A flight trajectory completion and prediction method based on time-frequency analysis

Abstract

The present invention provides a flight trajectory completion and prediction method based on time-frequency analysis. By analyzing aircraft trajectory data, the flight trajectory completion and future trajectory prediction are completed. This process aims to improve the efficiency of flight management and operation, especially when dealing with missing aircraft trajectories and predicting future flight paths. In view of the problem that aircraft trajectory data has complex time-frequency characteristics and some data is missing, a flight trajectory completion and prediction method based on time-frequency analysis is proposed. In view of the time and frequency domain characteristics of aircraft trajectories, a flight trajectory reconstruction model is introduced, which includes a backbone network and a reconstruction network. The backbone network is responsible for extracting the features of the input data, and the reconstruction network guides the model to pay more attention to the time characteristics and frequency domain characteristics of the aircraft trajectory through the trajectory reconstruction module and the frequency domain reconstruction module, thereby improving the accuracy of trajectory reconstruction.

Description

Technical Field

[0001] The present invention relates to the field of air traffic management, and in particular to a flight trajectory completion and prediction method based on time-frequency analysis. Background Art

[0002] In the air traffic sector, trajectory prediction is a key technology that supports air traffic management, including flight delay prediction, fuel consumption prediction, and flight trajectory prediction. Accurate trajectory prediction significantly improves the efficiency of air traffic controllers in real-time flight capacity management, further ensuring aircraft safety. However, traditional trajectory sequence prediction models rely on complete aircraft trajectory sequences during training. Furthermore, the real-time collection of actual flight data often results in significant missing data, which in turn limits the reliability and performance of downstream air traffic control tasks. Summary of the Invention

[0003] The purpose of this invention is to study an integrated flight trajectory completion and prediction method to address the common problem of trajectory loss in air traffic control. An encoder enhancement pre-training strategy, wavelet attention, and loss function are proposed to achieve integrated prediction and completion, striving to ensure flight trajectory prediction performance when there are missing input sequences, and improving the usability of the results in real-world scenarios.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A flight trajectory completion and prediction method based on time-frequency analysis includes the following steps:

[0006] S1: Obtain the original aircraft trajectory sequence-random masked trajectory sequence data pair to generate the original data set;

[0007] S2: Preprocess the collected aircraft trajectory data and divide it into training, validation, and test sets; S3: Construct a flight trajectory reconstruction model, including a backbone network and a reconstruction network;

[0008] The backbone network is used to perform feature processing on the input data, and the reconstruction network is used to guide the model to pay more attention to the time characteristics and frequency domain characteristics of the aircraft trajectory. The backbone network includes a multi-layer perceptron and an encoder module; the reconstruction network includes a trajectory reconstruction module and a frequency domain reconstruction module.

[0009] S4: Pre-train the flight trajectory reconstruction model, introduce the mean square error, form a new joint loss function, train the flight trajectory reconstruction model, and retain the weight of the best model;

[0010] S5: Based on the flight trajectory reconstruction model, a flight trajectory prediction model is constructed. Specifically, for the flight trajectory reconstruction model, the backbone network is retained, the trajectory reconstruction module in the reconstruction network is removed, and a new discrete wavelet transform module, decoder group, and inverse discrete wavelet transform module are designed.

[0011] S6: Set the loss function, train the flight trajectory prediction model, and retain the weight of the best model;

[0012] S7: Test the flight trajectory reconstruction model, input aircraft sequence data with missing points, and realize integrated completion and prediction of flight trajectories.

[0013] As a preferred embodiment of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the encoder in step 3 is:

[0014] The encoder is composed of Transformer modules. After preprocessing, the data is passed to the multi-layer perceptron to obtain V. V is then passed to the Transformer input layer. After passing through the attention mechanism and feedforward neural network module, the high-dimensional matrix F1 is obtained. Specifically, the data processing steps are as follows:

[0015] S3-1: Flatten the matrix data into a vector sequence. Connect the elements in the matrix in row order to form a one-dimensional vector sequence;

[0016] The input matrix is ​​V, and the flattened vector sequence is M;

[0017] M=[V[0,0],V[0,1],...,V[0,n-1],V[1,0],V[1,1],...V[1,n-1],...,V[m-1,0],V[m-1,1],...,V[m-1,n-1]](1)

[0018] Among them, m represents the number of rows of the matrix, and n represents the number of columns of the matrix;

[0019] S3-2: Add positional encoding to each element in the matrix in the Transformer model, using sine / cosine positional encoding.

