An aircraft parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm

Abstract

The application provides an aircraft parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm, which combines the GRU neural network model and the Gauss-Newton optimization algorithm and is used for solving a complex aircraft parameter identification problem. The GRU neural network model is designed to model aircraft dynamics by directly establishing a nonlinear function mapping relationship between measurement input and output of the aircraft system without any dynamic prior assumption. The Gauss-Newton optimization algorithm is combined with the trained GRU network model, and the optimal parameter identification result is obtained by minimizing the cost function related to unknown aerodynamic parameters in an iterative manner.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of time-domain aircraft system identification method, in particular to an aircraft aerodynamic parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm. BACKGROUND

[0002] Aircraft aerodynamic parameter identification describes a process of obtaining the most likely value of the unknown aerodynamic parameter representing the dynamic aircraft system, which helps to accurately and comprehensively understand the aerodynamic model structure of the target aircraft and is crucial for diagnosing and improving the design of the aircraft. In the past few decades, parameter identification methods based on the maximum likelihood principle (the most commonly used methods: output error method and filter error method) have been widely used to capture aerodynamic information closely related to the dynamic behavior of the aircraft system from flight data through deterministic analysis. However, both the output error method and the filter error method not only require prior assumptions of the dynamics of the aircraft system, but also require multiple numerical integrations of the assumed dynamic model. Therefore, the output error method or the filter error method is not suitable for parameter identification problems where the dynamics of the aircraft system is not fully understood (such as: aircraft parameter identification problems under complex flight conditions (stall hysteresis, high angle of attack flight, and large amplitude time-varying maneuvers), parameter identification problems of morphing aircraft with large range of morphing wing motion, etc.), and is likely to encounter integration divergence problems.

[0003] Artificial neural networks provide a comprehensive framework for non-linear function mapping within the input-output subspace and have been proven to be a reliable non-linear function approximator. In addition, the potential and effectiveness of artificial neural network-based parameter identification methods in solving complex problems related to aircraft parameter identification have been proven. Although current artificial neural network-based identification methods have brought benefits to aircraft parameter identification by not requiring dynamic assumptions, these methods mostly rely on feedforward neural networks to map the dynamics of the aircraft system. Unlike standard recurrent neural networks, feedforward neural networks have no feedback connections between nodes / units and layers, so they cannot handle input sequences of arbitrary length. However, it is extremely challenging to train standard recurrent neural networks with stable convergence while avoiding the occurrence of gradient vanishing or explosion problems.

[0004] Improved recurrent neural networks not only outperform feedforward neural networks in handling long time series data, but also avoid the gradient explosion or vanishing problems that may occur in standard recurrent neural networks. Therefore, it is necessary and valuable to explore the potential and effectiveness of improved recurrent neural networks in the field of aircraft parameter identification. SUMMARY

[0005] In order to solve the problem that the parameter identification method based on the maximum likelihood principle needs the prior assumption of the aircraft dynamics in the process of dealing with the complex aircraft parameter identification, and overcome the convergence problem of the existing parameter identification method based on the feedforward neural network or the standard recurrent neural network in dealing with long time flight data, the application provides a parameter identification method based on a gated recurrent unit (GRU) neural network, which combines the GRU neural network model and the Gauss-Newton optimization algorithm, and is used for solving the complex aircraft parameter identification problem. The GRU neural network model is designed to model the aircraft dynamics by directly establishing a nonlinear function mapping relationship between the measured input and output of the aircraft system without any prior assumption of dynamics. The Gauss-Newton optimization algorithm is combined with the trained GRU network model, and the optimal parameter identification result is obtained by minimizing the cost function related to the unknown aerodynamic parameters in an iterative manner.

