A trajectory prediction method and system based on fast transfer combined with LSTM neural network

Abstract

This invention discloses a trajectory prediction method and system based on fast transfer combined with an LSTM neural network. When an aircraft is maneuvering, it first uses an LSTM neural network to predict maneuvers based on radar data. When radar data is missing and cannot form a training dataset for the LSTM neural network, a fast transfer method is further used to directly approximate the target's flight dynamics and kinematics model and obtain approximate values ​​of the control quantities during the target's maneuver. Then, the target's flight state is predicted to supplement radar data and further provide a training dataset for the LSTM network. Since the LSTM network can obtain relatively accurate maneuver prediction results, the fast transfer method can assist the LSTM network in performing maneuver prediction even when radar data is missing.

Description

Technical Field

[0001] This invention belongs to the field of aerospace, specifically relating to a trajectory prediction method and system based on fast transfer combined with LSTM neural network. Background Technology

[0002] With the continuous development of aerospace technology and the increasing demands of missions, the prediction of target aircraft state parameters under high-maneuverability conditions has become increasingly important, and its crucial role in influencing the course of warfare is constantly being validated. Specifically, aircraft state parameter prediction refers to using radar observation data, treating this data as historical data, to predict the future state parameters of the aircraft. One traditional method is to use the classic LSTM network, using historical radar observation data as the training dataset for the LSTM network. After training, the LSTM network can predict aircraft maneuver parameters in real time. However, in reality, radar may lose motion data due to various unforeseen factors (electronic interference, silence, high target maneuverability, etc.), making it difficult to construct a training dataset for the LSTM network, thus hindering the prediction of future aircraft state parameters. Summary of the Invention

[0003] The purpose of this invention is to provide a trajectory prediction method and system based on rapid target maneuvering conditions, in order to overcome the problem in the prior art that radar will lose motion data of the observed object due to various uncontrollable factors (electronic interference, silence, target maneuvering, etc.), which makes it difficult to construct the training dataset of LSTM network and thus difficult to predict the state parameters of future aircraft.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A trajectory prediction method based on fast pass-through combined with an LSTM neural network includes the following steps:

[0006] S1: Establish a kinematic model of the target maneuvering flight;

[0007] S2: Establish the target maneuver dynamics model;

[0008] S3: Construct a mathematical model for the fast transfer method and LSTM network;

[0009] S4: Use radar to acquire the motion parameters of enemy aircraft, and then use a mathematical model that combines the maneuvering flight kinematics model, the maneuvering dynamics model, and the fast transfer method with the LSTM network to predict the target's trajectory.

[0010] Preferably, the method for establishing the target maneuvering flight kinematic model in S1 is as follows: based on the construction of the corresponding northeast coordinate system of our carrier aircraft and the enemy target aircraft, the target maneuvering flight kinematic model is derived according to the geometric and angular relationship between our carrier aircraft and the enemy target aircraft.

[0011] Preferably, the target maneuver dynamics model in S2 is represented by the following two equations:

[0012]

[0013]

[0014] In the formula, n x n y γ and θ represent the tangential overload, normal overload, and roll angle about the velocity axis, respectively; V, θ, and ψ represent the aircraft's flight speed, track inclination angle, and heading angle corresponding to the velocity vector, respectively. These are the derivatives of the flight speed, the track inclination angle, and the heading angle of the corresponding velocity vector, respectively.

[0015] Preferably, the mathematical model of the fast transfer method in S3 is as follows:

[0016] First, obtain the set of state variables parameters, determine a central state variable nominal point, calculate the deviation value between the central state variable nominal point and the other state points, then perform a one-step integration on the central state variable nominal value to obtain the state variable nominal point at the next time step, transform the deviation value to obtain all the deviation values ​​at the next time step, and then substitute the deviations into the state variables at the next time step to obtain all the state variable parameter sets at the next time step, thus completing the relevant modeling of the fast transfer method.

