CN114462293A - Method for predicting medium and long-term trajectory of hypersonic target - Google Patents

Method for predicting medium and long-term trajectory of hypersonic target Download PDF

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CN114462293A
CN114462293A CN202111564646.9A CN202111564646A CN114462293A CN 114462293 A CN114462293 A CN 114462293A CN 202111564646 A CN202111564646 A CN 202111564646A CN 114462293 A CN114462293 A CN 114462293A
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刘滔
赵暾
张显才
侯金鑫
郑凤麒
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention relates to the technical field of hypersonic targets, in particular to a method for predicting medium and long-term tracks of hypersonic targets, which comprises the following steps: step 1, obtaining position and speed state information of a target through a filtering algorithm according to information of a radar detection target; step 2, calculating a pneumatic parameter sequence alpha through historical state information obtained by target trackingVTCThen establishing an LSTM prediction model; step 3, predicting alpha by using the trained LSTM modelVTCThen, acquiring a medium-long term predicted track of the target according to a prediction result; step 4, when the target enters the maneuvering mode again or the maneuvering mode is changed, generating a new sequence alpha according to the step 1 and the step 2VTCAnd updating the LSTM model accordingly, and then returning to step 3. The invention can better predict the medium and long-term track.

Description

Method for predicting medium and long-term trajectory of hypersonic target
Technical Field
The invention relates to the technical field of hypersonic speed targets, in particular to a method for predicting a medium-long-term track of a hypersonic speed target.
Background
The hypersonic flight vehicle generally has a high lift-drag ratio or a medium lift-drag ratio, and can utilize aerodynamic control to perform long-distance unpowered maneuver gliding in an adjacent space after obtaining a certain height and speed. The aircraft has the capabilities of hypersonic speed and autonomous maneuvering, has the advantages of long reentry flight time, large flight altitude change range, flexible and changeable trajectory, difficulty in interception and the like, and brings great threat and challenge to the current defense system. The method is a problem which needs to be solved by a defense party urgently, and can find the target as early as possible, accurately predict the motion track of the target and implement effective interception.
For a defensive party, the target attribute of the track prediction belongs to a non-cooperative target, and the information such as the pneumatic parameter, the stress characteristic, the maneuvering mode, the maneuvering capability, the maneuvering range and the like of the target are unknown; and the hypersonic aircraft has high flying speed, adopts a non-inertial trajectory, cannot be applied by adopting a trajectory type target interception method, and can only intercept by a prediction hit point method, so that the target trajectory needs to be accurately tracked and predicted. The method is characterized in that the trajectory of the hypersonic aircraft is predicted based on the precondition that the target of the hypersonic aircraft is intercepted by the predicted hit point, and the prediction of the hypersonic aircraft refers to the estimation of the trajectory of the hypersonic aircraft at the future moment according to a certain rule or method on the basis of the existing information. The difference of the trajectory prediction method is essentially different from the known target trajectory related information recognition method. Trajectory prediction methods can be generally classified into three categories: the first category is analytical methods. Ballistic targets have a clear analytical formula, and trajectory prediction is generally performed by an analytical method. The analytic method has the advantages of high calculation speed and good real-time performance, but for the glide section of the hypersonic aircraft, the flight path is non-inertial, the dynamic modeling or characteristic parameter fitting is carried out on the flight path by analyzing the stress condition of the flight path, and the trajectory of the hypersonic aircraft is reversely designed according to the flight constraints such as dynamic pressure, heat flow, overload and the like, so that the analytic form of the motion path is obtained. At present, the method does not have enough prior information, people only obtain analytical solutions under certain assumptions (such as a lift-drag ratio is constant, heat flow is constant, and the like), and the method is limited in precision and cannot be used for track prediction. The second type is geometric. The method has the advantages that the form is simple by analyzing the curve characteristics of the target motion track, the short-term prediction precision is high, the long-term track characteristics of the target cannot be reflected due to the fact that the target track obtained by tracking is limited in duration, and the long-term prediction precision is low. The third category is numerical integration. The method allows the modeling and analysis of the target motion model to be carried out, can reflect the motion characteristics of the target, and has stronger pertinence and higher prediction precision. The numerical integration method has the advantages that various complex influence factors are allowed to be considered, and the track prediction precision is high; however, for the interception defense party, the target pneumatic parameters are unknown, accurate integral operation cannot be performed, and the method has large limitation.
