Unmanned aerial vehicle aerodynamic parameter identification method based on improved maximum likelihood estimation method

Abstract

The application discloses a method for identifying aerodynamic parameters of a UAV based on improved maximum likelihood estimation, and is implemented as follows: an initial aerodynamic coefficient table is generated by using DATCOM, a mathematical expression of the aerodynamic parameters is obtained by using a nonlinear least square polynomial fitting method, and a modeling difficulty of measured data is solved; a modeling process is simplified by combining a confidence interval and aerodynamic physical constraints, and complexity and interpretability of the model are balanced; a high-order coupling term of a polynomial is used to represent system uncertainty, iterative calculation is simplified, a gradient and a Hessian matrix are solved, an LM algorithm is introduced, and problems of covariance singularity, low efficiency and unstable convergence of traditional MLE in processing high-dimensional aerodynamic parameters are solved. The method is improved from three dimensions of aerodynamic model construction, optimization criterion function reconstruction and iterative algorithm optimization, is suitable for identifying aerodynamic parameters of a UAV under high dynamic maneuvering states, and has a 14 times higher calculation efficiency and a relative error of less than 7% compared with traditional MLE.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic parameter identification technology for unmanned aerial vehicles (UAVs), specifically to the identification of aerodynamic parameters of UAVs using an improved maximum likelihood estimation method, which is applicable to aerodynamic modeling under highly dynamic maneuvering flight conditions. Background Technology

[0002] Accurate acquisition of aerodynamic parameters is fundamental to the design of UAV flight control laws. Traditional wind tunnel testing and CFD computation are costly and time-consuming. System identification methods based on flight test data, especially maximum likelihood estimation (MLE), are widely used due to their excellent statistical properties. However, as UAVs perform high-dynamic maneuvering tasks (such as large-angle obstacle avoidance), their aerodynamic characteristics become highly nonlinear, leading to a sharp increase in the dimensionality of the aerodynamic parameters to be identified (often exceeding 100 dimensions). Traditional MLE methods face severe challenges in handling such high-dimensional parameters: 1) enormous computational cost, especially the calculation of gradients and Fisher information matrices, which involves complex sensitivity equations; 2) poor numerical stability, as high-dimensional parameters easily lead to deterioration or even singularity of the Hessian condition number, causing the algorithm to fail to converge; 3) sensitivity to initial values, as Newton-like algorithms are prone to getting trapped in local optima if the initial value deviation is large. Therefore, there is an urgent need for a high-dimensional aerodynamic parameter estimation method that can balance computational efficiency and convergence stability. Summary of the Invention

[0003] To address the aforementioned technical problems, the present invention aims to provide a method for identifying aerodynamic parameters of unmanned aerial vehicles based on improved maximum likelihood estimation. By simplifying the model structure and algorithm operators, the method solves the problems of computational time consumption and convergence in high-dimensional parameter identification.

[0004] This invention is achieved through the following technical solution: a method for identifying aerodynamic parameters of unmanned aerial vehicles based on an improved maximum likelihood estimation method, comprising the following steps:

[0005] S1: Input the UAV's geometric parameters using the DATCOM program, calculate the aerodynamic forces and torques of each component of the UAV, and generate an initial aerodynamic coefficient lookup table; at the same time, acquire sensor observation data of the UAV during actual flight, the observation data including at least three-axis specific force, three-axis angular rate, attitude angle and airspeed;

[0006] S2: Establish the UAV state equation based on the rigid body dynamics equation, and introduce a polynomial model to characterize the aerodynamic coefficients; the polynomial model includes a single-factor polynomial term that depends only on a single state parameter, and a two-factor coupled polynomial term that depends on the product of two state parameters; use the nonlinear least squares method to curve fit the initial aerodynamic coefficient lookup table generated in step S1, solve for the values ​​of the coefficients in the polynomial model, and use these values ​​as the initial values ​​of the parameters to be identified in the subsequent improved maximum likelihood estimation;

[0007] S3: Filter the terms of the polynomial model: First, based on the physical constraints of the aerodynamics, retain the terms that conform to the symmetry and physical mechanism; second, calculate the 95% confidence interval of the parameters through the residual analysis of the nonlinear least squares fitting, and remove redundant terms whose confidence interval contains zero or whose contribution to the model is lower than the preset threshold, and determine the final parameter vector to be identified.

