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

Abstract

A method for estimating the trajectory of a complex maneuvering aircraft based on a learnable extended Kalman filter, and the invention relates to a method for estimating the trajectory of an aircraft. The invention solves the problem that the existing track estimation method has low precision under complex maneuvering conditions of the target aircraft. The technical points of the present invention are: establishing a dynamic model of the aircraft, and further establishing a maneuvering model of the aircraft; building a learnable extended Kalman filter algorithm for aircraft track estimation, and designing and training the input modification network and gain modification therein. network. The learnable extended Kalman filter algorithm used in the aircraft track estimation in the present invention is obtained by training based on the existing track data, more fully utilizes the prior information of the motion characteristics of the aircraft, and can more accurately describe the complexity of the aircraft The maneuvering mode improves the accuracy of track estimation. This method is suitable for the field of information calculation based on knowledge and patterns.

Description

A Trajectory Estimation Method for Complex Maneuvering Aircraft Based on Learnable Extended Kalman Filter

technical field

The invention relates to a trajectory estimation method of an aircraft, in particular to a learnable extended Kalman filtering method based on a cyclic neural network, and belongs to the field of information estimation based on knowledge and patterns.

Background technique

For aircraft with complex maneuvering forms such as high-speed gliding aircraft, the trajectory estimation is more complicated than that of general aircraft. Most of the current aircraft trajectory estimation methods use constant velocity (CV), constant acceleration (CA), current statistics, Singer and other models to describe the target maneuver, and are based on extended Kalman filter (EKF), adaptive Kalman filter (AEKF), etc. method to achieve track estimation. When faced with such complex maneuvering forms of aircraft trajectory estimation, limited by the accuracy of the model, the existing trajectory estimation methods cannot adequately adapt to the complex motion modes of the aircraft, resulting in low estimation accuracy.

The patent document with the document number CN107504972A provides a method for aircraft trajectory planning based on the pigeon flock algorithm. First, a trajectory prediction model containing uncertainty is established, and then the path to be optimized in a specified area is determined. And compass operation and landmark operation, iteratively obtain the optimal path, and finally output the parameters of the obtained optimal path. The prior art derives and calculates the trajectory prediction model, and the path obtained by using the model has good stability, robustness and feasibility; and adopts the pigeon flock intelligent optimization method to solve the complex continuous optimization problem, and the calculation and search process has parallelism , feasibility, and strong robustness. But it did not indicate how to solve the problem of low accuracy under complex maneuvering conditions of the target aircraft.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a trajectory estimation method suitable for an aircraft with complex maneuvering form, so as to solve the problem of low accuracy of the existing method under the complex maneuvering condition of the target aircraft, and further provide a learnable extended Kalman filter based method A method for estimating the trajectory of complex maneuvering aircraft.

The technical scheme that the present invention takes for solving the above-mentioned technical problems is:

A method for estimating the trajectory of a complex maneuvering aircraft based on the learnable extended Kalman filter, the method is implemented according to the following steps:

Step 1: Build the maneuvering model of the aircraft

Assuming that the earth is a perfect sphere, under the condition of ignoring the rotation, the three-dimensional dynamic model of the aircraft is obtained:

和

为飞行器升阻比最大时的升力系数和阻力系数，c_l为标准化升力系数，σ为飞行器的倾侧角；Among them, r is the distance from the center of mass of the aircraft to the center of the earth, θ is the longitude, φ is the latitude, v is the velocity, γ is the ballistic inclination, ψ is the ballistic declination, m is the mass of the aircraft, _Re = 6,378,135m is the radius of the earth, g ₀ is the gravitational acceleration, S _ref is the characteristic area of the aircraft, ρ=ρ ₀ e ^-βh is the atmospheric density,

and

is the lift coefficient and drag coefficient when the lift-drag ratio of the aircraft is the largest, c _l is the standardized lift coefficient, and σ is the tilt angle of the aircraft;

Use the Singer maneuver model to describe the lateral maneuver of the aircraft:

Among them, T _s is the time constant of maneuver;

Combined (1), (2) to get the maneuvering model of the aircraft:

Step 2: Estimate the motion state of the aircraft according to the measurement (r, θ, φ), and use the learnable extended Kalman filter algorithm to estimate the motion state of the aircraft.