[0020] Let the position code be d,

[0021]

[0022] Among them, pos represents the position of the token in the sequence. If the sequence length is L, then pos = 0, 1, ..., L-1; d is the position vector of the token, d(pos, 2i) represents the i-th element in this position vector, i represents odd dimensions, 2i represents even dimensions, d modelRepresents the dimension of the token (that is, the dimension of each vector in our sequence); S3-3: Add the flattened matrix data to the position encoding element by element and perform a bitwise operation with the attention mask to obtain the input vector representation of the encoder.

[0023] Let the summed vector sequence be X, the attention mask be M_mask, and x be the masked vector sequence.

[0024]

[0025] Among them, * represents bitwise operation;

[0026] S3-4: The input vector representation is fed into the encoder and decoder of the Transformer model for forward propagation. The model performs self-attention calculations based on the position and relationship of elements in the sequence, thereby generating context-aware representations and outputs.

[0027] Assume that the input vector is represented as X, the forward propagation of the encoder is Encoder(X), and the forward propagation of the decoder is Decoder(X).

[0028]

[0029] S3-5: Use linear transformation method to convert the output vector into the target high-dimensional matrix.

[0030] Let the weight matrix of the linear transformation be W and the output vector be F1.

[0031] F1=decoder_output*W (5)

[0032] Here, * represents matrix multiplication.

[0033] As a preferred embodiment of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the trajectory reconstruction module and the frequency domain reconstruction module in step S3 are:

[0034] The trajectory reconstruction module is composed of an LSTM module; the frequency domain reconstruction module is composed of a self-attention module. Specifically, there are the following steps:

[0035] First, pass F1 into the input layer of the trajectory reconstruction module to obtain P′ (1) , that is, P′ (1) =LSTM(F1);

[0036] Secondly, f1 is passed into the input layer of the frequency domain reconstruction module to obtain f2; at the same time, the real trajectory vector P is subjected to discrete Fourier transform to obtain F3 (F3=FFT(P N-M:N-1 )),

[0037] The formula for discrete Fourier transform is:

[0038]

[0039] where X k is the transformed complex sequence, k = 0, 1, ..., N-1 represents the different frequency components in the frequency domain, i is the imaginary unit, x n is the sampled analog signal, and is the rotation factor;

[0040] The output of the fast Fourier transform will be a complex sequence representing the frequency components in the frequency domain, that is,

[0041]

[0042] Among them, i represents the frequency index and j represents the feature dimension;

[0043] As a preferred embodiment of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the aircraft reconstruction model training in step S4 is specifically as follows:

[0044] S4-1: Set the loss function with mean square error (MSE);

[0045] S4-2: For the trajectory reconstruction module, through the real trajectory sequence P and P' (1) As the loss function, it is marked as L1, L1 = MSE(P,P′ (1) );

[0046] S4-3: For the frequency domain reconstruction module, the real trajectory vector P is subjected to discrete Fourier transform to obtain F3 (F3 = FFT (P N-M:N-1 )), the loss function is obtained by F2 and F3, marked as L2, L2 = MSE (F2, F3); S4-4: Jointly optimize the multi-layer perceptron, encoder, trajectory reconstruction module and frequency domain reconstruction module, and set the joint loss function L 重建 =L1+L2 for optimization training and save the weight of the optimal aircraft reconstruction model;

[0047] As a preferred embodiment of the present invention, the integrated flight trajectory completion and prediction method based on wavelet time-frequency analysis described in step 4 is characterized in that the aircraft prediction model in step S5 is specifically modified as follows:

[0048] First, for the reconstruction network of the aircraft reconstruction module, the trajectory reconstruction module is removed from the network, and a convolutional layer is added after the self-attention module in the frequency domain reconstruction module. At the same time, the new frequency domain reconstruction module has a one-to-one correspondence with each decoder in the decoder group;

[0049] Secondly, for the backbone network of the aircraft reconstruction model, a discrete wavelet transform module, a decoder group and an inverse discrete wavelet transform module are added;

[0050] Finally, the serial order of the overall model is: discrete wavelet transform module, multi-layer perceptron, encoder, frequency domain reconstruction module, decoder, inverse discrete wavelet transform module;

[0051] As a preferred embodiment of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the S5 aircraft prediction model specifically processes the data stream as follows:

[0052] S5-1: Input the processed aircraft trajectory sequence, pass it through the multi-layer perceptron, encoder, and frequency domain reconstruction module to obtain F2, and then perform dimensionality-upgrading on F2 to obtain F5. The dimension of F5 is the same as the matrix dimension D in step S2-1.

