A guided shell dynamics parameter identification method based on double-layer game UKF

Abstract

The application provides a kind of guided artillery shell dynamics parameter identification method based on double-layer game UKF, this method mainly includes filter model construction and UKF filtering improvement two parts, according to six degrees of freedom trajectory dynamics model and aerodynamic extension equation, filter model is constructed, so as to obtain system state equation, according to the parameter coupling relationship between guided artillery shell dynamics model and inertial device, decoupling is obtained gyro output angular velocity and accelerometer output specific force, so as to construct system observation equation;Based on the innovation of filter model and prior observation data, design a kind of double-layer game improved UKF method, inner game is composed of noise mapping method and Sage-Husa method, for evaluating the dynamic relationship between prediction and actual measurement;Outer game assesses two kinds of adaptive methods by calculating Mahalanobis distance, which reflects the game between the predicted observation covariance and the actual measurement covariance.The application can adapt to unknown noise environment, self-adapting adjustment observation noise covariance, improve guided artillery shell parameter identification precision.

Description

Technical Field

[0001] This invention belongs to the field of high-dynamic guided projectile navigation technology, and relates to a method for identifying the dynamic parameters of guided projectiles based on two-layer game theory UKF. Background Technology

[0002] Currently, guided projectiles are affected by complex external environmental disturbances and the interactions between aerodynamic parameters, making it difficult to obtain their ballistic parameters during flight. Aerodynamic forces and aerodynamic moments are the main factors affecting projectile trajectory. Before designing the flight trajectory of a guided projectile, its aerodynamic forces and moments must be calculated. Without specific aerodynamic parameters beforehand, it is impossible to perform ballistic calculations for the guided projectile. Therefore, the identification of aerodynamic parameters of guided projectiles is of great significance for improving their firing accuracy and promoting their development.

[0003] In guided projectile design, aerodynamic parameters are primarily obtained through three methods: theoretical calculation, wind tunnel testing, and flight testing. Theoretical calculation involves establishing a mathematical model to calculate aerodynamic parameters. However, this method is computationally complex and cannot fully account for external influencing factors, often resulting in significant discrepancies between the calculated and actual aerodynamic parameters. Wind tunnel testing measures the forces acting on the test model under different Mach numbers in a wind tunnel using various measuring devices, calculating the model's aerodynamic parameters. However, the translational motion of the test model in the wind tunnel's virtual flight is constrained, leading to flight dynamics drastically different from free flight. Flight testing verifies the results of theoretical models and wind tunnel tests by observing and recording projectile behavior under real flight conditions. However, this method is costly, and the experimental conditions are subject to various constraints, making repeated verification difficult. Summary of the Invention

[0004] This invention addresses the problems of high nonlinearity and unknown noise caused by the complex flight environment of guided projectiles. It proposes a method for identifying the dynamic parameters of guided projectiles based on a two-layer game UKF, which can accurately estimate the trajectory impact point and identify key aerodynamic parameters, effectively improving the accuracy and robustness of inertial measurement-assisted trajectory parameter identification.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF), applicable to the identification of dynamic parameters during the flight process of guided projectiles, including:

[0007] A filtered model is constructed based on the six-degree-of-freedom ballistic dynamics model and the aerodynamic extended equations to obtain the system state equations.

[0008] Based on the parameter coupling relationship between the guided projectile dynamics model and the inertial devices, the gyroscope output angular velocity and the accelerometer output specific force are decoupled and the system observation equations are constructed.

[0009] Based on the system state equation and system observation equation, the noise evaluation function is determined, and an internal and external two-layer game strategy is designed.

[0010] The UKF method is combined with an internal and external two-layer game strategy to calculate the Kalman gain, and the state variables and state estimation error covariance are updated to estimate the ballistic dynamic parameters.

[0011] Furthermore, the six-degree-of-freedom ballistic dynamics model is as follows:

[0012]

[0013] in, This indicates the velocity of the projectile's center of mass. Indicates the elevation angle of velocity. Velocity azimuth angle, , , This represents the three-axis angular velocity of the projectile revolving around its center of mass. Indicates the elevation angle of the spring shaft. Indicates the azimuth angle of the spring shaft. Indicates the roll angle. , , Indicates the position of the three axes of the shell. , , Indicates the external torque at The three-axis components in the coordinate system , , This represents the three-axis components of the external force in the velocity coordinate system. , , These represent the projectile mass, polar moment of inertia, and equatorial moment of inertia, respectively. Indicates atmospheric pressure. Indicates air density, Represents gravitational acceleration. , , , , These represent the derivatives of the drag coefficient, lift coefficient, static moment coefficient, extreme damping moment coefficient, and Magnus moment coefficient, respectively.