[0017] Preferably, the mathematical model method for constructing the LSTM network in S3 is as follows:

[0018] We construct specific mathematical expressions for the forget gate, update gate, and output gate in the LSTM network. At the same time, we construct specific mathematical expressions for the internal weight update formula of the LSTM network based on the gradient descent method, so that the network forms a closed loop and can continuously iterate, thus completing the relevant modeling of the LSTM network.

[0019] Preferably, the mathematical expression for the forget gate is:

[0020] f t =σ(W xf x t +W hf h t-1 +b f )

[0021] Among them, f t Indicates the output of the forget gate; W xf Whf These represent the current network state and the weights of the network cell inputs to the forgetting gate pathway at the previous time step, respectively; x t and h t-1 These represent the network state and the network cell from the previous time step, respectively; b f This represents the bias layer parameters of the forget gate.

[0022] Preferably, the mathematical expression for updating the gate output is as follows:

[0023] i t =σ(W xi x t +W hi h t-1 +b i )

[0024] g t =tanh(W xg x t +W hg h t-1 +b g )

[0025] u t =i t g t

[0026] Where u t Indicates updating the gate output; W xi W hi W represents the current network state and the weights of the network cells input to the sigmoid function in the update gate at the previous time step, respectively. xg W hg Let b represent the current network state and the weights of the tanh function input from the network cell in the previous time step into the update gate, respectively. i and b g These represent the bias layer parameters of the sigmoid and tanh function paths in the update gate, respectively.

[0027] Preferably, the mathematical expression for the output gate is:

[0028] o t =σ(W xo x t +W ho h t-1 +b o )

[0029] h t =tanh(C t )*o t

[0030] Where h tIndicates the output gate output; W xo W ho These represent the current network state and the weights of the input-output gate pathways of the network cells at the previous time step, respectively; b o This represents the bias layer parameters of the output gate; Ct is the cell state value at the current moment of the network.

[0031] Preferably, the specific implementation method of S4 is as follows:

[0032] First, radar is used to acquire the target aircraft's motion parameters at nine consecutive time points. When any of these motion parameters are missing, a fast transfer method is used to directly approximate the target's flight dynamics and kinematics models, obtaining approximate values ​​of the control quantities during the target's maneuvering process. Then, the target's flight state is predicted, and the missing motion parameters at the time points are estimated to supplement the motion parameters at the nine consecutive time points. After online data training, an LSTM network is used to predict the target's state information at the tenth time point. If the motion parameters at the nine consecutive time points are not missing, the LSTM network is directly used after online data training to obtain the target's state information prediction at the tenth time point, completing the complete trajectory prediction.

[0033] A trajectory prediction system for targets under high-maneuver conditions based on rapid transfer, based on the aforementioned trajectory prediction method combining rapid transfer and LSTM neural network, is characterized by comprising:

[0034] Kinematics model acquisition module: used to establish the kinematics model of the target's maneuvering flight;

[0035] Dynamics model acquisition module: used to establish the target maneuver dynamics model;

[0036] The integrated model acquisition module is used to construct mathematical models for fast propagation methods and LSTM networks.

[0037] Trajectory prediction module: Used to acquire the motion parameters of enemy aircraft using radar, and then perform trajectory prediction based on a mathematical model that combines a maneuvering flight kinematics model, a maneuvering dynamics model, a fast transfer method, and an LSTM network.

[0038] Compared with existing technologies, the present invention has the following advantages: The present invention provides a trajectory prediction method for large maneuvering conditions of targets based on rapid transfer. When the aircraft is maneuvering, the motion parameters of the enemy aircraft are first obtained based on radar, and the maneuver prediction is performed using an LSTM neural network. When radar data is missing and cannot form a training dataset for the LSTM neural network, the rapid transfer method is further used to directly approximate the solution of the target flight dynamics and kinematic model and obtain approximate values ​​of the control quantities during the target maneuver. Then, the target flight state is predicted to supplement radar data and further provide a training dataset for the LSTM network. This allows the LSTM network to still obtain relatively accurate maneuver prediction results even when radar data is lost. In other words, the rapid transfer method can assist the LSTM network in maneuver prediction under the condition of missing radar data. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the ground coordinate system and the aircraft coordinate system;