[0053] S5-2: F5 passes through the self-attention module in the decoder, and the self-attention calculation formula is used to substitute the above-obtained F5 into Q, and F1 into K and V respectively, to calculate F6; the self-attention formula is as follows:

[0054] F6=Self-Attention(F5,F1,F1) (8)

[0055] S5-3: Since multiple decoders are designed, each corresponding to a wavelet component of different frequencies, it is assumed here that for the i+1 decoder, F6 is input to the convolution module of the decoder to obtain F7. i+1 ;

[0056] Among them, the convolution operation is used to embed the enhanced trajectory into F6, and the formula is expressed as:

[0057] F7 i =σ(Convld(F6)) (9)

[0058] Among them, F7 i+1 The time dimension of is determined by the resolution of the wavelet component corresponding to the i+1th decoder, where the length of the wavelet component is calculated as follows:

[0059]

[0060] h L =h L-1 (12)

[0061] Among them, L is the level of wavelet analysis, l is half of the wavelet filter length, M is the number of historical trajectory points, WTC i Represents wavelet components of different frequencies, Represents high-frequency WTC L-iThe length of time. L Represents the time length of low-frequency WTC0;

[0062] S5-4: F7 i+1 As the wavelet component at a certain resolution, at this time, let the final wavelet component obtained by different decoders be F;

[0063] As a preferred solution of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the training of the S6 aircraft prediction model has the following specific loss function settings: S6-1: find missing sequence points by extension and downsampling, and give them higher weights. Set the loss function L 预测 for:

[0064]

[0065] Where k represents the kth WTC, h L-k Representing WTC k length, It is WTC k The estimated value of the jth attribute of the i-th element of is the true value, It is a custom weight value, which completes the overall training of the model by resetting the loss function.

[0066] S6-2: The corresponding pre-processed original trajectory sequence P is subjected to discrete wavelet transform to obtain the wavelet component F8, and the F and F8 described in S5-4 are used as the prediction loss function L 预测 ,After the overall training of the model, the most suitable parameters for the model are found.

[0067] As a preferred embodiment of the present invention, a flight trajectory completion and prediction method based on time-frequency analysis is characterized in that the test in step S7 is specifically as follows:

[0068] First, input the aircraft trajectory sequence data P containing missing points l ;

[0069] Secondly, P l After passing through the model, the trajectory is completed and a complete trajectory sequence P containing the next time step is output c .

[0070] Preferably, an integrated flight trajectory completion and prediction method of a flight trajectory prediction method based on wavelet time-frequency analysis includes at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute any of the above methods.

[0071] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0072] 1. By introducing the encoder enhancement pre-training strategy and wavelet attention mechanism, the model can better capture the time and frequency characteristics of flight trajectories, and effectively improve the prediction accuracy of flight trajectories even when there are missing input sequences.

[0073] 2. The method of the present invention realizes the functions of flight trajectory completion and prediction in the same model, which solves the challenges brought by trajectory loss in traditional methods and provides a more comprehensive and consistent solution.

[0074] 3. By designing a trajectory reconstruction module and a frequency domain reconstruction module, and combining pre-training and joint training, the model can more effectively fill in missing data, thereby reducing the impact of trajectory loss on the overall prediction performance.

[0075] 4. The present invention is not only applicable to trajectory prediction under ideal conditions, but can also ensure the reliability and accuracy of trajectory prediction in real application scenarios, significantly improving the practical applicability of the technical solution.

[0076] 5. The present invention adopts discrete wavelet transform (DWT) and inverse discrete wavelet transform (IDWT) modules to optimize the computational efficiency of the model while maintaining high-precision prediction, ensuring its operability in large-scale data processing.

