An Online Prediction Method for Hypersonic Vehicle Trajectory Based on Parameter Extrapolation

Abstract

The present invention relates to the technical field of on-line prediction of aircraft trajectories, and particularly to an on-line prediction method for hypersonic aircraft trajectories based on parameter extrapolation. Select hypersonic aircraft trajectory prediction parameters; estimate the hypersonic aircraft trajectory prediction parameters based on a dynamic tracking model; denoise the hypersonic aircraft trajectory prediction parameters based on ensemble empirical mode decomposition, construct a data set, and train a pre-constructed attention time series neural network model according to the data in the data set; input the data set into the trained attention time series neural network model to obtain the predicted trajectory of the hypersonic aircraft. On-line prediction of aircraft trajectories is carried out based on ensemble empirical mode decomposition and attention time series neural network. This method uses deep learning technology to model the laws of prediction parameters and denoise the prediction parameters before prediction, effectively improving the prediction accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of on-line prediction of aircraft trajectories, and in particular to an on-line prediction method for hypersonic aircraft trajectories based on parameter extrapolation. Background Art

[0002] Hypersonic aircraft generally refer to aircraft with a speed above 5 Ma and a flight altitude between 20 km and 100 km. Such aircraft have become an important means of strategic balance between countries with their characteristics of high maneuverability, high speed, and high precision, and play an important role in future battlefield situations. The world's major military powers are engaged in a fierce arms race around the research and development of hypersonic aircraft. The continuous development of hypersonic aircraft poses new severe challenges to the aerospace security of each country. Therefore, the research on hypersonic aircraft trajectory prediction is of great significance for aerospace defense interception and determination of combat intentions.

[0003] Trajectory prediction refers to predicting the motion trajectory or trend of a target within a certain period in the future. The existing research on air target trajectory prediction mainly focuses on airplanes and ballistic missiles, and there are few literatures on the research of hypersonic aircraft trajectory prediction. Since airplanes have a low speed, regular flight routes, and a large amount of historical trajectory information, which provides a good data basis for trajectory prediction, most of the existing literatures adopt methods such as polynomial modeling, machine learning, and data-driven to mine the historical trajectory rules; although ballistic missiles have a high speed, their trajectories are relatively stable, and the ballistic and landing points can be deduced according to their state variables, and mainly adopt analytical methods, numerical integration methods, regression analysis, etc. for solution. Hypersonic aircraft belong to non-inertial trajectories. Not only do they have a "jumping" characteristic longitudinally, but they can also maneuver widely laterally. Their trajectory prediction usually adopts the idea of parameter identification, which mainly includes three parts: prediction parameter selection, state estimation, and prediction method. However, due to the high maneuverability of hypersonic aircraft, the predicted parameters obtained after tracking are often non-linear and contain unknown noise, which leads to two problems: one is that it is difficult to accurately characterize the non-linear law by modeling the predicted parameters through methods such as the least squares method or linear prediction model; the other is that directly using these noisy predicted parameters for prediction will interfere with the prediction model and affect the prediction performance. Summary of the Invention

[0004] The purpose of the present invention is to aim at the defects of the existing technology and provide an on-line prediction method for hypersonic aircraft trajectories based on parameter extrapolation, which performs on-line prediction of aircraft trajectories based on ensemble empirical mode decomposition and attention time series neural network. This method uses deep learning technology to model the rules of predicted parameters and denoises the predicted parameters before prediction, effectively improving the prediction accuracy.

[0005] An online trajectory prediction method for hypersonic vehicles based on parameter extrapolation, the technical solution of which includes:

[0006] Step 1: Select the trajectory prediction parameters of the hypersonic vehicle;

[0007] Step 2: Estimate the trajectory prediction parameters of the hypersonic vehicle based on the dynamic tracking model;

[0008] Step 3: Denoise the trajectory prediction parameters of the hypersonic vehicle based on ensemble empirical mode decomposition, construct a data set, and train a pre-constructed attention time series neural network model according to the data in the data set;

[0009] Step 4: Input the data set into the trained attention time series neural network model to obtain the predicted trajectory of the hypersonic vehicle.

[0010] Preferably, the trajectory prediction parameter of the hypersonic vehicle selected in Step 1 is the aerodynamic acceleration of the vehicle.

