Air target trajectory prediction system based on time sequence decomposition and reconstruction model

Abstract

The invention provides an air target trajectory prediction system based on a time sequence decomposition and reconstruction model. The system comprises a sensor, a database and a trajectory prediction unit. The sensor is used for collecting track data of an aerial target in real time and transmitting the track data to the database for storage and management, and the integrity and real-time performance of the data are ensured. The trajectory prediction unit is composed of a data preprocessing module, an online decomposition module, a component prediction module and a data reconstruction module. The data preprocessing module performs cleaning, abnormal value detection and normalization processing on trajectory data, the online decomposition module decomposes the data into a trend item, a season item and a residual item, the component prediction module predicts the decomposed data through a deep learning model, and the data reconstruction module performs weighted combination on each component to generate a final prediction result. High-precision and real-time prediction of the future trajectory of the air target is realized by cleaning, decomposing, predicting and reconstructing the trajectory data of the air target. The method has the advantages of high prediction precision, high real-time processing capability and the like, and is suitable for trajectory prediction in a complex aerial environment.

Description

Technical Field

[0001] The present invention belongs to the fields of data processing, deep learning, and aerial target trajectory prediction, and in particular relates to an aerial target trajectory prediction system based on a time series decomposition and reconstruction model. Background Art

[0002] Trajectory prediction of aerial targets is of great significance in many fields such as civil aviation and unmanned aerial vehicle systems.

[0003] In the field of civil aviation, aerial target trajectory prediction helps with flight scheduling and route optimization, especially in high-density airspace. Accurately predicting the aircraft's operating path is crucial to avoiding flight conflicts and improving airspace utilization.

[0004] In addition, in drone systems, trajectory prediction of aerial targets is also used to achieve functions such as obstacle avoidance, formation flying, and automatic navigation. Especially in the execution of automated tasks by drones, trajectory prediction can significantly improve the mission success rate and system stability. In environmental monitoring and disaster emergency response, trajectory prediction can help drones better perform tasks in complex natural environments, such as monitoring air quality, tracking pollution sources, and conducting post-disaster assessments. In addition, in the field of scientific research, trajectory prediction can also assist meteorological research, such as more accurately collecting atmospheric data by predicting the trajectory of balloons or drones.

[0005] In these different application scenarios, the accuracy, real-time and robustness of the prediction model directly affect the overall performance and safety of the system. Existing trajectory prediction methods mainly include methods based on physical models, statistical methods and machine learning methods. Methods based on physical models usually make predictions based on the dynamic model of the aircraft. When facing complex changes in the air environment, the assumptions of the physical model are often too idealized and difficult to adapt to emergencies and variable external interference. Methods based on statistics and deep learning use historical trajectory data to predict future motion trajectories through statistical techniques such as time series analysis and deep learning models. However, these methods are highly dependent on data and have difficulty in dealing with irregular motion and nonlinear changes. The prediction accuracy often cannot meet the requirements, especially the response to emergencies and irregular motion is relatively slow. Secondly, the trade-off between the complexity and real-time performance of the model often leads to a decrease in the system's response speed and the inability to quickly adapt to rapidly changing air situations. Therefore, there is an urgent need for a trajectory prediction model that can have both high accuracy and real-time performance in complex environments to better cope with the dynamic changes of aerial targets. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the prior art and provide an aerial target trajectory prediction system based on a time series decomposition and reconstruction model.

[0007] The objective of the present invention is achieved through the following technical scheme: an aerial target trajectory prediction system based on a time series decomposition and reconstruction model, the system consisting of a sensor, a database and a trajectory prediction unit, which are connected in sequence and work together; the sensor includes a radar sensor, an optical sensor, an infrared sensor and a GPS sensor; the trajectory prediction unit includes a data preprocessing module, an online decomposition module, a component prediction module and a data reconstruction module.

[0008] Furthermore, the sensor is responsible for collecting the monitored aerial target trajectory data and transmitting the data to the database in real time via a wireless network;

[0009] The database is used to sort and index the received aerial target trajectory data according to timestamps, obtain the processed aerial target trajectory data X and transmit it to the trajectory prediction unit;

[0010] The trajectory prediction unit is used to process and predict the received processed aerial target trajectory data X to obtain predicted reconstruction data.

[0011] Furthermore, the trajectory prediction unit is used to process and predict the received processed aerial target trajectory data X to obtain predicted reconstruction data, which specifically includes the following sub-steps:

[0012] (1) After the trajectory prediction unit receives the processed aerial target trajectory data X, the processed aerial target trajectory data X is first input into a data preprocessing module for outlier detection and data normalization processing to obtain preprocessed aerial target trajectory data Y;

[0013] (2) Then, the preprocessed aerial target trajectory data Y is input into the online decomposition module, and the preprocessed aerial target trajectory data Y is decomposed into the seasonal term vector τ 1～t , trend term vector s 1～t and the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ];

[0014] (3) Then the decomposed Y = [τ 1～t ,s 1～t ,r 1～t ] is input to the component prediction module 6 to obtain the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector

[0015] (4) Then the preprocessed aerial target trajectory data Y and the seasonal term prediction vector for the next k time steps are Trend term prediction vector and the residual prediction vector Input to the data reconstruction module to generate the final predicted reconstruction signal for the next k time steps

[0016] Furthermore, the step (1) specifically includes the following sub-steps:

[0017] (1.1) After the trajectory prediction unit receives the processed aerial target trajectory data X, it first inputs the processed aerial target trajectory data X into a data preprocessing module;

[0018] The processed aerial target trajectory data X is defined as a time series: X = {x1, x2, ..., x i ,...,x t}, where x i represents the observation value at the i-th time point, and t is the length of the time series;

[0019] First, the processed aerial target trajectory data X is used to detect outliers using the sliding window and standard deviation outlier detection method:

[0020] For each time point, the observed value x i Select a sliding window W of length w around and calculate the observation value x i The mean and standard deviation of :

[0021]

[0022] in, is the mean of the data in the window, is the standard deviation, w is the window length;

[0023] x that satisfies formula (3) i Considered as detected outliers:

[0024]

[0025] For the detected outlier x i , the linear interpolation method based on adjacent points is used to replace the observed value x after anomaly detection i ′, the linear interpolation formula is:

[0026]

[0027] x that does not satisfy formula (3) iNot considered as an outlier detected, for an outlier value x that is not considered as an outlier detected i , no replacement is performed, that is, x i ′=x i ;

[0028] After the outlier detection is completed on the processed aerial target trajectory data X, the aerial target trajectory data X′ after anomaly detection is obtained: X′={x1′,x2′,...,x i ′,...,x t '};

[0029] (1.2) Then, the air target trajectory data X′ after anomaly detection is normalized to obtain the preprocessed air target trajectory data Y: Y = {y1, y2, ..., y i ,...,y t}, using the Min-Max normalization method, the formula is:

[0030]

[0031] Among them, y i is the normalized observation value at the i-th time point; x min is the minimum value of the aerial target trajectory data X′ after anomaly detection, x max It is the maximum value in the aerial target trajectory data X′ after anomaly detection.

