A track prediction method and device based on multi-resolution analysis and wavelet packet reconstruction

Abstract

The present invention discloses a track prediction method and device based on multi-resolution analysis and wavelet packet reconstruction, comprising the following steps: Step 1: Obtain track data, and after decoding, extraction, and preprocessing, construct a training set, a validation set, and a test set; Step 2: Construct a track prediction model based on multi-resolution analysis and wavelet packet reconstruction, and the track prediction model includes an encoder module, an attention module, a decoder module, a wavelet embedding module, and a wavelet packet reconstruction module arranged in sequence; Step 3: Train the prediction model using the training set and a loss function, and evaluate the prediction effect using the validation set to obtain the prediction model; Step 4: Real-time collect historical track data, and after decoding and preprocessing, input it into the prediction model trained and adjusted in Step 3 to obtain the prediction result; The present invention is based on multi-resolution analysis and wavelet analysis tools, improving the prediction accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of air traffic management, and in particular to a flight track prediction method and device based on multi-resolution analysis and wavelet packet reconstruction. Background Art

[0002] Flight track prediction, as a key technology in the field of air traffic management, plays a very important role in applications such as air traffic flow prediction, conflict detection, and scheduling decision-making. Due to the wide airspace, high aircraft speeds, and poor spatial perception ability for long-distance visual observation, flight track prediction methods based on deep learning generally rely on dynamic parameters such as the positions and speeds of aircraft captured by navigation satellites in the past period of time for prediction. A more accurate flight track prediction method can often improve the work efficiency of air traffic controllers and ensure the safety of aircraft during flight. However, most traditional deep learning-based flight track prediction methods directly perform temporal modeling on each feature of the flight track points, without considering that the movement process of an aircraft can be decomposed into a macroscopic trend and local changes. The time series of each feature is actually composed of multiple complex components, and thus deeper pattern information is not fully extracted, limiting the prediction accuracy. Summary of the Invention

[0003] The present invention discloses a flight track prediction method, device, and computer-readable storage medium based on multi-resolution analysis and wavelet packet reconstruction with high prediction accuracy.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A flight track prediction method based on multi-resolution analysis and wavelet packet reconstruction, comprising the following steps:

[0006] Step 1: Obtain flight track data, and after decoding, extraction, and preprocessing, construct a training set, a validation set, and a test set;

[0007] Step 2: Construct a flight track prediction model based on multi-resolution analysis and wavelet packet reconstruction, where the flight track prediction model includes an encoder module, an attention module, a decoder module, a wavelet embedding module, and a wavelet packet reconstruction module arranged in sequence;

[0008] The encoder module is used to map the features of historical flight track points into flight track embedding vectors, and model and output the state vectors at each historical moment according to the flight track embedding vectors;

[0009] The attention module is used to extract context information of multiple groups of wavelet coefficients from the state vectors at each historical moment;

[0010] The decoder module is used to construct multiple wavelet coefficient embedding vectors of all historical flight track points and the next moment's flight track points according to the context information of multiple groups of wavelet coefficients;

[0011] The wavelet embedding module is used to perform a linear mapping on multiple wavelet coefficient embedding vectors to obtain multiple groups of wavelet components corresponding to the track point features respectively;

[0012] The wavelet packet reconstruction module is used to reconstruct the eigenvalue of all historical track points and the track point at the next moment according to multiple groups of wavelet components;

[0013] Step 3: Use the training set and the loss function to train the prediction model constructed in Step 2, use the validation set to evaluate the prediction effect, and adjust the hyperparameters of the prediction model according to the evaluation result, then the track prediction model based on multi-resolution analysis and wavelet packet reconstruction can be obtained;

[0014] Step 4: Real-time collect historical track data, after decoding and preprocessing, input it into the prediction model trained and adjusted in Step 3, then the prediction result can be obtained.