[0011] Preferably, in Step 2, estimating the trajectory prediction parameters of the hypersonic vehicle includes estimating the aerodynamic drag acceleration, climbing force acceleration, and turning force acceleration of the vehicle.

[0012] Preferably, estimating the aerodynamic drag acceleration, climbing force acceleration, and turning force acceleration of the vehicle includes:

[0013] Convert the aerodynamic acceleration of the vehicle from the VTC coordinate system to the north-east-down ENU coordinate system;

[0014] Model the drag acceleration and lift acceleration of the vehicle as damped oscillation models, and model the sine value of the bank angle as an exponential decay model. Among them, the state equation of the target is The non-linear equation f(X) is expressed as;

[0015]

[0016] Use the formula Discretize f(X);

[0017] Among them, v x 、v y 、v z are the velocity components of the vehicle along each coordinate axis in the ENU coordinate system, μ is the gravitational constant of the earth, R e is the equivalent radius of the earth, B0 is the geographical latitude where the radar is located, ω e is the earth's rotation speed, r is the distance between the vehicle and the earth's center, They are the components of the aerodynamic acceleration in the ENU coordinate system, α D , β D , α L , β L They are the attenuation coefficients and maneuver period frequencies corresponding to the aerodynamic drag acceleration and aerodynamic lift acceleration respectively. ε is the model parameter corresponding to the sine value of the bank angle. T is the sampling interval. F(X(k)) is the Jacobian matrix of f(X(k)) with respect to X(k).

[0018] More preferably, the denoising of the hypersonic vehicle trajectory prediction parameters based on ensemble empirical mode decomposition in step three includes:

[0019] Adding Gaussian white noise to the aerodynamic acceleration signal a(t) to obtain

[0020] Performing EMD decomposition on the signal s(t) with added Gaussian white noise to obtain n IMF components and a residue where c ij (t) is the i-th IMF component obtained from the j-th EMD decomposition, and e j (t) is the residue;

[0021] Repeating the above operations M times and calculating the average values of the corresponding IMF components and residues, where the average value of the IMF components The average value of the residue is

[0022] Reconstructing the aerodynamic acceleration signal according to the average value c i (t) of the IMF components and the residue average e

[0023] More preferably, the reconstruction of the aerodynamic acceleration signal includes:

[0024] Sorting the IMF components in descending order of energy and starting to accumulate them one by one from the IMF components with higher rankings until the energy occupied reaches 90% of the original signal, obtaining the reconstructed and denoised signal, and regarding the remaining unaccumulated IMF components as noise.

[0025] More preferably, the construction of the attention time series neural network model includes:

[0026] Designing the encoder as a bidirectional LSTM model through the following formula:

[0027]

[0028] Assuming that the sequence input generated at the previous moment is The corresponding decoder is designed as:

[0029]

[0030] where x t represents the current input, h t represents the hidden layer state at the current moment, and represent the forward hidden state and the backward hidden state respectively, θ E is the adaptation parameter, T represents matrix transpose, C t-1 is the context vector, u t is the current decoder hidden state, and LSTM(·) represents the LSTM network;

[0031] The attention mechanism is added to calculate the weights of each state of the encoder, so as to increase the judgment ability when the decoder outputs. The score calculation formula e of the i-th feature vector t = v T tanh(W T h t + b), where v, W, and b are the weight matrix and the bias vector respectively, and h t is the hidden layer state;

[0032] From this, the attention probability α t = softmax(e i );

[0033] The weighted sum of the hidden layer states is calculated as where k is the length of the array.

[0034] The beneficial effects of the present invention are as follows: From the perspective of the defense side, the pneumatic acceleration is selected as the prediction parameter, and an online prediction method for the trajectory of a hypersonic vehicle based on ensemble empirical mode decomposition and attention time series neural network is proposed. This method uses deep learning technology to model the law of the prediction parameter, and denoises the prediction parameter before prediction, which can effectively improve the prediction accuracy.