[0014] The filtering model is as follows:

[0015]

[0016] Where X is the augmented state variable. This refers to the computational error generated during the numerical calculation of the state equations.

[0017] Furthermore, the ratio of the gyroscope output angular velocity to the accelerometer output force is:

[0018]

[0019] In the formula, The gyroscope output angular velocity represents the ballistic parameters in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the gyroscope output angular velocity. This indicates the noise level measured by the gyroscope. Indicates the three-axis acceleration of the projectile. This represents the three-axis velocity expressed by ballistic parameters in the navigation system. This represents the projection of the Earth's rotational angular velocity onto the navigation frame. This indicates the rotation of the navigation frame relative to the Earth system. This is local gravitational acceleration. This represents the coordinate transformation matrix from the navigation frame to the vehicle frame. This represents the specific force output by the accelerometer in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the specific force output by the accelerometer. This indicates the noise level measured by the accelerometer.

[0020] Furthermore, the system observation equation is:

[0021]

[0022] in, The nonlinear function representing the inertial information (gyroscope output angular velocity, accelerometer output specific force) retrieved from the ballistic dynamics model. This refers to the measurement noise of inertial equipment.

[0023] Furthermore, the noise evaluation function is:

[0024]

[0025] In the formula, This represents the estimated value observed at the current time. This represents the actual observed value at the current moment. This represents the actual observed value at the previous moment. It is used to measure the degree of error between the observed estimate and the actual observed value.

[0026] Furthermore, the inner game of the inner and outer two-layer game strategy consists of a noise mapping method and a Sage-Husa method, which are used to evaluate the dynamic relationship between the prediction and the actual measurement. The outer game selects the optimal noise from the noise mapping method and the Sage-Husa method by calculating the Mahalanobis distance.

[0027] Furthermore, the noise mapping method specifically includes:

[0028] Based on the noise evaluation function, the noise mapping function is constructed as follows:

[0029]

[0030] In the formula, Indicates noise evaluation indicators The noise mapping function, , These represent the amplification factor for noise with anomalies less than the threshold and the amplification factor for noise with anomalies greater than the threshold, respectively. Indicators of error evaluation The mean;

[0031] The observed noise covariance is updated using the noise mapping function value. , Represents the noise mapping function at the current time. .

[0032] Furthermore, the Sage-Husa method updates the observation noise covariance as follows:

[0033]

[0034] In the formula, b is the forgetting factor. These are weighting coefficients. The information is the difference between the actual measured value and the observed estimated value at the current time.

[0035] Furthermore, the formula for calculating the Mahalanobis distance is:

[0036]

[0037] In the formula, Indicates the covariance weights in the UKF. This represents the observation noise covariance at the current moment. This represents the covariance of the predicted observations at the current moment.

[0038] Furthermore, the update of the state variables and the state estimation error covariance is performed using the fourth-order Runge-Kutta method.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] This invention, within the UKF framework, formulates a two-layer game strategy. The inner layer dynamically adjusts the noise covariance based on the predicted and measured trends, while the outer layer uses Mahalanobis distance to select the optimal noise strategy in real time. This method achieves adaptive adjustment of the noise covariance, accurately estimates the ballistic impact point, and identifies key aerodynamic parameters, effectively improving the accuracy and robustness of inertial measurement-assisted ballistic parameter identification. Attached Figure Description

[0041] Figure 1 Framework diagram of the two-layer game-based improved UKF ballistic dynamics parameter identification method.

[0042] Figure 2 Framework diagram for constructing a guided projectile / inertial measurement filter model with aerodynamic parameters extended.

[0043] Figure 3 Framework diagram of the improved UKF algorithm with two-layer game theory. Detailed Implementation

[0044] The implementation of the present invention will now be described in detail with reference to the accompanying drawings.

