Projectile trajectory and launching point recursive prediction method based on deep learning

Abstract

The invention relates to a projectile trajectory and launching point recursive prediction method based on deep learning. Comprising the following steps: performing numerical simulation on a modified particle trajectory equation under different sampling conditions by adopting a fourth-order Runge-Kutta algorithm to obtain data; sorting and dividing the data into a training set and a test set; building a forward projectile trajectory recursive prediction algorithm model and a projectile launching point recursive prediction model with data set reverse input; respectively inputting the training set into a forward projectile trajectory prediction algorithm model and a projectile launching point prediction model with the reversely input data set for training; and carrying out recursive prediction on the trajectory and the launching point of the projectile. According to the method, one network structure is adopted for training two prediction models for the first time, and the launching point of the projectile can be predicted by adjusting the format of input data; and the anti-guide interception capability and the attack capability on the enemy basis are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of recursive prediction of uncontrolled projectile trajectories of artillery, and specifically relates to a recursive prediction method for projectile trajectories and launch points based on deep learning. Background Art

[0002] The research on the recursive prediction of the trajectory and launch point of incoming projectiles is of great significance. Accurate prediction results can significantly improve the responsiveness and interception accuracy of air defense and anti-missile systems. In modern warfare, the key to ensuring victory in battle is to quickly identify and accurately predict the trajectory of incoming enemy projectiles. By using advanced algorithms and models to conduct real-time analysis of the flight path of incoming projectiles, the threat level can be effectively assessed, thereby providing a scientific basis for the defense system and formulating optimized interception strategies. At the same time, the recursive prediction of the launch point helps to determine the source of the enemy's attack and provide important clues for target strikes and counterattacks. This technological advancement not only enhances the flexibility and accuracy of combat command, but also reduces the risk of misjudgment and accidental injury, and improves the overall combat effectiveness.

[0003] Compared with traditional prediction algorithms, deep learning can automatically extract features from large amounts of data without having to manually design complex feature extraction algorithms. This self-learning ability enables deep learning models to handle complex nonlinear relationships, is highly adaptable, and can better capture dynamic changes and environmental impacts during projectile flight, thereby improving prediction accuracy. Traditional methods often rely on simplified mathematical models and may not be able to effectively cope with complex and uncertain battlefield environments.

[0004] Among them, the article "Projectile Trajectory Prediction Based on Convolutional Neural Network and Long Short-Term Memory Neural Network" published by Zheng Zhiwei, Guan Xueyuan and others in the Acta Ordnance in 2023 adopts a multi-step prediction method, which is difficult to extend the prediction time without ensuring accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a recursive prediction method for projectile trajectory and launch point based on deep learning, which solves the problem of extending the prediction time while ensuring accuracy. At the same time, a network structure is proposed for the first time, two models are trained, and they are used for future trajectory prediction and reverse launch point prediction respectively.

[0006] The technical solution to achieve the purpose of the present invention is: a projectile trajectory and launch point recursive prediction method based on deep learning, comprising the following steps:

[0007] Step (1): using the fourth-order Runge-Kutta algorithm to perform numerical simulation on the modified particle trajectory equation under different sampling conditions to obtain data;

[0008] Step (2): Organize the data into training set and test set;

[0009] Step (3): Build a forward projectile trajectory recursive prediction algorithm model and a projectile launch point recursive prediction model with reverse input of the data set;

[0010] Step (4): input the training set into the forward projectile trajectory prediction algorithm model and the projectile launch point prediction model with the data set reversely input for training;

[0011] Step (5): Input the test set into the trained forward projectile trajectory prediction algorithm model and the reverse launch point prediction model to perform recursive predictions on the trajectory and launch point of the projectile respectively.

[0012] Furthermore, the modified particle trajectory equation in step (1) is:

[0013]

[0014]

[0015] V ry =V y (20)

[0016] V rz =V z -W z (twenty one)

[0017] V rx =V x -W x (twenty two)

[0018] The parameters involved in the formula are defined as follows:

[0019]

[0020] Furthermore, the sampling conditions in step (1) are:

[0021] parameter Sample value Sampling interval Initial velocity / (m / s) (700,1000] 5 Angle of incidence / (°) (35,55] 1 .