Further, using the learnable extended Kalman filter algorithm to estimate the motion state of the aircraft described in step 2, the specific process is:

Step 21: Set state x _k =[r _k ,θ _k ,φ _k ,v _k ,γ _k ,ψ _k ,σ _k ] ^T , input u _k =[ _cl,k ,T _s,k ] ^T , Measure z _k = [r _k , θ _k , φ _k ] ^T , rewrite the model shown in equation (3) into the form of a nonlinear discrete system

下标k表示k时刻；in,

The subscript k represents time k;

t _s represents the step size of the discrete system, x _{1 in x 1, k- 1} corresponds to r (ie x _{1, k-1} corresponds to r _k-1 ), x 2 in x _{2 , k-1} corresponds to θ (ie x _2,k-1 corresponds to θ _k-1 ), and so on;

Step 22: Modify the input _uk through the Input Modification Network (IMN)

为修饰后的输入；Among them, * represents element-wise multiplication, κ _k is the input modification parameter,

is the modified input;

Step 23: State and Covariance Prediction

为状态方程f(x,u)的雅克比矩阵，

为k-1时刻的状态，P_k-1|k-1为k-1时刻状态

协方差矩阵，

和P_k|k-1分别为对状态和协方差矩阵的一步预测；where Q _k is the covariance matrix of the process noise,

is the Jacobian matrix of the equation of state f(x,u),

is the state at time k-1, and P _k-1|k-1 is the state at time k-1

covariance matrix,

and P _k|k-1 are one-step predictions for the state and covariance matrix, respectively;

Step 24: Calculate the suboptimal Kalman gain

为量测方程h(x)的雅克比矩阵，

为量测残差，S_k为残差的协方差矩阵，K_k为次优卡尔曼增益；where R _k is the covariance matrix of the measurement noise,

is the Jacobian matrix of the measurement equation h(x),

is the measurement residual, S _k is the covariance matrix of the residual, and K _k is the suboptimal Kalman gain;

Step 25: The Gain Modification Network (GMN) modifies the suboptimal Kalman gain K _k

为修饰后的次优卡尔曼增益；Among them, G _k is the gain modification parameter,

is the modified suboptimal Kalman gain;

Step 26: Update state and covariance estimates

Among them, I is the unit matrix.

Further, the specific process of establishing the input modification network (IMN) described in step 22 is:

输出为编码后的特征；第二层的输入为第一层的输出，输出为对模型输入u_k的修饰参数κ_k。Build a two-layer Long Short Term Memory (LSTM) network, the input of the first layer is the model input _{uk , the measurement z k ,} and the state estimation of the previous step

The output is the encoded feature; the input of the second layer is the output of the first layer, and the output is the modification parameter κ _k of the model input _uk .

Further, the specific process of establishing the Gain Modification Network (GMN) described in step 25 is:

上一步的状态估计

输出为编码后的特征；第二层的输入为第一层的输出，输出为对次优卡尔曼增益K_k的修饰参数G_k。Build a two-layer Long Short Term Memory (LSTM) network, and the input of the first layer is the modified model input

State estimation from the previous step

The output is the encoded feature; the input of the second layer is the output of the first layer, and the output is the modification parameter G _{k for the suboptimal Kalman gain K k .}

The beneficial effects of the present invention are as follows: the present invention establishes the dynamic model of the aircraft, and further establishes the maneuvering model of the aircraft; builds a learnable extended Kalman filter algorithm for the track estimation of the aircraft, and designs and trains the input modification network therein and gain modification network. For the trajectory estimation problem of complex maneuvers, the key to improving the estimation accuracy is to improve the adaptability to model/parameter uncertainty and accurately describe the characteristics of the target maneuver.

Compared with the existing track estimation methods, this method has the following advantages:

(1) Compared with the traditional AEKF algorithm, the learnable extended Kalman filter algorithm used in the aircraft track estimation in the present invention can adapt to a wide range of target motion models and parameter uncertainties.

(2) The learnable extended Kalman filter algorithm used in the aircraft track estimation in the present invention is obtained by training based on the existing track data, and the prior information of the motion characteristics of the aircraft is more fully utilized, which can describe more accurately The complex maneuvering mode of the aircraft improves the accuracy of track estimation.

(3) The estimation performance of the learnable extended Kalman filter algorithm used in the aircraft track estimation in the present invention is not sensitive to the two parameters of the process and the measurement noise covariance matrix (it is only required to ensure the convergence of the filtering algorithm), extremely This greatly simplifies the parameter tuning of the filtering algorithm.