[0015] Further, the data decoding in Step 1 is to decode the track data of the route to obtain the plaintext information, and extract the valid information from the plaintext information; the valid information includes the timestamp, longitude, latitude, altitude, longitude direction speed, latitude direction speed and vertical direction speed of each track point in the route; the track data includes the flight trend, climb, descent, hold, and turn of the aircraft; the data preprocessing includes the following processes:

[0016] S11: For the track segment with missing values, if the missing value is greater than the set threshold, discard the track segment, if the missing value is not greater than the set threshold, use the Lagrange interpolation method for interpolation;

[0017] S12: Eliminate the track segments containing outliers;

[0018] S13: Normalize the valid information;

[0019] The construction methods of the training set, validation set and test set are as follows:

[0020] Extract the training set, validation set and test set from the preprocessed data in a ratio of 7:1:2 respectively;

[0021] When constructing data pairs in the dataset, if N historical track points are used for prediction, then for each route in the route set, use a sliding window with a window size of N + 1, and use 1 track point as the step length to intercept the data pairs; the data pairs include N historical track points and the target track point at the next moment; the N historical track points and the target track point at the next moment include track point features.

[0022] Further, the encoder module includes a fully connected layer and an LSTM neural network.

[0023] Furthermore, the attention module includes multiple attention networks, the number of wavelet analysis layers is m, and the number of attention networks is 2 m The context information extraction process is as follows:

[0024] H is the state vector of each historical moment, and the context information of the jth wavelet coefficient extracted by the i-th attention network is context i,j ;

[0025]

[0026] Where: is the linear transformation matrix, is the bias vector, X j is the position embedding vector of the j-th wavelet coefficient, Q i,j is the query matrix, K i is the keyword matrix, K i is the content matrix, e i,j is the attention vector, d is the vector dimension, concat is the connection operator, and softmax(M) is the function calculation; where X j It is composed of an all-1 vector with the last Z 1s set to 0; Z satisfies the following formula:

[0027]

[0028] Where: h is the number of wavelet coefficients that need to extract context information;

[0029] The softmax(M) calculation formula is as follows:

[0030]

[0031] Where: M i is the i-th element of vector M.

[0032] Furthermore, the decoder module includes 2 m LSTM neural networks, each LSTM neural network uses h context information extracted by the corresponding attention network in the attention module as input and predicts h wavelet coefficient embedding vectors:

[0033]

[0034] Where: N is the number of historical track points, n is half the length of the wavelet basis filter selected in discrete wavelet transform, g m (N) Use the second and third formulas to iterate and calculate continuously, and obtain h after m iterations.

[0035] Furthermore, the wavelet embedding module includes 2 mA wavelet embedding network, each wavelet embedding network includes a layer normalization layer and a fully connected layer.

[0036] Further, the wavelet reconstruction module is composed of MISO-FIR filters; the wavelet packet reconstruction module performs wavelet reconstruction layer by layer on the wavelet components output by the wavelet embedding module according to the wavelet basis and the signal extension method; when the wavelet packet reconstruction module performs wavelet reconstruction on a certain feature, it uses 2 m sets of wavelet components of the corresponding feature extracted by the wavelet embedding module, and performs wavelet reconstruction layer by layer according to the wavelet packet decomposition paths of the 2 m sets of wavelet components.

[0037] Further, the loss function L in step 3 includes a time domain error L traj and a wavelet component error L wavelet ; the loss function satisfies the following formula:

[0038]

[0039] In the formula: α is the weight of the time domain error, β is the weight of the wavelet component error, γ l is the weight of the wavelet component error of the l-th group, m is the number of wavelet analysis layers, and respectively represent the true value and the predicted value of the i-th feature of the k-th track point in the j-th sample, and respectively represent the true value and the predicted value of the k-th coefficient in the l-th group of wavelet components after the i-th feature in the j-th sample is decomposed by m-layer wavelet packet decomposition, M is the number of track point features, N is the number of samples in a batch, H is the number of historical track points, and S is the number of coefficients in the wavelet components; is the time domain error of the i-th track point, is the wavelet component error of the l-th group of wavelet components.