From the perspective of an algorithm, the trajectory prediction problem is a time sequence prediction problem, the realization algorithm mainly comprises gray prediction, curve fitting, neural network prediction and the like, the algorithms establish a prediction or fitting model by using historical data, the short-term prediction precision is high, the medium-term prediction precision and the long-term prediction precision are low, and particularly when a target maneuvering mode is changed, the prediction precision cannot meet the requirement.
Disclosure of Invention
It is an object of the present invention to provide a method for mid-and long-term trajectory prediction of hypersonic targets that overcomes some or some of the deficiencies of the prior art.
The invention discloses a method for predicting a medium-long term trajectory of a hypersonic target, which comprises the following steps:
step 1, obtaining position and speed state information of a target through a filtering algorithm according to information of a radar detection target;
step 2, calculating a pneumatic parameter sequence alpha through historical state information obtained by target trackingVTCThen establishing an LSTM prediction model;
step 3, predicting alpha by using the well-trained LSTM modelVTCThen, acquiring a medium-long term predicted track of the target according to a prediction result;
step 4, when the target enters the maneuvering mode again or the maneuvering mode is changed, generating a new sequence alpha according to the step 1 and the step 2VTCAnd updating the LSTM model accordingly, and then returning to step 3.
Preferably, the sequence of pneumatic parameters αVTCThe calculation method is as follows:
setting: (1) the sideslip angle is zero; (2) regarding the earth as a sphere, the gravity of the earth is inversely proportional to the distance between the aircraft and the earth center; (3) neglecting the earth's rotation; the system of equations for the motion of the center of mass of the object in three-dimensional space
Figure BDA0003421431890000031
Comprises the following steps:
Figure BDA0003421431890000032
in the formula, the state variable
Figure BDA0003421431890000033
Where r represents the distance of the aircraft from the center of the earth, phi,
Figure BDA0003421431890000034
respectively representing latitude and longitude, theta, psi respectively representing a track inclination angle and a track deflection angle, and g is gravity acceleration; the pneumatic parameter a can be deduced according to the mass center motion equation setVTCThe calculation formula of (2):
Figure BDA0003421431890000035
in the VTC coordinate systemAerodynamic acceleration of aVTCIs air pressure intensity and pneumatic parameter alphaVTC＝[αd,αdktd,αdkcd]T＝[αV αT αC]Can be expressed here as:
Figure BDA0003421431890000036
from the above formula
Figure BDA0003421431890000037
In the formula, alphadAs a resistance parameter, the mass m and the reference area S of the aircraftaDetermining speed, height, length-to-diameter ratio and air viscosity coefficient; ρ is the air density; creep resistance ratio kcdThe ratio of climbing force to resistance force, the ratio of rotation to resistance ktdIs the ratio of the bending force to the resistance; lift-to-drag ratio krFor the ratio of lift to drag, assuming that the target lateral maneuver is the BTT mode, then
Figure BDA0003421431890000038
Preferably, in the LSTM prediction model, the LSTM memorizes information for a long period of time through three gates, and the LSTM includes:
1) forget the door:
f(t)＝σ(Wf[αVTC(t),h(t-1)]+bf)；
in the formula, alphaVTC(t) is a current moment pneumatic parameter; wfThe weight coefficient of a forgetting gate f is, sigma is a sigmoid activation function, h is the output of an LSTM, and b is a bias term;
2) an input gate:
i(t)＝σ(Wi[αVTC(t),h(t-1)]+bi)；
Figure BDA0003421431890000041
input gate i (t) controls the current timeSelect state
Figure BDA0003421431890000042
Which information needs to be saved; wiRepresents the input weight, W, corresponding to the input gate icRepresenting the state weight corresponding to the cell state c;
3) and (3) updating the cell state:
Figure BDA0003421431890000043
the forgetting gate output f (t) is multiplied by the last state of the cell c (t-1) to forget and add the new candidate
Figure BDA0003421431890000044
Scaling according to the update value determined for each state;
Figure BDA0003421431890000045
4) an output gate:
o(t)＝σ(Wo[aVTC(t),h(t-1)]+bo)；
h(t)＝o(t)·tanh(c(t))；
the output gate o (t) controls the information output of the cell state c (t) at the current moment.