[0008] S4: Based on the assumption of low-altitude flight environment, the process noise in the state equation is set to zero, transforming the stochastic system into a deterministic system; a negative log-likelihood criterion function containing only the statistical characteristics of observation noise is constructed.

[0009] S5: Obtain the state prediction and innovation vector by integrating the state equation using the fourth-order Runge-Kutta method; based on the deterministic model, simplify the calculation formulas for the gradient vector and the approximate Hessian matrix; introduce the dynamic damping factor, and use the improved Levenberg-Marquardt LM algorithm to update the parameters to be identified until the convergence condition is met, and output the final aerodynamic parameter estimates.

[0010] Furthermore, in step S2, the polynomial aerodynamic model is included in the aerodynamic force and moment equations, which are described by the following equation:

[0011] ;

[0012] Among them, resistance Lateral force Lift The components of the total aerodynamic force in the airflow coordinate system; rolling moment. Pitch moment , yaw moment Let be the component of the total aerodynamic torque in the body coordinate system. Dynamic pressure ( air density, (Airspeed), Wing reference area ,span Mean aerodynamic chord length ; For the selection matrix; , These are the dimensionless roll rate, pitch rate, and yaw rate, respectively. For the angle of attack, Sideslip angle, These represent the aileron, elevator, and rudder deflection angles, respectively; symbols This refers to the polynomial aerodynamic coefficient model under different components, based on the selection matrix. Choose the value to replace with ; , Describe longitudinal and lateral effects. , , Describe the rudder surface effect. , , Describe the angular rate damping effect.

[0013] , , , Classified as a single-factor polynomial term, it is used for aerodynamic coefficients that depend on only a single state parameter, with the corresponding state variable being the angle of attack. The general expression is described as follows:

[0014] ;

[0015] in Substitute , , , , For the coefficients of the polynomial model, ;

[0016] , , , Classified as a two-factor coupled polynomial term, it is used for aerodynamic coefficients that depend on the coupling of two parameters. Its general expression is described as follows:

[0017] ;

[0018] in, Substitute , , , , For the coefficients of the polynomial model, Angle of attack , Substitute , , , .

[0019] Furthermore, in step S3, the aerodynamic physical constraints are specifically structural pruning based on polynomial parity, including:

[0020] For the lateral force coefficient and yaw moment coefficient Only the sideslip angle is retained. Odd-power polynomial terms;

[0021] For the rolling moment coefficient and yaw moment coefficient Only information regarding aileron deflection is retained. and rudder deflection Odd-power polynomial terms;

[0022] For drag coefficient Only information regarding elevator deflection angle is retained. The even-power polynomial terms.

[0023] Furthermore, in step S4, under the assumption of a normal distribution, after ignoring the constant term, the negative log-likelihood criterion function... :

[0024] ;

[0025] in, To identify the aerodynamic parameters, For the total number of data points, the new information , For the first The observation data vector at each sampling point For the first Model calculation data for each sampling point To observe the noise covariance matrix.

[0026] Furthermore, in step S5, the gradient vector The Each component and the approximate Hessian matrix The Line number The formula for calculating column elements is simplified to:

[0027] ;

[0028] ;

[0029] in, Gradient vector The One portion, In the approximate Hessian matrix No. Line number Column elements; and These represent the vectors of aerodynamic parameters to be identified. The first in The and the first Each component.

[0030] Furthermore, in step S5, the improved Levenberg-Marquardt LM algorithm is as follows:

[0031]

[0032] in, aerodynamic parameter vector to be identified The iterative correction amount, This is the Hessian approximation matrix. The damping factor, Let the gradient vector be the criterion function; if the parameters are updated... ,but To accelerate convergence; otherwise To reduce the step size.