[0040] A device includes at least one memory and at least one processor;

[0041] 0]The memory is used to store computer-executable instructions;

[0042] The processor is used to run the computer-executable instructions, and the computer-executable instructions run to implement the track prediction method.

[0043] A computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed, the track prediction method is implemented.

[0044] The beneficial effects of the present invention are:

[0045] (1) The present invention utilizes the framework of multi-resolution analysis and wavelet analysis tools to extract the overall trend information and local detail information describing the characteristics of track points, converts complex time series into different wavelet components, and the prediction of each part at a specific resolution is relatively easy, thereby improving the prediction accuracy.

[0046] (2) The present invention establishes a wavelet coefficient attention mechanism to extract the similarities and differences between wavelet components and time series information at specific wavelet decomposition paths and specific scales, enhances the multi-resolution analysis ability of the prediction model, and is conducive to improving the prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic flow chart of the track prediction method of the present invention.

[0048] Figure 2 It is a schematic structural diagram of the prediction model in the present invention.

[0049] Figure 3 It is a schematic structural diagram of the LSTM neural network in the prediction model of the present invention.

[0050] Figure 4 It is a schematic diagram of the calculation method of the context information of the attention model in the prediction model of the present invention.

[0051] Figure 5 It is a schematic diagram of the device for implementing the track prediction method in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0053] As Figure 1 shown, a track prediction method based on multi-resolution analysis and wavelet packet reconstruction includes the following steps:

[0054] Step 1: Obtain track data, and after decoding, extraction and preprocessing, construct a training set, a validation set and a test set;

[0055] Extract the track data of several routes from the ATC system, decode the track data of several routes to obtain plaintext information, organize the plaintext information of each route into a TXT file, then extract the effective information from the information of each route's TXT file, and perform data preprocessing to construct a training set, a validation set and a test set.

[0056] Read the TXT files of each flight route and extract the valid information of each track point, including the timestamp, longitude, latitude, altitude, longitudinal velocity, latitudinal velocity, and vertical velocity of each track point in the flight route; to ensure that the track prediction model based on multi-resolution analysis and wavelet packet reconstruction has good generalization ability, the track data includes the motion trends of the aircraft such as climbing, descending, maintaining, and turning.

[0057] Data preprocessing includes the following processes:

[0058] S11: To ensure that the time interval of track points in each flight route remains unchanged, with the timestamp of each track point as a reference, for a track segment with missing values in one of the 6 features of the track point, if it is not greater than the set threshold, Lagrange interpolation method is used for interpolation, and if the missing value is greater than the set threshold, the track segment is discarded;

[0059] S12: Eliminate the track segments in which one of the 6 features of the track point contains outliers;

[0060] S13: Normalize the valid information, and use the maximum-minimum normalization method to normalize the 6 features of each track point respectively.

[0061] Construct the training set, validation set, and test set: First, extract the flight route sets of the training set, validation set, and test set from several flight route data after data preprocessing in a ratio of 7:1:2; then construct data pairs from the flight route sets. In this experiment, 9 historical track points are used for prediction. For each flight route in the flight route set, a sliding window with a window size of 10 is used, and with a step size of 1 track point, data pairs are intercepted; the data pairs include 9 historical track points and the target track point at the next moment, and the 9 historical track points and the target track point at the next moment contain 6 features, namely longitude, latitude, altitude, longitudinal velocity, latitudinal velocity, and vertical velocity.