[0035] 1. A dynamic tracking model is established on the basis of fully analyzing the maneuvering characteristics of hypersonic vehicles. In this dynamic tracking model, the aerodynamic drag acceleration and the lift acceleration are modeled as decaying oscillation models, and the sine value of the bank angle is modeled as an exponential decay model. It is an 11-dimensional tracking model that can estimate the value of the prediction parameter according to the relationship between the position information measured by the radar and the pneumatic acceleration, providing a data basis for trajectory prediction.

[0036] 2. A trajectory prediction method based on ensemble empirical mode decomposition and attention time series neural network (EEMD-ATSN) is proposed. This method denoises the estimated aerodynamic acceleration through ensemble empirical mode decomposition, uses the attention time series neural network to learn the features of the denoised data, and predicts the values of the aerodynamic acceleration in the future for a period of time. This model combining denoising and prediction can effectively improve the accuracy of trajectory prediction and has good prediction performance for highly maneuverable targets such as hypersonic vehicles.

[0037] 3. The research perspective of this method is based on the defender, that is, assuming that the mass, area, control amount and aerodynamic force of the hypersonic vehicle are unknown, only using radar measurement information to predict the vehicle trajectory, which is different from the previous perspective of the cooperation party. In addition, the prediction mentioned in this method is a multi-step prediction, that is, by using the predicted result as the input for the next prediction and continuously cycling, multiple time-step predictions can be obtained, which can provide an important basis for implementing aerospace defense interception and combat intention determination. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic flow chart of an online prediction method for hypersonic vehicle trajectory based on parameter extrapolation;

[0039] Figure 2 It is a schematic diagram of hypersonic vehicle trajectory;

[0040] Figure 3 It is the mode setting of the angle of attack of the hypersonic vehicle in the simulation experiment;

[0041] Figure 4 It is the maneuvering trajectory and observation trajectory of the hypersonic vehicle in the simulation experiment;

[0042] Figure 5 、 6 、7 is the EEMD decomposition diagram of the aerodynamic acceleration of the hypersonic vehicle in the simulation experiment;

[0043] Figure 8 It is the denoising effect diagram of the aerodynamic drag acceleration of the hypersonic vehicle in the simulation experiment;

[0044] Figures 9 - 11 It is the RMSE of the 180s future prediction of the aerodynamic acceleration of the hypersonic vehicle in the simulation experiment; Figure 12 It is the trajectory prediction diagram of the hypersonic vehicle in the simulation experiment. DETAILED DESCRIPTION OF THE INVENTION

[0045] In order to make the technical problems, technical solutions and beneficial effects to be solved by this application more clear and understandable, the following further details this application in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0046] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0047] It should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to this application.

[0048] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of this application, "a plurality" means two or more, unless otherwise specifically defined.

[0049] The present invention provides a method for online prediction of hypersonic vehicle trajectories based on parameter extrapolation. First, based on the six-degree-of-freedom motion equation of the hypersonic vehicle, its maneuvering characteristics and aerodynamic change laws are analyzed. Secondly, a dynamic tracking model is established to update the state information of the hypersonic vehicle according to radar measurements and to estimate the prediction parameters in real time. Then, the ensemble empirical mode decomposition is used to decompose and reconstruct the estimated prediction parameters to weaken the noise influence and avoid interference with the prediction model. Finally, the denoised prediction parameter data is used to train the attention time series neural network, and then the future aerodynamic acceleration data is predicted and the future trajectory of the hypersonic vehicle is reconstructed to achieve online prediction of the trajectory.

[0050] Embodiment 1

[0051] Figure 1 shows a preferred embodiment of this application ( Figure 1The flowchart of a hypersonic vehicle trajectory online prediction method based on parameter extrapolation provided by the first embodiment of the present application is shown. For the sake of convenience of description, only the parts related to this embodiment are shown and are described in detail as follows:

[0052] Step 1: Select hypersonic vehicle trajectory prediction parameters;

[0053] Step 2: Estimate the hypersonic vehicle trajectory prediction parameters based on the dynamic tracking model;

[0054] Step 3: Denoise the hypersonic vehicle trajectory prediction parameters based on ensemble empirical mode decomposition, construct a data set, and train a pre-constructed attention time series neural network model according to the data in the data set;

[0055] Step 4: Input the data set into the trained attention time series neural network model to obtain the predicted trajectory of the hypersonic vehicle.