[0006] The technical scheme of the application is:

[0007] An aircraft parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm, comprising the following steps:

[0008] Step 1: constructing and training a GRU neural network prediction model;

[0009] Step 1.1: establishing a GRU neural network prediction model; the GRU neural network prediction model comprises an input layer, L GRU layers and an output layer; a Dropout layer is added in the GRU layer;

[0010] The input of the GRU neural network prediction model is X=[X1, X2,..., X N-1 ], the output is Y=[Y2, Y3,..., Y N ], and the input vector X t at time t is used to predict the output vector Y t+1 at time t+1, t=1, 2,..., N-1; wherein N represents the total number of discrete time points contained in the flight data;

[0011] Step 1.2: training the GRU neural network prediction model established in step 1.1:

[0012] Through flight test, the data collected by the aircraft sensors are collected, including the angle of attack, the angle of sideslip, the attitude angle, the attitude angular velocity, the flight speed and the three-axis acceleration under the body axis system, the three direction angular accelerations of the aircraft around the body axis system are calculated by using the numerical differentiation method, and the aerodynamic force coefficients and moment coefficients of the aircraft are calculated by using Newton's law, so as to obtain the observation matrix Z=[Z2, Z3,..., Z N ] and the input matrix X=[X1, X2,..., X N-1]; the meaning of the vectors in the observation matrix is ​​the same as that of the vectors in the output matrix;

[0013] Use the input matrix X and observation matrix Z to train the GRU neural network prediction model;

[0014] Step 2: Combine the trained GRU network with the Gauss-Newton optimization algorithm to implement the aircraft parameter identification function:

[0015] Step 2.1: Select the appropriate aerodynamic model structure based on the actual maneuverability of the selected aircraft during the flight test;

[0016] Step 2.2: Set the initial value of the aerodynamic parameter vector Θ to be identified in the aerodynamic model;

[0017] Step 2.3: Use the initial values ​​of the aircraft's motion state variables obtained by sensors from the flight data and calculate the corresponding aerodynamic force and torque coefficients based on the aerodynamic model. Combine the initial values ​​of the aircraft's motion state variables obtained by sensors with the aerodynamic force and torque coefficients calculated based on the aerodynamic model to obtain the input vector X1 at the initial time.

[0018] Step 2.4: Input the input vector X1 at the initial moment into the trained GRU neural network prediction model, and combine the aerodynamic model to solve the aerodynamic force and torque coefficient at each time point, and predict the output matrix Y = [Y2, Y3, ..., Y N ]; Calculate the measurement noise covariance matrix R;

[0019] Step 2.5: Minimize the cost function J(Θ) using the standard unconstrained Gauss-Newton algorithm and one-dimensional line search, and iteratively update the aerodynamic parameter vector Θ:

[0020] J(Θ)=det(R)

[0021] where FΔΘ=-G

[0022]

[0023] Where i represents the number of iterations; represents a dimensionless parameter, whose value is determined by the one-dimensional line search algorithm in each iteration; F and G represent the information matrix and gradient vector respectively; ΔΘ represents the change vector of the aerodynamic parameter to be identified;

[0024] Step 2.6: Return to step 2.3 until the convergence condition is met and the aerodynamic parameter vector is obtained.

[0025] Furthermore, in step 1.1, the Dropout layer is used to quantify the probability of units in each GRU layer being discarded or excluded.

[0026] Further, for longitudinal flight data, the input vector X t and the output vector Y t+1 of the GRU neural network prediction model are respectively represented as:

[0027] X t,纵向 = [V(t), a(t), q(t), C D (t), C L (t), C m (t)] T

[0028]

[0029] where V represents the flight speed, a represents the angle of attack, q represents the pitch rate, C D is the drag coefficient, C L is the lift coefficient, C m is the pitch moment coefficient, a x represents the x-direction acceleration component of the aircraft under the body axis system, a z represents the z-direction acceleration component of the aircraft under the body axis system.

[0030] For lateral flight data, the input vector X t and the output vector Y t+1 of the GRU neural network prediction model are respectively represented as:

[0031] X t,横航向 = [b(t), p(t), r(t), C y (t), C l (t), C n (t)] T

[0032]

[0033] where b represents the side slip angle, p represents the roll angle, r represents the yaw angle, p represents the roll rate, r represents the yaw rate, C y represents the side force coefficient, C l represents the roll moment coefficient, C n represents the yaw moment coefficient, p represents the roll angle acceleration, r y represents the y-direction acceleration component of the aircraft under the body axis system.

[0034] Further, in step 1.2, the GRU neural network prediction model is trained using the root mean square propagation algorithm, and the neural network prediction accuracy is evaluated by the root mean square error and the determination coefficient.

[0035] Further, in step 2.1, if the aircraft performs longitudinal maneuver in small angle of attack state, the linear longitudinal aerodynamic model is selected; if the aircraft performs longitudinal maneuver in large angle of attack state, the nonlinear longitudinal aerodynamic model with time effect is selected; if the aircraft performs lateral maneuver, the lateral aerodynamic model is selected.