[0032] Furthermore, the step (2) specifically includes the following sub-steps:

[0033] (2.1) Then, the preprocessed aerial target trajectory data Y is input into an online decomposition module, which first divides the preprocessed aerial target trajectory data Y into Y=Y1+Y2, where Y1={y1, y2, ..., y d ,...,y N}, in,

[0034] Set Y1 = {y1, y2, ..., y d ,...,y N} is used to initialize the decomposition, and the decomposition objective function expression is:

[0035]

[0036] Among them, the parameter τ d and d Respectively represent the normalized observation value y at the dth time point dThe trend term and seasonal term obtained by decomposition, T represents the size of the cycle corresponding to the seasonal term; λ1 represents the parameter controlling the first-order smoothness of the trend term, λ2 represents the parameter controlling the second-order smoothness of the trend term; τ represents the trend term of the entire time series: τ=[τ1,τ2,…,τ d ,…,τ N ]; s represents the seasonal term of the entire time series: s = [s1, s2, …, s d ,…,s N ];

[0037] In order to optimize formula (6), the online decomposition module introduces auxiliary variables Transform formula (6) into:

[0038]

[0039] Among them, the auxiliary variable p d represents the value of variable p at the dth time point; q d represents the value of variable q at the dth time point;

[0040] Initialize auxiliary variables p and q to 1:

[0041]

[0042] The iterative process of the initialization phase will last for I iterations, and the auxiliary variables p and q will be gradually updated after each iteration to ensure that the estimates of the trend term and the seasonal term gradually converge; the specific update steps in each iteration are:

[0043] In each iteration, new trend terms and seasonal terms are first calculated based on the current auxiliary variables p and q; in order to efficiently solve the optimization problem, the matrix form in the objective function is defined as:

[0044]

[0045] Among them, matrices B1, B2, B3, and B4 are defined as:

[0046]

[0047] According to the above matrix definition, construct the linear system Ax = b and solve x: x = {x1,…,x N ,x N+1 ,…,x 2N}, thereby updating the trend term τ, seasonal term s and residual term r of this iteration:

[0048] τ={x1,…,x N} s={x N+1 ,…,x 2N} r = Y1 - τ - s (12);

[0049] Update the auxiliary variables p and q using the updated trend term:

[0050]

[0051] These update formulas are designed to ensure that trend items change smoothly while adapting to dynamic changes in data;

[0052] After I iterations, we get Y1 = {y1, y2, ..., y d ,...,y N The final trend term component corresponding to Seasonal Component and the residual component

[0053] (2.2) Then the online decomposition phase is carried out. After each online decomposition, the latest seasonal term will be saved in the sliding window and used for future updates. For ease of processing, the seasonal buffer is named And initialize it to v = [s N-T ,...,s N ] T ; Then, the components of the seasonal term in formula (6) are redefined and the problem is transformed into:

[0054]

[0055] Where M is the number of newly arrived data points, which are the ones that need to be decomposed online; j%T is the modulo operation used to ensure that when j>T, v j％T It can be correctly returned to the vector v, thus enabling the reuse of seasonal data;

[0056] First, the auxiliary variable and initialization:

[0057]

[0058] in, and are the initial values ​​at the beginning of the iteration, which are used to control the smoothness of the first-order difference and the second-order difference of the trend term; and Indicates that the auxiliary variables after the bth iteration will be gradually updated during the iteration process;

[0059] The iterative process of the online update phase will last for I iterations, with b=0 initialized and the value of b increasing by 1 in each iteration; the specific update steps in each iteration are:

[0060] First, in the bth iteration, based on the current and Calculate new trend terms and seasonal terms; in order to efficiently solve the optimization problem, define the matrix form in the objective function:

[0061]

[0062] in, N+t0 represents the time point of the current processing; The matrices C1, C2, C3, and C4 are defined as:

[0063]

[0064] According to the above matrix definition, construct the linear system And solve for the vector Thus, the trend item of the bth iteration is updated Seasonal Items and the residual

[0065]

[0066] in, Representation vector The second to last value in Representation vector The first to last value in the

[0067] According to formula (20) and formula (21), the b-th iteration is calculated and

[0068]

[0069] Repeat this process until b=I-1, and the iteration ends to obtain the trend item at time point N+t0. Seasonal Items and the residual decomposition;

[0070] In this way, the online update of the decomposition module can be completed. When new time series data enters, it is decomposed according to the above iteration to obtain The corresponding final trend term component Seasonal Component and the residual component

[0071] (2.3) After the initialization phase and the online update phase, the preprocessed aerial target trajectory data Y is decomposed into the seasonal term vector τ 1～t , Trend Items 1～tand the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ],in,

[0072] Furthermore, the step (3) is specifically as follows:

[0073] Then the decomposed Y=[τ 1～t ,s 1～t ,r 1～t ] is input into the component prediction module, which uses the Informer model to decompose the time series component Y = [τ 1～t ,s 1～t ,r 1～t ] to make predictions;

[0074] First, the linear transformation is mapped to the high-dimensional space d model :

[0075] H0=[τ 1～t ,s 1～t ,r 1～t ]W e +b e (twenty two);

[0076] in, is the embedding matrix, is the bias term; then position encoding is added to introduce timing information, and the position encoding is generated using sine and cosine functions:

[0077]

[0078] Through formula (23), we get the position code PE: PE = {PE (t,1) ,…,PE (t,i) ,…,PE (t,t)};

[0079] The position encoding PE is then added to the embedded features to introduce temporal position information into the model:

[0080] H t =H0+PE (24);

[0081] For each time step, the feature representation H t , generate the query matrix Q through linear transformation t , key matrix K t Sum value matrix V t :

[0082] Q t =H t W Q,K t =H t W K ,V t =H t W V (25);

[0083] in, is the transformation matrix, d k is the dimension of the key vector; query-key pairs with larger norm are queried to select those query-key pairs that have the greatest impact on the prediction results:

[0084] Q t ≥threshold (26);

[0085] For the sparse query-key pairs selected by formula (26), the attention weight is calculated using the standard attention mechanism formula:

[0086]

[0087] Then the value matrix V t Perform weighted summation;

[0088] After the self-attention calculation, residual connections and layer normalization are used to make the model more stable and maintain information transfer:

[0089] H1=LayerNorm(H t +Attention(Q t ,K t ,V t )) (28);

[0090] Residual connections allow gradients to flow, and layer normalization ensures numerical stability, preventing gradients from exploding or vanishing;

[0091] The Distilling layer reduces the length T of the input sequence to T / 2 through average pooling or other downsampling strategies:

[0092]

[0093] Here It is the time series representation after downsampling;

[0094] The encoder of the Informer model contains multiple ProbSparse self-attention layers and feed-forward neural network layers; the encoder uses an h-head self-attention mechanism, and each head performs attention calculations independently:

[0095] MultiHead(Q t ,K t ,Vt )=Concat(head1,head2,...,head h )W O (30);

[0096] The attention of each head is calculated as follows:

[0097]