[0033] The advantages of this invention are mainly reflected in the following aspects:

[0034] Significantly improved computational efficiency: By ignoring process noise and simplifying gradient / Hessian matrix calculations, the iteration of the state covariance matrix and sensitivity calculations in Kalman filtering are avoided, resulting in a significant improvement in computational efficiency compared to traditional MLE (experimental data show an improvement of approximately 14 times).

[0035] Enhanced convergence stability: By simplifying the model, parameter collinearity is reduced. Combined with the damping adjustment mechanism of the LM algorithm, the singularity problem of Hessian matrix caused by high-dimensional parameters is effectively overcome, ensuring that the algorithm can still converge stably when the initial value deviation is large.

[0036] High model accuracy: Key high-order coupling terms (such as the coupling between large angle of attack and angular rate) are retained, enabling the identified model to accurately reproduce the high-dynamic maneuvering flight characteristics of the UAV, with an average relative error of less than 7%. The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0037] Figure 1 This is a complete iterative flowchart of the maximum likelihood method parameter estimation;

[0038] Figure 2 This is a schematic diagram of the architecture of the UAV flight data generation simulation platform used in this embodiment of the invention;

[0039] Figure 3 This is a curve comparing the convergence of the MMLE algorithm of this invention with the traditional MLE algorithm;

[0040] Figure 4 This refers to the comparison of relative errors of aerodynamic parameters and the iterative convergence characteristics in the embodiments of the present invention;

[0041] Figure 5 This is a comparison diagram of the fitting of key state variables under coupled maneuvering conditions according to an embodiment of the present invention. Detailed Implementation

[0042] Step S1: Constructing the prior aerodynamic model and acquiring flight data

[0043] 1. Initial Lookup Table Generation: Using the Digital DATCOM tool. Input the core geometric parameters of the UAV (such as NACA-1410 wing airfoil, aspect ratio 6.3, angle of installation 1°, etc.). The DATCOM program decomposes the aircraft into basic components such as fuselage, wings, horizontal stabilizer, and vertical stabilizer, calculates the aerodynamic forces and moments of each component, and performs superposition corrections to generate an initial aerodynamic coefficient lookup table, the classification of which is shown in Table 1.

[0044] Table 1. Classification of Major Aerodynamic Coefficients Output by DATCOM

[0045]

[0046] 2. Flight Data Acquisition: Actual flight data can be acquired through onboard sensors with a sampling period of 0.002s. Observation vectors include: three-axis specific force (measured by accelerometers), three-axis angular rate (measured by gyroscopes), attitude angles, and airspeed. For flight data acquisition used for simulation verification, [the following is used]. Figure 2 The UAV flight data generation simulation platform shown is used for data collection. The simulation scenarios are designed with two typical operating conditions: steady-state level flight and pitch / roll coupled maneuver, respectively simulating stable flight in cruise mode and nonlinear motion characteristics during high-dynamic maneuver processes. The flight parameter constraints for each operating condition are listed in Table 2.

[0047] Table 2 Simulation Working Condition Design Table

[0048]

[0049] The visualization system and data inspector based on the Simulink VR Sink provide real-time curve plotting, which assists in achieving typical flight conditions of the target by giving remote control commands.

[0050] Step S2: Establishing a polynomial aerodynamic coefficient model and obtaining initial values

[0051] 1. Polynomial model construction:

[0052] In this embodiment, to accurately capture the nonlinear aerodynamic characteristics of the UAV under high-dynamic maneuvers, the traditional linear aerodynamic derivative model is abandoned, and a nonlinear polynomial model based on Taylor series expansion is adopted. The polynomial aerodynamic model is included in the aerodynamic force and moment equations, which are described by the following equation:

[0053] (1)