[0045] See appendix Figure 1 This invention proposes a method for identifying the dynamic parameters of guided projectiles based on a two-layer game-theoretic UKF (Unscented Kalman Filter). The core of this method consists of two main parts: (1) construction of a guided projectile / inertial measurement filtering model with aerodynamic parameter extension; and (2) design of a two-layer game-theoretic improved UKF (Unscented Kalman Filter) algorithm. First, a filtering model is constructed based on a six-degree-of-freedom ballistic dynamics model and the aerodynamic extension method to obtain the system state equation. The inertial measurement information is then inverted from the ballistic dynamics model to obtain the observation equation. Next, a two-layer game-theoretic improved UKF algorithm is designed. The inner game consists of a noise mapping method and a Sage-Husa method, used to evaluate the dynamic relationship between prediction and actual measurement; the outer game evaluates the two adaptive methods by calculating Mahalanobis distance, reflecting the game between the predicted observation covariance and the actual measurement covariance. The proposed method can adapt to unknown noise environments, adaptively adjust the observation noise covariance, and improve the accuracy of guided projectile parameter identification.

[0046] The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) proposed in this invention specifically includes:

[0047] (1) Based on the six-degree-of-freedom ballistic dynamics model and the aerodynamic extended equations, a filter model is constructed to obtain the system state equations;

[0048] The aerodynamic parameter extended guided projectile dynamics model is as follows:

[0049]

[0050] in, This indicates the velocity of the projectile's center of mass. Indicates the elevation angle of velocity. Velocity azimuth angle, , , This represents the three-axis angular velocity of the projectile revolving around its center of mass. Indicates the elevation angle of the spring shaft. Indicates the azimuth angle of the spring shaft. Indicates the roll angle. , , Indicates the position of the three axes of the shell. , , Indicates the external torque at The three-axis components in the coordinate system , , This represents the three-axis components of the external force in the velocity coordinate system. , , These represent the projectile mass, polar moment of inertia, and equatorial moment of inertia, respectively. Indicates atmospheric pressure. Indicates air density, Represents gravitational acceleration. , , , , These represent the derivatives of the drag coefficient, lift coefficient, static moment coefficient, extreme damping moment coefficient, and Magnus moment coefficient, respectively.

[0051] The augmented complete state variables are

[0052]

[0053] The state equation of the filter model can be expressed by the following equation:

[0054]

[0055] The update process of the state equation is completed using the fourth-order Runge-Kutta method, as shown below:

[0056]

[0057] In the formula, Represents the state vector. Representing the independent variable of time, Indicates the time step. Represents the slope at different points. This represents a nonlinear dynamic model with extended aerodynamic parameters.

[0058] (2) Based on the parameter coupling relationship between the guided projectile dynamics model and the inertial devices, the gyroscope output angular velocity and accelerometer output specific force are decoupled and the system observation equations are constructed; see [link to relevant documentation]. Figure 2 Specifically, this includes:

[0059] Based on the conversion relationship between attitude angles in the navigation coordinate system and angular velocities in the carrier coordinate system in strapdown inertial navigation, the conversion relationship between attitude angles and angular velocities in the ballistic model can be derived.

[0060] The equation for the gyroscope's output angular velocity is as follows:

[0061]

[0062] In the formula, The gyroscope output angular velocity represents the ballistic parameters in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the gyroscope output angular velocity. This indicates the noise level measured by the gyroscope. Indicates the three-axis acceleration of the projectile. This represents the three-axis velocity expressed by ballistic parameters in the navigation system. This represents the projection of the Earth's rotational angular velocity onto the navigation frame. This indicates the rotation of the navigation frame relative to the Earth system. This is local gravitational acceleration. This represents the coordinate transformation matrix from the navigation frame to the vehicle frame. This represents the specific force output by the accelerometer in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the specific force output by the accelerometer. This indicates the noise level measured by the accelerometer.

[0063] Based on further derivation of the ballistic model and combined with the velocity differential equation in the navigation coordinate system of strapdown inertial navigation, the output specific force equation of the accelerometer derived from the ballistic model can be obtained. The three-axis acceleration of the projectile can be obtained by taking the second derivative of its three-axis position, and expressed in terms of ballistic parameters, as shown in the following equation:

[0064]

[0065] According to the velocity differential equation of the strapdown inertial navigation system, we can obtain:

[0066]

[0067] In the formula, Indicates the three-axis acceleration of the projectile.

[0068] This represents the three-axis velocity expressed by ballistic parameters in the navigation system. This represents the projection of the Earth's rotational angular velocity onto the navigation frame. This indicates the rotation of the navigation frame relative to the Earth system. This is local gravitational acceleration. The coordinate transformation matrix from the navigation system to the vehicle system can be represented by the following formula.

[0069]

[0070] The accelerometer output specific force equation, expressed in terms of ballistic parameters, is as follows:

[0071]

[0072] In the formula, This represents the specific force output by the accelerometer in the carrier coordinate system. A nonlinear equation representing the relationship between ballistic parameters and the specific force output by the accelerometer. This indicates the noise level measured by the accelerometer.