[0098] Then concatenate the outputs of each head and pass the linear transformation matrix W O Mapping back to d model Dimension;

[0099] After each self-attention layer, there is a feedforward neural network that performs independent nonlinear transformations on the features at each time point; the FFN contains two layers of linear transformations and a ReLU activation function:

[0100] FFN(x)=ReLU(xW1+b1)W2+b2 (32);

[0101] Where FFN(·) represents the processing of the feedforward neural network, and x represents the input of the feedforward neural network;

[0102] The first layer maps the input to a higher dimensional space, and the second layer maps it back to d model The original space; each layer in the encoder uses residual connection and layer normalization to ensure the stability of training and the normal flow of gradients:

[0103]

[0104] The output H3 of the third layer is then input to the decoder in the Informer model; the decoder part is composed of multiple decoder layers stacked together; each decoder layer has three core components: self-attention mechanism, encoder-decoder attention mechanism and feedforward neural network. In addition, each layer has residual connection and layer normalization to ensure that the model can be stably trained in deep networks;

[0105] At each layer of the decoder, the self-attention mechanism first generates a query matrix for each time step Key Matrix Sum value matrix V t 3 :

[0106]

[0107] in, is the transformation matrix; through these linear transformations, the decoder will extract features from the output generated in the previous time step;

[0108] In the decoder, to ensure that each time step can only see the time step before it and not the time step in the future, the decoder's self-attention mechanism applies a mask matrix; this mask matrix ensures that each time step only pays attention to the time step before it:

[0109]

[0110] The mask matrix M marks future time steps as negative infinity to ensure that these time steps do not affect the current attention calculation. This mechanism is very important because in the decoding stage, the model generates outputs step by step and cannot see future time steps in advance.

[0111] After applying the mask, the decoder's self-attention mechanism uses a similar calculation as the encoder to capture the dependencies between time steps; the specific calculation is as follows:

[0112]

[0113] In the second attention layer of the decoder, the model combines the global information output by the encoder through the encoder-decoder attention; in the encoder-decoder attention, the query matrix Q generated by the decoder d The key matrix K generated by the encoder e Sum value matrix V e The specific calculation is as follows:

[0114]

[0115] Similar to self-attention, the encoder-decoder attention is calculated as:

[0116]

[0117] This step ensures that the decoder can refer to information from the entire input time series when generating predictions for future time steps;

[0118] At the end of each decoder layer, the feature vector processed by the attention mechanism is further processed by a feedforward neural network; the feedforward neural network consists of two layers of linear transformation and a ReLU activation function;

[0119] The first layer of the feed-forward network maps the input features to a higher dimension, and the second layer maps it back to the original dimension;

[0120] Each layer in the decoder uses residual connections and layer normalization to ensure the stability of training and the normal flow of gradients:

[0121]

[0122] The output of the decoder is mapped back to the original dimension D through a linear layer to generate the prediction result; predicting the data of the next k time steps, the output of the decoder is:

[0123]

[0124] Here, W out is the weight matrix of the output layer, b out is the bias term; W out Contains three sub-matrices, each used to generate predictions for a specific component:

[0125] W out =[W τ W s W r ] (41);

[0126] By matrix multiplying the decoder output H3 with these sub-matrices, we get the prediction for each component:

[0127]

[0128] Get the output of the component prediction module, which is the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector

[0129] Furthermore, the step (4) specifically includes the following sub-steps:

[0130] (4.1) Then Y = [τ 1～t ,s 1～t ,r 1～t ] and the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector Input into the data reconstruction module, first the weight training phase is carried out;

[0131] Weight training stage: The weight training model accepts the input signal Y = [τ 1～t ,s 1～t ,r 1～t ];

[0132] First, the input [τ 1～t ,s 1～t ,r 1～t ] is mapped to the hidden layer representation h1, and the hidden representation is generated through linear transformation and ReLU activation function:

[0133] h1=ReLU(W1[τ 1～t ,s1～t ,r 1～t ]+b1) (43);

[0134] in is the weight matrix that maps the input to the hidden layer, is the corresponding bias term;

[0135] Next, the hidden layer representation h1 is mapped to the output weight vector w:

[0136] w=W2h1+b2 (44);

[0137] in is the matrix that maps hidden layers to output weights, is the corresponding bias term;

[0138] In order to ensure that the generated weights w are reasonable and applicable to different components, the weight training model performs weight w = {w τ ,w s ,w r} Make the following adjustments to constrain the weights of the trend and residual through the sigmoid function to ensure that they are in the range of [0,1]:

[0139] w τ =σ(w τ ), w r =σ(w r ) (45);

[0140]

[0141] After generating weights, the weight training model performs a weighted combination of the three components of the input and

[0142]

[0143] Here τ ′、w s ′ and w r ′ are the weighting coefficients of trend, seasonality and residual respectively;

[0144] The goal of the weight training model is to minimize the reconstruction signal The error between the true signal Y and the loss function Using mean square error:

[0145]

[0146] in,

[0147] The training process uses the Adam optimizer to update the weight parameters of the weight training model through the gradient descent method to minimize the loss function;

[0148] During the training of the weight training model, after 100 iterations, the weight training model gradually adjusts its parameters so that the weights generated in each iteration can better reconstruct the signal; in each iteration, the weight training model calculates the current reconstructed signal through forward propagation, and updates the weights of the weight training model through back propagation according to the loss between the reconstructed signal and the true signal; this process is carried out through the Adam optimizer to gradually reduce the loss function value;

[0149] At the end of the 100th iteration, the weight training model has adjusted the weight matrices W1 and W2 multiple times through optimization and obtained the final weights and

[0150] (4.2) The forecast reconstruction phase is then performed: the seasonal term forecast vector for the next k time steps is received Trend term prediction vector and the residual prediction vector And the final weight of the output of the weight training part and Generate the final predicted reconstruction signal for the next k time steps

[0151]

[0152] The beneficial effects of the present invention are: 1. Through time series decomposition and reconstruction technology, the trend, seasonality and residual characteristics in the trajectory of aerial targets can be captured more accurately, thereby improving the accuracy of prediction; 2. The system design is modular and has real-time data processing capabilities, which can quickly respond to changes in the trajectory of aerial targets and ensure the real-time and reliability of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0153] Figure 1 It is a structural diagram of an aerial target trajectory prediction system based on a time series decomposition and reconstruction model;

[0154] In the figure, 1-sensor; 2-database; 3-trajectory prediction unit; 4-data preprocessing module; 5-online decomposition module; 6-component prediction module; 7-data reconstruction module. DETAILED DESCRIPTION

[0155] In order to make the purpose, technical scheme and advantages of the present invention more clear, the present invention is further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0156] Example 1

[0157] like Figure 1 As shown, the present invention provides an aerial target trajectory prediction system based on a time series decomposition and reconstruction model, the system consists of a sensor 1, a database 2 and a trajectory prediction unit 3, which are connected in sequence and work together; the sensor 1 includes a radar sensor, an optical sensor, an infrared sensor and a GPS sensor; the trajectory prediction unit 3 includes a data preprocessing module 4, an online decomposition module 5, a component prediction module 6 and a data reconstruction module 7.

