CN109858137B - Complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering - Google Patents

Complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering Download PDF

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CN109858137B
CN109858137B CN201910078778.7A CN201910078778A CN109858137B CN 109858137 B CN109858137 B CN 109858137B CN 201910078778 A CN201910078778 A CN 201910078778A CN 109858137 B CN109858137 B CN 109858137B
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郑天宇
贺风华
姚郁
杨宝庆
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Harbin Institute of Technology
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Abstract

The invention discloses a complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering, and relates to a track estimation method of an aircraft. The invention solves the problem that the existing flight path estimation method has lower precision under the complex maneuvering condition of the target aircraft. The technical points of the invention are as follows: establishing a dynamic model of the aircraft, and further establishing a maneuvering model of the aircraft; and constructing a learnable extended Kalman filtering algorithm for estimating the flight path of the aircraft, and designing and training an input modification network and a gain modification network in the learnable extended Kalman filtering algorithm. The learnable extended Kalman filtering algorithm used in the flight path estimation of the aircraft is obtained by training according to the existing flight path data, so that the prior information of the motion characteristics of the aircraft is more fully utilized, the complex maneuvering mode of the aircraft can be more accurately described, and the flight path estimation precision is improved. The method is suitable for the field of information calculation based on knowledge and modes.

Description

Complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering
Technical Field
The invention relates to a flight path estimation method of an aircraft, in particular to a learnable extended Kalman filtering method based on a recurrent neural network, and belongs to the field of information calculation based on knowledge and modes.
Background
For an aircraft with a complex maneuvering form, such as a high-speed gliding aircraft, the flight path estimation is more complex than that of a general aircraft. Most of the existing aircraft track estimation methods describe target maneuvers by using models such as Constant Velocity (CV), Constant Acceleration (CA), current statistics and Singer, and realize track estimation based on Extended Kalman Filtering (EKF), adaptive Kalman filtering (AEKF) and other methods. When the problem of flight path estimation of the aircraft with a complex maneuvering form is faced, the model precision is limited, and the existing flight path estimation method cannot be fully adapted to the complex motion mode of the aircraft, so that the estimation precision is low.
The patent document with the reference number of CN107504972A provides an aircraft track planning method based on a pigeon swarm algorithm, which comprises the steps of firstly establishing a track prediction model containing uncertainty, then determining a path to be optimized in a specified area, adopting the pigeon swarm algorithm, obtaining an optimal path through iteration through map, compass operation and landmark operation, and finally outputting each parameter of the obtained optimal path. In the prior art, a track prediction model is deduced and calculated, and a path obtained by using the model has good stability, robustness and feasibility; and the intelligent optimization method of the pigeon group is adopted, the problem of complex continuous optimization is solved, and the calculation searching process has the characteristics of parallelism, feasibility and strong robustness. But does not indicate how to solve the problem of low precision in the complex maneuvering conditions of the target aircraft.
Disclosure of Invention
The invention aims to provide a flight path estimation method suitable for an aircraft with a complex maneuver form, which aims to solve the problem that the existing method is low in precision under the complex maneuver condition of a target aircraft, and further provides a complex maneuver aircraft flight path estimation method based on learnable extended Kalman filtering.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering is realized according to the following steps:
the method comprises the following steps: building a maneuver model of an aircraft
Assuming that the earth is a regular sphere, a three-dimensional dynamic model of the aircraft is obtained under the condition of neglecting autorotation:
Figure GDA0003590448730000021
wherein R is the distance from the centroid of the aircraft to the geocentric, theta is the longitude, phi is the latitude, v is the velocity, gamma is the ballistic inclination angle, psi is the ballistic declination angle, m is the aircraft mass, R is the aircraft masse6,378,135m is the radius of the earth, g0As acceleration of gravity, SrefFor a characteristic area of an aircraft, ρ ═ ρ0e-βhIn order to be at the density of the atmosphere,
Figure GDA0003590448730000022
and
Figure GDA0003590448730000023
the lift coefficient and the drag coefficient when the lift-drag ratio of the aircraft is maximum, clTo normalize the lift coefficient, σ is the roll angle of the aircraft;
lateral maneuver of the aircraft was described using the Singer maneuver model:
Figure GDA0003590448730000024
wherein, TsA time constant for the maneuver;
and (2) obtaining a maneuvering model of the aircraft by the united vertical type (1) and the united vertical type (2):
Figure GDA0003590448730000025
step two: and estimating the motion state of the aircraft according to the measurement (r, theta, phi), and estimating the motion state of the aircraft by using a learnable extended Kalman filtering algorithm.
