removed, and the remaining hyperparameters are the same as those of SATF.

[0155] (2) A2: The channel feature recalibration module is removed, and the remaining hyperparameters are the same as those of SATF.

[0156] (3) A3: The frequency time-frequency learner is removed, and the remaining hyperparameters are the same as those of SATF.

[0157] The results in Table 5 show that removing any single module leads to a decrease in prediction accuracy on all evaluation metrics, thus verifying the positive contribution of each component. Additionally, removing the feature decoupling or channel feature recalibration module (A1 or A2) in the spatial perception learner results in more significant prediction errors within a shorter prediction time horizon (τ ∈ {2, 4, 12}), highlighting the crucial role of spatial dependency learning in short-term prediction. However, as the prediction time horizon extends (τ = 20), removing the frequency-time learner (A3) causes relatively larger prediction errors in all metrics except for the RMSE of height. This indicates that the role of the frequency-time learner becomes more important when the prediction time horizon extends, emphasizing the importance of capturing temporal dependencies in trajectory sequences.

[0158] Table 5 Ablation experiment results of the method of the present invention

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[0160]

[0161] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A flight trajectory prediction method integrating spatial perception and time-frequency conversion, characterized in that: include: Constructing a flight trajectory data set; the flight trajectory data set includes a plurality of complete flight trajectories in the form of automatic dependent surveillance broadcast (ADS-B), each trajectory consisting of a plurality of discrete trajectory points; Preprocessing the complete flight trajectory in the flight trajectory dataset to obtain a flight trajectory sequence, generating training samples for deep learning model training from the flight trajectory sequence, and obtaining a preprocessed flight trajectory dataset; The preprocessed flight trajectory dataset is divided into training set, validation set and test set according to the set ratio; Constructing a flight trajectory prediction model; the flight trajectory prediction model expands the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory; learning the spatial structure dependency and time dependency in the high-dimensional feature representation of the flight trajectory sequence to generate a final flight trajectory prediction result; According to the flight trajectory data in the training set, a loss function of the flight trajectory prediction model is constructed based on the idea of ​​supervised learning, and the constructed flight trajectory prediction model is trained to obtain a trained flight trajectory prediction model; The trained flight trajectory prediction model is verified using the flight trajectory in the validation set to obtain the final flight trajectory prediction model; The flight trajectory sequence for which prediction results are to be generated is input into the final flight trajectory prediction model to automatically generate the flight trajectory prediction results.

2. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 1 is characterized in that: The flight trajectory prediction model includes a trajectory representation module, a spatial perception learner, a frequency-time learner and a prediction mapping module; The trajectory representation module uses a representation learning method to expand the feature dimension of the flight trajectory sequence to obtain a high-dimensional feature representation of the flight trajectory that carries more semantic information; The spatial perception learner learns the spatial structure dependency in the high-dimensional feature representation of the flight trajectory sequence; the frequency-time learner performs time-frequency conversion on the output result of the spatial perception learner to learn the time dependency in the high-dimensional feature representation of the flight trajectory sequence; The prediction mapping module performs mapping prediction on the output results of the frequency-time learner through a two-layer feedforward neural network to generate the final flight trajectory prediction result.

3. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 2 is characterized in that: The spatial perception learner adopts a feature decoupling module and a channel feature recalibration module to learn the spatial structure dependency in the high-dimensional feature representation of the flight trajectory sequence; The input of the feature decoupling module is the high-dimensional representation of the flight trajectory output by the trajectory representation module. The feature decoupling module performs feature separation in the feature dimension of the trajectory representation, and performs feature decoupling operation on the trajectory sequence in each feature representation slice, thereby enhancing the model's learning ability for different features and reducing mutual interference between features. The channel feature recalibration module dynamically selects relatively important semantic features in the high-dimensional representation of trajectory features containing different scales and different levels of abstraction, further capturing the channel-by-channel spatial dependencies in the flight trajectory data and enhancing the spatial interaction capability of trajectory representation.

4. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 3 is characterized in that: The frequency-time learner includes a domain conversion module, a frequency domain learning module and a domain inverse conversion module; The input of the domain conversion module is the output result of the spatial perception learner, and the real number representation of the flight trajectory in the time domain is converted into a complex number representation in the frequency domain through Fourier transform; The frequency domain learning module performs frequency domain learning on the real part and the imaginary part of the domain conversion result of the domain conversion module through two frequency domain multilayer perceptrons respectively, and stacks the real part and the imaginary part obtained after learning to output a frequency domain signal; The domain inverse conversion module performs inverse Fourier transform on the stacked frequency domain signals to restore them to time domain signals.

5. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 4 is characterized in that: The trajectory characterization module processes the input flight trajectory sequence data X t With a learnable weight vector Perform matrix multiplication, where d is the embedding dimension; Get an implicit representation that carries more semantic information As the input of the spatial perception learner, N and L are the number of features and trajectory points of the flight trajectory sequence, respectively.

6. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 5 is characterized in that: The feature decoupling module of the spatial perception learner targets the nth feature channel of the implicit representation G output by the trajectory representation module The feature decoupling process is as follows: Query=G (n) ·W Q Key=G (n) ·W K Value=G (n) ·W V Weigh=Softmax(Score) U (n) =Weigh·Value in, are three with characteristic channel G (n) The corresponding query, key and value matrices, is a trainable parameter matrix, Score is the attention score in the attention mechanism, calculated by Query and Key; h is the dimension of the hidden layer in the fully connected layer, U (n) is the feature decoupling result of the nth feature channel; The decoupling results of all feature channels are combined into the output U of the feature decoupling module through the Concat operation.

7. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 6 is characterized in that: The channel feature recalibration module of the spatial perception learner is for the d'th feature channel of the output U of the feature decoupling module d' is a variable, and its value is any integer in the closed interval [1,128]. The channel feature recalibration process is as follows: Compress U in the spatial dimension N×L to generate a statistic where the d'th element z (d') It is calculated as follows: The statistic z is F compress The output of is interpreted as a set of local descriptors, the statistics of which can express the spatial characteristics of the entire trajectory representation; F compress It is a function operation that performs global average pooling on the N×L two-dimensional training samples, that is, finding the arithmetic mean of the N×L elements and using this value to represent the information on the entire N×L feature slice; In order to make full use of the F compress (·) The information aggregated after the operation is gated and activated to fully capture the dependencies between channels, that is, to capture the spatial relationships in the flight trajectory, and obtain the activation value of z to represent s; The final output of the channel feature recalibration module is obtained by using the activation value s (d') To U (d') Rescaling is performed to obtain the feature recalibration result of the d'th feature channel, as shown in the following formula: H (d') =F scale (U (d') ,s (d') )=s (d') U (d') Among them, H (d') Represents the feature recalibration result of the d'th feature channel; synthesize several two-dimensional feature slices to obtain the final three-dimensional representation of the trajectory feature F scale (U (d') ,s (d') ) represents the activation value s (d') With feature map Channel-by-channel multiplication between scale The (·) operation maps a particular input z to a set of channel weights.

8. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 7 is characterized in that: The domain conversion module of the frequency-time learner converts the time domain input H into a frequency domain representation H: Where v is the time domain integral variable, f is the frequency domain component, and j is the imaginary unit, defined as the square root of -1; yes The real part of yes The imaginary part of .

9. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 8, characterized in that: The frequency domain learning module of the frequency-time learner is for complex input Given a complex weight matrix and complex bias The frequency domain multilayer perceptron of the frequency domain learning module is expressed as: in, is the final output of the frequency domain multilayer perceptron, represents the frequency domain multilayer perceptron layer, σ represents the ReLU activation function, It is the 0th layer of the frequency domain multilayer perceptron; because and All are complex numbers. According to the complex multiplication rule, the frequency domain multilayer perceptron is further expanded to: in, and The domain inverse conversion module of the frequency-time learner uses the following inverse conversion formula to convert the frequency domain signal Convert back to the time domain: Here, f is used as the integration variable.

10. The flight trajectory prediction method integrating spatial perception and time-frequency conversion according to claim 9, characterized in that: The prediction mapping module uses the spatial and temporal dependencies learned by the frequency-time learner to predict the flight trajectory for the next τ timestamps through a two-layer feedforward network. The two-layer feedforward network performs only one forward propagation step, as shown in the following formula: in, is the output of the frequency-time learner, σ is the Leaky ReLU activation function, and is the weight matrix, and is the bias term, d h is the hidden layer dimension size of a two-layer feed-forward network.

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