[0158] The sensor 1 is responsible for collecting the trajectory data of the monitored aerial target and transmitting the data to the database 2 in real time via a wireless network; the transmission process can use the data cache in the sensor to ensure the continuity of the data and avoid signal interference or breakpoints.

[0159] The database 2 is used to sort and index the received aerial target trajectory data according to timestamps to obtain processed aerial target trajectory data X, so as to ensure that subsequent processing modules can quickly read and operate related data; then the processed aerial target trajectory data X is transmitted to the trajectory prediction unit 3, and batch processing is adopted to optimize the computing efficiency and ensure that the data can be seamlessly connected between different processing modules.

[0160] The trajectory prediction unit 3 is used to process and predict the received processed aerial target trajectory data X to obtain predicted reconstruction data, which specifically includes the following sub-steps:

[0161] (1) After the trajectory prediction unit 3 receives the processed aerial target trajectory data X, it first inputs the processed aerial target trajectory data X into the data preprocessing module 4 for outlier detection and data normalization processing to obtain the preprocessed aerial target trajectory data Y.

[0162] The data preprocessing module 4 is responsible for the preliminary processing of the aerial target trajectory data in the database to ensure the quality and consistency of the data. The functions of this module include outlier detection and data normalization, which aims to remove noise, correct erroneous data and unify the data scale.

[0163] The step (1) specifically includes the following sub-steps:

[0164] (1.1) After the trajectory prediction unit 3 receives the processed aerial target trajectory data X, it first inputs the processed aerial target trajectory data X into the data preprocessing module 4;

[0165] The processed aerial target trajectory data X is defined as a time series: X = {x1, x2, ..., x i ,...,x t}, where x i represents the observation value at the i-th time point, and t is the length of the time series;

[0166] First, the processed aerial target trajectory data X is used to detect outliers using the sliding window and standard deviation outlier detection method:

[0167] For each time point, the observed value x i Select a sliding window W of length w around and calculate the observation value x i The mean and standard deviation of :

[0168]

[0169] in, is the mean of the data in the window, is the standard deviation, and w is the window length.

[0170] Assuming that the data distribution is approximately normal, data points beyond the 99% confidence interval can be considered outliers, and x that satisfies formula (3) i Considered as detected outliers:

[0171]

[0172] For the detected outlier x i , the linear interpolation method based on adjacent points is used to replace the observed value x after anomaly detection i ′, the linear interpolation formula is:

[0173]

[0174] x that does not satisfy formula (3) i Not considered as an outlier detected, for an outlier value x that is not considered as an outlier detected i , no replacement is performed, that is, x i ′=x i .

[0175] After the outlier detection is completed on the processed aerial target trajectory data X, the aerial target trajectory data X′ after anomaly detection is obtained: X′={x1′,x2′,...,x i′,...,x t ′}.

[0176] (1.2) For time series that have been detected for outliers, data normalization is performed to eliminate the dimensional differences of different data features and ensure that the data is calculated at the same scale in subsequent processing.

[0177] Then, the air target trajectory data X′ after anomaly detection is normalized to obtain the preprocessed air target trajectory data Y: Y = {y1, y2, ..., y i ,...,y t}, using the Min-Max normalization method, the formula is:

[0178]

[0179] Among them, y i is the normalized observation value at the i-th time point; x min is the minimum value of the aerial target trajectory data X′ after anomaly detection, x max is the maximum value in the aerial target trajectory data X′ after anomaly detection. The normalization process scales all trajectory data to the interval [0,1], so that data with different features can be processed by the model at the same scale, thereby improving the prediction accuracy.

[0180] (2)) Then, the preprocessed aerial target trajectory data Y is input into the online decomposition module 5, and the preprocessed aerial target trajectory data Y is decomposed into a seasonal term vector τ 1～t , trend term vector s 1～t and the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ].

[0181] The online decomposition module 5 is responsible for decomposing the time series of the preprocessed aerial target trajectory data Y into seasonal terms, trend terms and residual terms, obtaining the initial trend and seasonal components through the initialization phase, and dynamically updating the trend and seasonal components at each moment after receiving new data points. This module can accurately capture the long-term trends and short-term periodic changes in the data, decompose complex time series data into more regular components, and has the ability to update online, thereby more accurately predicting trajectory data.

[0182] The step (2) specifically includes the following sub-steps:

[0183] (2.1) Then, the preprocessed aerial target trajectory data Y is input into the online decomposition module 5, and the online decomposition module 5 first divides the preprocessed aerial target trajectory data Y into Y=Y1+Y2, where Y1={y1, y2, ..., y d ,...,y N}, in,

[0184] Set Y1 = {y1, y2, ..., y d ,...,y N} is used to initialize the decomposition, and the decomposition objective function expression is:

[0185]

[0186] Among them, the parameter τ d and d Respectively represent the normalized observation value y at the dth time point d The trend term and seasonal term obtained by decomposition, T represents the size of the cycle corresponding to the seasonal term; λ1 represents the parameter controlling the first-order smoothness of the trend term, λ2 represents the parameter controlling the second-order smoothness of the trend term; τ represents the trend term of the entire time series: τ=[τ1,τ2,…,τ d ,…,τ N ]; s represents the seasonal term of the entire time series: s = [s1, s2, …, s d ,…,s N ].

[0187] In order to optimize formula (6), the online decomposition module 5 introduces auxiliary variables Transform formula (6) into:

[0188]

[0189] Among them, the auxiliary variable p d represents the value of variable p at the dth time point; q d represents the value of variable q at the dth time point. By introducing p d and q d Adjustments have enhanced the ability to respond to changes in different trends.

[0190] Initialize auxiliary variables p and q to 1:

[0191]

[0192] These initial values ​​are used to control the smoothness of the trend and seasonal terms in the first iteration.

[0193] The iterative process of the initialization phase will last for I iterations, and the auxiliary variables p and q are gradually updated after each iteration to ensure that the estimates of the trend term and the seasonal term gradually converge. The specific update steps in each iteration are:

[0194] In each iteration, new trend terms and seasonal terms are first calculated based on the current auxiliary variables p and q. In order to efficiently solve the optimization problem, the matrix form in the objective function is defined as:

[0195]

[0196] Among them, matrices B1, B2, B3, and B4 are defined as:

[0197]

[0198] According to the above matrix definition, construct the linear system Ax = b and solve x: x = {x1,…,x N ,x N+1 ,…,x 2N}, thereby updating the trend term τ, seasonal term s and residual term r of this iteration:

[0199] τ={x1,…,x N} s={x N+1 ,…,x 2N} r = Y1 - τ - s (12);

[0200] Update the auxiliary variables p and q using the updated trend term:

[0201]

[0202]

[0203] These update formulas are designed to ensure that trend items change smoothly while adapting to dynamic changes in data.