[0073] The complete observation equation based on inertial measurement is as follows:

[0074]

[0075] (3) Based on the system state equation and system observation equation, determine the noise evaluation function and design an internal and external two-layer game strategy; see appendix. Figure 3 This invention constructs a filter model with extended aerodynamic parameters and designs a two-layer game strategy. The inner layer dynamically adjusts the noise covariance based on the predicted and measured trends, while the outer layer uses Mahalanobis distance to select the optimal noise strategy in real time, reflecting the dynamic game relationship between the predicted observation covariance and the actual measurement covariance. This method achieves adaptive adjustment of the noise covariance, accurately estimates the ballistic impact point, and identifies key aerodynamic parameters, effectively improving the accuracy and robustness of inertial measurement-assisted ballistic parameter identification.

[0076] (4) The UKF method is combined with an internal and external two-layer game strategy to calculate the Kalman gain, and the state variables and state estimation error covariance are updated to estimate the ballistic dynamics parameters. The specific implementation of this step is as follows:

[0077] Step 1, Initialize state variables and state estimation error covariance Sigma points are generated through unscented transformation.

[0078] Step 2: The Sigma points are used to make a one-step prediction of the state variables and the state estimation error covariance using the 4-RK method, and then a new Sigma point is generated by unscented transformation.

[0079] Step 3: The new Sigma point is entered into the observation equation to complete the measurement update and calculate the new information.

[0080] Step 4, the inner game consists of two methods: the noise mapping method and the Sage-Husa method, which reflects the dynamic game relationship between the prediction and the actual measurement, as detailed below.

[0081] Noise mapping method:

[0082] (1) Calculate the degree of error between the observed estimated value and the actual observed value based on the difference between the current information and the current observation, and define the comprehensive error evaluation index as shown in the following formula.

[0083]

[0084] In the formula, This represents the estimated value observed at the current time. This represents the actual observed value at the current moment. This represents the actual observed value at the previous moment, therefore, It is used to measure the degree of error between the estimated and actual observed values. The larger the value, the higher the degree of error. The closer it is to 1, the smaller the degree of error.

[0085] (2) Construct a noise mapping function, through The degree of error is reflected by adaptively smoothing the noise covariance R, thereby improving the stability and consistency of the filtered values. The noise mapping function is shown in the following equation:

[0086]

[0087] In the formula, , These represent the amplification factor under noise with a low degree of anomaly and the amplification factor under noise with a high degree of anomaly, respectively. Indicators of error evaluation The mean is shown in the following formula:

[0088]

[0089] (3) Update of observation noise covariance

[0090]

[0091] Sage-Husa method:

[0092] The adaptive method for the observation noise covariance R is shown in the following equation:

[0093]

[0094] In the formula, b is the forgetting factor. These are weighting coefficients. The innovation is the difference between the actual measured value and the observed estimated value at the current time. By updating R in real time using the innovation, we can adapt to unknown noise environments, improving estimation accuracy and robustness.

[0095] Step 5. Outer Game Design: Calculate the Mahalanobis distance between the actual measured value and the observed estimated value at the current time. The Mahalanobis distance evaluates the two adaptive methods, reflecting the game between the predicted observed covariance and the actual measured covariance, as shown in the following equation:

[0096]

[0097] In the formula, Indicates the covariance weights in the UKF. This represents the observation noise covariance at the current moment.

[0098] Finally, the Mahalanobis distances corresponding to the noise mapping method and the Sage-Husa method were calculated respectively. and The strategy with the smaller Mahalanobis distance is selected as the optimal noise estimate for the current time.

[0099]

[0100] Step 6. Calculate the Kalman gain and update the state variables and state estimation error covariance to achieve high-precision identification of the parameters of the guided projectile dynamic model.

[0101] This invention constructs a guided projectile filtering model with extended aerodynamic parameters, inverts the inertial measurement information of the guided projectile, defines a noise evaluation function, and formulates an inner and outer two-layer game strategy. The inner game consists of a noise mapping method and a Sage-Husa method, used to evaluate the dynamic relationship between predictions and actual measurements. The outer game evaluates two adaptive methods by calculating Mahalanobis distance, reflecting the game between the predicted observation covariance and the actual measurement covariance. Combined with UKF, data fusion is completed to accurately estimate ballistic parameters. The proposed method can adapt to unknown noise environments, adaptively adjust the observation noise covariance, and improve the accuracy of guided projectile parameter identification.