Preferably, in step 3, the data is normalized before prediction;
Figure BDA0003421431890000046
in the formula (I), the compound is shown in the specification,
Figure BDA0003421431890000047
is alphaVTC(t) the normalized value of the signal,
Figure BDA0003421431890000048
are each alphaVTC(t) mean and deviation, wherein:
Figure BDA0003421431890000051
Figure BDA0003421431890000052
after the trained model is used for prediction, inverse normalization needs to be performed on the prediction result, and the formula of the inverse normalization is as follows:
Figure BDA0003421431890000053
the invention provides a medium-long term track prediction strategy of a hypersonic speed target based on LSTM pneumatic parameter sequence prediction, which is characterized in that a medium-long term track prediction problem is converted into a long term sequence prediction problem, and then a time sequence prediction result is integrated through a dynamic model to obtain medium-long term track prediction of the target. Firstly, a pneumatic parameter sequence which is approximately linear to a target posture is obtained through coordinate conversion relation and formula derivation, then, long-short-term memory (LSTM) is utilized to predict the pneumatic parameter sequence, the predicted pneumatic parameter sequence is substituted into a dynamic model to obtain a medium-long term predicted track, and meanwhile, the prediction model is updated according to the target maneuver so as to reduce the track prediction error caused by the target complex abrupt maneuver. The prediction algorithm provided by the invention can provide certain theoretical support for the interception strategy based on the prediction hit point.
Drawings
Fig. 1 is a flowchart of a method for predicting a medium-long term trajectory of a hypersonic target in embodiment 1;
FIG. 2(a) is a graph showing the pneumatic parameters a in the case where the target control amounts α and β are both constant values in example 1VTCA time-dependent profile;
FIG. 2(b) is a graph showing the pneumatic parameter α in the case where the target control amounts α and β are both constant values in example 1VTCA time-dependent profile;
FIG. 3 is a schematic diagram showing the RNN structure in example 1;
FIG. 4 is a schematic view of the LSTM structure in example 1;
FIG. 5 is a UKF filtering algorithm tracking target trajectory curve when the target in embodiment 1 adopts maneuver mode 2;
FIG. 6(a) is a view showing the pneumatic parameter α in the case of the maneuver 1 in example 1VTCThe medium-long term prediction result is shown schematically;
FIG. 6(b) is a schematic diagram of a three-dimensional trajectory of a target in the maneuvering mode 1 in example 1;
FIG. 6(c) is a schematic diagram of the tracking and medium-and long-term prediction errors of the target in the maneuver 1 of example 1;
FIG. 7(a) is a view showing the aerodynamic parameter α in the case of the maneuvering mode 2 in example 1VTCThe medium-long term prediction result is shown schematically;
FIG. 7(b) is a schematic diagram of a three-dimensional trajectory of a target in the case of adopting the maneuver mode 2 in example 1;
fig. 7(c) is a schematic diagram of the tracking and medium-and long-term prediction errors of the target in the maneuver 2 of example 1.
Detailed Description
For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not limiting.
Example 1
Hypersonic target maneuvering characteristic analysis
To predict the trajectory of the hypersonic velocity target, firstly, a dynamic model and a kinematic model of the hypersonic velocity target are analyzed according to the stress condition of the hypersonic velocity target, the maneuvering characteristics of the hypersonic velocity target are further researched, constraint conditions such as the maneuvering mode and the maneuvering capability of the hypersonic velocity target are analyzed, the trajectory prediction range is narrowed, and the trajectory prediction precision is improved.