[0204] After I iterations, we get Y1 = {y1, y2, ..., y d ,…,y N The final trend term component corresponding to Seasonal Component and the residual component

[0205] In the initialization phase, the online decomposition module 5 converts Y1={y1,y2,...,y d ,...,y N}Decompose into trend terms Seasonal Items and the residual Therefore, when the online updating phase decomposes the first data point, the online decomposition module 5 has already obtained the seasonal components of the previous data points.

[0206] (2.2) Then the online decomposition phase is carried out. After each online decomposition, the latest seasonal term will be saved in the sliding window and used for future updates. For ease of processing, the seasonal buffer is named And initialize it to v = [s N-T ,...,s N ] T Subsequently, the components of the seasonal term in formula (6) are redefined and the problem is transformed into:

[0207]

[0208] Where M is the number of newly arrived data points that need to be decomposed online. j%T is a modulo operation to ensure that when j>T, v j％T It can be correctly returned to the vector v, thus realizing the reuse of seasonal data. Formula (15) prevents the model from becoming too complicated when fitting historical data by redefining the seasonal term and introducing dynamic updates to new data, thereby maintaining the simplicity and robustness of the model. At the same time, the formula transforms the iterative update of new data into an optimization problem, greatly improving the computational efficiency when processing real-time data, especially when facing large-scale data, which can significantly improve the response speed and adaptability of the model.

[0209] First, the auxiliary variable and initialization:

[0210]

[0211] in, and are the initial values ​​at the beginning of the iteration, which are used to control the smoothness of the first-order difference and the second-order difference of the trend term. and Indicates that the auxiliary variables after the bth iteration will be gradually updated during the iteration process.

[0212] The iterative process of the online update phase will last for I iterations, with b = 0 initialized and the value of b increasing by 1 in each iteration. The specific update steps in each iteration are:

[0213] First, in the bth iteration, based on the current and Calculate new trend terms and seasonal terms. In order to efficiently solve the optimization problem, the matrix form in the objective function is defined as:

[0214]

[0215] in, N+t0 represents the time point of the current processing; The matrices C1, C2, C3, and C4 are defined as:

[0216]

[0217] According to the above matrix definition, construct the linear system And solve for the vector Thus, the trend item of the bth iteration is updated Seasonal Items and the residual

[0218]

[0219] in, Representation vector The second to last value in Representation vector The first to last value in the

[0220] According to formula (20) and formula (21), the b-th iteration is calculated and

[0221]

[0222] Repeat this process until b=I-1, and the iteration ends to obtain the trend item at time point N+t0. Seasonal Items and the residual decomposition.

[0223] In this way, the online update of the decomposition module can be completed. When new time series data enters, it is decomposed according to the above iteration to obtain The corresponding final trend term component Seasonal Component and the residual component

[0224] (2.3) After the initialization phase and the online update phase, the preprocessed aerial target trajectory data Y is decomposed into the seasonal term vector τ 1～t , Trend Items 1～t and the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ],in,

[0225] (3) Then the decomposed Y = [τ 1～t ,s 1～t ,r 1～t ] is input to the component prediction module 6 to obtain the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector

[0226] The step (3) is specifically:

[0227] Then the decomposed Y=[τ 1～t ,s 1～t ,r 1～t ] is input to the component prediction module 6, and the component prediction module 6 uses the Informer model to decompose the time series component Y=[τ 1～t ,s 1～t ,r 1～t ] to make predictions;

[0228] First, the linear transformation is mapped to the high-dimensional space d model , making it easier for the model to handle complex features:

[0229] H0=[τ 1～t ,s 1～t ,r 1～t ]W e +b e (twenty two);

[0230] in, is the embedding matrix, is the bias term. This step maps the data of each time step from 3D to d model dimensional space to enhance the representation ability of the model. Then position encoding is added to introduce temporal information. Position encoding is generated using sine and cosine functions:

[0231]

[0232] Through formula (23), we get the position code PE: PE = {PE (t,1) ,...,PE (t,i) ,...,PE (t,t)}.

[0233] The position encoding PE is then added to the embedded features to introduce temporal position information into the model:

[0234] H t =H0+PE (24);

[0235] This layer allows the model to capture the order of time points in the time series.

[0236] For each time step, the feature representation H t , generate the query matrix Q through linear transformation t (Query), key matrix K t (Key) and value matrix V t (Value):

[0237] Q t =H t W Q ,K t =H t W K ,V t =H t W V (25);

[0238] in, is the transformation matrix, d k is the dimension of the key vector. The purpose of generating these matrices is to find correlations between time steps. Query with query-key pairs with larger norm to pick those query-key pairs that have the greatest impact on the prediction results:

[0239] Q t ≥threshold (26);

[0240] For the sparse query-key pairs selected by formula (26), the attention weight is calculated using the standard attention mechanism formula:

[0241]

[0242] in, It is the dot product of query and key divided by d k The square root of , to maintain numerical stability. Then the value matrix V t Perform weighted summation.

[0243] After the self-attention calculation, residual connections and layer normalization are used to make the model more stable and maintain information transfer:

[0244] H1=LayerNorm(H t +Attention(Q t ,K t ,V t )) (28);

[0245] Residual connections allow gradients to flow, and layer normalization ensures numerical stability, preventing gradients from exploding or vanishing.

[0246] Through average pooling or other downsampling strategies, the Distilling layer shortens the length T of the input sequence to T / 2, thereby reducing the computational complexity of subsequent layers of the model:

[0247]

[0248] Here It is the time series representation after downsampling. This step retains the main feature information while reducing the sequence length and improving efficiency.

[0249] The encoder of the Informer model contains multiple ProbSparse self-attention layers and feed-forward neural network layers (FFN) to extract deep features in time series.

[0250] The encoder uses an h-head self-attention mechanism, which means it applies multiple self-attention modules in parallel on different projection spaces. Each head performs attention calculations independently:

[0251] MultiHead(Q t ,K t ,V t )=Concat(head1,head2,...,head h )W O (30);

[0252] The attention of each head is calculated as follows:

[0253]

[0254] Then concatenate the outputs of each head and pass the linear transformation matrix W O Mapping back to d model Dimension.

[0255] After each self-attention layer, there is a feedforward neural network that performs independent nonlinear transformations on the features at each time point. FFN contains two layers of linear transformations and a ReLU activation function:

[0256] FFN(x)=ReLU(xW1+b1)W2+b2 (32);

[0257] Where FFN(·) represents the processing of the feedforward neural network, and x represents the input of the feedforward neural network;

[0258] The first layer maps the input to a higher dimensional space, and the second layer maps it back to d model Each layer in the encoder uses residual connections and layer normalization to ensure the stability of training and the normal flow of gradients:

[0259]

[0260] The output H3 of the third layer is then input to the decoder in the Informer model; the decoder part is composed of multiple decoder layers stacked together. Each decoder layer has three core components: self-attention mechanism, encoder-decoder attention mechanism and feedforward neural network. In addition, each layer has residual connection and layer normalization to ensure that the model can be stably trained in deep networks.

[0261] At each layer of the decoder, the self-attention mechanism first generates a query matrix for each time step Key Matrix Sum value matrix V t 3 (Value):

[0262]

[0263] in, is the transformation matrix. Through these linear transformations, the decoder extracts features from the output generated in the previous time step.

