CN114048889B - Aircraft trajectory prediction method based on long-term and short-term memory network - Google Patents

Abstract

The invention relates to the fields of air combat environment, data processing, deep learning and the like, and provides a method for realizing aircraft trajectory prediction by using a long-short term memory network (LSTM) under the uncertain perception condition. Therefore, the technical scheme adopted by the invention is that a method for predicting the aircraft track based on a long-term and short-term memory network utilizes Kalman filtering to eliminate the noise interference carried by the sensor characteristic vector; for the directly acquired state parameters, data preprocessing is carried out, including down-sampling, invalid value elimination and missing value complementation, in addition, in order to improve the calculation stability, the data is subjected to normalization processing, and the value range of the input data is included in a [0,1] interval; and constructing a locus prediction model based on the LSTM, defining input and output of the network, and carrying out supervision training on the network. The method is mainly applied to occasions for predicting the flight path of the unmanned aerial vehicle.

Description

A method of aircraft trajectory prediction based on long short-term memory network

technical field

The invention relates to the fields of air combat environment, data processing, deep learning and the like, and solves the problem of predicting the flight trajectory of an aircraft under uncertain perception conditions. Specifically, it relates to a method of aircraft trajectory prediction based on long short-term memory network.

Background technique

In the current international environment, air force strength is the embodiment of a country's overall combat strength. In the actual air combat environment, the pilot needs to grasp the flight status of the enemy aircraft in real time according to the real-time data information of the airborne sensors. If we can predict the future state information of the enemy aircraft in advance based on the existing sensor state parameter information, including possible future positions and possible flight trajectories, it will help us to implement combat strategies such as interception, strike, and evasion in advance, and improve the Our win rate. Therefore, it is of great strategic significance to dynamically and accurately predict the position of the enemy aircraft at the next moment through known information. However, the traditional trajectory prediction method has the problems of serious model simplification, few factors to be considered, and it is difficult to deal with the coupled state information, so it is difficult to give more accurate prediction results. As an emerging forecasting method, compared with traditional forecasting methods, neural network's powerful fitting ability can describe complex nonlinear relationships.

Trajectory prediction refers to using the existing historical trajectory data information to construct a prediction model to obtain the location points in the future. At present, there are three main methods for constructing trajectory prediction models:

One is trajectory prediction based on association rules ^[1] . The association rules are constructed by mining frequently occurring items, and then the sequence matching method is used to predict the trajectory. Trajectory prediction using association rules is mainly divided into two sub-tasks: the first part is the mining of frequent itemsets, which is to find out the locations with high frequency from the existing historical data, and call these locations as frequent items. is called frequent itemsets; the second part is to generate association rules. In the frequent itemsets in the first part, calculate the probability that one position appears and another position occurs. This probability is called confidence. When the current position is input into When the rule base is used, the position with the highest confidence is output as the trajectory prediction result. Among the association rule algorithms, the Apriori ^[2] algorithm is typical, which can quickly and accurately mine association rules, but it needs to repeatedly scan the database, resulting in a large number of useless feature sets, and the computational complexity is large. The Prefix Span algorithm calculates the frequent items and association rules according to the order of the trajectory, and uses the prefix projection technology to find the subsequent position of a certain position in chronological order to form a frequent itemset, so that the frequent itemsets of positions have a certain continuity. Reference [3] combines the FP-Tree algorithm and the Prefix Span algorithm to mine frequent trajectories, match the existing trajectories with the motion rule library, and establish a probability model of object positions. This type of research only considers the historical trajectory information. Although the frequent items excavated have a certain continuity, some positions will be skipped in the middle, resulting in a low accuracy of the prediction results.

The second is the trajectory prediction based on the Markov model. By constructing a state transition matrix, the probability of a certain position point to other position points is calculated, the current position is input into the constructed matrix, and the next position is determined according to the maximum probability, so as to obtain the prediction result. The first-order Markov model has only a transition probability matrix of one position. In order to obtain more comprehensive information, Yang J ^[4] designed a high-order Markov model, which uses the state information of n positions to predict the position at the next moment. , which improves the prediction accuracy. The Hidden Markov-based trajectory prediction algorithm HMTP proposed by Qiao SJ ^[5] improves the problem that the speed of moving objects changes quickly and is difficult to predict, and can predict the continuous trajectory of objects. This type of research is based on the assumption that the location information at the current moment is only related to the previous moment, and the obtained local optimal solutions are all local optimal solutions. However, the high-order Markov computational complexity is relatively large, and it is not suitable for real-time prediction requirements.