[0077] 6. By jointly optimizing the trajectory reconstruction loss function and the frequency domain reconstruction loss function, the model can better capture the characteristics of the input data in the time and frequency domains, effectively improving the overall performance of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The present invention will be described in more detail below based on embodiments and with reference to the accompanying drawings, wherein:

[0079] Figure 1 This is a structural diagram of the flight trajectory reconstruction model of the method proposed in the present invention;

[0080] Figure 2 This is a structural diagram of the flight trajectory prediction model of the method proposed in this invention. DETAILED DESCRIPTION

[0081] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] The present invention will be further described below with reference to the accompanying drawings and examples.

[0083] A flight trajectory completion and prediction method based on time-frequency analysis, characterized by comprising the following steps:

[0084] S1: Collect aircraft trajectory sequence data;

[0085] The original aircraft trajectory dataset is derived from the multi-source Secondary Surveillance Radar (SSR) and Automatic Dependent Surveillance-Broadcast (ADS-B) in China's actual ATC system;

[0086] S2: Preprocess the collected aircraft trajectory data and divide it into training set, validation set and test set;

[0087] The raw data was preprocessed through data verification, multi-source data analysis, track point and flight registration, multi-source data alignment, data filtering and fusion. The original binary data was used to analyze the timestamp, position and velocity attributes in the three-dimensional earth space to obtain the data set text collection.

[0088] Assume that n-1 pre-processed track data are used for prediction, and a sliding window with a window size of n is used with a step size of 1 track point to intercept the track data as a data pair, which consists of the observation values ​​of the first n-1 track points;

[0089] By random masking, a sequence of aircraft trajectories with a missing point is obtained. Then, the completed sequence of aircraft trajectories is obtained through interpolation. The two corresponding sequences are regarded as a sequence group.

[0090] The dataset is divided into training set, validation set and test set according to 9:1:1;

[0091] S3: Construct a flight trajectory reconstruction model, including a backbone network and a reconstruction network. The backbone network is used to perform feature processing on the input data, while the reconstruction network is used to guide the model to pay more attention to the temporal and frequency domain characteristics of the aircraft trajectory.

[0092] The backbone network includes a multi-layer perceptron and an encoder module; the reconstruction network includes a trajectory reconstruction module and a frequency domain reconstruction module;

[0093] First, we build a multilayer perceptron (MLP), which consists of two convolutional layers and a nonlinear layer. The convolutional layers extract local features from the input data, while the nonlinear layers introduce nonlinear transformations through activation functions, enhancing the model's ability to represent complex features. This allows the MLP to gradually extract deep features from the aircraft trajectory data, providing effective feature representation for subsequent reconstruction and prediction.

[0094] Specifically, the multi-layer perceptron consists of two convolutional layers and a nonlinear layer. The original data with a dimension of 2048x10x6 is input into the multi-layer perceptron to obtain the feature-expanded data with a dimension of 2048x10x64 as the input of the encoder.

[0095] Next, we construct the encoder, which consists of Transformer layers. The Transformer layer uses a self-attention mechanism to capture temporal dependencies in the aircraft trajectory data, effectively modeling long-range dependencies. The encoder's self-attention mechanism allows the model to flexibly focus on important trajectory features across time steps while reducing interference from irrelevant information. This allows the encoder to better extract temporal patterns and underlying features in the aircraft trajectory data, providing a more accurate input representation for subsequent trajectory reconstruction and prediction.

[0096] Next, we constructed the trajectory reconstruction module and the frequency domain reconstruction module. The trajectory reconstruction module, composed of an LSTM module, primarily processes the temporal characteristics of the aircraft trajectory. The LSTM module captures the long-term and short-term dependencies of the trajectory sequence through its internal memory cells, effectively addressing missing points and discontinuities in the trajectory, thereby achieving high-precision trajectory completion.

[0097] The frequency domain reconstruction module, comprised of a self-attention module, primarily processes the frequency domain features of trajectory data. Through this self-attention mechanism, the frequency domain reconstruction module captures the correlations between different frequency components in the frequency dimension, highlighting important frequency features while suppressing irrelevant noise frequencies. This enables the model to more comprehensively understand the frequency domain variations of aircraft trajectories, improving the accuracy and robustness of overall trajectory reconstruction.