Further, the aircraft motion state estimation in the second step is carried out by using a learnable extended kalman filter algorithm, and the specific process is as follows:
step two is as follows: let state xk＝[rk,θk,φk,vk,γk,ψk,σk]TInput uk＝[cl,k,Ts,k]TMeasuring zk＝[rk,θk,φk]TThe model shown in the formula (3) is rewritten into a form of a nonlinear discrete system
Figure GDA0003590448730000031
Wherein,
Figure GDA0003590448730000032
Figure GDA0003590448730000033
subscript k denotes time k;
tsstep size, x, representing a discrete system1,k-1X in (2)1Corresponds to r (i.e. x)1,k-1Corresponds to rk-1)，x2,k-1X in (2)2Corresponds to theta (i.e. x)2,k-1Corresponds to thetak-1) The rest is analogized in the same way;
step two: input u is Input through Input Modification Network (IMN)kMake a modification
Figure GDA0003590448730000041
Figure GDA0003590448730000042
Where denotes multiplication by element, κkIn order to input the parameters for the modification,
Figure GDA0003590448730000043
is a modified input;
step two and step three: state and covariance prediction
Figure GDA0003590448730000044
Figure GDA0003590448730000045
Wherein Q iskIs a covariance matrix of the process noise,
Figure GDA0003590448730000046
the Jacobian matrix of the equation of state f (x, u),
Figure GDA0003590448730000047
state at time k-1, Pk-1|k-1Is a state at the time k-1
Figure GDA0003590448730000048
The covariance matrix is then used to generate a covariance matrix,
Figure GDA0003590448730000049
and Pk|k-1Respectively, one-step prediction of the state and covariance matrices;
step two, four: computing suboptimal Kalman gain
Figure GDA00035904487300000410
Figure GDA00035904487300000411
Figure GDA00035904487300000412
Wherein R iskIn order to measure the covariance matrix of the noise,
Figure GDA00035904487300000413
to measure the Jacobian matrix of equation h (x),
Figure GDA00035904487300000414
for measuring residual errors, SkCovariance matrix, K, being the residualkSuboptimal Kalman gain;
step two and step five: gain Modification Network (GMN) pair suboptimal Kalman Gain KkMake a modification
Figure GDA00035904487300000415
Figure GDA00035904487300000416
Wherein G iskIn order to gain-modify the parameters,
Figure GDA00035904487300000417
the modified suboptimal Kalman gain is obtained;
step two, step six: updating state and covariance estimates
Figure GDA00035904487300000418
Figure GDA0003590448730000051
Wherein I is a unit array.
Further, the specific process of establishing the input decoration network (IMN) in the second step is as follows:
establishing a two-layer Long Short Term Memory (LSTM) network, the input of the first layer being the model input ukMeasuring zkEstimation of the State of the last step
Figure GDA0003590448730000052
The output is the coded features; the input of the second layer is the output of the first layer, and the output is the input u to the modelkModification parameter of (k)k。
Further, the specific process of establishing the Gain Modified Network (GMN) described in the second five steps is as follows:
establishing a two-layer Long Short Term Memory (LSTM) network, wherein the input of the first layer is modified model input
Figure GDA0003590448730000053
State estimation of the previous step
Figure GDA0003590448730000054
The output is the coded features; the input of the second layer is the output of the first layer, and the output is the suboptimal Kalman gain KkModification parameter G ofk。
The invention has the beneficial effects that: the invention establishes a dynamic model of the aircraft and further establishes a maneuvering model of the aircraft; and constructing a learnable extended Kalman filtering algorithm for estimating the flight path of the aircraft, and designing and training an input modification network and a gain modification network in the learnable extended Kalman filtering algorithm. For the flight path estimation problem of complex maneuvering, the key for improving the estimation precision is to improve the adaptability to model/parameter uncertainty and accurately describe the characteristics of target maneuvering.
Compared with the existing track estimation method, the method has the advantages that,
(1) compared with the traditional AEKF algorithm, the learnable extended Kalman filtering algorithm used in the aircraft track estimation can adapt to a large-range target motion model and parameter uncertainty.