[0036] Further, in step 2.1, for the longitudinal aerodynamic model, the to-be-identified aerodynamic parameter vector

[0037] Θ 纵向 = [C D0 , C L0 , C Lα , C Lq , C Lδe , C m0 , C mα , C mq , C mδe ] T

[0038] For the lateral aerodynamic model, the to-be-identified aerodynamic parameter vector

[0039] Θ 横航向 = [C y0 , C yβ , C yr , C yp , C yδr , C l0 , C lβ , C lr , C lp ,

[0040] C lδa , C lδr , C n0 , C nβ , C nr , C np , C nδr ] T

[0041] In the formula, C ·0 represents the aerodynamic coefficient bias term, C ·α and C ·β represent the static stability aerodynamic derivative term, C ·p , C ·q and C ·r represent the dynamic aerodynamic derivative term, and denotes the static aerodynamic derivative term related to control surface deflection, and • the symbols D, L, m, y, l and n.

[0042] Advantages

[0043] The application provides a vehicle parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm. The application trains a gated recurrent unit neural network model GRU based on real flight collected data, and is used for directly establishing a nonlinear mapping relationship between vehicle system input and output, thereby effectively avoiding the uncertainty problem of vehicle dynamics modeling. Then, the trained GRU neural network is used to predict an output matrix Y, a cost function based on a predicted noise covariance matrix and a gradient are constructed, the cost function J(Theta) is iteratively optimized through the Gauss-Newton optimization algorithm and one-dimensional line search, until the cost function residual satisfies the iteration convergence condition, thereby completing the complete parameter identification process. The application is a parameter identification method combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm, and the gated recurrent unit neural network can effectively avoid the problems of inaccurate dynamics modeling and integral divergence, and is suitable for solving the parameter identification problems of various vehicles.

[0044] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0045] The above and / or additional aspects and advantages of the application will become apparent and be readily appreciated from the description of the embodiments, taken in conjunction with the following drawings in which:

[0046] Figure 1 : Flow chart of the GRU-GN method;

[0047] Figure 2 : Structure of the gated recurrent unit neural network (GRU);

[0048] Wherein: Figure 2 (a) shows the unfolded structure of the GRU network; Figure 2 (b) shows the detailed structure of a certain hidden unit in the Lth layer of the GRU at time t;

[0049] Figure 3 : Application example of the GRU-GN method in parameter identification of a small unmanned aerial vehicle;

[0050] Wherein: Figure 3 (a) shows a real photo of the aerial flight data collected in the air by a small unmanned aerial vehicle; Figure 3 (b) shows the waveform of the elevator (delta e ) excitation of the small unmanned aerial vehicle; Figure 3(c) shows the verification of the recognition effect of the GRU-GN method. DETAILED DESCRIPTION

[0051] The embodiments of the present application are described in detail below, which are exemplary and intended to explain the present application, and cannot be understood as a limitation of the present application.

[0052] As shown in Figure 1 , the present application is a kind of aircraft parameter identification method combining gated recurrent unit neural network model and Gauss-Newton optimization algorithm, including gated recurrent unit neural network model (GRU) training and Gauss-Newton parameter identification method combined with GRU;The specific steps are as follows:

[0053] Step 1: build and train GRU neural network prediction model;Including the following steps:

[0054] Step 1.1: GRU neural network prediction model modeling:

[0055] Build the GRU neural network structure as shown in Figure 2 . Figure 2 (a) shows the unfolded structure of GRU neural network, including input layer, L layer GRU layer and output layer; Figure 2 (b) represents the detailed structure of a hidden unit in the L layer GRU layer at t time.

[0056] In the present application, the Dropout layer is added to the GRU layer of the neural network to prevent network overfitting, and the Dropout layer is used to quantify the probability of each GRU layer unit being discarded or excluded. Specifically from Figure 2 (b) can be seen, there are two gates (i.e. update gate and reset gate ) in the hidden unit, represents the output vector of the hidden unit in the L layer GRU layer, represents the output vector of the hidden unit in the L-1 layer GRU layer. At t time, the mathematical form of the hidden unit in the L layer GRU layer is:

[0057]

[0058] In the formula, σ and tanh represent sigmoid function and hyperbolic tangent function respectively; and respectively represent the input weight matrix in the L layer GRU layer; and respectively represent the cycle weight matrix in the L layer GRU layer; and respectively represent the offset vector in the L layer GRU layer.