The invention establishes the dynamic model of the aircraft, and further establishes the maneuvering model of the aircraft; constructs a learnable extended Kalman filter algorithm for the track estimation of the aircraft, and designs and trains the input modification network and gain modification network therein. The invention solves the problem that the existing track estimation method cannot cope with the complex maneuvering form of the aircraft, improves the accuracy of the track estimation, and simplifies the parameter adjustment of the track estimation algorithm. This method is suitable for the field of information calculation based on knowledge and patterns. It can be seen from FIG. 4 that the method of the present invention and the traditional EKF and AEKF methods have similar position estimation accuracy, but the result is better and smoother. It can be seen from Fig. 5 that the method of the present invention is more accurate in estimating the speed of the aircraft than the traditional EKF and AEKF methods.

The aircraft with complex maneuvering forms targeted by the present invention has various maneuvering forms such as quasi-balanced gliding, jump gliding, avoidance, penetration, etc., and the flight path is constrained by factors such as heat flow, dynamic pressure, overload, etc., its maneuvering form is difficult to be described above. An accurate description of the maneuvering model.

Description of drawings

Fig. 1 is the algorithm structure diagram of the present invention,

Figure 2 is the structure diagram of the input decoration network,

Figure 3 is the structure diagram of the gain modification network,

Fig. 4 is the result of the position estimation of the aircraft, comparing the method of the present invention with the traditional EKF and AEKF methods,

FIG. 5 is the result of aircraft speed estimation, comparing the method of the present invention with the traditional EKF and AEKF methods.

Detailed ways

The learnable extended Kalman filter method for estimating complex maneuvering target tracks described in this embodiment is implemented according to the following steps:

Step 1: Build a maneuver model of the target

Assuming that the earth is a true sphere, ignoring the rotation, the three-dimensional dynamic model of the aircraft is obtained:

和

为飞行器升阻比最大时的升力系数和阻力系数， c_l为标准化升力系数，σ为飞行器的倾侧角。Among them, r is the distance from the center of mass of the aircraft to the center of the earth, θ is the longitude, φ is the latitude, v is the velocity, γ is the ballistic inclination, ψ is the ballistic declination, m is the mass of the aircraft, _Re = 6,378,135m is the radius of the earth, g ₀ is the gravitational acceleration, S _ref is the characteristic area of the aircraft, ρ=ρ ₀ e ^-βh is the atmospheric density,

and

is the lift coefficient and drag coefficient when the lift-drag ratio of the aircraft is the largest, _cl is the standardized lift coefficient, and σ is the tilt angle of the aircraft.

Use the Singer maneuver model to describe the lateral maneuver of the target:

Among them, T _s is the time constant of maneuvering.

Combined formulas (1) and (2) get the maneuvering model of the target:

Step 2: Estimate the motion state of the target according to the measurements (r, θ, φ).

A learnable extended Kalman filter algorithm is constructed to estimate the target motion state described in step 2. The specific process is as follows:

Step 21: Set state x _k =[r _k ,θ _k ,φ _k ,v _k ,γ _k ,ψ _k ,σ _k ] ^T , input u _k =[ _cl,k ,T _s,k ] ^T , Measure z _k = [r _k , θ _k , φ _k ] ^T , rewrite the model shown in equation (3) into the form of a nonlinear discrete system

下标k表示k时刻。in,

The subscript k represents time k.

Step 22: Modify the input _uk through the Input Modification Network (IMN)

为修饰后的输入。Among them, * represents element-wise multiplication, κ _k is the input modification parameter,

is the modified input.

Step 23: State and Covariance Prediction

为状态方程f(x,u)的雅克比矩阵，

为k-1时刻的状态，P_k-1|k-1为k-1时刻状态

协方差矩阵，

和P_k|k-1分别为对状态和协方差矩阵的一步预测。where Q _k is the covariance matrix of the process noise,

is the Jacobian matrix of the equation of state f(x,u),

is the state at time k-1, and P _k-1|k-1 is the state at time k-1

covariance matrix,

and P _k|k-1 are one-step predictions for the state and covariance matrices, respectively.

Step 24: Calculate the suboptimal Kalman gain

为量测方程h(x)的雅克比矩阵，

为量测残差，S_k为残差的协方差矩阵，K_k为次优卡尔曼增益。where R _k is the covariance matrix of the measurement noise,

is the Jacobian matrix of the measurement equation h(x),

In order to measure the residual, S _k is the covariance matrix of the residual, and K _k is the suboptimal Kalman gain.

Step 25: The Gain Modification Network (GMN) modifies the suboptimal Kalman gain K _k

为修饰后的次优卡尔曼增益。Among them, G _k is the gain modification parameter,

is the modified suboptimal Kalman gain.