(2) The learnable extended Kalman filtering algorithm used in the flight path estimation of the aircraft is obtained by training according to the existing flight path data, so that the prior information of the motion characteristics of the aircraft is more fully utilized, the complex maneuvering mode of the aircraft can be more accurately described, and the flight path estimation precision is improved.
(3) The estimation performance of the learnable extended Kalman filtering algorithm used in the aircraft track estimation is insensitive to two parameters of a process and a measurement noise covariance matrix (the convergence of the filtering algorithm can be ensured only by requiring the two parameters), and the tuning parameters of the filtering algorithm are greatly simplified.
The invention establishes a dynamic model of the aircraft and further establishes a maneuvering model of the aircraft; a learnable extended Kalman filtering algorithm for estimating the flight path of the aircraft is constructed, and an input modification network and a gain modification network are designed and trained. The method solves the problem that the existing flight path estimation method cannot cope with the complex maneuvering form of the aircraft, improves the precision of flight path estimation, and simplifies the parameter adjustment of the flight path estimation algorithm. The method is suitable for the field of information calculation based on knowledge and modes. It can be seen from fig. 4 that the method of the present invention has similar position estimation accuracy to the conventional EKF and AEKF methods, but the result is better smooth. Fig. 5 shows that the method of the invention is more accurate in estimating the speed of the aircraft than the conventional EKF and AEKF methods.
The aircraft with complex maneuvering forms aimed by the invention has multiple maneuvering forms such as quasi-equilibrium gliding, jumping gliding, evasion, sudden defense and the like, and the flight path is restrained by heat flow, dynamic pressure, overload and other factors, and the maneuvering forms are difficult to be accurately described by the maneuvering model.
Drawings
Figure 1 is a block diagram of the algorithm of the present invention,
figure 2 is a block diagram of an input grooming network,
figure 3 is a block diagram of a gain modification network,
FIG. 4 is the result of an aircraft position estimation, comparing the method of the present invention with conventional EKF, AEKF methods,
FIG. 5 is the result of an aircraft speed estimation comparing the method of the present invention with conventional EKF, AEKF methods.
Detailed Description
The learnable extended Kalman filtering method for estimating the flight path of the complex maneuvering target is implemented according to the following steps:
the method comprises the following steps: building a mobility model of an object
Assuming that the earth is a regular sphere, neglecting autorotation, obtaining a three-dimensional dynamic model of the aircraft:
Figure GDA0003590448730000061
wherein R is the distance from the centroid of the aircraft to the geocentric, theta is the longitude, phi is the latitude, v is the velocity, gamma is the ballistic inclination angle, psi is the ballistic declination angle, m is the aircraft mass, R is the aircraft masse6,378,135m is the radius of the earth, g0As acceleration of gravity, SrefFor a characteristic area of an aircraft, ρ ═ ρ0e-βhIn order to be at the density of the atmosphere,
Figure GDA0003590448730000062
and
Figure GDA0003590448730000063
the lift coefficient and the drag coefficient when the lift-drag ratio of the aircraft is maximum, clTo normalize the lift coefficient, σ is the roll angle of the aircraft.
Lateral maneuver of the target was described using the Singer maneuver model:
Figure GDA0003590448730000071
wherein, TsIs the time constant of the maneuver.
Obtaining a maneuvering model of a target by the joint type (1) and (2):
Figure GDA0003590448730000072
step two: the motion state of the object is estimated from the measurements (r, theta, phi).
Constructing a learnable extended Kalman filtering algorithm to carry out the target motion state estimation in the second step, wherein the specific process is as follows:
step two, firstly: let state xk＝[rk,θk,φk,vk,γk,ψk,σk]TInput uk＝[cl,k,Ts,k]TMeasuring zk＝[rk,θk,φk]TThe model shown in the formula (3) is rewritten into a form of a nonlinear discrete system
Figure GDA0003590448730000073
Wherein,
Figure GDA0003590448730000081
Figure GDA0003590448730000082
the subscript k denotes the time k.
Step two: input u is Input through Input Modification Network (IMN)kMake a modification
Figure GDA0003590448730000083
Figure GDA0003590448730000084
Wherein denotes multiplication by element, κkIn order to input the parameters for the modification,
Figure GDA0003590448730000085
is the modified input.