The third is the trajectory prediction based on neural network. The neural network usually consists of an input layer, a hidden layer, and an output layer. The network output is calculated by forward propagation, and the error between the output and the true value is calculated by back propagation, thereby updating the network weights. After multiple parameter updates, you can get A predictive model that fits the true model better. Payeur ^[6] et al. proposed to use artificial neural network (Artificial Neural Networks, ANN) to predict the motion trajectory of the robot, using the six recent measurements of the robot coordinates as the input of the network, and using several neurons to predict the future trajectory position Make predictions; Huang ^[7] et al. proposed a trajectory prediction model based on Deep Belief Network (DBN), the bottom of the model is a deep belief layer for unsupervised training, and the top is a multi-task learning layer for supervised learning; Zhang Tao ^[8] and others proposed to use Elman neural network to predict the trajectory of the fighter, and selected the position points in three directions as the position vector, sampling the fighter flight trajectory every 0.25 seconds, and using the first five position points to predict the Based on Elman neural network, Wang Jianchen ^[9] used particle swarm algorithm and gradient algorithm to optimize the weight of the network, and better predicted the landing trajectory of the UAV. The prediction speed and prediction accuracy of the model are improved; Qian Kui et al. ^[10] used the adaptive K-means algorithm to perform cluster analysis on the target track group when predicting the flight trajectory of the aircraft to find out the specific activity area of a certain target. , and then use the BP neural network to train the track group, establish a prediction model, and complete the prediction of the track; Yang Rennong ^[11] proposed a prediction model based on Bi-LSTM when predicting the trajectory of the UAV. , distance and other parameters are used as the input of the model, and the position at the next moment is used as the output, and the training network completes the prediction of the UAV flight trajectory. Experiments show that this method is more accurate than the trajectory prediction result based on Elman neural network.

The trajectory prediction of aircraft is essentially the prediction of time series data. Due to the complex and changeable environment, the flight trajectory has a high degree of uncertainty. The traditional prediction method uses a small amount of data and does not consider the difference between aircraft. Due to the mutual influence of position and attitude, it is difficult to accurately learn the flight laws of aircraft affected by multiple factors, so a more intelligent prediction model is required. The idea of reference [11], using a data-based method, transforms the trajectory prediction problem into the prediction problem of time series data, simply starting from the flight data, regardless of the physical model of the aircraft, using the long short-term memory network (LSTM)-based network. In the deep learning prediction model, at the same time, when selecting the network input feature quantity, in addition to considering the state parameters of the other party obtained by the sensor, it is also necessary to add the state parameters of the own party, so that the prediction model can fit the flight trajectory of the aircraft affected by multiple factors to the greatest extent.

SUMMARY OF THE INVENTION

In order to overcome the deficiencies of the prior art, the present invention aims to propose a method for realizing aircraft trajectory prediction by using a long short-term memory network (LSTM) under uncertain perception conditions. To this end, the technical solution adopted in the present invention is that, in the method for predicting the trajectory of an aircraft based on a long short-term memory network, Kalman filtering is used to eliminate the noise interference carried by the sensor feature vector; Data preprocessing is performed, including downsampling, invalid value elimination, and missing value complementing. In addition, in order to improve calculation stability, the data is normalized, and the value range of the input data is included in the [0,1] interval; The trajectory prediction model of LSTM defines the input and output of the network, and supervised training of the network.

Specific steps are as follows:

The first step is to obtain the original state information from the airborne sensors, and select a total of twenty-three-dimensional feature quantities as the input of the prediction model;

The second step is to preprocess the data: first, the original sensor parameters contain a certain amount of noise interference, and the Kalman filtering method is used to eliminate it; secondly, in order to improve the data utilization rate and reduce the calculation cost, the original data is treated according to 1: 5 Perform downsampling and normalize the data; finally, remove the invalid values, fill in the missing values, and complete the data preprocessing; then select the input and label values: use the sliding window method to complete the data set. Segmentation, the input of the network is obtained by iterative selection of the original data, starting from 0 to the first time_step, because the time_step selected for this training is 20, that is, from 0 to 19 is the first input, and 1 to 20 is the second input, and so on; the dimension of the input data is (N, 20, 23), where N depends on the size of the sample set, 20 refers to the time_step value of the LSTM, 23 is the dimension of the feature vector, and the training network needs to use the label Data, since the purpose of this model is to predict the trajectory of the aircraft in the next step, therefore, for the first 0-19 input, select 1-20 longitude and latitude of the carrier aircraft as the label, for the second 1-20 input, select The latitude and longitude height of the carrier of 2-21 is used as a label, and so on;

The third step is to build a trajectory prediction model based on LSTM. The constructed model includes two layers of LSTM layers. After each layer of LSTM layer, a dropout layer is added to avoid overfitting. After a fully connected layer, transform the dimensions to the desired output dimension.