[0040] Figure 2 A flowchart illustrating the algorithm for rapid evolution of uncertain parameters;

[0041] Figure 3 Flowchart for rapid evolutionary maneuver trajectory prediction;

[0042] Figure 4 A schematic diagram of the maneuver trajectory, data points, and corresponding control variables;

[0043] Figure 5 This is a schematic diagram of a maneuver prediction algorithm based on a combination of a fast transfer method and an LSTM network.

[0044] Figure 6 This is a motion prediction method that combines a fast transfer method with an LSTM network. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0046] A trajectory prediction method based on fast pass-through combined with an LSTM neural network, characterized by the following steps:

[0047] S1: Establish a kinematic model of the target maneuvering flight;

[0048] S2: Establish the target maneuver dynamics model;

[0049] S3: Construct a mathematical model for the fast transfer method and LSTM network;

[0050] S4: Target trajectory prediction based on mathematical models of maneuvering flight kinematics, maneuvering dynamics, fast transfer methods, and LSTM networks.

[0051] The specific method for establishing the target maneuvering flight kinematic model in S1 is as follows: Based on the construction of the corresponding northeast coordinate system of our carrier aircraft and the enemy target aircraft, the target maneuvering flight kinematic model is derived according to the geometric and angular relationship between our carrier aircraft and the enemy target aircraft.

[0052] The method for calculating the target's position coordinates relative to the ground is as follows:

[0053] The target's position coordinates relative to the ground (N) t E t D t As shown in the following formula:

[0054]

[0055] Where, N p E p D p Let α and β be the coordinates of our carrier aircraft in the ground coordinate system, respectively, and let R be the relative distance between the target aircraft and the carrier aircraft.

[0056] The target's velocity relative to the ground inertial coordinate system is as follows:

[0057]

[0058] Where V Nt V Et V Dt V represents the velocity relative to the ground in the target aircraft's ground inertial coordinate system, oriented north, east, and at the geocentric direction. Np V Ep V Dp The velocity relative to the ground in the geographic north, geographic east, and geocentric direction of our aircraft's ground inertial coordinate system; These are the differentials of the azimuth angle and the elevation angle of the geographic system, respectively.

[0059] The target maneuver dynamics model in S2 is represented by the following two equations:

[0060]

[0061]

[0062] In the formula, n x n yγ and θ represent the tangential overload, normal overload, and roll angle about the velocity axis, respectively; V, θ, and ψ represent the aircraft's flight speed, track inclination angle, and heading angle corresponding to the velocity vector, respectively. These are the derivatives of the flight speed, the track inclination angle, and the heading angle of the corresponding velocity vector, respectively.

[0063] The target maneuver dynamics model is a three-degree-of-freedom dynamics model.

[0064] The mathematical model for constructing the fast transfer method and LSTM network in S3 is as follows:

[0065] For the fast propagation method, the state variable parameter set is first obtained, a central state variable nominal point is determined, and the deviation values ​​between the central state variable nominal point and the other state points are calculated. Then, the central state variable nominal point is integrated in one step to obtain the state variable nominal point at the next time step. The deviation values ​​are transformed to obtain all the deviation values ​​at the next time step. The deviations are then substituted into the state variables at the next time step to obtain all the state variable parameter sets at the next time step, thus completing the relevant modeling of the fast propagation method. The method used to transform the deviation values ​​to obtain all the deviation values ​​at the next time step is the Taylor polynomial expansion method. For the modeling method of LSTM networks, it is necessary to construct the specific mathematical expressions of the "forget gate", "update gate", and "output gate" involved in the LSTM network. At the same time, based on the gradient descent method, the specific mathematical expression of the internal weight update formula of the LSTM network is constructed so that the network forms a closed loop and can continuously iterate, thus completing the relevant modeling of the LSTM network.