Step two and step three: state and covariance prediction
Figure GDA0003590448730000086
Figure GDA0003590448730000087
Wherein Q iskIs a covariance matrix of the process noise,
Figure GDA0003590448730000088
the Jacobian matrix of the equation of state f (x, u),
Figure GDA0003590448730000089
state at time k-1, Pk-1|k-1Is a state at the time k-1
Figure GDA00035904487300000810
The covariance matrix is then used to determine the covariance matrix,
Figure GDA00035904487300000811
and Pk|k-1One step prediction of the state and covariance matrices, respectively.
Step two, four: computing sub-optimal Kalman gain
Figure GDA0003590448730000091
Figure GDA0003590448730000092
Figure GDA0003590448730000093
Wherein R iskIn order to measure the covariance matrix of the noise,
Figure GDA0003590448730000094
to measure the Jacobian matrix of equation h (x),
Figure GDA0003590448730000095
to measure residual errors, SkCovariance matrix, K, being the residualkSuboptimal kalman gain.
Step two, five: gain Modification Network (GMN) pair suboptimal Kalman Gain KkMake a modification
Figure GDA0003590448730000096
Figure GDA0003590448730000097
Wherein G iskIn order to gain-modify the parameters,
Figure GDA0003590448730000098
the modified suboptimal Kalman gain.
Step two, step six: updating state and covariance estimates
Figure GDA0003590448730000099
Figure GDA00035904487300000910
Wherein I is a unit array.
In the implementation process, the existing track data of the aircraft are collected and collated, a data set is established to train the learnable extended Kalman filtering algorithm, and the training is completed on a Python3.6 + Tensorflow + CUDA + CUDnn platform by using a weighted RMSE loss function and an RMSprop optimizer shown in the formula.
Figure GDA00035904487300000911
Wherein, the weight w is [1,10 ]6,106,0.2,200,200,100]。
As shown in fig. 2, the specific process of establishing the input decorated network (IMN) in step two is as follows:
establishing a two-layer Long Short Term Memory (LSTM) network, identifying the used sequence length of 200, wherein the first LSTM layer contains 128 neurons, and the input is the model input ukMeasuring zkEstimation of the State of the last step
Figure GDA00035904487300000912
The output is the coded features; the second LSTM layer contains 2 neurons (u)kDimension of) is input as output to the first layer, and output is input to the model ukModification parameter of (k)k。
As shown in fig. 3, the specific process of establishing the Gain Modified Network (GMN) in step two and five is as follows:
establishing a two-layer Long Short Term Memory (LSTM) network, identifying the used sequence length of 200, wherein the first LSTM layer contains 256 neurons, and the input is modified model input
Figure GDA0003590448730000101
State estimation of the previous step
Figure GDA0003590448730000102
The output is the coded features; the second LSTM layer contains 21 neurons (K)kDimension of) with the input as the output of the first layer and the output as the sub-optimal Kalman gain KkModification parameter G ofk。
The simulation experiment process of the invention is as follows:
taking a flight path of jumping and gliding and periodic maneuvering and defense as an example for simulation, the maneuvering parameter (c) thereofll,Ts) With a random uncertainty not greater than 3 times the true maneuver parameters, the method of the present invention was performed as described above, using a pre-collected data set containing 1000 traces to train the IMN and GMN, and comparing the results with conventional EKF and AEKF methods to obtain the simulation test results shown in FIGS. 4 and 5.