[0062] Step 2: As Figure 2 shown, construct a track prediction model based on multi-resolution analysis and wavelet packet reconstruction. The track prediction model includes an encoder module, an attention module, a decoder module, a wavelet embedding module, and a wavelet packet reconstruction module set in sequence;

[0063] The encoder module includes a fully connected layer and an LSTM neural network. The input dimension of the fully connected layer is 6, the output dimension is 144, the number of layers of the LSTM neural network is 4, the input dimension is 144, and the dimension of the hidden state vector is 144, as Figure 3 shown. The LSTM neural network (as Figure 3As shown in the figure, it consists of an input gate, a forget gate, a candidate memory, an output gate, and multiple operators. The candidate memory stores the information at the current moment. The forget gate controls how much information of the memory cell vectors at historical moments is retained. The input gate controls how much candidate memory is adopted. The output gate calculates the output value at the current moment. The fully connected layer maps the 6 features of the track points at each historical moment to a high-dimensional space through linear transformation to obtain the track embedding vector at each historical moment. The track embedding vector at each historical moment integrates the position information and motion trend of the aircraft at each historical moment, enhances the representation ability of the track data, and further improves the prediction effect.

[0064] The LSTM neural network uses the track embedding vector at each historical moment as input, performs temporal modeling on the motion pattern of the aircraft in the past period of time, and outputs the state vector at each historical moment, as well as the hidden state vector and memory cell vector at the last time step.

[0065] The attention module includes multiple attention networks. The number of wavelet analysis layers is m, and the number of attention networks is 2 m In this embodiment, the number of wavelet analysis layers is 2, and there are 4 attention networks. The 4 wavelet attention networks extract the context information between the wavelet coefficients under different wavelet packet decomposition paths and different scales and the state vector at each historical moment. As Figure 4 shown, the process of extracting context information is as follows:

[0066] H is the state vector at each historical moment. The context information of the j-th wavelet coefficient extracted by the i-th attention network is context i,j ;

[0067]

[0068] In the formula: is the linear transformation matrix, is the bias vector, X j is the position embedding vector of the j-th wavelet coefficient, Q i,j is the query matrix, K i is the key matrix, K i is the content matrix, e i,j is the attention vector, d is the vector dimension, concat is the concatenation operator, and softmax(M) is the function calculation; where X j consists of an all-ones vector with the last Z ones set to 0; Z satisfies the following formula:

[0069]

[0070] In the formula: h is the number of wavelet coefficients for which context information needs to be extracted;

[0071] The calculation formula of softmax(M) is as follows:

[0072]

[0073] In the formula: M i is the i-th element of vector M.

[0074] Construct a decoder module, which includes 4 LSTM neural networks. Each LSTM neural network has 4 layers, an input dimension of 288, and a hidden state vector dimension of 144. The 4 LSTM neural networks all use the hidden state vector and memory cell vector of the last time step output by the encoder module as the initial hidden state vector and initial memory cell vector. The 4 LSTM neural networks focus on the prediction of wavelet coefficient embedding vectors under different wavelet packet decomposition paths and different scales. The number of historical track points adopted in this experiment is 9, the selected wavelet basis is the Haar wavelet, and the number of wavelet analysis layers is 2. Therefore, the prediction step h = 3. Then, in the 4 LSTM neural networks, each LSTM neural network uses 3 context information extracted by the corresponding wavelet attention network in the attention module as input to predict 3 wavelet coefficient embedding vectors. h satisfies the following formula:

[0075]

[0076] Among them: m = 2 is the number of wavelet analysis layers, n = 1 is the general length of the Haar wavelet basis filter in the discrete wavelet transform, and N = 9 is the number of historical track points. g m (N) is continuously iteratively calculated using the second and third formulas, and h is obtained after m iterations.

[0077] Construct a wavelet embedding module. The wavelet embedding module has a total of 4 wavelet embedding networks. Each wavelet embedding network consists of a layer normalization layer and a fully connected layer. The input dimension of the fully connected layer is 144, and the output dimension is 6. The normalization layer can avoid the problems of gradient disappearance or gradient explosion, and ensure the stability of training the track prediction model based on wavelet packet reconstruction. The 4 wavelet embedding networks obtain wavelet components under different wavelet packet decomposition paths and different scales through linear mapping. Among them, each wavelet embedding network maps the 3 wavelet coefficient embedding vectors predicted by the corresponding decoder network in the decoder module into 6 groups of wavelet components of track point features. Each feature has 1 group of wavelet components, and this wavelet component represents the wavelet component obtained from the time series data of this feature under a certain wavelet packet decomposition path among all historical moments and the next moment track points.