[0056] Preferably, Step 1 specifically includes the following steps:

[0057] Step 1.1, establish the motion equation of the hypersonic vehicle in the glide phase;

[0058] In the semi-velocity (VTC) coordinate system, ignoring the influence of the earth's oblateness, the motion equation of the hypersonic vehicle in the glide phase is established as

[0059]

[0060] In the formula, r, λ, ζ, V, σ are all vehicle state variables, representing geocentric distance, longitude, latitude, speed, speed inclination angle and azimuth angle respectively. α and υ are control variables, representing angle of attack and bank angle respectively. a D 、a L are drag acceleration and lift acceleration respectively. The expressions of lift acceleration and drag acceleration are

[0061]

[0062] In the formula, L and D are lift and drag respectively, C L (α), C D (α) are lift coefficient and drag coefficient respectively, S is the target equivalent cross-sectional area, ρ is the atmospheric density, and m is the target mass.

[0063] Step 1.2, select hypersonic vehicle trajectory prediction parameters;

[0064] When selecting the trajectory prediction parameters of a hypersonic vehicle, the following two aspects are mainly considered: First, whether the prediction parameters can contain the control information of the hypersonic vehicle so as to enable trajectory prediction; second, whether the prediction parameters have relatively stable variation laws for easy mathematical description. According to Equations (2) and (3), the aerodynamic acceleration can fully contain the information of the control variables, and the trajectory can be reconstructed using the aerodynamic acceleration data and the vehicle state information. Next, the regularity of the aerodynamic acceleration is analyzed.

[0065] As Figure 2 shown, there are two maneuvering modes for hypersonic vehicles. The present invention mainly studies the skip-glide maneuver of the vehicle. When a hypersonic vehicle performs a skip-glide maneuver, it is mainly affected by gravity, aerodynamic drag, and aerodynamic lift. When the vehicle is in the upward climbing stage, as the vehicle altitude increases, the air density gradually decreases, and the lift force on the vehicle gradually decreases. When it rises to a certain altitude, affected by gravity and aerodynamic drag, the direction of the resultant force on the vehicle becomes downward, and the upward speed of the vehicle will gradually slow down until it becomes zero, and then it starts to move downward. As the altitude decreases, the air density gradually increases, and the aerodynamic lift gradually increases. When it descends to a certain altitude, the direction of the resultant force on the vehicle becomes upward, and the downward speed of the vehicle will gradually slow down until it becomes zero, and then it starts to climb upward again, completing one cycle of the skip maneuver. Therefore, the magnitudes of the aerodynamic drag and aerodynamic lift on the vehicle also show quasi-periodic changes with the skip state of the vehicle. It can be seen that the aerodynamic drag acceleration and aerodynamic lift acceleration of the vehicle also have quasi-periodic characteristics. The aerodynamic turning force acceleration and aerodynamic climbing force acceleration, as components of the aerodynamic lift acceleration, are related to the aerodynamic lift acceleration as shown in Equation (3). It can be seen that the aerodynamic turning force acceleration and aerodynamic climbing force acceleration are actually relationships about the aerodynamic lift acceleration and the bank angle. And the cosine or sine value of the bank angle within a short time can be regarded as a certain constant in the interval [-1, 1]. Based on this, the aerodynamic turning force acceleration and aerodynamic climbing force acceleration should have similar characteristics to the aerodynamic lift acceleration, that is, they have quasi-periodicity. Therefore, the aerodynamic acceleration contains both the control variable information and has a relatively stable variation law, so the aerodynamic acceleration is selected as the prediction parameter for the trajectory of the hypersonic vehicle.

[0066]

[0067] More preferably, the process of step two is specifically as follows:

[0068] After selecting the aerodynamic acceleration as the prediction parameter, it is also necessary to obtain the value of the aerodynamic acceleration in real time. From the analysis of the maneuvering characteristics of the hypersonic vehicle described in Step 1, the aerodynamic drag acceleration and lift acceleration of the hypersonic vehicle are modeled as damped oscillation models, the sine value of the bank angle is modeled as an exponential decay model, and based on the relationship between the components of the aerodynamic acceleration, the value of the aerodynamic acceleration can be estimated in real time during the tracking process.