[0022] Furthermore, the time, range, altitude and lateral position information of each trajectory are saved to construct a data set. The format of the saved data set is Traj = {T1, T2, ..., T 1200}, where any trajectory is represented by Where i is the i-th coordinate point, n is the n-th trajectory, and t is the timestamp corresponding to the current coordinate point;

[0023] The data set is divided into training set, test set and validation set according to the ratio of 8:1:1;

[0024] The trajectory set should be normalized before training;

[0025] The normalization formula is as follows:

[0026]

[0027] In the formula, T is a track in the data set. The data in T are normalized separately. min and T max is the minimum and maximum value of the corresponding data, T N The data are normalized.

[0028] Furthermore, the forward projectile trajectory recursive prediction algorithm model in step (3) adopts the CNN-BiLSTM model, and an attention mechanism is added to the CNN-BiLSTM model;

[0029] The CNN-BiLSTM model has two convolutional layers. The number of convolution kernels in the first layer is set to 32 and the length is 3. The number of convolution kernels in the second layer is set to 64 and the length is 3. Two independent LSTM layers are used to perform forward propagation and backward propagation according to the time series, respectively, to form BiLSTM.

[0030] The features extracted by CNN are used as the initial input of BiLSTM, BiLSTM is used to extract temporal features, and the number of neurons in the BiLSTM layer is set to 64.

[0031] Furthermore, the learning process of BiLSTM consists of four parts: forget gate, input gate, update memory unit and output gate. The calculation method involved in these four parts is as follows:

[0032] Forget Gate

[0033] f t =σ(W f ·[h t-1 ,x t ]+b f ) (twenty four)

[0034] Input Gate

[0035] i t =σ(W i ·[h t-1 ,x t ]+b i ) (25)

[0036]

[0037] Update memory unit

[0038]

[0039] Output Gate

[0040] O t =σ(W O ·[h t-1 ,x t ]+b O ) (28)

[0041] h t =O t *tanh(C t ) (29)

[0042] Where σ is the sigmoid function, W k ,b k (k=f,i,c,o) are the weight matrices and bias terms of the forget gate, input gate, and output gate respectively, h t is the hidden state output of the time step, i t and O t are the activation values ​​of the input gate and the output gate, is the candidate value vector.

[0043] Furthermore, the attention mechanism is as follows:

[0044] Calculate the similarity between Query and Key

[0045] e ij =D(q i ,p j ) (30)

[0046] Normalize the similarity

[0047] a ij =softmax(e ij ) (31)

[0048] Weighted Sum

[0049]

[0050] The D operation represents the dot product function, q is the query element, p is the element address, e is the similarity between elements, and c is the weight;

[0051] Finally, a fully connected layer is added. Since the prediction result is the coordinate of three-dimensional space, the number of neurons in the fully connected layer is set to 3.

[0052] Furthermore, step (4) specifically includes the following steps:

[0053] Step (41): For the prediction of the future trajectory of the projectile, the processed data set is directly input into the training of the recursive prediction model of the future trajectory of the projectile;

[0054] Step (42): Launch point prediction requires the training set to be reversely arranged and input into the projectile launch point recursive prediction model, thereby realizing the advantage of training two models with one network structure.

[0055] Furthermore, step (5) specifically includes the following steps:

[0056] Step (51): For the test set of the future trajectory prediction of the projectile, the The trajectory points are input into the recursive prediction model of the future trajectory of the projectile for prediction.

[0057] Step (52): The test set for projectile launch point prediction will use the first detected by the radar The trajectory points are input into the projectile launch point recursive prediction model for prediction in turn;

[0058] Step (53): Output prediction results

[0059] Compared with the prior art, the present invention has the following significant advantages:

[0060] The present invention can ensure the prediction accuracy while increasing the prediction time length, can provide sufficient response time for missile interception, and effectively improve the missile interception probability.

[0061] This paper integrates the advantages of models such as convolutional neural network (CNN) feature extraction, bidirectional long short-term memory network (BiLSTM) and attention mechanism (Attention), and proposes a recursive prediction model. At the same time, the present invention proposes a network structure, trains two models, and uses them for future trajectory prediction and reverse emission point prediction respectively. This scheme can achieve accurate prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is the prediction result of the future trajectory of the projectile of the present invention.