[0066] The specific implementation method of S4 is as follows:

[0067] Based on four consecutive time points, the target's motion state at each of the four moments is acquired. First, the airborne radar of our aircraft acquires the position and velocity of the fighter jet from the first time point to the second time point. Based on the target's maneuvering flight kinematics model, the position and velocity of the target fighter jet in the ground coordinate system are calculated. Based on the target's maneuvering dynamics model, the control quantity at the first time point is calculated. Then, the target's motion state at the third time point is acquired using a rapid transfer method. The control quantity at the second time point is determined based on the target's motion state at the third time point. Finally, based on the target's motion state at the third time point and the control quantity at the second time point, the target's state information at the fourth time point is obtained, thus completing the target's maneuver prediction. The calculation method for the control quantity at the first time point is as follows:

[0068]

[0069]

[0070] Where V, θ, and ψ are the aircraft's flight speed, track inclination angle, and heading angle of the corresponding velocity vector, respectively. The derivatives of the flight speed, the track inclination angle, and the corresponding velocity vector heading angle, respectively, n x n y γ and γ are the control parameters at the first time point.

[0071] Example:

[0072] A trajectory prediction method for targets under high-speed maneuvering conditions based on rapid transmission:

[0073] Step 1: Establish a kinematic model of the target's maneuvering flight;

[0074] Step 2: Establish the target maneuver dynamics model;

[0075] Step 3: Construct the mathematical model of the fast transmission method and LSTM network;

[0076] Step 4: Predict target maneuvering based on the mathematical model of maneuvering flight kinematics, maneuvering dynamics, and rapid transfer method.

[0077] In step 1, attached Figure 1 This refers to the ground coordinate system for the aircraft and the fighter jet, specifically the northeast-northeast coordinate system.

[0078] The position coordinates (N) of the target fighter relative to the ground can be obtained from geometric relationships. t E t D t As shown in the following formula:

[0079]

[0080] In the formula, α and β are the azimuth and elevation angles in the geographic system, respectively. R is the relative distance between the target aircraft and the carrier aircraft, given by radar data.

[0081] Differentiating both sides of equation (1), we obtain the velocity of the target relative to the ground inertial coordinate system as follows:

[0082]

[0083] First, the radar data is processed to obtain the position of our fighter jet, the radial distance and speed between our fighter jet and the enemy fighter jet, and the azimuth and pitch angles of our fighter jet relative to the geographic coordinate system. The position and speed of the enemy fighter jet relative to the ground coordinate system can be obtained through equation (2).

[0084] In step 2, in the ground inertial coordinate system, the fighter jet model adopts a three-degree-of-freedom dynamic / kinematic model, expressed by the following two equations:

[0085]

[0086]

[0087] In the formula, V represents the target's flight speed.

[0088] In step 3, attach Figure 2 This is a flowchart illustrating the algorithm for rapid evolution (rapid propagation) of uncertain parameters. Assume that the sampling label for a certain uncertain parameter is... The parameters of the remaining N associated sampling points are Assume the state vector increment of N associated sampling points is Right now The set of state deviations arising from the evolution of N uncertain parameters can be represented as: Since the nominal state parameter x0 has been obtained from the evolution of the uncertain parameters, and the state deviation Δx0 of each uncertain parameter evolution has also been obtained, each point used in the range of uncertain parameters can be described as an associated individual x related to the nominal state x0. i Then any sampling point within the range of this uncertain parameter can be described as:

[0089]

[0090] In the formula, the symbol [·] indicates that the variable within the square brackets has a polynomial form.

[0091] Furthermore, a Taylor expansion is performed on the performance evaluation evolution function near the nominal point x0; and a Runge-Kutta integrator in polynomial form is used to map the initial polynomial state to the orbital state at a specific moment, obtaining a polynomial solution [x] with the initial state deviation Δx0 as the variable. f That is, an approximate solution to solution (1):

[0092]

[0093] In the formula, j = j1 + ... + j6 is the order of each term in the polynomial approximation solution, d represents the index value of the state vector, and x f =Φ(t) f ;t0,x0) means that at t f The time corresponds to the state of the uncertain point x0, [x f ] represents the solution of the polynomial. The corresponding Taylor expansion coefficients are given directly by the polynomial calculation tool.