[0069] Assume the state variables of the vehicle are

[0070]

[0071] where [x, y, z, v x , v y , v z are the position and velocity of the vehicle in the ENU coordinate system, are the aerodynamic acceleration, sine value of the bank angle, and jerk components of the vehicle in the VTC coordinate system.

[0072] Model the drag acceleration and lift acceleration of the vehicle as damped oscillation models, and model the sine value of the bank angle as an exponential decay model. Then the state equation of the target is:

[0073]

[0074] The nonlinear equation f(X) can be expressed as:

[0075]

[0076] where μ is the gravitational constant of the earth, R e is the equivalent radius of the earth, B0 is the geographical latitude where the radar is located, ω e is the earth's rotation speed, represents the distance between the vehicle and the center of the earth. is the component of the aerodynamic acceleration in the ENU coordinate system. α D , β D , α L , β L are the attenuation coefficients and maneuvering period frequencies corresponding to the aerodynamic drag acceleration and aerodynamic lift acceleration respectively, and ε is the model parameter corresponding to the sine value of the bank angle.

[0077] Assume the sampling interval is T, and discretize the above formula to obtain

[0078]

[0079] where F(X(k)) is the Jacobian matrix of f(X(k)) with respect to X(k).

[0080] By using the above kinetic tracking model to track and filter the aircraft, the real-time estimated values of the aerodynamic drag acceleration, climbing force acceleration, and turning force acceleration of the aircraft can be obtained. According to formulas (2) and (3), the aerodynamic acceleration contains information on unknown control variables such as the angle of attack and bank angle, as well as information on the airframe such as the aircraft mass and aircraft area. Therefore, based on the position information at the prediction starting point and the data information of the aerodynamic acceleration within a certain period of time in the future, the aircraft motion trajectory can be reconstructed using formula (1), and then trajectory prediction can be achieved.

[0081] In step three, the estimated value of the aerodynamic acceleration of the aircraft obtained through the kinetic tracking model described in step two often contains unknown noise. Directly using the estimated value for prediction will be interfered by the noise, reducing the prediction accuracy and resulting in a large prediction error. Therefore, it is necessary to denoise the information on the estimated aerodynamic acceleration components first. The present invention processes it through the method of ensemble empirical mode decomposition (EEMD). First, the estimated value of the aerodynamic acceleration is decomposed into multiple intrinsic mode functions (IMFs) through EEMD. Secondly, the energy magnitudes contained in each IMF component are calculated, and the IMF components are sorted according to the energy magnitudes. Finally, the IMF components with the first 90% energy are selected for signal reconstruction to obtain the denoised estimated value of the aerodynamic acceleration.

[0082] More preferably, step three specifically includes the following steps:

[0083] Step 3.1, ensemble empirical mode decomposition;

[0084] Ensemble empirical mode decomposition is based on empirical mode decomposition. Gaussian white noise is added to the aerodynamic acceleration. Utilizing the characteristic that the spectrum distribution of white noise is uniform, the aerodynamic acceleration with added white noise is decomposed by EMD multiple times, and the average value of the IMF components in the same frequency band after decomposition is obtained as the final IMF component, overcoming the mode mixing problem. The specific steps are as follows:

[0085] a. Consider the aerodynamic acceleration as a non-stationary and non-linear signal. Add Gaussian white noise to this signal a(t) to obtain

[0086]

[0087] b. Perform EMD decomposition on the signal s(t) with added Gaussian white noise to obtain n IMF components and a residue as

[0088]

[0089] where c ij (t) is the i-th IMF component obtained from the j-th EMD decomposition, and e j (t) is the residue.

[0090] c. Repeat the operations in Step 1 and Step 2 for multiple times. Here, a total of M repeated decompositions are performed, and then the average values of the corresponding IMF components and the residue are obtained and used as the final decomposition results.

[0091]

[0092] After decomposition, the original signal reconstruction formula is

[0093]

[0094] Step 3.2, Reconstruct the data after denoising;

[0095] The energy magnitude of the IMF components directly reflects the proportion of the IMF components in the original signal. After the aerodynamic acceleration is decomposed by EEMD, several IMF components can be obtained. The IMF components are sorted in descending order of energy, and the IMF components are accumulated one by one starting from the IMF with the highest ranking until the energy accounts for 90% of the original signal. The reconstructed and denoised signal is obtained, and the remaining unaccumulated IMF components are regarded as noise.