[0098] Specifically, the trajectory reconstruction module and the frequency domain reconstruction module are composed of: the trajectory reconstruction module is composed of an LSTM module; the frequency domain reconstruction module is composed of a self-attention module. Specifically, there are the following steps:

[0099] 1) Pass F1 into the input layer of the trajectory reconstruction module to obtain P′ (1) , that is, P′ (1) =LSTM(F1);

[0100] 2) F1 is passed into the input layer of the frequency domain reconstruction module to obtain F2; at the same time, the true trajectory vector P is subjected to discrete Fourier transform to obtain F3 (F3 = FFT (P N-M:N-1 )), where the discrete Fourier transform formula is:

[0101]

[0102] where X k is the transformed complex sequence, k = 0, 1, ..., N-1 represents the different frequency components in the frequency domain, i is the imaginary unit, x n is the sampled analog signal, and is the rotation factor;

[0103] The output of the fast Fourier transform will be a complex sequence representing the frequency components in the frequency domain, that is,

[0104]

[0105] Among them, i represents the frequency index and j represents the feature dimension;

[0106] S4: Pre-train the flight trajectory reconstruction model, introduce the mean square error, form a new joint loss function, train the flight trajectory reconstruction model, and retain the weight of the best model;

[0107] The specific steps for aircraft trajectory reconstruction model training are as follows:

[0108] Set the loss function to mean square error (MSE);

[0109] For the trajectory reconstruction module, the real trajectory sequences P and P′ are (1) As the loss function, it is marked as L1, L1 = MSE(P,P′ (1) );

[0110] For the frequency domain reconstruction module, the real trajectory vector P is subjected to discrete Fourier transform to obtain F3 (F3 = FFT (P N-M:N-1 )), the loss function is obtained by F2 and F3, denoted as L2, L2 = MSE (F2, F3);

[0111] Jointly optimize the multilayer perceptron, encoder, trajectory reconstruction module and frequency domain reconstruction module, and set the joint loss function L 重建 =L1+L2 for optimization training and save the weight of the optimal aircraft reconstruction model;

[0112] S5: Based on the flight trajectory reconstruction model, a flight trajectory prediction model is constructed. Specifically, for the flight trajectory reconstruction model, the backbone network is retained, the trajectory reconstruction module in the reconstruction network is removed, and a new discrete wavelet transform module, decoder group, and inverse discrete wavelet transform module are designed.

[0113] The specific steps for changing the aircraft prediction model are:

[0114] 1) For the reconstruction network of the aircraft reconstruction module, the trajectory reconstruction module is removed from the network, and a convolutional layer is added after the self-attention module in the frequency domain reconstruction module. At the same time, the new frequency domain reconstruction module has a one-to-one correspondence with each decoder in the decoder group;

[0115] 2) For the backbone network of the aircraft reconstruction model, a discrete wavelet transform module, a decoder group, and an inverse discrete wavelet transform module are added;

[0116] 3) The serial order of the overall model is: discrete wavelet transform module, multi-layer perceptron, encoder, frequency domain reconstruction module, decoder, inverse discrete wavelet transform module;

[0117] S6: Set the loss function, train the flight trajectory prediction model, and retain the weight of the best model;

[0118] The loss function is specifically set as follows:

[0119] 1) Find the missing sequence points by extension and downsampling, and give them higher weights. Set the loss function L 预测 for:

[0120]

[0121] Where k represents the kth WTC, h L-k Representing WTC k length, It is WTC k The estimated value of the jth attribute of the i-th element of is the true value, It is a custom weight value, which completes the overall training of the model by resetting the loss function.

[0122] 2) The corresponding pre-processed original trajectory sequence P is subjected to discrete wavelet transform to obtain the wavelet component F8, and the F and F8 described in S5-4 are used as the prediction loss function L 预测 ,After the overall training of the model, the most suitable parameters for the model are found.

[0123] S7: Test the flight trajectory reconstruction model by inputting aircraft sequence data with missing points to achieve integrated completion and prediction of flight trajectories;

[0124] The test is as follows:

[0125] 1) Input the aircraft trajectory sequence data P containing missing points l ;

[0126] 2)P l After passing through the model, the trajectory is completed and a complete trajectory sequence P containing the next time step is output c .