[0063] Figure 2 It is the predicted value of the projectile range direction of the present invention.

[0064] Figure 3 It is the predicted value of the projectile shooting height direction of the present invention.

[0065] Figure 4 It is the predicted value of the lateral deviation direction of the projectile of the present invention.

[0066] Figure 5 It is the predicted value of the range direction of the projectile launching point of the present invention.

[0067] Figure 6 It is the predicted value of the high direction of the projectile launch point shooting of the present invention.

[0068] Figure 7It is the predicted value of the lateral deviation direction of the projectile launching point of the present invention. DETAILED DESCRIPTION

[0069] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0070] The present invention provides a recursive prediction method for projectile trajectory and launch point based on deep learning, which solves the problem of extending the prediction time while ensuring accuracy. At the same time, a network structure is proposed for the first time, and two models are trained and used for future trajectory prediction and reverse launch point prediction respectively. The specific steps include:

[0071] Step (1): using the fourth-order Runge-Kutta algorithm to perform numerical simulation on the modified particle trajectory equation under different sampling conditions to obtain data;

[0072] Step (2): Organize the data into training set and test set, and perform data preprocessing;

[0073] Step (3): Build a forward projectile trajectory recursive prediction algorithm model and a projectile launch point recursive prediction model with reverse input of the data set;

[0074] Step (4): input the training set into the forward projectile trajectory prediction algorithm model and the projectile launch point prediction model with the data set reverse input respectively;

[0075] Step (5): Input the test set into the trained forward projectile trajectory prediction algorithm model and the reverse launch point prediction model to perform recursive predictions on the trajectory and launch point of the projectile respectively.

[0076] Furthermore, step (1) "using the fourth-order Runge-Kutta algorithm to perform numerical simulation on the modified particle trajectory equation under different sampling conditions to obtain data" is specifically as follows:

[0077] The modified particle trajectory equation is:

[0078]

[0079]

[0080] V ry =V y (20)

[0081] V rz =V z -W z (twenty one)

[0082] V rx =V x -W x (twenty two)

[0083] The parameters involved in the formula are defined as follows:

[0084]

[0085] The sampling conditions are determined as follows:

[0086] parameter Sample value Sampling interval Initial velocity / (m / s) (700,1000] 5 Angle of incidence / (°) (35,55] 1

[0087] Furthermore, step (2) "dividing the data into a training set and a test set, and performing data preprocessing operations" is specifically as follows:

[0088] The data set is divided as follows:

[0089] The time, range, altitude, and lateral deviation of each trajectory are saved to construct a data set. The format of the saved data set is Traj = {T1, T2, ..., T 1200}, any trajectory can be expressed as Where i is the i-th coordinate point, n is the n-th trajectory, and t is the timestamp corresponding to the current coordinate point. The dataset is divided into training set, test set, and validation set according to the ratio of 8:1:1.

[0090] The data preprocessing method is:

[0091] Before training, the trajectory set should be normalized. Normalization can unify data of different dimensions and ranges to a standard scale, thereby eliminating the magnitude differences between data and avoiding certain features dominating the learning process of the model. It helps to accelerate convergence and improve the training efficiency of the model. The formula is as follows:

[0092]

[0093] In the formula, T is a track in the data set. The data in T are normalized separately. min and T max is the minimum and maximum value of the corresponding data, T N The data are normalized.

[0094] Furthermore, step (3) "building a forward projectile trajectory recursive prediction algorithm model and a projectile launch point recursive prediction model with reverse input of the data set" is specifically as follows:

[0095] The network model is:

[0096] In the trajectory prediction model, the convolution layer in the CNN module can extract local features of the trajectory data. Its feature extraction capability is constrained by the size of the convolution kernel. The pooling layer is used to reduce the feature dimension and discard irrelevant features to reduce the complexity of the model. In order to balance the computing resources and prediction effect, two convolution layers are set. The number of convolution kernels in the first layer is set to 32 and the length is 3. The number of convolution kernels in the second layer is set to 64 and the length is 3.

[0097] Currently, LSTM is often used in forward trajectory prediction, but LSTM mainly processes past information. Therefore, two independent LSTM layers are used to perform forward propagation and backward propagation according to the time series, thus forming BiLSTM to enhance the model's ability to learn time series features.