[0094] Then, substitute the sets of states of other associated sampling points into the polynomial solution (6). It is possible to obtain the i-th sampling point at t f The set of approximate numerical solutions of the state at time t. Within the framework of polynomial algebra, the traditional Runge-Kutta numerical integration method can be easily generalized to its polynomial form, transforming all nonlinear solutions into polynomial operations. Meanwhile, in step 3, according to the appendix... Figure 3 For modeling LSTM networks, it is necessary to construct specific mathematical expressions for the network's gates, such as the "forget gate," "update gate," and "output gate," as shown below:

[0095] The mathematical expression output by the "forget gate" is as follows:

[0096] f t =σ(W xf x t +W hf h t-1 +b f (13)

[0097] Where f t Indicates the "Forgot Gate" output; W xf W hf x represents the current network state and the weights of the network cell inputs to the "forget gate" pathway at the previous time step, respectively; t and h t-1 These represent the network state and the network cell from the previous time step, respectively; b f The bias layer parameters represent the "forget gate"; σ represents the sigmoid function, with the following expression:

[0098]

[0099] The mathematical expression output by the "update gate" is as follows:

[0100]

[0101] Where u t Indicates the "update gate" output; W xi W hi W represents the current network state and the weights of the network cell inputs to the sigmoid function in the "update gate" pathway, respectively. xg W hg b represents the current network state and the weights of the tanh function input from the network cell in the previous time step into the "update gate" pathway, respectively. i and b g These represent the bias layer parameters of the sigmoid and tanh function paths in the "update gate," respectively; the specific expression for tanh is:

[0102]

[0103] The mathematical expression output by the "output gate" is as follows:

[0104]

[0105] Where h t Indicates the output of the "output gate"; W xo W ho These represent the current network state and the weights of the network cell inputs to the "output gate" pathway at the previous time step, respectively; b o The bias layer parameters represent the "output gate"; Ct represents the cell state value at the current moment in the network. For the input-output training of the LSTM network, taking the x-direction of the fighter jet's motion as an example, the input matrix of the sliding module is constructed as follows:

[0106]

[0107] The output matrix is ​​as follows:

[0108] [x(6) x(7) x(8) x(9)] (19)

[0109] Where x(i), i = 1, 2, ..., 9, refers to t. i The x-coordinate of the fighter jet is determined by the radar. After acquiring nine x-coordinate data points of the fighter jet, they are numbered 1-9. The input-output training set is constructed according to equations (18) and (19). After training, the trained LSTM network is used to input the x-coordinate sequence [x(5) x(6) x(7) x(8) x(9)]. T Then, the predicted value of data x (10) numbered 10 can be obtained. After the radar acquires the 10th data point, the input-output training set of data points numbered 2-10 is constructed according to equations (18) and (19) to predict the predicted value of data x (11) numbered 11. After the 11th data point is acquired, the training dataset of data points numbered 3-11 is constructed for training and prediction, and so on.