[0102] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0103] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF), characterized in that, include: A filtered model is constructed based on the six-degree-of-freedom ballistic dynamics model and the aerodynamic extended equations to obtain the system state equations. Based on the parameter coupling relationship between the guided projectile dynamics model and the inertial devices, the gyroscope output angular velocity and the accelerometer output specific force are decoupled and the system observation equations are constructed. Based on the system state equation and system observation equation, the noise evaluation function is determined, and an internal and external two-layer game strategy is designed. The UKF method is combined with an internal and external two-layer game strategy to calculate the Kalman gain, and the state variables and state estimation error covariance are updated to estimate the ballistic dynamic parameters.

2. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 1, characterized in that, The six-degree-of-freedom ballistic dynamics model is as follows: in, This indicates the velocity of the projectile's center of mass. Indicates the elevation angle of velocity. Velocity azimuth angle, , , This represents the three-axis angular velocity of the projectile revolving around its center of mass. Indicates the elevation angle of the spring shaft. Indicates the azimuth angle of the spring shaft. Indicates the roll angle. , , Indicates the position of the three axes of the shell. , , Indicates the external torque at The three-axis components in the coordinate system , , This represents the three-axis components of the external force in the velocity coordinate system. , , These represent the projectile mass, polar moment of inertia, and equatorial moment of inertia, respectively. Indicates atmospheric pressure. Indicates air density, Represents gravitational acceleration. , , , , These represent the derivatives of the drag coefficient, lift coefficient, static moment coefficient, extreme damping moment coefficient, and Magnus moment coefficient, respectively. The filtering model is as follows: Where X is the augmented state variable. This refers to the computational error generated during the numerical calculation of the state equations.

3. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 2, characterized in that, The ratio of the gyroscope output angular velocity to the accelerometer output force is: In the formula, The gyroscope output angular velocity represents the ballistic parameters in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the gyroscope output angular velocity. This indicates the noise level measured by the gyroscope. This indicates the three-axis acceleration of the projectile. This represents the three-axis velocity expressed by ballistic parameters in the navigation system. This represents the projection of the Earth's rotational angular velocity onto the navigation frame. This indicates the rotation of the navigation frame relative to the Earth system. This is local gravitational acceleration. This represents the coordinate transformation matrix from the navigation frame to the vehicle frame. This represents the specific force output by the accelerometer in the carrier coordinate system. The nonlinear equation representing the relationship between ballistic parameters and the specific force output by the accelerometer. This indicates the noise level measured by the accelerometer.

4. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 3, characterized in that, The system observation equation is: in, The nonlinear function representing the inertial information (gyroscope output angular velocity, accelerometer output specific force) retrieved from the ballistic dynamics model. This refers to the measurement noise of inertial equipment.

5. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 1, characterized in that, The noise evaluation index is: In the formula, This represents the estimated value observed at the current time. This represents the actual observed value at the current moment. This represents the actual observed value at the previous moment. It is used to measure the degree of error between the observed estimate and the actual observed value.

6. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 1, characterized in that, The inner game of the aforementioned two-layer game strategy consists of a noise mapping method and a Sage-Husa method, which are used to evaluate the dynamic relationship between predictions and actual measurements. The outer game selects the optimal noise from the noise mapping method and the Sage-Husa method by calculating Mahalanobis distance.

7. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 6, characterized in that, The noise mapping method specifically includes: Based on the noise evaluation function, the noise mapping function is constructed as follows: In the formula, Indicates noise evaluation indicators The noise mapping function, , These represent the amplification factor for noise with anomalies less than the threshold and the amplification factor for noise with anomalies greater than the threshold, respectively. Indicators of error evaluation The mean; The observed noise covariance is updated using the noise mapping function value. , Represents the noise mapping function at the current time. .

8. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 6, characterized in that, The Sage-Husa method updates the observation noise covariance as follows: In the formula, b is the forgetting factor. These are weighting coefficients. The information is the difference between the actual measured value and the observed estimated value at the current time.

9. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 6, characterized in that, The formula for calculating the Mahalanobis distance is: In the formula, Indicates the covariance weights in the UKF. This represents the observation noise covariance at the current moment. This represents the covariance of the predicted observations.

10. The method for identifying the dynamic parameters of guided projectiles based on two-layer game theory (UKF) according to claim 1, characterized in that, The state variables and state estimation error covariance are updated using the fourth-order Runge-Kutta method.

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