[0059] The input and output of the GRU network model are represented by the matrix X = [X1, X2, ..., X N-1 ] and matrix Y=[Y2,Y3,…,Y N ], where N represents the total number of discrete time points contained in the flight data. The function of the GRU network prediction model is: using the input vector X at time t t To predict the output vector Y at time t+1 t+1 (t=1,2,…,N-1).

[0060] For longitudinal flight data, the input vector X t And the output vector Y t+1 Respectively expressed as:

[0061] X t,纵向 =[V(t),α(t),θ(t),q(t),C D (t),C L (t),C m (t)] T

[0062]

[0063] Where V is the flight speed, α is the angle of attack, θ is the pitch angle, q is the pitch angular velocity, and C D is the drag coefficient, C L is the lift coefficient, C m is the pitching moment coefficient, represents the pitch angular acceleration, a x represents the acceleration component of the aircraft in the x direction under the body axis system, a z It represents the acceleration component of the aircraft in the z direction under the body axis system.

[0064] For lateral and heading flight data, input vector X t And the output vector Y t+1 They are respectively expressed as:

[0065] X t,横航向 =[β(t),φ(t),ψ(t),p(t),r(t),C y (t),C l (t),C n (t)] T

[0066]

[0067] Where β represents the sideslip angle, φ represents the roll angle, ψ represents the yaw angle, p represents the roll angular velocity, r represents the yaw angular velocity, and C y represents the lateral force coefficient, C ldenotes the roll moment coefficient, C n denotes the yaw moment coefficient, denotes the roll angle acceleration, denotes the yaw angle acceleration, a y denotes the aircraft y-direction acceleration component in the body axis system.

[0068] Step 1.2: Before realizing the prediction function of the network model, the network model needs to undergo training. Through flight tests, data collected by aircraft sensors, including angle of attack, sideslip angle, attitude angle, attitude angular velocity, flight speed, and three-axis acceleration in the body axis system, are used to calculate the three direction angular accelerations of the aircraft around its body axis system by numerical differentiation, and the aerodynamic force coefficients and moment coefficients of the aircraft are calculated by Newton's law, so as to obtain the observation matrix Z = [Z2, Z3,..., Z N ] and the input matrix X = [X1, X2,..., X N-1 ]; the meaning of the vectors in the observation matrix is the same as that in the output matrix.

[0069] Using the input matrix X and the observation matrix Z, the GRU neural network prediction model is trained using the root mean square propagation (RMSProp) algorithm, and the neural network prediction accuracy is evaluated by the root mean square error (RMSE) and the determination coefficient (R 2 ).

[0070]

[0071] Step 2: Combine the trained GRU network with the Gauss-Newton optimization algorithm to realize the aircraft parameter identification function:

[0072] Step 2.1: According to the actual maneuvering flight conditions of the selected aircraft in the flight test, select the corresponding aerodynamic model structure; for example, if the aircraft performs longitudinal maneuvering at a small angle of attack, select a linear longitudinal aerodynamic model; if the aircraft performs longitudinal maneuvering at a large angle of attack, select a nonlinear longitudinal aerodynamic model with time effect; if the aircraft performs lateral and longitudinal maneuvering, select a lateral and longitudinal aerodynamic model.

[0073] In the aerodynamic model, the aerodynamic parameters to be identified are:

[0074] For the longitudinal aerodynamic model, the aerodynamic parameter vector to be identified is

[0075]

[0076] For the lateral and longitudinal aerodynamic model, the aerodynamic parameter vector to be identified is

[0077]

[0078] In the above formula, C·0 denotes the aerodynamic coefficient bias term, C ·α and C ·β denotes the static stability aerodynamic derivative term, C ·p , C ·q and C ·r denotes the dynamic aerodynamic derivative term, C ·δe , C ·θm and C ·δr denotes the static aerodynamic derivative term related to control surface deflection, · denotes the symbols D, L, m, y, l and n, which are all well-known concepts in the field of flight mechanics.

[0079] Step 2.2: Set the initial value of the aerodynamic parameter vector Θ to be identified in the aerodynamic model.