[0110] In step 4, attach Figure 4 This is a flowchart for predicting maneuver trajectories. (Attached) Figure 4 This is a schematic diagram of the maneuver trajectory, data points, and corresponding control variables. (Based on the attached diagram...) Figure 5 It can be seen that there are four time points, and the fighter jet corresponds to three state variables X at times t1-t3 respectively. t1 ,X t2 ,X t3 The state quantity corresponds to the fighter jet's position and velocity, i.e., X. ti =[P i V iThis method, based on a three-degree-of-freedom particle dynamics model, can use the relevant data at the third time point as initial values ​​to predict the aircraft positions at the fourth, fifth, and sixth time points, enabling multi-step prediction. However, its accuracy is slightly lower than that of LSTM network prediction. For trajectory prediction based on LSTM networks, the principle is to use the target's motion state at nine consecutive time points acquired by radar. After online data training, the target state information at the tenth time point can be obtained. However, due to the characteristics of LSTM neural networks, they can only predict the target position at the tenth time point and cannot further predict the aircraft positions at the eleventh time point and subsequent time points; that is, they can only perform single-step prediction and not multi-step prediction. During radar observation, target loss often occurs, leading to missing radar observation data. When data is missing, it is difficult to construct a training dataset for the LSTM neural network, causing the LSTM network prediction algorithm to fail. In this case, a maneuver prediction method based on the fast transfer method should be considered. If prediction accuracy is still required, a combination of the fast transfer method and the LSTM neural network maneuver prediction method can be further considered. Figure 6 This is a maneuver prediction method that combines the fast transfer method with an LSTM network. When the radar loses data points, the maneuver prediction algorithm based on the fast transfer method is used to predict the aircraft position at the fourth, fifth, and sixth time points, in order to supplement the lost radar data. After the lost radar data is supplemented, the maneuver prediction algorithm based on the LSTM neural network can be used to further predict the aircraft position.

[0111] A trajectory prediction system based on fast pass-through combined with an LSTM neural network includes:

[0112] Kinematics model acquisition module: used to establish the kinematics model of the target's maneuvering flight;

[0113] Dynamics model acquisition module: used to establish the target maneuver dynamics model;

[0114] The integrated model acquisition module is used to construct mathematical models for fast propagation methods and LSTM networks.

[0115] Trajectory prediction module: Used to acquire the motion parameters of enemy aircraft using radar, and then perform trajectory prediction based on a mathematical model that combines a maneuvering flight kinematics model, a maneuvering dynamics model, a fast transfer method, and an LSTM network.

[0116] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by the specification, can make many other modifications without departing from the scope of the claims of the present invention, and all of these modifications are within the scope of protection of the present invention.

Claims

1. A trajectory prediction method based on fast pass-through combined with an LSTM neural network, characterized in that, Includes the following steps: S1: Establish a kinematic model of the target maneuvering flight; S2: Establish the target maneuver dynamics model; S3: Construct a mathematical model for the fast transfer method and LSTM network; S4: Use radar to acquire the motion parameters of enemy aircraft, and then use a mathematical model that combines the maneuvering flight kinematics model, the maneuvering dynamics model, and the fast transfer method with the LSTM network to predict the trajectory of the target. The specific mathematical model of the fast transfer method in S3 is as follows: First, obtain the set of state variables parameters, determine a central state variable nominal point, calculate the deviation value between the central state variable nominal point and the other state points, then perform a one-step integration on the central state variable nominal value to obtain the state variable nominal point at the next time step, transform the deviation value to obtain all the deviation values ​​at the next time step, and then substitute the deviations into the state variables at the next time step to obtain all the state variable parameter sets at the next time step, thus completing the relevant modeling of the fast transfer method. The detailed steps are as follows: Assume that the sampling label of a certain uncertain parameter is called the remaining The parameters of the associated sampling points are: ,assumed The state vector increment of each associated sampling point is ,Right now , , , , , , The set of state deviations arising from the evolution of uncertain parameters can be represented as: Due to nominal state parameters The state deviations of the evolution of each uncertain parameter have been obtained. It has also been determined that, therefore, each point used in the range of uncertain parameters can be described as relative to the nominal state. Related individuals Then any sampling point within the range of this uncertain parameter can be described as: （1） In the formula, the symbol This indicates that the variable within the square brackets has a polynomial form; At the nominal point The efficiency evaluation evolution function is subjected to a Taylor expansion; and a Runge-Kutta integrator in polynomial form is used to map the initial polynomial state to the orbital state at a specific moment, obtaining the initial state deviation. The solution in polynomial form for variables That is, an approximate solution to solution (1): （2） In the formula, Let the order of each term in the approximate solution of the polynomial be the order of the term. The index value Y represents the state vector. Indicates in The time corresponds to the uncertain adoption point state, Represents the solution of the polynomial. The corresponding Taylor expansion coefficients are given directly by the polynomial calculation tool.

2. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 1, characterized in that, The specific method for establishing the target maneuvering flight kinematic model in S1 is as follows: Based on the construction of the corresponding northeast coordinate system of our carrier aircraft and the enemy target aircraft, the target maneuvering flight kinematic model is derived according to the geometric and angular relationship between our carrier aircraft and the enemy target aircraft.

3. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 1, characterized in that, The target maneuver dynamics model in S2 is represented by the following two equations: In the formula, , γ and γ represent the tangential overload, normal overload, and roll angle about the velocity axis, respectively; , and These are the fighter jet's flight speed, track inclination angle, and the heading angle corresponding to the velocity vector. These are the derivatives of the flight speed, the track inclination angle, and the heading angle of the corresponding velocity vector, respectively.

4. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 1, characterized in that, The specific mathematical model method for constructing LSTM networks in S3 is as follows: We construct specific mathematical expressions for the forget gate, update gate, and output gate in the LSTM network. At the same time, we construct specific mathematical expressions for the internal weight update formula of the LSTM network based on the gradient descent method, so that the network forms a closed loop and can continuously iterate, thus completing the relevant modeling of the LSTM network.

5. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 4, characterized in that, The mathematical expression for the forget gate is: in, f t Indicates the output of the forget gate; W xf , W hf These represent the current network state and the weights of the network cell inputs to the forget gate pathway at the previous time step, respectively. x t and h t-1 These represent the network state and the network cell at the previous time step, respectively. b f This represents the bias layer parameters of the forget gate.

6. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 4, characterized in that, The mathematical expression for the update gate output is as follows: in u t This indicates an update to the gate output; W xi , W hi These represent the current network state and the weights of the network cells input to the sigmoid function in the update gate, respectively. W xg , W hg Let represent the current network state and the weights of the tanh function input to the update gate from the previous network cell, respectively. b i and b g These represent the bias layer parameters of the sigmoid and tanh function paths in the update gate, respectively.

7. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 4, characterized in that, The mathematical expression for the output gate is: in h t Indicates the output of the output gate; W xo , W ho These represent the network state at the current moment and the weights of the input-output gate pathways of the network cells at the previous moment, respectively. b o This represents the bias layer parameters of the output gate; Ct is the cell state value at the current moment of the network.

8. The trajectory prediction method based on fast pass-through combined with LSTM neural network according to claim 1, characterized in that, The specific implementation method of S4 is as follows: First, radar is used to acquire the target aircraft's motion parameters at nine consecutive time points. When any of these motion parameters are missing, a fast transfer method is used to directly approximate the target's flight dynamics and kinematics models, obtaining approximate values ​​of the control quantities during the target's maneuvering process. Then, the target's flight state is predicted, and the missing motion parameters at the time points are estimated to supplement the motion parameters at the nine consecutive time points. After online data training, an LSTM network is used to predict the target's state information at the tenth time point. If the motion parameters at the nine consecutive time points are not missing, the LSTM network is directly used after online data training to obtain the target's state information prediction at the tenth time point, completing the complete trajectory prediction.

9. A trajectory prediction system for targets under high-maneuver conditions based on rapid transfer, based on the trajectory prediction method based on rapid transfer combined with LSTM neural network as described in any one of claims 1-8, characterized in that, include: Kinematics model acquisition module: used to establish the kinematics model of the target's maneuvering flight; Dynamics model acquisition module: used to establish the target maneuver dynamics model; The integrated model acquisition module is used to construct mathematical models for fast propagation methods and LSTM networks. Trajectory prediction module: Used to acquire the motion parameters of enemy aircraft using radar, and then perform trajectory prediction based on a mathematical model that combines a maneuvering flight kinematics model, a maneuvering dynamics model, a fast transfer method, and an LSTM network.

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