The detailed steps are as follows:

First of all, the required characteristic data is obtained from the aircraft confrontation simulation platform. Considering that the trajectory of the aircraft is affected by various factors such as itself, the battlefield environment, and the enemy's motivation, it is concluded that the trajectory of the aircraft has three characteristics: continuity, timing, and interactivity. Features:

①Continuity means that the trajectory of the UAV changes continuously rather than intermittently;

②Timing means that the trajectory data is temporal, and the position of the next moment is related to the position of the previous moment, so the trajectory data is essentially a time series data;

③Interactivity refers to the complex process of dynamic changes between multiple aircraft in the actual environment. The maneuver of one aircraft will affect the maneuver of another aircraft, and the position of one aircraft will also affect the position of another aircraft;

Therefore, in the trajectory prediction, in addition to considering the position, attitude and speed of the enemy aircraft, due to the interaction, the 23-dimensional feature vectors of the two aircraft should also be considered:

Longitude, Latitude, Altitude, Pitch, Roll, Yaw, Azimuth, Azimuth Velocity, Pitch Velocity, North Velocity, Sky Velocity, East Velocity, North Acceleration, Sky Acceleration, East Acceleration, Horizontal Entry Angle, Relative distance, relative distance change rate, relative altitude, radar status recognition result, radial velocity, true heading, ground speed;

Secondly, after the feature vector is obtained, since the raw data obtained from the sensor cannot be directly used as network input, it needs to be preprocessed, and the data is down-sampled according to the sampling interval of 1:5, and invalid values in the data are removed. Eliminate, use the mean filling method to make up for missing values. In addition, due to the large value of some parameters used, in order to improve the stability of the calculation, the data is normalized, and the value range of the input data is included in [0,1 ] interval, the normalization formula is:

In the formula, X is the actual value of a certain feature quantity, X _max and X _min are the maximum and minimum values of X in all data, respectively, and Y is the normalized result;

Use the trained prediction model to de-normalize the prediction results, so as to compare and analyze the error with the actual value. The formula for de-normalization is:

X=(X _max -X _min )Y+X _min (2)

After the data processing is completed, a standardized sample data set that can be used by the neural network is obtained. At this time, the input and output of the LSTM network need to be constructed according to the actual needs. When selecting the label data, the longitude, The latitude and height are used as the feature labels of the current moment, and the sliding window method is used to complete the segmentation of the data set. The input of the network is obtained by iterative selection of the original data, starting from 0 to the first time_step, because the time_step selected for this training is 20 , that is, from 0 to 19 is the first input, 1 to 20 is the second input, and so on; the dimension of the input data is (N, 20, 23), where N depends on the size of the sample set, 20 means The time_step value of LSTM, 23 is the dimension of the feature vector, the training network needs to use the label data, because the purpose of this model is to predict the trajectory of the aircraft in the next step, therefore, for the first 0-19 input, select 1-20 The latitude and longitude of the carrier is used as the label. For the second input of 1-20, the latitude and longitude of the carrier of 2-21 is selected as the label, and so on, so the dimension of the output data is (N, 20, 3), where N depends on Due to the size of the sample set, 20 refers to the time_step value of LSTM, and 3 corresponds to the output dimension, that is, the longitude, latitude, and altitude of the aircraft;

作为输入，第二层输出

经过一个全连接层之后，得到最终的网络输出Y，在每一层LSTM网络中添加了Dropout层，利用其控制隐含层节点权重，避免某些轨迹特征只在固定组合下生效，有意识地让网络去学习轨迹普遍的共性，对LSTM输出的特征量经过一个全连接层后，将维度转化为所需的输出纬度；Finally, the LSTM network is constructed, using LSTM as the main part of the model, by constructing a multi-layer network structure, learning the relationship between the input trajectory-related feature quantity and the label of the next moment position, and predicting the possible position in the future. The prediction model mainly includes LSTM layer, Dropout layer, fully connected layer, two layers of LSTM are selected for model building: the LSTM network of the first layer takes twenty-three-dimensional feature quantities as input, and the second layer takes the output of the first layer

As input, the second layer outputs

After a fully connected layer, the final network output Y is obtained, and a Dropout layer is added to each layer of the LSTM network, which is used to control the node weight of the hidden layer, so as to avoid certain trajectory features only taking effect under a fixed combination, and consciously let The network learns the general commonality of trajectories. After the feature quantity output by LSTM passes through a fully connected layer, the dimension is converted into the required output dimension;

In addition to determining the network structure and input and output, the network is trained with the training sample set, and the mean square error function shown in equation (3) is selected as the loss function:

Among them, N represents the number of batch samples in a training process, Y _pred represents the predicted value output by the neural network, and Y _i represents the corresponding real value. The neural network training is the process of updating the weights. The optimization goal of the network is to make E approach At 0, during network training, the adaptive moment estimation method (Adam) is selected. The steps of the adaptive moment estimation method are as follows:

First of all, considering that in the traditional backpropagation algorithm, the update direction of the weight only depends on the gradient obtained by the current sample, so we draw on the concept of momentum in physics, that is, when updating the weight, the previous update direction is retained to a certain extent, and the current update direction is added at the same time. The gradient of the sample to get the final update direction, that is

In the formula, s is called momentum, which is also the first-order moment estimation of the gradient, and β ₁ is called the first-order momentum decay coefficient;

In the formula, v is called the velocity quantity, which is also the second-order moment estimation of the gradient, and β ₂ is called the second-order momentum decay coefficient, which is generally taken as β ₂ =0.999;

In order to further realize the adaptive adjustment of the learning rate, that is, a larger ε update is used for the weights that are updated slowly, and a smaller ε update is used for the weights that update faster, so the learning rate ε is adjusted:

δ is a constant to prevent the denominator from being zero, generally take δ=10 ^-8 ;

On this basis, unbiased corrections are made to the first and second moment estimates of the gradient:

Finally, the weight update formula based on Adam algorithm is obtained:

According to the above steps, the training of the LSTM network is completed, the trained model is saved locally, and the sample mean and variance parameters are saved in the format of txt files. When experimenting with new samples to be tested, these local files are directly called;

During model training and testing, the values of network structure parameters are shown in the following table:

Table 1 LSTM network parameters

For the trained prediction model, input new data to be tested to verify the prediction accuracy of the model;

When selecting a sample data set, in the simulation confrontation environment, each time a simulation confrontation is completed, a set of experimental data can be obtained, that is, a trajectory curve. Considering that there are too few feature points in a single curve, it is not conducive to the learning of the neural network, so many times In the experiment, the trajectories are spliced, and finally time series data containing 10600 points are obtained, each point contains twenty-three-dimensional feature quantities. After dimensionality reduction, a sample set with a dimension of (21200, 23) is obtained, according to 0.75: The ratio of 0.25 divides the training set and the test set, and the sample dimension of the test set is (5300,23);

In order to prevent the model from overfitting within the set epoch range, in addition to adding the dropout layer when designing the model, the sample data is also processed. For the training data, a part of it is selected as the validation data (valid data), The ratio of the validation set data to the training set data is defined as valid_data_rate=0.15, and a patience value of patience=5 is set. If the number of iterations of the validation set exceeds 5 and the training accuracy and loss are not improved, the training will be terminated in advance, which is called "" "Early Stopping", by adding a validation set, can avoid overfitting and improve model selection.

The characteristics and beneficial effects of the present invention are:

When predicting the trajectory of the aircraft, due to the complexity of the environment where the aircraft is located, the high maneuverability of the aircraft and the interaction between the aircraft, it is difficult for traditional prediction methods to obtain accurate prediction results. The present invention adopts a deep learning prediction model based on LSTM network, which can process a large amount of aircraft data information, fit a motion model of the aircraft from it, and then give a high-precision prediction result. At the same time, the model is purely from the data point of view, ignoring the influence of the physical model of the aircraft, which simplifies the complexity of model construction to a certain extent. Twenty-three-dimensional feature quantities related to trajectory prediction are selected from the three-hundred multi-dimensional sensor state parameters. Through the data preprocessing module, filtering, downsampling, missing value complementing, outlier elimination and normalization are realized; the sliding window method is used. Select the input amount and label value; after the model is built, use the input amount and label data to perform supervised learning on the network and optimize the network parameters. For the trained network, input new data to be tested, you can get the following: The prediction result of the trajectory at a moment.

The present invention mainly has the following characteristics and advantages:

(1) According to the actual selection of the twenty-three-dimensional feature quantities of the aircraft of both parties, the influencing factors of the aircraft trajectory of the aircraft can be described to the maximum extent, and the prediction model can be fitted.

(2) The division of input amount and label value, the longitude, latitude, and altitude of the next moment are regarded as the label value of the current moment, and the prediction result can be obtained directly when new data is input.

(3) The prediction model composed of multi-layer LSTM can fit complex nonlinear trajectories, and at the same time avoid the phenomenon of over-fitting.

Description of drawings:

Figure 1. Flow chart of trajectory prediction.

Figure 2 Schematic diagram of input quantity and label value.

Figure 3. The network structure diagram of the trajectory prediction model.

Figure 4 Training loss curve.

Figure 5. The result of the trajectory prediction of the aircraft.

Detailed ways

In view of the above background and problems, the present invention aims to provide a method for realizing aircraft trajectory prediction using a long short-term memory network (LSTM) under uncertain perception conditions. For the noise interference carried by the sensor feature vector, Kalman filtering is used to eliminate it; for the directly obtained state parameters, data preprocessing is performed, including downsampling, invalid value elimination, and missing value complementing. In addition, in order to improve the calculation stability The data is normalized, and the value range of the input data is included in the [0,1] interval; a trajectory prediction model based on LSTM is constructed, the input and output of the network are defined, and the network is supervised and trained.

The functions and features of the present invention are as follows:

(1) The present invention selects the state parameter information of the 23-dimensional aircraft on both sides as the input vector of the network, and selects the three vectors of longitude, latitude and height as the output of the network according to the characteristics of the interactivity of the aircraft trajectory under the actual air combat environment. .

(2) The present invention proposes a method for network input and label determination. Using the sliding window method, the longitude, latitude and altitude of the next moment are regarded as the feature labels of the current moment to complete the segmentation of the data set.

(3) Based on the LSTM network, the present invention proposes an aircraft trajectory prediction model, including an LSTM layer, a Dropout layer, and a fully connected layer. A Dropout layer is added to the LSTM network of each layer, and the Dropout layer is used to control the node weight of the hidden layer, avoiding that some trajectory features only take effect under a fixed combination, and consciously let the network learn the general commonality of the trajectory.