[0054] Among them, resistance Lateral force Lift The components of the total aerodynamic force in the airflow coordinate system; rolling moment. Pitch moment , yaw moment Let be the component of the total aerodynamic torque in the body coordinate system. Dynamic pressure ( air density, (Airspeed), Wing reference area ,span Mean aerodynamic chord length ; Item selection matrix; , These are the dimensionless roll rate, pitch rate, and yaw rate, respectively. For the angle of attack, Sideslip angle, These represent the aileron, elevator, and rudder deflection angles, respectively; symbols This refers to the polynomial aerodynamic coefficient model under different components, based on the selection matrix. Choose the value to replace with ; , Describe longitudinal and lateral effects. , , Describe the rudder surface effect. , , Describe the angular rate damping effect.

[0055] , , , Classified as a single-factor polynomial term, it is used for aerodynamic coefficients that depend on only a single state parameter, with the corresponding state variable being the angle of attack. The general expression is described as follows:

[0056] (2)

[0057] in Substitute , , , , For the coefficients of the polynomial model, ;

[0058] , , , Classified as a two-factor coupled polynomial term, it is used for aerodynamic coefficients that depend on the coupling of two parameters. Its general expression is described as follows:

[0059] (3)

[0060] in, Substitute , , , , For the coefficients of the polynomial model, Angle of attack , Substitute , , , .

[0061] 2. Obtaining initial values ​​for polynomial model parameters:

[0062] The lookup table output by DATCOM consists of discrete points and cannot be directly used as input to the MMLE algorithm. Therefore, this step utilizes nonlinear least squares (NLLS) to perform offline fitting of the lookup table in S1. The multinomial model closely matches the subdivided aerodynamic coefficient lookup table entries output by DATCOM. A small number of uncovered coefficients are initialized with zero, and subsequent parameter estimation will iteratively optimize their values ​​using observational data. This process effectively solves the problem of traditional MLE's sensitivity to initial values ​​and the difficulty in providing them arbitrarily.

[0063] Step S3: Model Simplification Based on Physical Constraints and Statistical Significance Tests: The initially constructed full-order 4th-degree polynomial model contains as many as 310 coefficients to be estimated. Direct identification would lead to serious overfitting and multicollinearity problems. This invention employs the following collaborative strategy to prune the model terms.

[0064] (1) Symmetry constraint:

[0065] a) Sideslip angle Related items: lateral force, yaw moment, etc. It exhibits odd function characteristics and retains Odd terms;

[0066] b) Surface deflection related terms: Ailerons and rudder exhibit odd function characteristics with respect to roll / yaw moments, retain Odd-order terms; the elevator's contribution to drag is retained. Even-order terms are used to reflect the symmetry characteristics of induced resistance.

[0067] (2) Statistical significance screening: The 95% confidence interval of the parameters is calculated by residual analysis of nonlinear least square fitting, and items with too small absolute values ​​of coefficients or confidence intervals containing 0 are eliminated.

[0068] (3) Physical interpretability: Retain terms directly related to aerodynamic mechanisms, such as... Reflects the modulation of the effective angle of attack by the deflection of the control surfaces. Capturing stall nonlinearity at high angles of attack The item embodies pitch damping characteristics.

[0069] Through the aforementioned streamlined process, the number of parameters to be estimated was significantly reduced from the initial 310 to 119, achieving a model simplification rate of 62%. This structure determination process significantly reduced the coupling and collinearity among parameters, greatly improving the numerical stability of subsequent optimization algorithms.

[0070] Step S4: Construct a deterministic likelihood criterion function that ignores process noise, simplifying the optimization objective. In traditional methods, the process noise covariance... Selecting sensitive parameters can easily lead to fitting noise or singular covariance. Considering the low-altitude flight scenario of drones, the impact of minor wind disturbances is negligible, thus reducing process noise. Right now The focus shifts to aerodynamic parameter errors, resulting in the following changes to the MLE:

[0071] (1) The state equation is simplified to a deterministic model. ;

[0072] (2) The new covariance matrix is ​​simplified to: It is determined solely by observation noise, without the need for iterative calculation of state covariance correlation quantities;

[0073] (3) The modified likelihood criterion function is:

[0074] (4)

[0075] in, To identify the aerodynamic parameters, For the total number of data points, the new information , For the first The observation data vector at each sampling point For the first Model calculation data for each sampling point To observe the noise covariance matrix.