[0096] Step 3.3, Construct a data set and train a pre-constructed attention time series neural network model according to the data in the data set;

[0097] Obtain the hypersonic vehicle prediction parameters according to Step 2. Denoise and reconstruct the prediction parameters according to Steps 3.1 and 3.2, and then use this data as the input data of the prediction model to train the model.

[0098] The trajectory of a hypersonic vehicle can be regarded as a time series. The problem of hypersonic vehicle trajectory prediction is essentially a time series prediction problem.

[0099] The construction process of the attention time series neural network model (ATSN) in this solution includes:

[0100] a. Construct a time series neural network with an encoder-decoder structure;

[0101] Design the encoder of the time series neural network as a bidirectional LSTM through the following formula:

[0102]

[0103] Assume that the sequence input generated at the previous moment is The corresponding decoder is designed as:

[0104]

[0105] In the formula, x t represents the current input, ht represents the hidden state of the current moment, and represent the forward hidden state and the backward hidden state respectively, θ E is the adaptation parameter, T represents matrix transpose, C t-1 is the context vector, u t is the current decoder hidden state, LSTM(·) represents the LSTM network;

[0106] b. Adding the attention mechanism

[0107] The attention mechanism mimics the human visual system's behavior when processing information. It automatically focuses on key and important information through attention, reducing the attention to unimportant information. Its essence is to amplify the role of important information and weaken the role of useless information by adjusting the probability distribution of information, thereby improving the model's performance. Here, since the information at different moments has different degrees of influence on the current output, usually the information closer to the current moment is more important. Therefore, the influence weights are determined according to the importance degrees of the information at different moments.

[0108] The scoring calculation formula for the i-th feature vector is

[0109] e t = v T tanh(W T h t + b) (17)

[0110] In the formula, v, W, and b are the weight matrix and the bias vector respectively.

[0111] Normalize the above formula:

[0112] α i = softmax(e i ) (18)

[0113] The final output of the attention mechanism is expressed as:

[0114]

[0115] In the formula, k is the length of the array.

[0116] After the ATSN model is trained, in step four, input the data set obtained in step 3 into the ATSN model for prediction, and the prediction parameters can be output.

[0117] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of this application.

[0118] Example 2

[0119] In this example, a specific numerical example is used to verify the above method, and the process is as follows:

[0120] The following simulation experiment scenario is designed in the present invention: A hypersonic vehicle is boosted to an altitude of 50 km by a launch rocket, and then continues to rise to the highest point by inertia, and then re-enters the atmosphere, enters the skip-glide phase, and maneuvers according to a preset mode. Assume that the geographical coordinates of the radar site are [1, 2°, 0.5°, 1 km], the sampling interval is 0.5 s, the azimuth angle and elevation angle errors are 0.15°, and the range error is 200 m. The bank angle of the hypersonic vehicle is constantly 5°, and the angle of attack is set as a continuous function related to the speed according to formula (20), such as Figure 3 shown. The unscented Kalman filter (UKF) is used for filtering during the tracking process. The target maneuvering trajectory and the observation trajectory are as Figure 4 shown. It should be noted that the prediction mentioned in this simulation refers to multi-step prediction, that is, the result obtained by prediction is used as the input for the next step of prediction, and the cycle is repeated continuously, so as to obtain the prediction of multiple time steps.

[0121]

[0122] wherein, V mid =(V1 + V2) / 2; α mid =(α max +α max_K ) / 2; α bal =(α max -α max_K ) / 2; α max =25°; α max_K =11°; V1 = 4000 m / s; V2 = 2000 m / s.