The technical scheme of the present invention is as follows:

The main purpose of the present invention is to realize one-step prediction of the trajectory of the aircraft, and the overall flow is shown in Figure 1 .

The first step is to obtain the original status information from the airborne sensors. There are usually more than 300 kinds of sensor information that can be obtained by the aircraft, which can be selected according to the actual use. In this invention, a total of twenty-three-dimensional feature quantities are selected as the input of the prediction model, as shown in Table 1.

The second step is to preprocess the data. First, the original sensor parameters contain a certain amount of noise interference, and the Kalman filtering method is used to eliminate it; secondly, in order to improve the data utilization rate and reduce the calculation cost, the original data is down-sampled according to 1:5, and the data is normalized. Uniform processing; finally, the invalid values are eliminated, and the missing values are filled to complete the data preprocessing. Then, according to the method shown in Figure 2, the selection of input and label value is performed.

The third step is to construct a trajectory prediction model based on LSTM. The constructed model is shown in Figure 3. It consists of two LSTM layers. After each LSTM layer, a dropout layer is added to avoid overfitting. After passing the output feature through a fully connected layer, the dimension is converted to the desired output dimension.

The present invention will be further described below with reference to the accompanying drawings.

The trajectory of the aircraft can be regarded as a series of time series data. Therefore, the data-based approach can be used to transform the trajectory prediction problem into a time series data prediction problem. Using the powerful data fitting ability of the LSTM network, select appropriate input samples to obtain the trajectory of the aircraft. one-step prediction results.

When predicting the trajectory of the aircraft, follow the process shown in FIG. 1 . It is mainly divided into four steps: (1) extracting valid data in adversarial simulation and establishing a training sample data set; (2) preprocessing the samples; (3) constructing network input and output, establishing a neural network, and using input and output to pair The network is supervised and trained, and the network structure parameters are adjusted according to the training results. (4) Using the trained network, input the new sample to be tested, obtain the prediction result, and compare it with the real value.

The first is to obtain the required characteristic data from the aircraft confrontation simulation platform. Considering that the trajectory of the aircraft is affected by various factors such as itself, the battlefield environment, and the enemy's motives, according to expert experience, it is concluded that the trajectory of the aircraft has three characteristics: continuity, timing, and interactivity ^[12] .

①Continuity means that the trajectory of the UAV changes continuously rather than intermittently.

② Timing means that the trajectory data is temporal, and the position of the next moment is related to the position of the previous moment, so the trajectory data is essentially a time series data.

③Interactivity refers to the complex process of dynamic changes between multiple aircraft in the actual environment. The maneuver of one aircraft will affect the maneuver of another aircraft, and the position of one aircraft will also affect the position of another aircraft.

Therefore, in the trajectory prediction, in addition to considering the position, attitude, and speed of the enemy aircraft, due to the interaction, the relative distance, relative height, and horizontal entry angle of the two aircraft should also be considered, a total of twenty-three-dimensional features, as shown in Table 2.

Table 2 Neural network input feature quantities

Second, after obtaining a total of twenty three-dimensional feature vectors, since the raw data obtained from the sensor cannot be directly used as network input, it needs to be preprocessed. The data is down-sampled according to the sampling interval of 1:5, the invalid values in the data are eliminated, and the missing values are filled by the mean filling method. , the data is normalized, and the value range of the input data is included in the [0,1] interval. The normalization formula is:

In the formula, X is the actual value of a feature quantity, X _max and X _min are the maximum and minimum values of X in all data, respectively, and Y is the normalized result.

Use the trained prediction model to de-normalize the prediction results, so as to compare and analyze the error with the actual value. The formula for de-normalization is:

X=(X _max -X _min )Y+X _min (2)

After the data processing is completed, the normalized sample data set that can be used by the neural network is obtained. At this time, the input and output of the LSTM network need to be constructed according to the actual needs. The ultimate purpose of this paper is to predict the longitude, latitude, and altitude of the aircraft at the next moment according to the twenty-three-dimensional feature quantities at the current moment. Feature label. The sliding window method is used to complete the segmentation of the dataset, as shown in Figure 2. Its meaning means: the input of the network is obtained by iterative selection of the original data, starting from 0 to the first time_step, because the time_step selected for this training is 20, that is, from 0 to 19 is the first input, and 1 to 20 is the first input. The second input, and so on. So the dimension of the input data is (N, 20, 23), where N depends on the size of the sample set, 20 refers to the time_step value of the LSTM, and 23 is the dimension of the feature vector. The training network needs to use the label data. Since the purpose of this model is to predict the trajectory of the aircraft in the next step, for the first input of 0-19, select the latitude and longitude height of the carrier aircraft of 1-20 as the label, for the second 1 The input of -20, select the latitude and longitude height of the carrier from 2-21 as the label, and so on. Therefore, the dimension of the output data is (N, 20, 3), where N depends on the size of the sample set, 20 refers to the time_step value of the LSTM, and 3 corresponds to the dimension of the output, that is, the longitude, latitude, and altitude of the aircraft.