[0076] This improvement increases the contribution of aerodynamic parameter errors to the innovation, eliminates the need to calculate state covariance and Kalman gain, improves computational efficiency by about 70%, and completely solves the problem of singularity in the covariance matrix.

[0077] Step S5: Introduce the Levenberg-Marquardt (LM) algorithm, utilize the simplified gradient and Hessian matrix calculation formulas, introduce the dynamic damping factor, solve the covariance singularity and convergence instability problems of high-dimensional parameters, and finally iterate to obtain the aerodynamic parameter identification results.

[0078] (1) Sensitivity and gradient calculation optimization. Traditional MLE gradient calculation needs to consider the sensitivity of both innovation and innovation covariance to the parameters. After simplification, and and Irrelevant, therefore The gradient formula is greatly simplified to the gradient vector of the first... One component:

[0079] (5)

[0080] Traditional Hessian matrix calculations are complex, and the residuals are small after parameter convergence. Therefore, the residual Jacobian product approximation is used, neglecting the presence of... The cross term, approximating the Hessian matrix, is the first... Line number Column elements (ignoring second derivative terms):

[0081] (6)

[0082] This optimization eliminates the need to calculate the sensitivity of the new information covariance to the parameters, further reducing the computational load by 60%, while maintaining the approximate accuracy to meet engineering requirements.

[0083] (2) The Levenberg-Marquardt iterative strategy is introduced to replace the Newton method. The traditional Newton method relies on the positive definiteness of the Hessian matrix, which is prone to iterative oscillations in 119-dimensional high-dimensional scenarios due to the non-positive definiteness of the matrix. The Levenberg-Marquardt (LM) algorithm is adopted, introducing a damping factor to balance the convergence speed and stability. The parameter update formula for the LM algorithm is:

[0084] (7)

[0085] in, aerodynamic parameter vector to be identified The iterative correction amount, This is the Hessian approximation matrix. Let be the damping factor, with an initial value of . , Let the gradient vector be the criterion function; if the parameters are updated... ,but To accelerate convergence; otherwise To reduce the step size.

[0086] Integrating the above improvements, the iterative process for estimating aerodynamic parameters for UAVs is as follows:

[0087] a) Initialization: Set the observation noise covariance matrix according to sensor calibration. Initial parameters are given by the DATCOM fitting results. Determine the initial value and initial state from the observation data. .

[0088] b) Forward simulation: The simulation state at each time step is obtained by using the fourth-order Runge-Kutta method integral state equation. .

[0089] c) New interest calculation: based on Calculate the residuals. This represents the measured observation data at time i.

[0090] d) Sensitivity calculation: Integral state sensitivity equation Obtain the sensitivity of the simulation state to the parameters. Combined with the observed Jacobian, the sensitivity of the innovation to the parameters is calculated.

[0091] (8)

[0092] e) Gradient and Hessian matrix calculation: Calculate the gradient according to equation (4). Calculate the Hessian approximation matrix according to equation (5). .

[0093] f) Parameter update and convergence judgment: Calculate the parameter update amount according to equation (6), and update the parameters. Adjust the damping factor according to the change in the criterion function value. If the relative rate of change of the likelihood criterion function is less than If the parameter update amount is less than the set threshold, then convergence is determined and iteration stops; otherwise, return to step b).

[0094] Each time, 2500 consecutive data points are randomly selected from flight data containing level flight and coupled maneuvers, and iterative calculation simulations of improved MLE parameter estimation are carried out. The results are evaluated from four dimensions: algorithm convergence, computational efficiency, parameter estimation accuracy, and data fitting accuracy.