[0078] Construct a wavelet reconstruction module, which is composed of a MISO-FIR filter; the wavelet basis selected in this embodiment is the Haar wavelet, the number of wavelet analysis layers is 2, and the signal extension method is symmetric extension. This module performs wavelet reconstruction on the wavelet components output by the wavelet embedding module layer by layer. Six features of historical track points and track points at the next moment are reconstructed, namely longitude, latitude, altitude, velocity in the longitude direction, velocity in the latitude direction, and velocity in the vertical direction. When the wavelet packet reconstruction module performs wavelet reconstruction on a certain feature, it uses four groups of wavelet components of the corresponding feature extracted by the wavelet embedding module, and performs wavelet reconstruction layer by layer according to the wavelet decomposition paths of the four groups of wavelet components.

[0079] Step 3: Use the training set and the loss function to train the prediction model constructed in Step 2, use the validation set to evaluate the prediction effect, and adjust the hyperparameters of the prediction model according to the evaluation results, then a track prediction model based on multi-resolution analysis and wavelet packet reconstruction can be obtained;

[0080] The loss function L includes the time-domain error L traj and the wavelet component error L wavelet ; the loss function satisfies the following formula:

[0081]

[0082] In the formula: α is the weight of the time-domain error, β is the weight of the wavelet component error, γ l is the weight of the l-th group of wavelet component errors, m is the number of wavelet analysis layers, and respectively represent the true value and the predicted value of the i-th feature of the k-th track point in the j-th sample, and respectively represent the true value and the predicted value of the k-th coefficient in the l-th group of wavelet components after the i-th feature in the j-th sample is decomposed by m layers of wavelet packets. M is the number of track point features, N is the number of samples in a batch, H is the number of historical track points, and S is the number of coefficients in the wavelet components; is the time-domain error of the i-th track point, is the wavelet component error of the l-th group of wavelet components.

[0083] The wavelet component error L wavelet describes the errors of the trend information and detail information at different scales in the features of all historical moments and track points at the next moment. However, due to the lack of the features of track points at the next moment, the training process is difficult and slow. Therefore, in order to accelerate the training process and improve the prediction accuracy, the time-domain error L traj is introduced to increase the supervision information of the track point features.

[0084] After each training session, use the validation set to evaluate the track prediction model based on multi-resolution analysis and wavelet packet reconstruction. Adjust the hyperparameters of the model according to the evaluation results to obtain a well-trained track prediction model based on multi-resolution analysis and wavelet packet reconstruction. The evaluation criteria adopted are the root mean square error (RMSE) and mean absolute error (MAE) of six features of the track points, as well as the average value of the mean square error (aveMSE) and the average value of the mean absolute error (aveMAE) of the six features. Specifically:

[0085]

[0086] where: a ij is the true value of the j-th feature of the i-th sample, a' ij is the predicted value of the j-th feature of the i-th sample, and n is the number of samples.

[0087] Step 4: For a certain flight route, collect historical track data from the ADS-B system in real time. After decoding and preprocessing, input it into the prediction model trained and adjusted in Step 3 to obtain the prediction results.

[0088] To illustrate the beneficial effects of the method of the present invention, a regression model of the LSTM neural network is used as a benchmark model for comparison. The number of layers of the LSTM neural network in the benchmark model is 8, the input dimension is 144, and the dimension of the hidden layer state vector is 144; after the hyperparameters of the two models are debugged using the validation set, the performance is evaluated using the test set. Nine historical track points are used as inputs to predict the features of the future 15-step track points, and the prediction results of the 1st, 3rd, 9th, and 15th steps are selected to calculate the root mean square error (RMSE) and mean absolute error (MAE) of each feature. Table 1 shows the comparison of the root mean square error (RMSE) of the two methods. It can be seen that in the three items of longitude, latitude, and altitude, the method proposed by the present invention has a smaller error compared with the benchmark model, and its superiority can be maintained even in multi-step prediction; Table 2 shows the comparison of the mean absolute error (MAE) of the two methods. It can be seen that in the three items of longitude, latitude, and altitude, the prediction effect of the method proposed by the present invention exceeds the benchmark method at different prediction steps.