作为输入，第二层输出

经过一个全连接层之后，得到最终的网络输出Y。由于网络结构层数和神经元个数都比较多，为了防止“过拟合”现象的发生，Hinton提出使用Dropout方法，它在训练过程中随机省略一些用于特征学习的神经元，减少因仅有特定的神经元起作用，在训练集上产生复杂的相互适应造成的过拟合。因此本文在每一层LSTM网络中添加了Dropout 层，利用其控制隐含层节点权重，避免某些轨迹特征只在固定组合下生效，有意识地让网络去学习轨迹普遍的共性。对LSTM输出的特征量经过一个全连接层后，将维度转化为所需的输出纬度。The last step is to construct the LSTM network. This paper uses LSTM as the main part of the model. By constructing a multi-layer network structure, it learns the relationship between the input trajectory-related feature quantity and the label of the next moment position, and predicts the possible future position. The prediction model mainly includes LSTM layer, Dropout layer, and fully connected layer. In this paper, two layers of LSTM are selected for model building, as shown in Figure 3: the LSTM network of the first layer takes twenty-three-dimensional feature quantities as input, and the second layer takes the output of the first layer as the input.

As input, the second layer outputs

After a fully connected layer, the final network output Y is obtained. Due to the large number of layers and neurons in the network structure, in order to prevent the occurrence of "overfitting", Hinton proposed to use the Dropout method, which randomly omits some neurons for feature learning during the training process, reducing the number of There are specific neurons at work that generate overfitting due to complex mutual adaptations on the training set. Therefore, this paper adds a Dropout layer to each layer of LSTM network, and uses it to control the node weight of the hidden layer, avoiding that some trajectory features only take effect under a fixed combination, and consciously let the network learn the general commonality of the trajectory. After the feature quantity output by LSTM is passed through a fully connected layer, the dimension is converted into the desired output dimension.

After the network structure and input and output are determined, the network can be trained with the training sample set, and the mean square error function shown in equation (3) is selected as the loss function:

Among them, N represents the number of batch samples in a training process, Y _pred represents the predicted value output by the neural network, and Y _i represents the corresponding real value. The neural network training is the process of updating the weights. The optimization goal of the network is to make E approach at 0. During network training, adaptive moment estimation (Adam) ^[13] is selected, and the steps are as follows:

First of all, considering that in the traditional backpropagation algorithm, the update direction of the weight only depends on the gradient obtained by the current sample, so we draw on the concept of momentum in physics, that is, when updating the weight, the previous update direction is retained to a certain extent, and the current update direction is added at the same time. The gradient of the sample to get the final update direction, that is

In the formula, s is called momentum, which is also the first-order moment estimation of the gradient, and β ₁ is called the first-order momentum decay coefficient, which is generally taken as β ₁ =0.9.

In the formula, v is called the velocity quantity, which is also the second-order moment estimation of the gradient, and β ₂ is called the second-order momentum decay coefficient, which is generally taken as β ₂ =0.999.

In order to further realize the adaptive adjustment of the learning rate, that is, a larger ε update is used for the weights that are updated slowly, and a smaller ε update is used for the weights that update faster, so the learning rate ε is adjusted:

δ is a constant that prevents the denominator from being zero, and generally takes δ=10 ^-8 .

On this basis, unbiased corrections are made to the first and second moment estimates of the gradient:

Finally, the weight update formula based on Adam algorithm is obtained:

According to the above steps, the training of the LSTM network is completed, the trained model is saved locally, and some parameters, such as sample mean, variance, etc., are also saved in the format of txt files. When experimenting with new samples to be tested, you can Directly call these local files to quickly complete simulation experiments.

During model training and testing, the network structure parameters are shown in Table 3. For the trained prediction model, input new data to be tested to verify the prediction accuracy of the model.

Table 3 LSTM network parameters

When selecting a sample data set, in the simulation confrontation environment, each time a simulation confrontation is completed, a set of experimental data can be obtained, that is, a trajectory curve. Considering that there are too few feature points in a single curve, it is not conducive to the learning of the neural network, so many times Experiment, splicing trajectories. Finally, time series data containing 10,600 points are obtained, and each point contains twenty-three-dimensional feature quantities. After dimensionality reduction, a sample set of dimension (21200, 23) is obtained. The training set and the test set are divided according to the ratio of 0.75:0.25, and the sample dimension of the test set is (5300, 23).

In order to prevent the model from overfitting within the set epoch range, in addition to adding the Dropout layer when designing the model, the sample data is also processed. For the training data, select a part of it as the validation data (valid data), the ratio of the validation set data to the training set data is defined as valid_data_rate=0.15, set a patience value of patience=5, if the number of iterations of the validation set exceeds 5, the training If the accuracy and loss are not improved, the training is terminated early, which is called "Early Stopping" ^[14] . By adding a validation set, overfitting can be avoided and model selection can be improved. For the training set and the validation set, as shown in the left figure of Figure 4, the loss under epoch is given. The red line is the loss of the training set, and the blue line is the loss of the validation set. It can be seen that the loss of the validation set and the training set increases with the The number of iterations increases and decreases, and the two are very close, and there is no overfitting. In order to analyze the loss of the model on the training set separately, for each batch of training, the first 1000 training loss values are saved, as shown in the right figure of Figure 4. It can be seen that as the number of model training increases, the model loss value gradually decreases and approaches 0, indicating that the model training effect is ideal.