[0095] For evaluating algorithm convergence, due to the different magnitudes of parameters, it is not suitable to use the norm of a single parameter update as a convergence criterion. Therefore, using the cumulative decrease rate of the likelihood criterion function as a convergence criterion is more in line with engineering practice. The cumulative decrease rate is defined as:

[0096] (9)

[0097] When two consecutive iterations The change is less than The algorithm is considered converged upon completion. For evaluating computational efficiency, single-condition computation time is defined as the average total time taken to complete the entire process of forward simulation, sensitivity calculation, and gradient iteration under the same data volume (2500 data points). For evaluating parameter estimation accuracy, the relative error of aerodynamic parameters is the primary focus. For evaluating data fitting accuracy, the root mean square error (RMSE) is used to assess the degree of fit between the model output corresponding to the estimated parameters and the actual flight data, defined as:

[0098] (10)

[0099] Improved MLE parameter estimation was performed using data from 100 flights. The average results were compared with those of the traditional MLE, as shown in Table 3.

[0100] (1) The improved MLE has an average single-condition execution time of 4.2s, which is only a fraction of the traditional MLE. Efficiency increased by more than 14 times.

[0101] (2) Traditional MLE cannot converge because the Hessian matrix is ​​non-positive definite under high-dimensional parameters, while the improved MLE only requires an average of 6.6 iterations to achieve a cumulative decrease rate of 96.16%, and the convergence stability is significantly improved. Figure 3 The typical iterative convergence process of improving MLE parameter estimation using level flight and coupled maneuver data is presented. The likelihood criterion function value decreases rapidly with the number of iterations. When the 8th iteration is reached, the convergence condition is met, proving the stable convergence characteristics of the algorithm under high-dimensional parameters and high-dynamic maneuver conditions of UAVs.

[0102] Table 3 Performance Comparison between Improved MLE and Traditional MLE

[0103]

[0104] (3) Figure 4 The relative error results of the improved MLE algorithm in high-dimensional aerodynamic parameter estimation are presented from three dimensions: sub- Figure 1-2 To optimize the relative error distribution of parameters before and after, sub Figure 3 The curves showing the variation of the average relative error of the parameters with the number of iterations are shown. The results indicate that the average relative error of the optimized aerodynamic parameters is less than 7%, and the average relative error of the parameters shows a continuous convergence trend as the number of iterations increases. This verifies the accuracy advantage of the algorithm in high-dimensional aerodynamic parameter estimation and also demonstrates its stable estimation capability under high dynamic conditions.

[0105] (4) Regarding fitting accuracy, the RMSE of specific force, angular rate, and attitude angle are all at a low level, meeting engineering requirements, and the estimated parameters can accurately reproduce the dynamic characteristics of the actual flight state. For example Figure 5As shown, taking the pitch-roll coupled maneuver state as an example, the time series of the original flight data and the model before and after optimization are compared. It can be seen that the model before optimization deviates significantly from the original data, while the model after optimization almost overlaps with the original data. The simulation results verify the improved MLE's fitting ability for high dynamic scenarios.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the present invention.