[0123] The dynamic tracking model in step 2 is used to track the maneuver of the vehicle, and the position state information and aerodynamic acceleration information of the vehicle can be obtained. The EEMD algorithm proposed in step 3 is used to decompose the aerodynamic acceleration estimated by the tracking, and multiple IMF components and residues are obtained. The results are as Figures 5 - 7 shown, where Figure 5 is the decomposition of the aerodynamic turning force acceleration, Figure 6 is the decomposition of the aerodynamic drag acceleration, Figure 7 is the decomposition of the aerodynamic climbing force acceleration. The energy proportion of each aerodynamic acceleration component obtained after the EEMD decomposition in the original signal is calculated respectively, and they are sorted in descending order, and the first 90% of the components are selected for reconstruction to obtain the denoised aerodynamic acceleration. Taking the aerodynamic drag acceleration as an example, its denoising result is as Figure 8As shown, it can be seen that the noise in the data after denoising is significantly reduced, and the overall curve becomes smoother.

[0124] The total tracking duration of this simulation is 430 s. The obtained aerodynamic acceleration data is denoised and used as a dataset. Among them, the aerodynamic acceleration data from 1 s to 250 s is selected as the training set, and the aerodynamic acceleration data from 251 s to 430 s (with a total duration of 180 s) is selected as the test set (i.e., the trajectory prediction segment). To eliminate the influence of dimensions and improve the convergence speed during model training, the denoised aerodynamic acceleration data is normalized and then input into the ATSN model for training.

[0125] The model code used in the present invention is written in Python 3.7.6 and implemented based on the TensorFlow framework. The experiment is carried out on a mobile workstation with an Intel Core i7-10510U processor and 16G of memory. The learning rate is set to 0.01, the time step is set to 90, the number of training times is 100, and the batch size is 36. The ReLU function is selected as the model activation function, and the optimizer is Adam.

[0126] The settings of the comparative experiment mainly consider two points: one is to verify the influence of data denoising on the model prediction performance. The LSTM model is trained with the undenosed data, and its prediction accuracy is compared with that of the prediction model (EEMD-ATSN) proposed in the present invention; the other is to verify the superiority of the model performance itself. The EEMD-CNN model, EEMD-LSTM model, and EEMD-RNN model are selected for comparison to compare the prediction accuracies of different models. The designs of the learning rate and time step of the comparative models are the same as those of the model proposed in the present invention.

[0127] The RMSE of the prediction of the aerodynamic acceleration for the next 180 s is as Figures 9 - 11 shown, where Figure 9 is the root mean square error of the prediction of the aerodynamic turning force acceleration, Figure 10 is the root mean square error of the prediction of the aerodynamic drag acceleration, Figure 11It is the root mean square error of the predicted aerodynamic climbing force acceleration. By comparing the RMSE values of the five models respectively, it is found that the prediction effect of the EEMD-CNN model is slightly inferior to that of the EEMD-LSTM model, indicating that the LSTM network can extract data features well and can play a good role in time series data prediction. However, the prediction performance of the EEMD-RNN model is inferior to that of the EEMD-CNN model and the EEMD-LSTM model, indicating that the recurrent neural network model cannot learn the long-term change features of data well during time series prediction and has a limited memory length. At the same time, compared with directly training with the undenoised data, the prediction performance of the AT-LSTM model is significantly inferior to that of the EEMD-ATSN model, indicating that data denoising can effectively improve the model prediction performance. Through comprehensive comparison, it can be found that the EEMD-ATSN model proposed in the present invention has better prediction performance than several existing typical time series prediction models, with the smallest prediction error value, and can effectively predict the future value of the aerodynamic acceleration.

[0128] The motion trajectory of the HGV can be reconstructed using the aerodynamic acceleration value predicted by the EEMD-ATSN model to obtain the predicted trajectory, as Figure 12 shown. It can be seen that the prediction accuracy of the prediction method proposed in the present invention is relatively higher.

[0129] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. An online prediction method for the trajectory of a hypersonic vehicle based on parameter extrapolation, characterized in that Including: Step 1: Select the hypersonic vehicle trajectory prediction parameters; Step 2: Estimate the hypersonic vehicle trajectory prediction parameters based on the dynamic tracking model; Step 3: Denoise the hypersonic vehicle trajectory prediction parameters based on ensemble empirical mode decomposition, construct a data set, and train a pre-constructed attention time series neural network model according to the data in the data set; Step 4: Input the data set into the trained attention time series neural network model to obtain the predicted trajectory of the hypersonic vehicle; After selecting the aerodynamic acceleration as the prediction parameter, the value of the aerodynamic acceleration is obtained in real time. The aerodynamic drag acceleration and lift acceleration of the hypersonic vehicle are modeled as a decaying oscillation model, and the sine value of the bank angle is modeled as an exponential decay model. According to the relationship between the aerodynamic acceleration components, the value of the aerodynamic acceleration is estimated in real time during the tracking process.