Figure 5 shows the prediction results of the aircraft in the three directions of longitude, latitude, and altitude. The red solid line is the actual aircraft trajectory, that is, the label value, and the blue dotted line is the aircraft trajectory predicted by the LSTM model. In the figure, there is a jump at the 2800th time. This is because the sample trajectory is spliced by a segment of small trajectories, so there will be a value jump at some moments. It can be seen from the simulation results that the difference between the predicted value and the actual value is small, and the model prediction accuracy is high.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

references

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Claims (2)

1. a method for predicting the trajectory of an aircraft based on a long short-term memory network, characterized in that, for the noise interference carried by the sensor feature vector, Kalman filtering is used to eliminate it; Processing, including downsampling, invalid value elimination, and missing value complement. In addition, in order to improve the stability of the calculation, the data is normalized, and the value range of the input data is included in the [0,1] interval; the trajectory based on LSTM is constructed. Predict the network model, define the input and output of the network model, and supervise the training of the network model; the detailed steps are as follows: First of all, the required characteristic data is obtained from the aircraft confrontation simulation platform. Considering that the trajectory of the aircraft is affected by various factors such as itself, the battlefield environment, and the enemy's motivation, it is concluded that the trajectory of the aircraft has three characteristics: continuity, timing, and interactivity. Features: ①Continuity means that the trajectory of the UAV changes continuously rather than intermittently; ②Timing means that the trajectory data is temporal, and the position of the next moment is related to the position of the previous moment, so the trajectory data is essentially a time series data; ③Interactivity refers to the complex process of dynamic changes between multiple aircraft in the actual environment. The maneuver of one aircraft will affect the maneuver of another aircraft, and the position of one aircraft will also affect the position of another aircraft; Therefore, in the trajectory prediction, in addition to considering the position, attitude and speed of the enemy aircraft, due to the interaction, the 23-dimensional feature vectors of the two aircraft should also be considered: Longitude, Latitude, Altitude, Pitch, Roll, Yaw, Azimuth, Azimuth Velocity, Pitch Velocity, North Velocity, Sky Velocity, East Velocity, North Acceleration, Sky Acceleration, East Acceleration, Horizontal Entry Angle, Relative distance, relative distance change rate, relative altitude, radar status recognition result, radial velocity, true heading, ground speed; Secondly, after the feature vector is obtained, since the raw data obtained from the sensor cannot be directly used as network input, it needs to be preprocessed, and the data is down-sampled according to the sampling interval of 1:5, and invalid values in the data are removed. Eliminate, use the mean filling method to make up for missing values. In addition, due to the large value of some parameters used, in order to improve the stability of the calculation, the data is normalized, and the value range of the input data is included in [0,1 ] interval, the normalization formula is:

In the formula, X is the actual value of a certain feature quantity, X _max and X _min are the maximum and minimum values of X in all data, respectively, and Y is the normalized result; Use the trained prediction model to de-normalize the prediction results, so as to compare and analyze the error with the actual value. The formula for de-normalization is: X=(X _max -X _min )Y+X _min (2) After the data processing is completed, a standardized sample data set that can be used by the neural network is obtained. At this time, the input and output of the LSTM network need to be constructed according to the actual needs. When selecting the label data, the longitude, The latitude and height are used as the feature labels of the current moment, and the sliding window method is used to complete the segmentation of the data set. The input of the network is obtained by iterative selection of the original data, starting from 0 to the first time_step, because the time_step selected for this training is 20 , that is, from 0 to 19 is the first input, 1 to 20 is the second input, and so on; the dimension of the input data is (N, 20, 23), where N depends on the size of the sample set, 20 means The time_step value of LSTM, 23 is the dimension of the feature vector, the training network needs to use the label data, since the purpose of this model is to predict the trajectory of the aircraft in the next step, therefore, for the first 0-19 input, select 1-20 The latitude and longitude of the carrier is used as the label. For the second input of 1-20, the latitude and longitude of the carrier of 2-21 is selected as the label, and so on, so the dimension of the output data is (N, 20, 3), where N depends on Due to the size of the sample set, 20 refers to the time_step value of LSTM, and 3 corresponds to the output dimension, that is, the longitude, latitude, and altitude of the aircraft; Finally, the LSTM network is constructed, using LSTM as the main part of the model, by constructing a multi-layer network structure, learning the relationship between the input trajectory-related feature quantity and the label of the next moment position, and predicting the possible future position. The prediction model mainly includes LSTM Layer, Dropout layer, and fully connected layer. Two layers of LSTM are selected for model building: the LSTM network of the first layer takes twenty-three-dimensional feature quantities as input, and the second layer takes the output of the first layer.