Claims (3)

1. A complex maneuvering aircraft track estimation method based on learnable extended Kalman filtering is characterized by being realized according to the following steps:
the method comprises the following steps: building a maneuver model of an aircraft
Assuming that the earth is a regular sphere, a three-dimensional dynamic model of the aircraft is obtained under the condition of neglecting autorotation:
Figure FDA0003557971490000011
wherein R is the distance from the centroid of the aircraft to the geocentric, theta is the longitude, phi is the latitude, v is the velocity, gamma is the ballistic inclination angle, psi is the ballistic declination angle, m is the aircraft mass, R is the aircraft masse6,378,135m is the radius of the earth, g0As acceleration of gravity, SrefFor a characteristic area of an aircraft, ρ ═ ρ0e-βhIs the density of the atmosphere and is,
Figure FDA0003557971490000012
and
Figure FDA0003557971490000013
the lift coefficient and the drag coefficient when the lift-drag ratio of the aircraft is maximum, clTo normalize the lift coefficient, σ is the roll angle of the aircraft;
lateral maneuver of the aircraft was described using the Singer maneuver model:
Figure FDA0003557971490000014
wherein, TsA time constant for the maneuver;
and (2) obtaining a maneuvering model of the aircraft by the united vertical type (1) and the united vertical type (2):
Figure FDA0003557971490000021
step two: estimating the motion state of the aircraft according to the measurement (r, theta, phi), and estimating the motion state of the aircraft by using a learnable extended Kalman filtering algorithm;
and (3) using a learnable extended Kalman Filter algorithm to carry out the estimation of the motion state of the aircraft in the second step, wherein the specific process is as follows:
step two, firstly: let state xk＝[rk,θk,φk,vk,γk,ψk,σk]TInput uk＝[cl,k,Ts,k]TMeasuring zk＝[rk,θk,φk]TThe model shown in the formula (3) is rewritten into a form of a nonlinear discrete system
Figure FDA0003557971490000022
Wherein,
Figure FDA0003557971490000031
Figure FDA0003557971490000032
subscript k denotes time k; t is tsRepresenting the step size of a discrete system; x is the number of1,k-1X in (2)1Corresponds to r, x1,k-1Corresponds to rk-1；x2,k-1X in (2)2Corresponding to theta, x2,k-1Corresponds to thetak-1(ii) a The rest is analogized in the same way;
step two: input u by input decoration network (IMN)kThe modification is carried out, and the modified protein,
Figure FDA0003557971490000033
Figure FDA0003557971490000034
wherein denotes multiplication by element, κkIn order to input the parameters for the modification,
Figure FDA0003557971490000035
is a modified input;
step two and step three: state and covariance prediction
Figure FDA0003557971490000036
Figure FDA0003557971490000037
Wherein Q iskIs a covariance matrix of the process noise,
Figure FDA0003557971490000038
the Jacobian matrix of the equation of state f (x, u),
Figure FDA0003557971490000039
state at time k-1, Pk-1|k-1Is a state at the time k-1
Figure FDA00035579714900000310
The covariance matrix is then used to determine the covariance matrix,
Figure FDA00035579714900000311
and Pk|k-1Respectively, one-step prediction of the state and covariance matrices;
step two: computing suboptimal Kalman gain
Figure FDA0003557971490000041
Figure FDA0003557971490000042
Figure FDA0003557971490000043
Wherein R iskIn order to measure the covariance matrix of the noise,
Figure FDA0003557971490000044
to measure the Jacobian matrix of equation h (x),
Figure FDA0003557971490000045
to measure residual errors, SkCovariance matrix, K, being the residualkSuboptimal Kalman gain;
step two and step five: gain Modified Network (GMN) versus suboptimal Kalman gain KkMake a modification
Figure FDA0003557971490000046
Figure FDA0003557971490000047
Wherein, GkIn order to gain the parameters for the modification of the gain,
Figure FDA0003557971490000048
the modified suboptimal Kalman gain is obtained;
step two, step six: updating state and covariance estimates
Figure FDA0003557971490000049
Figure FDA00035579714900000410
Wherein I is a unit array.
2. The method for estimating the flight path of the complex maneuvering aircraft based on the learnable extended kalman filter according to claim 1, characterized in that the specific process of establishing the input decoration network (IMN) in the second step is as follows:
establishing a two-layer long-time memory (LSTM) network, the input of the first layer being the model input ukMeasuring zkEstimation of the State of the last step
Figure FDA00035579714900000411
The output is the coded features; the input of the second layer is the output of the first layer, and the output is the input u to the modelkModification parameter of (2) < kappa > (K)k。
3. The method for estimating the flight path of the complex maneuvering aircraft based on the learnable extended kalman filter according to claim 2, characterized in that the specific process of establishing the Gain Modifying Network (GMN) in the second five steps is as follows:
establishing a two-layer long-time memory (LSTM) network, wherein the input of the first layer is modified model input
Figure FDA00035579714900000412
State estimation of the previous step
Figure FDA0003557971490000051
The output is the coded features; the input of the second layer is the output of the first layer, and the output is the suboptimal Kalman gain KkModification parameter G ofk。
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