[0089] Table 1. RMSE of Different Methods at Different Prediction Steps

[0090]

[0091] Table 2. MAE of Different Methods at Different Prediction Steps

[0092]

[0093]

[0094] An apparatus includes at least one memory and at least one processor;

[0095] The memory is used to store computer-executable instructions;

[0096] The processor is used to run the computer-executable instructions, and the running of the computer-executable instructions realizes a trajectory prediction method.

[0097] In this embodiment, the apparatus includes a processor, a memory, a display, input / output devices, and a power supply; the output / output devices include a keyboard, a mouse, a USB interface, and a network cable interface, and the power supply can be an external power supply or an internal battery.

[0098] A computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed, a trajectory prediction method is realized.

[0099] All or part of the steps of the above method embodiment can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps including the above method embodiment; and the foregoing storage medium includes: a removable storage device, a read-only memory (ROM), a magnetic disk, or an optical disc, etc., which can store program codes.

[0100] When the above integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the embodiments of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in the embodiments of the present invention. And the foregoing storage medium includes: a removable storage device, a ROM, a magnetic disk, or an optical disc, etc., which can store program codes.

[0101] The present invention adopts a multi-resolution analysis framework and wavelet analysis tools to predict the wavelet components of the features of all historical moments and the next moment's trajectory points at different scales, extract the trend information and detail information of each feature, and then reconstruct the feature values of all historical moments and the next moment's trajectory points, improving the prediction accuracy and having good application prospects.

Claims

1. A track prediction method based on multi-resolution analysis and wavelet packet reconstruction, characterized in that The following steps are involved: Step 1: Obtain track data, decode, extract, and preprocess the data to construct training sets, validation sets, and test sets; Step 2: Construct a track prediction model based on multi-resolution analysis and wavelet packet reconstruction. The track prediction model includes an encoder module, an attention module, a decoder module, a wavelet embedding module, and a wavelet packet reconstruction module. The encoder module is used to map the features of historical track points into track embedding vectors, and output the state vector of each historical moment based on the track embedding vector model; The attention module is used to extract the context information of multiple sets of wavelet coefficients from the state vectors at each historical moment; the attention module includes multiple attention networks, the number of wavelet analysis layers is m, and the number of attention networks is 2 m The process of extracting context information is as follows: H is the state vector at each historical moment, and the context information of the j-th wavelet coefficient extracted by the i-th attention network is context i,j ; Wherein: is a linear transformation matrix, is a bias vector, X j is the position embedding vector of the j-th wavelet coefficient, Q i,j is a query matrix, K i is a keyword matrix, K i is a content matrix, e i,j is an attention vector, d is the vector dimension, concat is a concatenation operator, softmax(M) is a function calculation; wherein X j is composed of an all-ones vector with the last Z 1s set to 0; Z satisfies the following formula: Where: h is the number of wavelet coefficients that need to extract context information; The softmax(M) calculation formula is as follows: Where: M i is the i-th element of vector M; The decoder module is used to construct multiple wavelet coefficient embedding vectors of all historical track points and next moment track points based on the context information of multiple groups of wavelet coefficients; The decoder module includes 2 m LSTM neural networks. Each LSTM neural network uses h context information extracted by the corresponding attention network in the attention module as input, and predicts h wavelet coefficient embedding vectors: Where: N is the number of historical track points, n is half of the length of the wavelet basis filter selected in the discrete wavelet transform, and g m (N) is continuously iteratively calculated using the second and third equations, and h is obtained after m iterations. The wavelet embedding module is used to perform linear mapping on multiple wavelet coefficient embedding vectors to obtain multiple groups of wavelet components corresponding to the track point features; The wavelet packet reconstruction module is used to reconstruct the characteristic values of all historical track points and the next moment track points based on multiple groups of wavelet components; Step 3: Use the training set and loss function to train the prediction model constructed in step 2, use the validation set to evaluate the prediction effect, and adjust the hyperparameters of the prediction model based on the evaluation results to obtain the track prediction model based on multi-resolution analysis and wavelet packet reconstruction; Step 4: Collect historical track data in real time, decode and preprocess it, and input it into the prediction model trained and adjusted in step 3 to obtain the prediction results.