As input, the second layer outputs

After a fully connected layer, the final network output Y is obtained, and a Dropout layer is added to each layer of the LSTM network, which is used to control the node weight of the hidden layer, so as to avoid certain trajectory features only taking effect under a fixed combination, and consciously let The network learns the general commonality of trajectories. After the feature quantity output by LSTM passes through a fully connected layer, the dimension is converted into the required output dimension; In addition to determining the network structure and input and output, the network is trained with the training sample set, and the mean square error function shown in equation (3) is selected as the loss function:

Among them, N represents the number of batch samples in a training process, Y _pred represents the predicted value output by the neural network, and Y _i represents the corresponding real value. The neural network training is the process of updating the weights. The optimization goal of the network is to make E approach At 0, during network training, the adaptive moment estimation method (Adam) is selected. The steps of the adaptive moment estimation method are as follows: First of all, considering that in the traditional backpropagation algorithm, the update direction of the weight only depends on the gradient obtained by the current sample, so we draw on the concept of momentum in physics, that is, when updating the weight, the previous update direction is retained to a certain extent, and the current update direction is added at the same time. The gradient of the sample to get the final update direction, that is

In the formula, s is called momentum, which is also the first-order moment estimation of the gradient, and β ₁ is called the first-order momentum decay coefficient;

In the formula, v is called the velocity quantity, which is also the second-order moment estimation of the gradient, and β ₂ is called the second-order momentum decay coefficient, which is generally taken as β ₂ =0.999; In order to further realize the adaptive adjustment of the learning rate, that is, a larger ε update is used for the weights that are updated slowly, and a smaller ε update is used for the weights that update faster, so the learning rate ε is adjusted:

δ is a constant to prevent the denominator from being zero, generally take δ=10 ^-8 ; On this basis, unbiased corrections are made to the first and second moment estimates of the gradient:

Finally, the weight update formula based on Adam algorithm is obtained:

According to the above steps, the training of the LSTM network is completed, the trained model is saved locally, and the sample mean and variance parameters are saved in the format of txt files. When experimenting with new samples to be tested, these local files are directly called; During model training and testing, the values of network structure parameters are shown in the following table: LSTM network parameter table

For the trained prediction model, input new data to be tested to verify the prediction accuracy of the model; When selecting a sample data set, in the simulation confrontation environment, each time a simulation confrontation is completed, a set of experimental data can be obtained, that is, a trajectory curve. Considering that there are too few feature points in a single curve, it is not conducive to the learning of the neural network, so many times In the experiment, the trajectories are spliced, and finally time series data containing 10600 points are obtained, each point contains twenty-three-dimensional feature quantities. After dimensionality reduction, a sample set with a dimension of (21200, 23) is obtained, according to 0.75: The ratio of 0.25 divides the training set and the test set, and the sample dimension of the test set is (5300,23); In order to prevent the model from overfitting within the set epoch range, in addition to adding the dropout layer when designing the model, the sample data is also processed, and a part of the training data is selected as the validation data (valid data), The ratio of the validation set data to the training set data is defined as valid_data_rate=0.15, and a patience value of patience=5 is set. If the number of iterations of the validation set exceeds 5 and the training accuracy and loss are not improved, the training will be terminated in advance, which is called "" "Early Stopping", by adding a validation set, can avoid overfitting and improve model selection. 2. the method for the aircraft trajectory prediction based on long short term memory network as claimed in claim 1, is characterized in that, concrete steps are as follows: The first step is to obtain the original state information from the airborne sensors, and select a total of twenty-three-dimensional feature quantities as the input of the prediction model; The second step is to preprocess the data: first, the original sensor parameters contain a certain amount of noise interference, and the Kalman filtering method is used to eliminate it; secondly, in order to improve the data utilization rate and reduce the calculation cost, the original data is treated according to 1: 5. Downsampling is performed and the data is normalized; finally, the invalid values are eliminated, the missing values are filled, and the data preprocessing is completed; then the input and label values are selected: the sliding window method is used to complete the data set. Segmentation, the input of the network is obtained by iterative selection of the original data, starting from 0 to the first time_step, because the time_step selected for this training is 20, that is, from 0 to 19 is the first input, and 1 to 20 is the second input, and so on; the dimension of the input data is (N, 20, 23), where N depends on the size of the sample set, 20 refers to the time_step value of the LSTM, 23 is the dimension of the feature vector, and the training network needs to use the label Data, since the purpose of this model is to predict the trajectory of the aircraft in the next step, therefore, for the first 0-19 input, select 1-20 longitude and latitude of the carrier aircraft as the label, for the second 1-20 input, select The latitude and longitude height of the carrier of 2-21 is used as a label, and so on; The third step is to build a trajectory prediction model based on LSTM. The constructed model includes two layers of LSTM layers. After each layer of LSTM layer, a dropout layer is added to avoid overfitting. After a fully connected layer, transform the dimensions to the desired output dimension.

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