[0080] Step 2.3: Use the aircraft state values obtained by sensors in the flight data, and calculate the corresponding aerodynamic force and moment coefficient values according to the aerodynamic model; combine the aircraft state values obtained by sensors with the aerodynamic force and moment coefficient values calculated according to the aerodynamic model to obtain the input vector X1 at the initial time.

[0081] For example, the aircraft performs longitudinal maneuver in small angle of attack state, uses longitudinal aerodynamic model, and the aerodynamic parameter vector to be identified is Θ 纵向 , and the input vector of the GRU network model is X t,纵向 , wherein V, a, θ, q at the initial time are obtained by sensors, and C D , C L , C m are calculated by the longitudinal aerodynamic model.

[0082] If the aircraft performs lateral directional maneuver, uses lateral directional aerodynamic model, and the aerodynamic parameter vector to be identified is Θ 横航向 , and the input vector of the GRU network model is X t,横航向 , wherein β, φ, ψ, p, r at the initial time are obtained by sensors, and C y , C l , C n are calculated by the lateral directional aerodynamic model.

[0083] Step 2.4: input the input vector X1 at the initial time into the trained GRU neural network prediction model, and combine the aerodynamic model to solve the aerodynamic force and moment coefficient at each time point, and predict the output matrix Y (=[Y2, Y3,..., Y N ]) to calculate the measurement noise covariance matrix R:

[0084]

[0085] Step 2.5: Minimize the cost function J(Θ) using the standard unconstrained Gauss- Newton (GN) algorithm and one-dimensional line search. The iterative update of the predicted aerodynamic parameter vector Θ involves the prediction of the output vector Y t and the computation of the response gradient The computation formulae are as follows:

[0086] J(Θ) = det(R)

[0087] where FΔΘ = -G

[0088]

[0089] In the above formula, i represents the iteration number; is a dimensionless parameter, the value of which is determined by the one-dimensional line search algorithm at each iteration; F and G represent the information matrix and the gradient vector, respectively; ΔΘ represents the variation vector of the aerodynamic parameters to be identified.

[0090] Step 2.6: Return to step 2.3 until the convergence condition is met:

[0091]

[0092] In the above formula, J(Θ)0represents the initial value of the cost function; J(Θ) represents the cost function value corresponding to the ith iteration; e0represents the relative error of J(Θ) i with respect to J(Θ) i-1 .

[0093] Although the embodiments of the present application have been shown and described above, it should be understood that the above-described embodiments are exemplary and are not to be construed as limiting the present application, and that those of ordinary skill in the art can make changes, modifications, replacements and variations to the above-described embodiments without departing from the principles and spirit of the present application within the scope of the present application.

Claims

1. A method for aircraft parameter identification combining a gated recurrent unit neural network model and a Gauss-Newton optimization algorithm, characterized by: The following steps are involved: Step 1: Build and train the GRU neural network prediction model; Step 1.1: Establish a GRU neural network prediction model; the GRU neural network prediction model includes an input layer, an L-layer GRU layer and an output layer; a Dropout layer is added to the GRU layer; The input of the GRU neural network prediction model is X = [X1, X2, ..., X N-1 ], the output is Y=[Y2,Y3,…,Y N ], using the input vector X at time t t To predict the output vector Y at time t+1 t+1 , t=1,2,…,N-1; where N represents the total number of discrete time points included in the flight data; Step 1.2: Train the GRU neural network prediction model established in step 1.1: The data collected by the aircraft sensors are collected through flight tests, including angle of attack, sideslip angle, attitude angle, attitude angular velocity, flight speed and three-axis acceleration under the body axis system. The angular acceleration of the aircraft in three directions around its body axis system is calculated using the numerical differentiation method, and the aerodynamic coefficient and torque coefficient of the aircraft are calculated using Newton's law, so as to obtain the observation matrix Z = [Z2, Z3, ..., Z N ] and the input matrix X=[X1,X2,...,X N-1 ]; the meaning of the vectors in the observation matrix is ​​the same as that of the vectors in the output matrix; Use the input matrix X and observation matrix Z to train the GRU neural network prediction model; Step 2: Combine the trained GRU network with the Gauss-Newton optimization algorithm to implement the aircraft parameter identification function: Step 2.1: Select the appropriate aerodynamic model structure based on the actual maneuverability of the selected aircraft during the flight test; Step 2.2: Set the initial value of the aerodynamic parameter vector Θ to be identified in the aerodynamic model; Step 2.3: Use the initial values ​​of the aircraft's motion state variables obtained by sensors from the flight data and calculate the corresponding aerodynamic force and torque coefficients based on the aerodynamic model. Combine the initial values ​​of the aircraft's motion state variables obtained by sensors with the aerodynamic force and torque coefficients calculated based on the aerodynamic model to obtain the input vector X1 at the initial moment. Step 2.4: Input the input vector X1 at the initial moment into the trained GRU neural network prediction model, and combine the aerodynamic model to solve the aerodynamic force and torque coefficient at each time point, and predict the output matrix Y = [Y2, Y3, ..., Y N ]; Calculate the measurement noise covariance matrix R; Step 2.5: Minimize the cost function J(Θ) using the standard unconstrained Gauss-Newton algorithm and one-dimensional line search, and iteratively update the aerodynamic parameter vector Θ: J(Θ)=det(R) Where FΔΘ=-G Where i represents the number of iterations; represents a dimensionless parameter, whose value is determined by the one-dimensional line search algorithm in each iteration; F and G represent the information matrix and gradient vector respectively; ΔΘ represents the change vector of the aerodynamic parameter to be identified; Step 2.6: Return to step 2.3 until the convergence condition is met and the aerodynamic parameter vector is obtained.