[0264] In the decoder, to ensure that each time step can only see the time step before it and not the time step in the future, the decoder's self-attention mechanism applies a mask matrix. This mask matrix ensures that each time step only pays attention to the time step before it:

[0265]

[0266] The mask matrix M marks future time steps as negative infinity to ensure that these time steps do not affect the current attention calculation. This mechanism is very important because in the decoding stage, the model generates outputs step by step and cannot see future time steps in advance.

[0267] After applying the mask, the decoder's self-attention mechanism uses a similar calculation as the encoder to capture the dependencies between time steps. The specific calculation is as follows:

[0268]

[0269] The function of this formula is to generate the context representation of the time step at the current time step t based on the representation value V of other time steps.

[0270] In the second attention layer of the decoder, the model combines the global information of the encoder output through encoder-decoder attention. In encoder-decoder attention, the query matrix Q generated by the decoder is d The key matrix K generated by the encodere Sum value matrix V e The specific calculation is as follows:

[0271]

[0272] In this way, the decoder is able to use the input time series information extracted by the encoder to help it generate predictions.

[0273] Similar to self-attention, the encoder-decoder attention is calculated as:

[0274]

[0275] This step ensures that the decoder can take into account information from the entire input time series when generating predictions for future time steps.

[0276] At the end of each decoder layer, the feature vector processed by the attention mechanism is further processed by a feed-forward neural network (FFN), which consists of two layers of linear transformation and a ReLU activation function.

[0277] The first layer of the feed-forward network maps the input features to a higher dimension, and the second layer maps them back to the original dimension.

[0278] Each layer in the decoder uses residual connections and layer normalization to ensure the stability of training and the normal flow of gradients:

[0279]

[0280] The output of the decoder is mapped back to the original dimension D through a linear layer to generate the prediction result. Forecasting the data for the next k time steps, the output of the decoder is:

[0281]

[0282] Here, W out is the weight matrix of the output layer, b out is the bias term. out Contains three sub-matrices, each used to generate predictions for a specific component:

[0283] W out =[W τ W s W r ] (41);

[0284] By matrix multiplying the decoder output H3 with these sub-matrices, we get the prediction for each component:

[0285]

[0286] The output of component prediction module 6 is obtained, which is the seasonal term prediction vector for the next k time steps. Trend term prediction vector and the residual prediction vector

[0287] (4) Then the preprocessed aerial target trajectory data Y and the seasonal term prediction vector for the next k time steps are Trend term prediction vector and the residual prediction vector Input to data reconstruction module 7 to generate the final predicted reconstruction signal for the next k time steps

[0288] The step (4) specifically includes the following sub-steps:

[0289] (4.1) Then Y = [τ 1～t ,s 1～t ,r 1～t ] and the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector The data is input into the data reconstruction module 7, and the weight training phase is first performed;

[0290] Weight training stage: The weight training model accepts the input signal Y = [τ 1～t ,s 1～t ,r 1～t ];

[0291] First, the input [τ 1～t ,s 1～t ,r 1～t ] is mapped to the hidden layer representation h1, and the hidden representation is generated through linear transformation and ReLU activation function:

[0292] h1=ReLU(W1[τ 1～t ,s 1～t ,r 1～t ]+b1) (43);

[0293] in is the weight matrix that maps the input to the hidden layer, is the corresponding bias term;

[0294] Next, the hidden layer representation h1 is mapped to the output weight vector w:

[0295] w=W2h1+b2 (44);

[0296] in is the matrix that maps hidden layers to output weights, is the corresponding bias term.

[0297] In order to ensure that the generated weights w are reasonable and applicable to different components, the weight training model performs weight w = {w τ ,w s ,w r} Make the following adjustments to constrain the weights of the trend and residual through the sigmoid function to ensure that they are in the range of [0,1]:

[0298] w τ ′=σ(w τ ), w r ′=σ(w r ) (45);

[0299] here is the sigmoid function, which compresses the input weight value to the range of [0,1]. This ensures that the weights of the trend and residual are reasonable, and there will be no excessive or small weights that affect the reconstruction effect.

[0300] For the seasonal component s 1～t The model uses the softmax function to normalize the weights of the seasonal components so that they have a more reasonable weight distribution among different components:

[0301]

[0302] Here, the role of softmax is to convert the weight values ​​into a probability distribution, ensuring that their sum is 1. The advantage of this is that it ensures that the weight of the seasonal component in the overall signal is not overly amplified or reduced.

[0303] After generating weights, the weight training model performs a weighted combination of the three components of the input and

[0304]

[0305] Here τ ′、w s ′ and w r ′ are weighted coefficients of trend, seasonality and residual respectively. Formula (50) reconstructs the signal by weighted combination of trend, seasonality and residual terms, so that the model can adapt to different patterns in the data more flexibly. In this way, it can capture long-term trends and cyclical fluctuations, and effectively deal with random fluctuations, thus improving the accuracy and robustness of the overall prediction.

[0306] The goal of the weight training model is to minimize the reconstruction signal The error between the true signal Y and the loss function Using mean square error:

[0307]

[0308] in,

[0309] The training process uses the Adam optimizer to update the weight parameters of the weight training model through the gradient descent method to minimize the loss function.

[0310] During the training of the weight training model, after 100 iterations, the weight training model gradually adjusts its parameters so that the weights generated in each iteration can better reconstruct the signal. In each iteration, the weight training model calculates the current reconstructed signal through forward propagation, and updates the weights of the weight training model through back propagation based on the loss between the reconstructed signal and the true signal. This process is performed through the Adam optimizer to gradually reduce the loss function value.

[0311] At the end of the 100th iteration, the weight training model has adjusted the weight matrices W1 and W2 multiple times through optimization and obtained the final weights and

[0312] (4.2) The forecast reconstruction phase is then performed: the seasonal term forecast vector for the next k time steps is received Trend term prediction vector and the residual prediction vector And the final weight of the output of the weight training part and Generate the final predicted reconstruction signal for the next k time steps

[0313]

[0314] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An aerial target trajectory prediction system based on a time series decomposition and reconstruction model, characterized in that: The system consists of sensors, a database and a trajectory prediction unit, which are connected in sequence and work together; the sensors include radar sensors, optical sensors, infrared sensors and GPS sensors; the trajectory prediction unit includes a data preprocessing module, an online decomposition module, a component prediction module and a data reconstruction module.

2. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 1 is characterized in that: The sensor is responsible for collecting the monitored air target trajectory data and transmitting the data to the database in real time via a wireless network; The database is used to sort and index the received aerial target trajectory data according to timestamps, obtain the processed aerial target trajectory data X and transmit it to the trajectory prediction unit; The trajectory prediction unit is used to process and predict the received processed aerial target trajectory data X to obtain predicted reconstruction data.

3. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 2 is characterized in that: The trajectory prediction unit is used to process and predict the received processed aerial target trajectory data X to obtain predicted reconstruction data, which specifically includes the following sub-steps: (1) After the trajectory prediction unit receives the processed aerial target trajectory data X, the processed aerial target trajectory data X is first input into a data preprocessing module for outlier detection and data normalization processing to obtain preprocessed aerial target trajectory data Y; (2) Then, the preprocessed aerial target trajectory data Y is input into the online decomposition module, and the preprocessed aerial target trajectory data Y is decomposed into the seasonal term vector τ 1～t , trend term vector s 1～t and the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ]; (3) Then the decomposed Y = [τ 1～t ,s 1～t ,r 1～t ] is input to the component prediction module 6 to obtain the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector (4) Then the preprocessed aerial target trajectory data Y and the seasonal term prediction vector for the next k time steps are Trend term prediction vector and the residual prediction vector Input to the data reconstruction module to generate the final predicted reconstruction signal for the next k time steps 4. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 3 is characterized in that: The step (1) specifically includes the following sub-steps: (1.1) After the trajectory prediction unit receives the processed aerial target trajectory data X, it first inputs the processed aerial target trajectory data X into a data preprocessing module; The processed aerial target trajectory data X is defined as a time series: X = {x1, x2, ..., x i ,...,x t }, where x i represents the observation value at the i-th time point, and t is the length of the time series; First, the processed aerial target trajectory data X is used to detect outliers using the sliding window and standard deviation outlier detection method: For each time point, the observed value x i Select a sliding window W of length w around and calculate the observation value x i The mean and standard deviation of : in, is the mean of the data in the window, is the standard deviation, w is the window length; x that satisfies formula (3) i Considered as detected outliers: For the detected outlier x i , the linear interpolation method based on adjacent points is used to replace the observed value x after anomaly detection i ′, the linear interpolation formula is: x that does not satisfy formula (3) i Not considered as an outlier detected, for an outlier value x that is not considered as an outlier detected i , no replacement is performed, that is, x i ′=x i ; After the outlier detection is completed on the processed aerial target trajectory data X, the aerial target trajectory data X′ after anomaly detection is obtained: X′={x1′,x2′,...,x i ′,...,x t '}; (1.2) Then, the air target trajectory data X′ after anomaly detection is normalized to obtain the preprocessed air target trajectory data Y: Y = {y1, y2, ..., y i ,...,y t }, using the Min-Max normalization method, the formula is: Among them, y i is the normalized observation value at the i-th time point; x min is the minimum value of the aerial target trajectory data X′ after anomaly detection, x max It is the maximum value in the aerial target trajectory data X′ after anomaly detection.

5. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 4 is characterized in that: The step (2) specifically includes the following sub-steps: (2.1) Then, the preprocessed aerial target trajectory data Y is input into an online decomposition module, which first divides the preprocessed aerial target trajectory data Y into Y=Y1+Y2, where Y1={y1, y2, ..., y d ,...,y N }, in, Set Y1={y1,y2,…,y d ,…,y N } is used to initialize the decomposition, and the decomposition objective function expression is: Among them, the parameter τ d and d Respectively represent the normalized observation value y at the dth time point d The trend term and seasonal term obtained by decomposition, T represents the size of the cycle corresponding to the seasonal term; λ1 represents the parameter controlling the first-order smoothness of the trend term, λ2 represents the parameter controlling the second-order smoothness of the trend term; τ represents the trend term of the entire time series: τ=[τ1,τ2,…,τ d ,…,τ N ]; s represents the seasonal term of the entire time series: s = [s1, s2, …, s d ,…,s N ]; In order to optimize formula (6), the online decomposition module introduces auxiliary variables Transform formula (6) into: Among them, the auxiliary variable p d represents the value of variable p at the dth time point; q d represents the value of variable q at the dth time point; Initialize auxiliary variables p and q to 1: The iterative process of the initialization phase will last for I iterations, and the auxiliary variables p and q will be gradually updated after each iteration to ensure that the estimates of the trend term and the seasonal term gradually converge; the specific update steps in each iteration are: In each iteration, new trend terms and seasonal terms are first calculated based on the current auxiliary variables p and q; in order to efficiently solve the optimization problem, the matrix form in the objective function is defined as: Among them, matrices B1, B2, B3, and B4 are defined as: According to the above matrix definition, construct the linear system Ax = b and solve x: x = {x1,…,x N ,x N+1 ,…,x 2N }, thereby updating the trend term τ, seasonal term s and residual term r of this iteration: τ={x1,…,x N } s={x N+1 ,…,x 2N } r=Y1-τ-s (12); Update the auxiliary variables p and q using the updated trend term: These update formulas are designed to ensure that trend items change smoothly while adapting to dynamic changes in data; After I iterations, we get Y1 = {y1, y2, ..., y d ,...,y N The final trend term component corresponding to Seasonal Component and the residual component (2.2) Then the online decomposition phase is carried out. After each online decomposition, the latest seasonal term will be saved in the sliding window and used for future updates. For ease of processing, the seasonal buffer is named And initialize it to v = [s N-T ,...,s N ] T ; Then, the components of the seasonal term in formula (6) are redefined and the problem is transformed into: Where M is the number of newly arrived data points, which are the ones that need to be decomposed online; j%T is the modulo operation used to ensure that when j>T, v j％T It can be correctly returned to the vector v, thus enabling the reuse of seasonal data; First, the auxiliary variable and initialization: in, and are the initial values ​​at the beginning of the iteration, which are used to control the smoothness of the first-order difference and the second-order difference of the trend term; and Indicates that the auxiliary variables after the bth iteration will be gradually updated during the iteration process; The iterative process of the online update phase will last for I iterations, with b=0 initialized and the value of b increasing by 1 in each iteration; the specific update steps in each iteration are: First, in the bth iteration, based on the current and Calculate new trend terms and seasonal terms; in order to efficiently solve the optimization problem, define the matrix form in the objective function: in, N+t0 represents the time point of the current processing; The matrices C1, C2, C3, and C4 are defined as: According to the above matrix definition, construct the linear system And solve for the vector Thus, the trend item of the bth iteration is updated Seasonal Items and the residual in, Representation vector The second to last value in Representation vector The first to last value in the According to formula (20) and formula (21), the b-th iteration is calculated and Repeat this process until b=I-1, and the iteration ends to obtain the trend item at time point N+t0. Seasonal Items and the residual decomposition; In this way, the online update of the decomposition module can be completed. When new time series data enters, it is decomposed according to the above iteration to obtain The corresponding final trend term component Seasonal Component and the residual component (2.3) After the initialization phase and the online update phase, the preprocessed aerial target trajectory data Y is decomposed into the seasonal term vector τ 1～t , Trend Items 1～t and the residual vector r 1～t :Y=[τ 1～t ,s 1～t ,r 1～t ],in, 6. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 5 is characterized in that: The step (3) is specifically: Then the decomposed Y=[τ 1～t ,s 1～t ,r 1～t ] is input into the component prediction module, which uses the Informer model to decompose the time series component Y = [τ 1～t ,s 1～t ,r 1～t ] to make predictions; First, the linear transformation is mapped to the high-dimensional space d model : H0=[τ 1～t ,s 1～t ,r 1～t ]IN e +b e (22); in, is the embedding matrix, is the bias term; then position encoding is added to introduce timing information, and the position encoding is generated using sine and cosine functions: Through formula (23), we get the position code PE: PE = {PE (t,1) ,…,PE (t,i) ,…,PE (t,t) }; The position encoding PE is then added to the embedded features to introduce temporal position information into the model: A t =H0+PE (24); For each time step, the feature representation H t , generate the query matrix Q through linear transformation t , key matrix K t Sum value matrix V t : Q t =H t W Q , K t =H t W K , V t =H t W V (25); in, is the transformation matrix, d k is the dimension of the key vector; query-key pairs with larger norm are queried to select those query-key pairs that have the greatest impact on the prediction results: Q t ≥ threshold (26); For the sparse query-key pairs selected by formula (26), the attention weight is calculated using the standard attention mechanism formula: Then the value matrix V t Perform weighted summation; After the self-attention calculation, residual connections and layer normalization are used to make the model more stable and maintain information transfer: H1=LayerNorm(H t +Attention(Q t ,K t ,V t )) (28); Residual connections allow gradients to flow, and layer normalization ensures numerical stability, preventing gradients from exploding or vanishing; The Distilling layer reduces the length T of the input sequence to T / 2 through average pooling or other downsampling strategies: Here It is the time series representation after downsampling; The encoder of the Informer model contains multiple ProbSparse self-attention layers and feed-forward neural network layers; the encoder uses an h-head self-attention mechanism, and each head performs attention calculations independently: MultiHead(Q t ,K t ,V t )=Concat(head1,head2,...,head h )W O (30); The attention of each head is calculated as follows: Then concatenate the outputs of each head and pass the linear transformation matrix W O Mapping back to d model Dimension; After each self-attention layer, there is a feedforward neural network that performs independent nonlinear transformations on the features at each time point; the FFN contains two layers of linear transformations and a ReLU activation function: FFN(x)=ReLU(xW1+b1)W2+b2 (32); Where FFN(·) represents the processing of the feedforward neural network, and x represents the input of the feedforward neural network; The first layer maps the input to a higher dimensional space, and the second layer maps it back to d model The original space; each layer in the encoder uses residual connection and layer normalization to ensure the stability of training and the normal flow of gradients: The output H3 of the third layer is then input to the decoder in the Informer model; the decoder part is composed of multiple decoder layers stacked together; each decoder layer has three core components: self-attention mechanism, encoder-decoder attention mechanism and feedforward neural network. In addition, each layer has residual connection and layer normalization to ensure that the model can be stably trained in deep networks; At each layer of the decoder, the self-attention mechanism first generates a query matrix for each time step Key Matrix Sum value matrix V t 3 : in, is the transformation matrix; through these linear transformations, the decoder will extract features from the output generated in the previous time step; In the decoder, to ensure that each time step can only see the time step before it and not the time step in the future, the decoder's self-attention mechanism applies a mask matrix; this mask matrix ensures that each time step only pays attention to the time step before it: The mask matrix M marks future time steps as negative infinity to ensure that these time steps do not affect the current attention calculation. This mechanism is very important because in the decoding stage, the model generates outputs step by step and cannot see future time steps in advance. After applying the mask, the decoder's self-attention mechanism uses a similar calculation as the encoder to capture the dependencies between time steps; the specific calculation is as follows: In the second attention layer of the decoder, the model combines the global information output by the encoder through the encoder-decoder attention; in the encoder-decoder attention, the query matrix Q generated by the decoder d The key matrix K generated by the encoder e Sum value matrix V e The specific calculation is as follows: Similar to self-attention, the encoder-decoder attention is calculated as: This step ensures that the decoder can refer to information from the entire input time series when generating predictions for future time steps; At the end of each decoder layer, the feature vector processed by the attention mechanism is further processed by a feedforward neural network; the feedforward neural network consists of two layers of linear transformation and a ReLU activation function; The first layer of the feed-forward network maps the input features to a higher dimension, and the second layer maps it back to the original dimension; Each layer in the decoder uses residual connections and layer normalization to ensure the stability of training and the normal flow of gradients: The output of the decoder is mapped back to the original dimension D through a linear layer to generate the prediction result; predicting the data of the next k time steps, the output of the decoder is: Here, W out is the weight matrix of the output layer, b out is the bias term; W out Contains three sub-matrices, each used to generate predictions for a specific component: IN out =[W τ IN s IN r ] (41); By matrix multiplying the decoder output H3 with these sub-matrices, we get the prediction for each component: Get the output of the component prediction module, which is the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector 7. The aerial target trajectory prediction system based on the time series decomposition and reconstruction model according to claim 6 is characterized in that: The step (4) specifically includes the following sub-steps: (4.1) Then Y = [τ 1～t ,s 1～t ,r 1～t ] and the seasonal term prediction vector for the next k time steps Trend term prediction vector and the residual prediction vector Input into the data reconstruction module, first the weight training phase is carried out; Weight training stage: The weight training model accepts the input signal Y = [τ 1～t ,s 1～t ,r 1～t ]; First, the input [τ 1～t ,s 1～t ,r 1～t ] is mapped to the hidden layer representation h1, and the hidden representation is generated through linear transformation and ReLU activation function: h1=ReLU(W1[τ 1～t ,s 1～t ,r 1～t ]+b1) (43); in is the weight matrix that maps the input to the hidden layer, is the corresponding bias term; Next, the hidden layer representation h1 is mapped to the output weight vector w: w=W2h1+b2 (44); in is the matrix that maps hidden layers to output weights, is the corresponding bias term; In order to ensure that the generated weights w are reasonable and applicable to different components, the weight training model performs weight w = {w τ ,w s ,w r } Make the following adjustments to constrain the weights of the trend and residual through the sigmoid function to ensure that they are in the range of [0,1]: w τ =σ(w τ ), w r =σ(w r ) (45); After generating weights, the weight training model performs a weighted combination of the three components of the input and Here τ ′、w s ′ and w r ′ are the weighting coefficients of trend, seasonality and residual respectively; The goal of the weight training model is to minimize the reconstruction signal The error between the true signal Y and the loss function Using mean square error: in, The training process uses the Adam optimizer to update the weight parameters of the weight training model through the gradient descent method to minimize the loss function; During the training of the weight training model, after 100 iterations, the weight training model gradually adjusts its parameters so that the weights generated in each iteration can better reconstruct the signal; in each iteration, the weight training model calculates the current reconstructed signal through forward propagation, and updates the weights of the weight training model through back propagation according to the loss between the reconstructed signal and the true signal; this process is carried out through the Adam optimizer to gradually reduce the loss function value; At the end of the 100th iteration, the weight training model has adjusted the weight matrices W1 and W2 multiple times through optimization and obtained the final weights and (4.2) The forecast reconstruction phase is then performed: the seasonal term forecast vector for the next k time steps is received Trend term prediction vector and the residual prediction vector And the final weight of the output of the weight training part and Generate the final predicted reconstruction signal for the next k time steps

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