Hypersonic velocity dynamics model
The aircraft acceleration expression is:
Figure BDA0003421431890000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003421431890000062
the ground center distance vector of the aircraft, a and g respectively represent the aerodynamic acceleration and the gravitational acceleration of the aircraft, omegaeIs the rotational angular velocity of the earth, -omegae×(ωeXr) is the bulk acceleration caused by inertial centrifugal force,
Figure BDA0003421431890000063
is the coriolis acceleration. The aerodynamic acceleration is generally resolved in the VTC coordinate system and can be expressed as:
a＝-aVeV+aTeT+aCeC (3)
in the formula, eV、eT、eCFor each coordinate axis unit vector in VTC coordinate system, let aVTC＝[aV aT aC]TAnd the components of the coordinates of the aircraft in the VTC coordinate axis system are represented.
2.1 hypersonic velocity target pneumatic acceleration model
For a hypersonic target, after data processing such as direct detection and tracking by a radar, the obtained information is usually the position, speed, acceleration and the like of the target. Hypersonic reentry gliding aircraft usually adopts a maneuver mode of bank turning, and the hypersonic target is taken as a mass point and then a three-dimensional space motion model of the hypersonic target in a northeast coordinate system is established. Based on the transient balance assumption, the motion of the aircraft can be divided into centroid motion and motion around the centroid. We assume that: (1) the sideslip angle is zero; (2) regarding the earth as a sphere, the gravity of the earth is inversely proportional to the distance between the aircraft and the earth center; (3) neglecting earth rotation. The system of the centroid motion equation of the target in the three-dimensional space is:
Figure BDA0003421431890000071
in the formula, the state variable
Figure BDA0003421431890000072
Where r represents the distance of the aircraft from the center of the earth, phi,
Figure BDA0003421431890000073
respectively, latitude and longitude, theta, psi respectively, track inclination and track declination, and g is gravitational acceleration. The pneumatic parameter a can be derived from equation (4)VTCThe calculation formula of (2):
Figure BDA0003421431890000074
aerodynamic acceleration a in VTC coordinate systemVTCIs air pressure intensity and pneumatic parameter alphaVTC＝[αd,αdktd,αdkcd]T＝[αV αT αC]Can be expressed here as:
Figure BDA0003421431890000081
from the above formula
Figure BDA0003421431890000082
In the formula, alphadAs a resistance parameter, the mass m and the reference area S of the aircraftaDetermining speed, height, length-to-diameter ratio, air viscosity coefficient and the like; ρ is the air density; creep resistance ratio kcdThe ratio of climbing force to resistance force, the ratio of rotation to resistance ktdIs the ratio of the bending force to the resistance; lift-to-drag ratio krFor lift to drag ratio, assuming the target lateral maneuver is in BTT mode, there are
Figure BDA0003421431890000083
In the prediction of the trajectory of the hypersonic target in the non-cooperative near space, the defensive party generally cannot obtain the m and S of the aircraftaThe long straight ratio, the lift drag coefficient, the air viscosity coefficient and the control quantity attack angle alpha and the roll angle beta can not be directly obtainedAnd acquiring the data through target tracking. FIG. 2(a) and FIG. 2(b) show the pneumatic parameter a when the target control amounts α and β are both constant valuesVTCAnd alphaVTCTime profile.
As can be seen in FIGS. 2(a) and 2(b), the aerodynamic parameter a is a for a fixed alpha, beta flight of the targetVTCComponent a ofV、aT、aCNon-linearly varying and irregular with time, and the aerodynamic parameter aVTCComponent a ofV、αT、αCApproximately linear in time, so to speak the aerodynamic parameter αVTCApproximately linear with the relative pose of the target at VTCCS.