Claims

1. A flight trajectory completion and prediction method based on time-frequency analysis, characterized in that: The following steps are involved: S1: Collect aircraft trajectory sequence data; S2: Preprocess the collected aircraft trajectory data and divide it into training set, validation set and test set; S3: Construct a flight trajectory reconstruction model, including a backbone network and a reconstruction network; The backbone network is used to perform feature processing on the input data, and the reconstruction network is used to guide the model to pay more attention to the time characteristics and frequency domain characteristics of the aircraft trajectory. The backbone network includes a multi-layer perceptron and an encoder module; the reconstruction network includes a trajectory reconstruction module and a frequency domain reconstruction module. S4: Pre-train the flight trajectory reconstruction model, introduce the mean square error, form a new joint loss function, train the flight trajectory reconstruction model, and retain the weight of the best model; S5: Based on the flight trajectory reconstruction model, a flight trajectory prediction model is constructed. Specifically, for the flight trajectory reconstruction model, the backbone network is retained, the trajectory reconstruction module in the reconstruction network is removed, and a discrete wavelet transform module, a decoder group, and an inverse discrete wavelet transform module are designed. S6: Set the loss function, train the flight trajectory prediction model, and retain the weight of the best model; S7: Test the flight trajectory reconstruction model, input aircraft sequence data with missing points, and realize integrated completion and prediction of flight trajectories.

2. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 1, characterized in that: The encoder in step S3 is: The encoder is composed of Transformer modules. After preprocessing, the data is fed into the multi-layer perceptron to obtain V. V is then passed to the Transformer input layer. After the attention mechanism and feedforward neural network module, the high-dimensional matrix F1 is obtained. Specifically, there are the following data processing steps: S3-1: Flatten the matrix data into a vector sequence, and connect the elements in the matrix in row order to form a one-dimensional vector sequence; The input matrix is ​​V, and the flattened vector sequence is M; M=[V[0,0],V[0,1],...,V[0,n-1],V[1,0],V[1,1],...V[1,n-1],...,V[m-1,0],V[m-1,1],...,V[m-1,n-1]](1)where m represents the number of rows and n represents the number of columns of the matrix; S3-2: Add positional encoding to each element in the matrix in the Transformer model, using sine / cosine positional encoding; Let the position code be d, Where pos represents the position of the token in the sequence. If the sequence length is L, then pos = 0, 1, ..., L-1; d is the position vector of the token, d(pos,2i) represents the i-th element in this position vector, i represents odd dimensions, 2i represents even dimensions, d model Represents the dimension of the token, that is, the dimension of each vector in our sequence; S3-3: Add the flattened matrix data to the positional encoding element-wise and perform a bitwise operation with the attention mask to obtain the input vector representation of the encoder; Let the summed vector sequence be X, the attention mask be M_mask, and x be the masked vector sequence; Among them, * represents bitwise operation; S3-4: The input vector representation is fed into the encoder and decoder of the Transformer model for forward propagation; the model performs self-attention calculations based on the position and relationship of elements in the sequence, thereby generating context-aware representations and outputs; Assume that the input vector is represented by X, the forward propagation of the encoder is Encoder(X), and the forward propagation of the decoder is Decoder(X); S3-5: Use linear transformation method to convert the output vector into the target high-dimensional matrix; Let the weight matrix of the linear transformation be W and the output vector be F1; F1=decoder_output*W (5) Here, * represents matrix multiplication.

3. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 2, characterized in that: The trajectory reconstruction module and frequency domain reconstruction module in step S3 are: The trajectory reconstruction module is composed of an LSTM module; the frequency domain reconstruction module is composed of a self-attention module. Specifically, there are the following steps: 1) Pass F1 into the input layer of the trajectory reconstruction module to obtain P′ (1) , that is, P′ (1) =LSTM(F1); 2) F1 is passed into the input layer of the frequency domain reconstruction module to obtain F2; at the same time, the true trajectory vector P is subjected to discrete Fourier transform to obtain F3, F3 = FFT(P N-M:N-1 ), where the discrete Fourier transform formula is: where X k is the transformed complex sequence, k = 0, 1, ..., N-1 represents the different frequency components in the frequency domain, i is the imaginary unit, x n is the sampled analog signal, and is the rotation factor; The output of the fast Fourier transform will be a complex sequence representing the frequency components in the frequency domain, that is, Among them, i represents the frequency index and j represents the feature dimension.

4. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 3, characterized in that: The specific training for the aircraft reconstruction model in step S4 is as follows: S4-1: Set the loss function with mean square error MSE; S4-2: For the trajectory reconstruction module, through the real trajectory sequence P and P' (1) As the loss function, it is marked as L1, L1 = MSE(P,P′ (1) ); S4-3: For the frequency domain reconstruction module, the real trajectory vector P is subjected to discrete Fourier transform to obtain F3, F3 = FFT (P N-M:N-1 ), the loss function is obtained by F2 and F3, denoted as L2, L2 = MSE (F2, F3); S4-4: Jointly optimize the multilayer perceptron, encoder, trajectory reconstruction module, and frequency domain reconstruction module, and set the joint loss function L 重建 =L1+L2 for optimization training and save the weights of the optimal aircraft reconstruction model.

5. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 1, characterized in that: The specific steps for changing the flight trajectory prediction model in step S5 are as follows: 1) For the reconstruction network of the aircraft reconstruction module, the trajectory reconstruction module is removed from the network, and a convolutional layer is added after the self-attention module in the frequency domain reconstruction module. At the same time, the new frequency domain reconstruction module has a one-to-one correspondence with each decoder in the decoder group; 2) For the backbone network of the aircraft reconstruction model, a discrete wavelet transform module, a decoder group, and an inverse discrete wavelet transform module are added; 3) The serial order of the overall model is: discrete wavelet transform module, multi-layer perceptron, encoder, frequency domain reconstruction module, decoder, inverse discrete wavelet transform module.

6. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 3, characterized in that: The specific data flow processing of the S5 flight trajectory prediction model is as follows: S5-1: Input the processed aircraft trajectory sequence, pass it through the multi-layer perceptron, encoder, and frequency domain reconstruction module to obtain F2, and then perform dimensionality-upgrading on F2 to obtain F5. The dimension of F5 is the same as the matrix dimension D in step S3-1. S5-2: F5 passes through the self-attention module in the decoder, and the self-attention calculation formula is used to substitute F5 into Q, and F1 into K and V respectively to calculate F6; the self-attention formula is as follows: F6=Self-Attention(F5,F1,F1) (8) S5-3: Design multiple decoders, which correspond to wavelet components of different frequencies. Assume that for the i+1th decoder, input F6 into the convolution module of the decoder to obtain F7 i+1 ; Among them, the convolution operation is used to embed the enhanced trajectory into F6, and the formula is expressed as: F7 i =σ(Convld(F6)) (9) Among them, F7 i+1 The time dimension of is determined by the resolution of the wavelet component corresponding to the i+1th decoder, The calculation formula for the length of the wavelet component is as follows: h L =h L-1 (12) Among them, L is the level of wavelet analysis, l is half of the wavelet filter length, M is the number of historical trajectory points, WTC i Represents wavelet components of different frequencies, Represents high-frequency WTC L-i The length of time; h L Represents the time length of low-frequency WTC0; S5-4: F7 i+1 As the wavelet component at a certain resolution, at this time, let the final wavelet component obtained by different decoders be F.

7. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 6, characterized in that: The specific loss function for training the S6 flight trajectory prediction model is set as: S6-1: Find the missing sequence points by extension and downsampling, and give them higher weights; set the loss function L 预测 for: Where k represents the kth WTC, h L-k Representing WTC k length, It is WTC k The estimated value of the jth attribute of the i-th element of is the true value, It is a custom weight value, which completes the overall training of the model by resetting the loss function; S6-2: The corresponding pre-processed original trajectory sequence P is subjected to discrete wavelet transform to obtain the wavelet component F8, and F and F8 are used as the prediction loss function L 预测 ,After the overall training of the model, the most suitable parameters for the model are found.

8. The flight trajectory completion and prediction method based on time-frequency analysis according to claim 1, characterized in that: The test in step S7 is as follows: 1) Input the aircraft trajectory sequence data P containing missing points l ; 2)P l After passing through the model, the trajectory is completed and a complete trajectory sequence P containing the next time step is output c .

9. A flight trajectory completion and prediction method based on time-frequency analysis, characterized in that: The invention comprises at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method according to any one of claims 1 to 8.

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