Step 26: Update state and covariance estimates

Among them, I is the unit matrix.

In the implementation process, collect and organize the existing track data of the aircraft, establish a data set to train the learnable extended Kalman filter algorithm, train the RMSE loss function weighted as shown in the formula and the RMSprop optimizer, in Python3.6+ Completed on the Tensorflow+CUDA+CUDnn platform.

Wherein, the weight w=[1, 10 ⁶ , 10 ⁶ , 0.2, 200, 200, 100].

As shown in Figure 2, the specific process of establishing the input modification network (IMN) described in step 22 is:

输出为编码后的特征；第二个LSTM层含有2个神经元(u_k的维度)，输入为第一层的输出，输出为对模型输入u_k的修饰参数κ_k。Build a two-layer Long Short Term Memory (LSTM) network, the sequence length used for recognition is 200, the first LSTM layer contains 128 neurons, the input is the model input _{uk , and the measurement z k ,} State estimation from the previous step

The output is the encoded feature; the second LSTM layer contains 2 neurons (dimension of _uk ), the input is the output of the first layer, and the output is the modification parameter κ _k of the model input _uk .

As shown in Figure 3, the specific process of establishing the Gain Modification Network (GMN) described in Step 25 is:

上一步的状态估计

输出为编码后的特征；第二个LSTM层含有21个神经元(K_k的维度)，输入为第一层的输出，输出为对次优卡尔曼增益K_k的修饰参数G_k。Build a two-layer Long Short Term Memory (LSTM) network, the sequence length used for recognition is 200, the first LSTM layer contains 256 neurons, and the input is the modified model input

State estimation from the previous step

The output is the encoded feature; the second LSTM layer contains 21 neurons (dimension of K _k ), the input is the output of the first layer, and the output is the modification parameter G _{k for the sub-optimal Kalman gain K k .}

The simulation experiment process of the present invention:

Taking a jumping and gliding track with periodic maneuvering penetration as an example to simulate, its maneuvering parameters (c _ll , T _s ) have random uncertainty not greater than 3 times the real maneuvering parameters. The inventive method uses a pre-collected data set containing 1000 tracks to train the IMN and GMN, and compares the obtained results with the traditional EKF and AEKF methods, and obtains the simulation test results shown in Figure 4 and Figure 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:

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 mass_e6,378,135m is the radius of the earth, g₀As acceleration of gravity, S_refFor a characteristic area of an aircraft, ρ ═ ρ₀e^-βhIs the density of the atmosphere and is,

and

the lift coefficient and the drag coefficient when the lift-drag ratio of the aircraft is maximum, c_lTo normalize the lift coefficient, σ is the roll angle of the aircraft;

lateral maneuver of the aircraft was described using the Singer maneuver model:

wherein, T_sA 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):

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 x_k＝[r_k,θ_k,φ_k,v_k,γ_k,ψ_k,σ_k]^TInput u_k＝[c_l,k,T_s,k]^TMeasuring z_k＝[r_k,θ_k,φ_k]^TThe model shown in the formula (3) is rewritten into a form of a nonlinear discrete system

Wherein,

subscript k denotes time k; t is t_sRepresenting the step size of a discrete system; x is the number of_1,k-1X in (2)₁Corresponds to r, x_1,k-1Corresponds to r_k-1；x_2,k-1X in (2)₂Corresponding to theta, x_2,k-1Corresponds to theta_k-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,

wherein denotes multiplication by element, κ_kIn order to input the parameters for the modification,

is a modified input;

step two and step three: state and covariance prediction

Wherein Q is_kIs a covariance matrix of the process noise,

the Jacobian matrix of the equation of state f (x, u),

state at time k-1, P_k-1|k-1Is a state at the time k-1

The covariance matrix is then used to determine the covariance matrix,

and P_k|k-1Respectively, one-step prediction of the state and covariance matrices;

step two: computing suboptimal Kalman gain

Wherein R is_kIn order to measure the covariance matrix of the noise,

to measure the Jacobian matrix of equation h (x),

to measure residual errors, S_kCovariance matrix, K, being the residual_kSuboptimal Kalman gain;

step two and step five: gain Modified Network (GMN) versus suboptimal Kalman gain K_kMake a modification

Wherein, G_kIn order to gain the parameters for the modification of the gain,

the modified suboptimal Kalman gain is obtained;

step two, step six: updating state and covariance estimates

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 u_kMeasuring z_kEstimation of the State of the last step

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 model_kModification 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

State estimation of the previous step

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 K_kModification parameter G of_k。

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