Pneumatic parameter track prediction strategy based on LSTM
For the pneumatic parameter alphaVTCThe three component analysis shows that the three components are mainly influenced by lift drag coefficients CL, CD and roll angle of the aircraft, and for a hypersonic aircraft target, CL and CD can be considered to be influenced by factors such as attack angle, Mach number, altitude and the like, particularly the attack angle. The attack angle in the reentry process of the aircraft has important influence on the flight distance, and the roll angle has influence on the target transverse maneuver. For the aerodynamic parameter αVTCLinearly varying object by fitting alphaVTCThe trajectory prediction of the trajectory target can be realized as shown in FIG. 2(b), αVTCThe time is basically linear, and the fitting method has good prediction effect. When α isVTCWhen the parameters are subjected to long-time nonlinear change, the simple fitting method only has a good short-time prediction effect, but has a poor medium-long time prediction effect. Long-term memory (LSTM) can well deal with the Long-term sequence prediction problem, and the embodiment predicts a target pneumatic parameter sequence by using the LSTM so as to predict a medium-term and Long-term trajectory of a target.
LSTM neural network model
Long-short term memory (LSTM) is a special Recurrent Neural Network (RNN). The feedback structure is added in the RNN hidden layer, namely the output at the current moment is not only related to the current input, but also related to the output at the previous moment, and the feedback structure is equivalent to a deep neural network developed on a time series and is more suitable for processing time series data. The RNN structure is shown in FIG. 3.
LSTM takes place as soon as the RNN cannot learn long-term dependence due to the disadvantages of gradient disappearance and gradient explosion. LSTM was proposed by Hochreiter and Schmidhuber and recently improved and generalized by Alex Graves. The LSTM can remember information in a long time period through three gates, and solves the problem of long-term dependence to a certain extent so as to solve the problems of gradient extinction and gradient explosion in the long sequence training process. LSTM is often used for trajectory prediction, action classification and semantic classification, and the embodiment utilizes LSTM to perform target pneumatic parameter sequence alphaVTCPredicting the target medium-long term trajectory by using the predicted target medium-long term trajectory, and predicting alpha by using LSTMVTCThe structure of (2) is shown in fig. 4.
According to the structure of fig. 4, it is possible to obtain:
1) forget the door:
f(t)＝σ(Wf[αVTC(t),h(t-1)]+bf)
in the formula, alphaVTCAnd (t) is a pneumatic parameter at the current moment. WfThe weight coefficient of the forgetting gate f is sigma activation function, h is LSTM output, and b is bias term.
2) An input gate:
i(t)＝σ(Wi[αVTC(t),h(t-1)]+bi)
Figure BDA0003421431890000091
input gate i (t) controls the candidate state at the current time
Figure BDA0003421431890000109
Which information needs to be saved. WfThe weight coefficient of the forgetting gate f is sigma activation function, h is LSTM output, and b is bias term.
3) Renewal of cell status
Figure BDA0003421431890000101
The forgetting gate output f (t) is multiplied by the state c (t-1) of the cell at the previous moment to forget what we need to forget, and a new candidate value is added
Figure BDA0003421431890000102
Scaling is done according to the update value we decide for each state.
Figure BDA0003421431890000103
4) An output gate:
o(t)＝σ(Wo[aVTC(t),h(t-1)]+bo)；
h(t)＝o(t)·tanh(c(t))；
the output gate o (t) controls the information output of the cell state c (t) at the current moment.
Trajectory prediction strategy based on pneumatic parameter sequence prediction
In the target reentry process, the position and angle information of a target is detected through a radar, then the track information of the target is obtained through radar data processing (a target state observer), and then the pneumatic parameter sequence alpha of the target is obtained by using the formula (5)VTC(T), T ═ 1, 2.., n + T', which is then used for training and prediction of the LSTM model.
To improve the stability of the calculation, the data are normalized (normal normalization), that is:
Figure BDA0003421431890000104
in the formula (I), the compound is shown in the specification,
Figure BDA0003421431890000105
is alphaVTC(t) the normalized value of the signal,
Figure BDA0003421431890000106
are each alphaVTC(t)Wherein:
Figure BDA0003421431890000107
Figure BDA0003421431890000108
after the trained model is used for prediction, the prediction result needs to be subjected to inverse normalization, and then the target track prediction can be continuously carried out by substituting the formula (4), wherein the formula of the inverse normalization is as follows:
Figure BDA0003421431890000111
as shown in FIG. 1, the pneumatic parameter α is predicted based on the LSTM methodVTCAnd sequencing to realize target medium and long term track prediction, wherein the specific steps are as follows:
step 1, obtaining state information such as position, speed and the like of a target through a filtering algorithm according to information of a radar detection target.