Claims

1. A method for identifying aerodynamic parameters of unmanned aerial vehicles based on an improved maximum likelihood estimation method, characterized in that: Includes the following steps: S1: Input the UAV's geometric parameters using the DATCOM program, calculate the aerodynamic forces and torques of each component of the UAV, and generate an initial aerodynamic coefficient lookup table; at the same time, acquire sensor observation data of the UAV during actual flight, the observation data including at least three-axis specific force, three-axis angular rate, attitude angle and airspeed; S2: Establish the UAV state equation based on the rigid body dynamics equation, and introduce a polynomial model to characterize the aerodynamic coefficients; the polynomial model includes a single-factor polynomial term that depends only on a single state parameter, and a two-factor coupled polynomial term that depends on the product of two state parameters; use the nonlinear least squares method to curve fit the initial aerodynamic coefficient lookup table generated in step S1, solve for the values ​​of the coefficients in the polynomial model, and use these values ​​as the initial values ​​of the parameters to be identified in the subsequent improved maximum likelihood estimation; S3: Filter the terms of the polynomial model: First, based on the physical constraints of the aerodynamics, retain the terms that conform to the symmetry and physical mechanism; second, calculate the 95% confidence interval of the parameters through the residual analysis of the nonlinear least squares fitting, and remove redundant terms whose confidence interval contains zero or whose contribution to the model is lower than the preset threshold, and determine the final parameter vector to be identified. S4: Based on the assumption of low-altitude flight environment, the process noise in the state equation is set to zero, transforming the stochastic system into a deterministic system; a negative log-likelihood criterion function containing only the statistical characteristics of observation noise is constructed. S5: Obtain the state prediction and innovation vector by integrating the state equation using the fourth-order Runge-Kutta method; based on the deterministic model, simplify the calculation formulas for the gradient vector and the approximate Hessian matrix; introduce the dynamic damping factor, and use the improved Levenberg-Marquardt LM algorithm to update the parameters to be identified until the convergence condition is met, and output the final aerodynamic parameter estimates.

2. The method according to claim 1, characterized in that: In step S2, the polynomial aerodynamic model is included in the aerodynamic force and moment equations, which are described by the following equation: ； Among them, resistance Lateral force Lift The components of the total aerodynamic force in the airflow coordinate system; rolling moment. Pitch moment , yaw moment Let be the component of the total aerodynamic torque in the body coordinate system. Dynamic pressure ( air density, (Airspeed), Wing reference area ,span Mean aerodynamic chord length ; For the selection matrix; , These are the dimensionless roll rate, pitch rate, and yaw rate, respectively. For the angle of attack, Sideslip angle, These represent the aileron, elevator, and rudder deflection angles, respectively; symbols This refers to the polynomial aerodynamic coefficient model under different components, based on the selection matrix. Choose the value to replace with ; , Describe longitudinal and lateral effects. , , Describe the rudder surface effect. , , Describe the angular velocity damping effect; , , , Classified as a single-factor polynomial term, it is used for aerodynamic coefficients that depend on only a single state parameter, with the corresponding state variable being the angle of attack. The general expression is described as follows: ； in Substitute , , , , For the coefficients of the polynomial model, ; , , , Classified as a two-factor coupled polynomial term, it is used for aerodynamic coefficients that depend on the coupling of two parameters. Its general expression is described as follows: ； in, Substitute , , , , For the coefficients of the polynomial model, Angle of attack , Substitute , , , .

3. The method according to claim 1, characterized in that: In step S3, the aerodynamic physical constraints are specifically structural trimming based on polynomial parity, including: For the lateral force coefficient and yaw moment coefficient Only the sideslip angle is retained. Odd-power polynomial terms; For the rolling moment coefficient and yaw moment coefficient Only information regarding aileron deflection is retained. and rudder deflection Odd-power polynomial terms; For drag coefficient Only information regarding elevator deflection angle is retained. The even-power polynomial terms.

4. The method according to claim 1, characterized in that: In step S4, under the assumption of normal distribution, after ignoring the constant term, the negative log-likelihood criterion function... : ； in, To identify the aerodynamic parameters, For the total number of data points, the new information , For the first The observation data vector at each sampling point For the first Model calculation data for each sampling point To observe the noise covariance matrix.

5. The method according to claim 1, characterized in that: In step S5, the gradient vector The Each component and the approximate Hessian matrix The Line number The formula for calculating column elements is simplified to: ； ； in, Gradient vector The One portion, In the approximate Hessian matrix No. Line number Column elements; and These represent the vectors of aerodynamic parameters to be identified. The first in The and the first Each component.

6. The method according to claim 1, characterized in that: In step S5, the improved Levenberg-Marquardt LM algorithm is as follows: ； in, aerodynamic parameter vector to be identified The iterative correction amount, This is the Hessian approximation matrix. The damping factor, Let the gradient vector of the criterion function be used; if the parameters are updated... ,but To accelerate convergence; otherwise To reduce the step size.

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