[0098] The learning process of BiLSTM is mainly composed of four parts: forget gate, input gate, update memory unit and output gate. The calculation methods involved in these four parts are as follows:

[0099] 1. Forget Gate

[0100] f t =σ(W f ·[h t-1 ,x t ]+b f ) (twenty four)

[0101] 2. Input Gate

[0102] i t =σ(W i ·[h t-1 ,x t ]+b i ) (25)

[0103]

[0104] 3. Update memory unit

[0105]

[0106] 4. Output Gate

[0107] O t =σ(W O ·[h t-1 ,x t ]+b O ) (28)

[0108] h t =O t *tanh(C t ) (29)

[0109] Where σ is the sigmoid function, W k ,b k (k=f,i,c,o) are the weight matrices and bias terms of the forget gate, input gate, and output gate respectively, h t is the hidden state output of the time step, i t and O t are the activation values ​​of the input gate and the output gate, is the candidate value vector.

[0110] If the input trajectory sequence is too long, LSTM will also have information loss problems. Therefore, the features extracted by CNN are used as the initial input of BiLSTM, BiLSTM is used to extract time features, and the number of neurons in the BiLSTM layer is set to 64. At the same time, adding an attention mechanism to the CNN-BiLSTM model enhances the model's ability to identify key turning points of the trajectory, reduces the prediction error, and improves the prediction accuracy. The calculation method involved in the attention mechanism is:

[0111] 1. Calculate the similarity between Query and Key

[0112] e ij =D(q i ,p j ) (30)

[0113] 2. Normalize the similarity

[0114] a ij =softmax(e ij ) (31)

[0115] 3. Weighted sum

[0116]

[0117] The D operation represents the dot product function, q is the query element, p is the element address, e is the similarity between elements, and c is the weight.

[0118] Finally, a fully connected layer is added. Since the predicted output is the coordinates of three-dimensional space, the number of neurons in the fully connected layer is set to 3.

[0119] Furthermore, step (4) "inputting the training set into the forward projectile trajectory prediction algorithm model and the projectile launch point prediction model with the data set reversely inputted" specifically includes the following steps:

[0120] Step (41): For the prediction of the future trajectory of the projectile, it is only necessary to directly input the processed data set into the training of the recursive prediction model of the future trajectory of the projectile;

[0121] Step (42): Launch point prediction requires the training set to be reversely arranged and input into the projectile launch point recursive prediction model, thereby realizing the advantage of training two models with one network structure.

[0122] Furthermore, step (5) "inputting the test set into the trained forward projectile trajectory prediction algorithm model and the reverse launch point prediction model to perform recursive prediction of the projectile trajectory and launch point respectively" specifically includes the following steps:

[0123] Step (51): For the test set of the future trajectory prediction of the projectile, the The trajectory points are input into the recursive prediction model of the future trajectory of the projectile for prediction.

[0124] Step (52): The test set for projectile launch point prediction will use the first detected by the radar The trajectory points are input into the projectile launch point recursive prediction model for prediction.

[0125] Recursive prediction is usually used to handle long-term series task prediction. Recursive prediction is a method that gradually utilizes single-step prediction results. It is flexible and interpretable. The mathematical expression of recursive prediction is as follows:

[0126]

[0127] Using the above recursive method, the prediction results are output step by step.

[0128] Example

[0129] The data in the simulation is the calculation result of the external ballistics of a 155mm howitzer under standard atmospheric conditions, where the Runge-Kutta time step is 0.01s. The data is sorted and divided, and then input into CNN, BiLSTM and Attention for training in turn, where the learning rate is set to 0.001 and the epoch is 20. The training model is saved, and the prediction samples are input in turn for prediction. Figure 2 , Figure 3 and Figure 4 They are the fitting effects of the range, altitude and lateral deviation in the forward projectile trajectory prediction results with the real data, which can accurately simulate the future flight trajectory of the projectile and improve the anti-missile interception capability. Figure 5 , Figure 6 and Figure 7 They are the prediction results of the projectile launch point, and the prediction error is small, so the enemy launch point can be effectively hit according to the prediction results.