Step 2, calculating a pneumatic parameter sequence alpha by substituting equations (4) to (6) through historical state information obtained by target trackingVTCThen, an LSTM prediction model is established.
Step 3, predicting alpha by using the well-trained LSTM modelVTCAnd then substituting the prediction result into an equation (4) to obtain the predicted track of the target in the medium and long term.
Step 4, when the target enters the maneuvering mode again or the maneuvering mode is changed, generating a new sequence alpha according to the step 1 and the step 2VTCAnd updating the LSTM model accordingly, and then returning to step 3.
Simulation analysis
1. Simulation condition setting
From the current state of research on hypersonic vehicles, it is known that, although hypersonic assisted gliding aircraft have lateral maneuvering capabilities, the typical lateral maneuvering patterns for certain tactical needs are not seen from the open literature in view of its control stability and maneuverability. To verify the performance of the LSTM algorithm to predict aerodynamic parameters and the effectiveness of the hypersonic target trajectory prediction method, we assume that the target always flies at the mission profile angle of attack (i.e., the angle of attack is a piecewise function of velocity), and give the following 2 target maneuvers:
mode 1: the target always flies at a roll angle of 30 degrees;
mode 2: the target roll angle maneuvers in a step wave with a period of 80s and an amplitude of 45 °.
The hypersonic aircraft target observer is an early warning radar, and the distance, the pitch angle and the azimuth angle between a detection point and a target can be obtained through the radar. The equation for early warning radar detection of the target is as follows:
Figure BDA0003421431890000121
in the formula, zk、h(xk) And σkRespectively an observation vector, a measurement equation and measurement noise of the early warning radar; sigmar、σθ、
Figure BDA0003421431890000122
The early warning radar radial distance, the pitch angle and the azimuth angle error are white noise sequences with the mean value of zero respectively. Here the initial state x of the target is given0＝[56.42km,0°,0°,4.0km/s,-2°,0°]TThe arrangement position of the early warning radar is 0 degrees and 0 degrees]TThe standard deviation of the measured noise is [50m,0.05 DEG ]]T。
For tracking of non-cooperative target with controlled quantity input, the present embodiment uses Unscented Kalman Filter (Unscented Kalman Filter, UKF) algorithm to track, and analyzes α according to the aboveVTCThe change is slow in the flying process, the embodiment takes the change as the control input of the target motion model, and the estimated value of the previous moment
Figure BDA0003421431890000123
And the control quantity is input as the control quantity of the current moment, and then filtering is carried out by using UKF. As shown in the figureAnd 5, when the target adopts a maneuvering mode 2, tracking a target track curve by a UKF filtering algorithm. In FIG. 5, height is height; latitude: latitude; longtitude: longitude; realjectory: an actual trajectory; the object projection: observing a track; ukfesitetrajectory: ukf estimate the trajectory.
2. Trajectory prediction simulation analysis
Firstly, tracking the track of the target adopting the two maneuvering modes by using a UKF algorithm to obtain alphaVTC(t), t 1,2, k, then using the LSTM algorithm to predict αVTC(T), T ═ k + 1.., k + T to obtain the medium and long term predicted trajectory of the target, and 50 monte carlo simulations were performed.
2.1 prediction accuracy analysis
Target pneumatic parameter alpha of two maneuvering tracksVTCThe results of the middle-long term prediction in (a) and (b) of fig. 6 are shown; fig. 6(b) and 7(b) show the three-dimensional trajectory of the target, and fig. 6(c) and 7(c) show the tracking and medium-and long-term prediction errors of the target. The trajectory1, trajectory 2, and trajectory3 in fig. 6(b) are curves from the predicted start time 400s, 500s, 600s, and 700s to the end time 791s, respectively, and the trajectory1, trajectory 2, and trajectory3 in fig. 7(b) are curves from the predicted start time 500s, 600s, and 700s to the end time 723s, respectively.