2. The method according to claim 1, wherein: In step 1.1, the Dropout layer is used to quantify the probability of a unit being dropped or excluded in each GRU layer.

3. The method according to claim 1, wherein: For longitudinal flight data, the input vector X of the GRU neural network prediction model is t And the output vector Y t+1 Respectively expressed as: X t,纵向 =[V(t),α(t),θ(t),q(t),C D (t),C L (t),C m (t)] T Where V is the flight speed, α is the angle of attack, θ is the pitch angle, q is the pitch angular velocity, and C D is the drag coefficient, C L is the lift coefficient, C m is the pitching moment coefficient, represents the pitch angular acceleration, a x represents the acceleration component of the aircraft in the x direction under the body axis system, a z It represents the acceleration component of the aircraft in the z direction under the body axis system; For lateral and heading flight data, input vector X t And the output vector Y t+1 They are respectively expressed as: X t,横航向 =[β(t),φ(t),ψ(t),p(t),r(t),C y (t),C l (t),C n (t)] T Where β represents the sideslip angle, φ represents the roll angle, ψ represents the yaw angle, p represents the roll angular velocity, r represents the yaw angular velocity, and C y represents the lateral force coefficient, C l Denotes the rolling moment coefficient, C n represents the yaw moment coefficient, is the roll angular acceleration, represents the yaw angular acceleration, a y It represents the acceleration component of the vehicle in the y direction in the body axis system.

4. The method according to claim 1, wherein: In step 1.2, the root mean square propagation algorithm is used to train the GRU neural network prediction model, and the neural network prediction accuracy is evaluated by the root mean square error and determination coefficient.

5. The method according to claim 1, wherein: In step 2.1, if the aircraft performs longitudinal maneuvers at a small angle of attack, the linear longitudinal aerodynamic model is selected; when the aircraft performs longitudinal maneuvers at a large angle of attack, the nonlinear longitudinal aerodynamic model with time effect is selected; if the aircraft performs lateral maneuvers, the lateral aerodynamic model is selected.

6. The method according to claim 5, characterized in that: In step 2.1, for the longitudinal aerodynamic model, the aerodynamic parameter vector to be identified is Θ 纵向 =[C D0 ,C L0 ,C Lα ,C Lq ,C Lδe ,C m0 ,C mα ,C mq ,C mδe ] T For the lateral aerodynamic model, the aerodynamic parameter vector to be identified is Θ 横航向 =[C y0 ,C yβ ,C yr ,C yp ,C yδr ,C l0 ,C lβ ,C lr ,C lp , Where C ·0 represents the aerodynamic coefficient deviation term, C ·α and C ·β represents the static stability aerodynamic derivative term, C ·p 、C ·q and C ·r represents the dynamic aerodynamic derivative term, and represents the static aerodynamic derivative term related to the control surface deflection, and · represents the symbols D, L, m, y, l, and n.

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