Claims

1. A projectile trajectory and launch point recursive prediction method based on deep learning, characterized in that: The steps include: Step (1): using the fourth-order Runge-Kutta algorithm to perform numerical simulation on the modified particle trajectory equation under different sampling conditions to obtain data; Step (2): Organize the data into training set and test set; Step (3): Build a forward projectile trajectory recursive prediction algorithm model and a projectile launch point recursive prediction model with reverse input of the data set; Step (4): input the training set into the forward projectile trajectory prediction algorithm model and the projectile launch point prediction model with the data set reversely input for training; Step (5): Input the test set into the trained forward projectile trajectory prediction algorithm model and the reverse launch point prediction model to perform recursive predictions on the trajectory and launch point of the projectile respectively.

2. The method according to claim 1, characterized in that The modified particle trajectory equation in step (1) is: x2=(a a -a b )b y V r 2 (14) V ry =V y (20) V rz =V z -W z (21) V rx =V x -W x (22) The parameters involved in the formula are defined as follows:

3. The method according to claim 2, characterized in that The sampling conditions in step (1) are: 。 4. The method according to claim 3, characterized in that The time, range, altitude and lateral position information of each trajectory are saved to construct a data set. The format of the saved data set is Traj = {T1, T2, ..., T 1200 }, where any trajectory is represented by Where i is the i-th coordinate point, n is the n-th trajectory, and t is the timestamp corresponding to the current coordinate point; The data set is divided into training set, test set and validation set according to the ratio of 8:1:1; The trajectory set should be normalized before training; The normalization formula is as follows: In the formula, T is a track in the data set. The data in T are normalized separately. min and T max is the minimum and maximum value of the corresponding data, T N The data are normalized.

5. The method according to claim 4, characterized in that The forward projectile trajectory recursive prediction algorithm model in step (3) adopts the CNN-BiLSTM model, and adds an attention mechanism to the CNN-BiLSTM model; The CNN-BiLSTM model has two convolutional layers. The number of convolution kernels in the first layer is set to 32 and the length is 3. The number of convolution kernels in the second layer is set to 64 and the length is 3. Two independent LSTM layers are used to perform forward propagation and backward propagation according to the time series, respectively, to form BiLSTM. The features extracted by CNN are used as the initial input of BiLSTM, BiLSTM is used to extract temporal features, and the number of neurons in the BiLSTM layer is set to 64.

6. The method according to claim 5, characterized in that The learning process of BiLSTM consists of four parts: forget gate, input gate, update memory unit and output gate. The calculation method involved in these four parts is as follows: Forget Gate f t =σ(W f ·[h t-1 ,x t ]+b f ) (24) Input Gate i t =σ(W i ·[h t-1 ,x t ]+b i ) (25) Update memory unit Output Gate The t =σ(W O ·[h t-1 ,x t ]+b O ) (28) h t =O t *tanh(C t ) (29) Where σ is the sigmoid function, W k ,b k (k=f,i,c,o) are the weight matrices and bias terms of the forget gate, input gate, and output gate respectively, h t is the hidden state output of the time step, i t and O t are the activation values ​​of the input gate and the output gate, is the candidate value vector.

7. The method according to claim 6, characterized in that The attention mechanism is as follows: Calculate the similarity between Query and Key e ij =D(q i ,p j ) (30) Normalize the similarity the ij =softmax(e ij ) (31) Weighted Sum The D operation represents the dot product function, q is the query element, p is the element address, e is the similarity between elements, and c is the weight; Finally, a fully connected layer is added. Since the prediction result is the coordinate of three-dimensional space, the number of neurons in the fully connected layer is set to 3.

8. The method according to claim 7, characterized in that Step (4) specifically includes the following steps: Step (41): For the prediction of the future trajectory of the projectile, the processed data set is directly input into the training of the recursive prediction model of the future trajectory of the projectile; Step (42): Launch point prediction requires the training set to be reversely arranged and input into the projectile launch point recursive prediction model, thereby realizing the advantage of training two models with one network structure.

9. The method according to claim 8, characterized in that Step (5) specifically includes the following steps: Step (51): For the test set of the future trajectory prediction of the projectile, the The trajectory points are input into the recursive prediction model of the future trajectory of the projectile for prediction. Step (52): The test set for projectile launch point prediction will use the first detected by the radar The trajectory points are input into the projectile launch point recursive prediction model for prediction in turn; Step (53): Output the prediction result.

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