As can be seen from fig. 6(b) and fig. 7(b), the target medium-and-long-term predicted trajectory can substantially coincide with the real trajectory of the target, which illustrates that the prediction method of the present embodiment can achieve a relatively ideal effect on the trajectory prediction of the target by using the maneuver manners 1 and 2. As can be seen from the tracking and predicting results of the target three-dimensional track, in the target tracking process, due to the fact that observation data are corrected in time, the tracking estimation result can well approach the real target track; and the error accumulation effect exists in the medium-long term prediction track, and the deviation of the error accumulation effect with the real track is continuously increased along with the increase of the prediction duration.
Compare α in FIG. 6(a) with FIG. 7(a)VTCTracking and predicting the result, aerodynamic parameter αVAnd alphaCApproximately piecewise linear variation with time; whereas for maneuver 2, the target aerodynamic parameter αTDue to the fact thatThe roll angle changes stepwise with a step change in time. α in FIGS. 6(a) and 7(a)VTCCan show that the LSTM network can basically predict alphaVTCBut the prediction error increases with time, particularly for the target aerodynamic parameter α in the maneuver mode 2TThe LSTM algorithm is well able to predict the step change.
The tracking error and the prediction error of the target state are contrastively analyzed, and the position error of 100s predicted within the range of 5km by knowing different maneuvering modes and different tracking durations. In particular, in the maneuvering mode 1 with a small maneuvering variation range, the position error of the predicted 100s duration is within the range of 2km, but the predicted position error increases sharply with the increase of the predicted time, which is considered to be caused by the cumulative effect of the predicted speed error. The speed error of the different predicted time periods of the two maneuvers is below 40m/s, and in addition, it should be noted that the tracking speed error increases significantly when the tracking time is shorter due to the larger initial model error, as can be seen from the speed tracking error curves in fig. 6(c) and fig. 7 (c).
2.2 real-time analysis
The operating environment of the embodiment comprises an AMD Ryzen 54500U 2.38.38 GHZ processor, an 8G memory and a Win 1064 Bit operating system, and the operating platform is MATLAB2020 b. The time required for tracking and predicting the two maneuver trajectories is shown in Table 1.
Knowing that the running step length of the program is 1s, the time consumed by adopting the UKF single step tracking is less than 10ms and far less than the predicted step length 1 s. From table 1, it is found that, when performing the medium-and-long-term trajectory prediction, the time length required for training 400s data is greater than 4s (>1s), but when actually performing the target trajectory prediction, we can adopt a batch training strategy to enable the medium-and-long-term trajectory prediction to meet the real-time requirement. The specific method is that the 400s data is divided into two batches, the first batch of data is 390s data, the second batch of data is 10s data, the time consumed for training the first batch of data is less than 4s, and the second batch of data only needs 100ms (<1s) for training, so that the requirement of predicting the track in real time can be met. The method can also be adopted in the later migration training, so that the trajectory prediction can meet the requirement of real-time performance.
TABLE 1
Figure BDA0003421431890000141
Conclusion
In the embodiment, a prediction method of the medium and long-term track of the hypersonic aircraft target is developed on the basis of prediction of a pneumatic parameter sequence of the hypersonic target. When a target motion model is constructed, parameters related to pneumatic stress are fused into a target state, and the influence of dynamic pressure in target pneumatic parameters is eliminated. And acquiring a new pneumatic parameter sequence with slow change, predicting the new pneumatic parameter sequence at the future moment by using a time sequence prediction model, and using the prediction result for target medium and long-term trajectory prediction. Simulation analysis shows that the trajectory prediction precision of the method of the embodiment under the target roll angle change can meet the requirement.
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.

Claims (4)

1. A method for predicting a medium-long term trajectory of a hypersonic target is characterized by comprising the following steps: the method comprises the following steps:
step 1, obtaining position and speed state information of a target through a filtering algorithm according to information of a radar detection target;
step 2, calculating a pneumatic parameter sequence alpha through historical state information obtained by target trackingVTCThen establishing an LSTM prediction model;
step 3, predicting alpha by using the well-trained LSTM modelVTCThen, acquiring a medium-long term predicted track of the target according to a prediction result;
step 4, when the target reenters the maneuvering mode or the maneuvering mode is changed, generating a new sequence alpha according to the step 1 and the step 2VTCAnd updating the LSTM model accordingly, and then returning to step 3.