2. The online trajectory prediction method for hypersonic vehicles based on parameter extrapolation according to claim 1, characterized in that The hypersonic vehicle trajectory prediction parameter selected in Step 1 is the aerodynamic acceleration of the vehicle.

3. The online trajectory prediction method for hypersonic vehicles based on parameter extrapolation according to claim 2, wherein In Step 2, the estimation of the hypersonic vehicle trajectory prediction parameters includes the estimation of the aerodynamic drag acceleration, climb force acceleration, and turning force acceleration of the vehicle.

4. The online trajectory prediction method for hypersonic vehicles based on parameter extrapolation according to claim 3, characterized in that, The estimation of the aerodynamic drag acceleration, climb force acceleration, and turning force acceleration of the vehicle includes: Convert the vehicle aerodynamic acceleration from the VTC coordinate system to the east-north-up ENU coordinate system; Model the drag acceleration and lift acceleration of the aircraft as damped oscillation models, and model the sine value of the bank angle as an exponentially decaying form. Among them, the state equation of the target is represented by the non-linear equation f(X); Discretize f(X) using the formula ; Among them, v x , v y , v z are the velocity components of the aircraft along each coordinate axis in the ENU coordinate system, μ is the Earth's gravitational constant, R e is the equivalent radius of the Earth, B0 is the geographical latitude where the radar is located, ω e is the Earth's rotation speed, r is the distance between the aircraft and the Earth's center, are the components of the aerodynamic acceleration in the ENU coordinate system, α D , β D , α L , β L are the attenuation coefficients and maneuvering period frequencies corresponding to the aerodynamic drag acceleration and aerodynamic lift acceleration respectively, ε is the model parameter corresponding to the sine value of the bank angle, T is the sampling interval, F(X(k)) is the Jacobian matrix of f(X(k)) with respect to X(k), S υ is the sine value of the bank angle.

5. The online prediction method for the hypersonic vehicle trajectory based on parameter extrapolation according to claim 1, wherein In Step 3, the denoising of the hypersonic vehicle trajectory prediction parameters based on ensemble empirical mode decomposition includes: Add Gaussian white noise to the pneumatic acceleration signal a(t) Obtain Perform EMD decomposition on the signal s(t) added with Gaussian white noise to obtain n IMF components and a residue as where, c ij (t) is the i-th IMF component obtained from the j-th EMD decomposition, and e j (t) is the residue; Repeat the above operation M times, and calculate the average values of the corresponding IMF components and the residue, where the average value of the IMF components The average value of the residue is According to the average value c of the IMF components i (t) and the average value e of the remainder to reconstruct the aerodynamic acceleration signal 6. The online prediction method for the hypersonic vehicle trajectory based on parameter extrapolation according to claim 5, characterized in that The reconstruction of the aerodynamic acceleration signal includes: Sort the IMF components in descending order of energy, and start accumulating them one by one from the IMF components with higher rankings until the energy occupied reaches 90% of the original signal, obtaining the reconstructed and denoised signal, and the remaining unaccumulated IMF components are regarded as noise.

7. The online trajectory prediction method for hypersonic vehicles based on parameter extrapolation according to claim 1, characterized in that The construction of the attention time series neural network model includes: Design the encoder as a bidirectional LSTM through the following formula: Assume that the sequence input generated at the previous moment is The corresponding decoder is designed as follows: where x t represents the current input, h t represents the hidden state of the current moment, and represent the forward hidden state and the backward hidden state respectively, θ E is the adaptation parameter, T represents matrix transpose C t-1 is the context vector, u t is the current decoder hidden state, LSTM(·) represents the LSTM network; The scoring calculation formula e for the i-th eigenvector t = v T tanh(W T h t + b), where v, W, and b are the weight matrix and bias vector respectively, and h t is the hidden layer state; The attention probability α can thus be obtained t = softmax(e i ); Through the formula the output of the attention mechanism is obtained, where k is the length of the array.

Images