2. The track prediction method based on multi-resolution analysis and wavelet packet reconstruction according to claim 1, characterized in that The data decoding in step 1 is to decode the track data of the route to obtain plain text information, and extract valid information from the plain text information; the valid information includes the timestamp, longitude, latitude, altitude, longitude speed, latitude speed and vertical speed of each track point in the route; the track data includes the aircraft movement trend, climb, descent, hold and turn; the data preprocessing includes the following steps: S11: For track segments with missing values, if the number of missing values is greater than the set threshold, the track segment is discarded; if the number of missing values is not greater than the set threshold, the Lagrange interpolation method is used for interpolation; S12: Eliminate track segments containing outliers; S13: normalize the valid information; The training set, validation set, and test set construction methods are as follows: The training set, validation set, and test set were extracted from the preprocessed data in a ratio of 7:1:2; When constructing data pairs in a dataset, if N historical track points are used for prediction, for each route in the route set, a sliding window with a window size of N+1 and a step size of 1 track point is used to extract data pairs; the data pair includes N historical track points and the target track point at the next moment; the N historical track points and the target track point at the next moment contain track point features.

3. A track prediction method based on multi-resolution analysis and wavelet packet reconstruction according to claim 1, characterized in that The encoder module includes a fully connected layer and an LSTM neural network.

4. A track prediction method based on multi-resolution analysis and wavelet packet reconstruction according to claim 1, characterized in that The wavelet embedding module includes 2 m wavelet embedding networks, and each wavelet embedding network includes a layer normalization layer and a fully connected layer.

5. A track prediction method based on multi-resolution analysis and wavelet packet reconstruction according to claim 4, characterized in that The wavelet packet reconstruction module is composed of MISO-FIR filters; the wavelet packet reconstruction module performs wavelet reconstruction layer by layer on the wavelet components output by the wavelet embedding module according to the wavelet basis and the signal extension method; when the wavelet packet reconstruction module performs wavelet reconstruction on a certain feature, it uses 2 m groups of wavelet components of the corresponding feature extracted by the wavelet embedding module, and performs wavelet reconstruction layer by layer according to the wavelet packet decomposition path of the 2 m groups of wavelet components.

6. A track prediction method based on multi-resolution analysis and wavelet packet reconstruction according to claim 1, characterized in that The loss function L in the said step 3 includes the time-domain error L traj and the wavelet component error L wavelet ; The loss function satisfies the following formula: where: α is the weight of the time-domain error, β is the weight of the wavelet component error, γ l is the weight of the l-th group of wavelet component errors, m is the number of wavelet analysis layers, and respectively represent the true value and the predicted value of the i-th feature of the k-th track point in the j-th sample, and respectively represent the true value and the predicted value of the k-th coefficient in the l-th group of wavelet components after the i-th feature in the j-th sample is decomposed by m-layer wavelet packet. M is the number of track point features, N is the number of samples in a batch, H is the number of historical track points, and S is the number of coefficients in the wavelet components; is the time-domain error of the i-th track point, is the wavelet component error of the l-th group of wavelet components.

7. A device, characterized in that, comprising at least one memory and at least one processor; The memory is used to store computer executable instructions; The processor is used to run the computer executable instructions, and the computer executable instructions are used to implement any one of the track prediction methods according to claims 1 to 6.

8. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores computer-executable instructions, which, when executed, implement any one of the trajectory prediction methods described in claims 1 to 6.

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