2. The method for predicting the medium-long term trajectory of the hypersonic target according to claim 1, characterized in that: sequence of pneumatic parameters alphaVTCThe calculation method is as follows:
setting: (1) the sideslip angle is zero; (2) regarding the earth as a sphere, the gravity of the earth is inversely proportional to the distance between the aircraft and the earth center; (3) neglecting the earth's rotation; the system of equations for the motion of the center of mass of the object in three-dimensional space
Figure FDA0003421431880000015
Comprises the following steps:
Figure FDA0003421431880000011
in the formula, the state variable
Figure FDA0003421431880000012
Where r represents the distance of the aircraft from the center of the earth, phi,
Figure FDA0003421431880000013
respectively representing latitude and longitude, theta, psi respectively representing a track inclination angle and a track deflection angle, and g is gravity acceleration; the pneumatic parameter a can be deduced according to the mass center motion equation setVTCThe calculation formula of (2):
Figure FDA0003421431880000014
aerodynamic acceleration a in VTC coordinate systemVTCIs air pressure intensity and pneumatic parameter alphaVTC＝[αd,αdktd,αdkcd]T＝[αVαT αC]Is composed ofThe number, here, can be expressed as:
Figure FDA0003421431880000021
from the above formula
Figure FDA0003421431880000022
In the formula, alphadAs a resistance parameter, the mass m and the reference area S of the aircraftaDetermining speed, height, length-to-diameter ratio and air viscosity coefficient; ρ is the air density; creep resistance ratio kcdThe ratio of climbing force to resistance force, the ratio of rotation to resistance ktdIs the ratio of the bending force to the resistance; lift-to-drag ratio krFor the ratio of lift to drag, assuming that the target lateral maneuver is the BTT mode, then
Figure FDA0003421431880000023
3. The method for predicting the medium-long term trajectory of the hypersonic target according to claim 2, characterized in that: in the LSTM prediction model, LSTM keeps track of information over long periods of time through three gates, the LSTM includes:
1) forget the door:
f(t)＝σ(Wf[αVTC(t),h(t-1)]+bf)；
in the formula, alphaVTC(t) is a current moment pneumatic parameter; wfThe weight coefficient of a forgetting gate f is, sigma is a sigmoid activation function, h is the output of an LSTM, and b is a bias term;
2) an input gate:
i(t)＝σ(Wi[αVTC(t),h(t-1)]+bi)；
Figure FDA0003421431880000024
input gate i (t) controls the candidate state at the current time
Figure FDA0003421431880000025
Which information needs to be saved; wiRepresents the input weight, W, corresponding to the input gate icRepresenting the state weight corresponding to the cell state c;
3) and (3) updating the cell state:
Figure FDA0003421431880000026
the forgetting gate output f (t) is multiplied by the last state of the cell c (t-1) to forget and add the new candidate
Figure FDA0003421431880000027
Scaling according to the update value determined for each state;
Figure FDA0003421431880000031
4) an output gate:
o(t)＝σ(Wo[aVTC(t),h(t-1)]+bo)；
h(t)＝o(t)·tanh(c(t))；
the output gate o (t) controls the information output of the cell state c (t) at the current moment.
4. The method for predicting the medium-long term trajectory of the hypersonic target according to claim 3, characterized in that: step 3, normalizing the data before prediction;
Figure FDA0003421431880000032
in the formula (I), the compound is shown in the specification,
Figure FDA0003421431880000033
is alphaVTC(t) normalizationThe value of the product after the conversion is shown,
Figure FDA0003421431880000034
are each alphaVTC(t) mean and deviation, wherein:
Figure FDA0003421431880000035
Figure FDA0003421431880000036
after the trained model is used for prediction, inverse normalization needs to be performed on the prediction result, and the formula of the inverse normalization is as follows:
Figure FDA0003421431880000037
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