A local battlefield average wind fast determination method based on a closed loop calibration system

Abstract

The application discloses a kind of local battlefield average wind fast determination method based on closed loop calibration system, with four degrees of freedom trajectory model as foundation, time-varying longitudinal wind and transverse wind are regarded as virtual control quantity to be solved, and local battlefield average wind trajectory optimization model is constructed.Radau pseudospectral method is used, and by arranging LGR discrete node, the average wind trajectory optimization model in continuous form is dispersed into nonlinear programming problem, and based on trajectory model, the reconstruction method of calibration head measurement data in sliding window trajectory fitting.Finally, the discrete nonlinear programming problem is solved by using interior point algorithm, and the optimal average wind value at each discrete node is obtained by optimization, and then the variation law of average wind with projectile flight time is obtained.The application can reduce the adverse effects caused by the loss of wireless communication data of closed loop calibration system to the greatest extent, efficiently capture the variation law of time-varying average wind, and provide a better basis for improving shooting accuracy without actual measurement of upper air meteorological data.

Description

Technical Field

[0001] This invention belongs to the fields of external ballistics ballistic correction theory, artillery firing science, and artillery weapon system applications, and in particular, it is a method for rapidly determining the local battlefield mean wind based on a closed-loop firing correction system. Background Technology

[0002] A closed-loop artillery firing correction system is a system capable of automatically measuring the projectile's impact coordinates and performing automatic firing correction. In this system, the projectile's position and velocity are measured in real time during flight, and this information is sent back to the artillery position for calculation to obtain the impact coordinates and firing data deviations, thereby adjusting the artillery for a more precise next shot.

[0003] In artillery firing, weather conditions are a crucial factor affecting accuracy. Actual wind speed and direction vary with altitude. In ballistics, for ease of correction, a constant mean wind (crosswind and longitudinal wind) is often used to replace the altitude-varying mean wind, ensuring its effect on range and sideslip is the same. Mean wind plays a vital role in initial firing parameter calculations and trajectory corrections, especially when applying differential methods. Traditional methods typically use accurate or approximate layer weights to calculate mean wind. After obtaining upper-air meteorological data, this method divides the trajectory into multiple layers, assigning different weights to each, and weighting the winds at different altitudes to obtain the mean wind. The mean wind calculated using traditional methods is constant, unchanging with altitude and distance. However, as weapon ranges increase, weather variations between the firing point and the target point become significant. Even for long-range artillery within a range of over 100 kilometers, the variation of weather conditions with distance remains quite complex due to the influence of terrain, air masses, and gusts. Therefore, using the constant average wind throughout the entire trajectory to replace the meteorological parameters of the ballistic trajectory will introduce significant errors, adversely affecting the calculation of initial firing parameters and trajectory correction. In particular, when upper-air meteorological measurement data is unavailable, even for average winds containing errors, traditional methods are difficult to calculate.

[0004] Therefore, there is an urgent need for a more accurate method for determining the average wind, especially in the absence of actual upper-air meteorological measurements, to still obtain a relatively accurate average wind, but there is no relevant description in the existing technology. Summary of the Invention

[0005] The purpose of this invention is to provide a solution for quickly determining the average wind on a local battlefield, especially the average wind that varies with distance, in the absence of measured meteorological data at high altitudes. Based on this, a method for solving the average wind in a closed-loop fire correction system is formed, providing a foundation for improving shooting accuracy.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A method for rapidly determining the local battlefield mean wind based on a closed-loop fire correction system includes the following steps:

[0008] Establish a set of ballistic motion equations including time-varying local mean wind: (The equations are then used to represent the longitudinal wind w.) x (t) and crosswind w z (t) is treated as a variable that varies with the projectile's flight time, and a four-degree-of-freedom ballistic model is established as the local battlefield mean wind calculation model.

[0009] Establish a local mean wind trajectory optimization model: This involves considering the time-varying longitudinal wind w. x (t), Time-varying crosswinds w z (t) is used as a virtual control input, and virtual control variables are introduced. By seeking the optimal control variables, the objective function is minimized, and a ballistic optimization model is constructed.

[0010] Discretize the local average wind trajectory optimization model;

[0011] Reconstructing the measurement data of the calibration head: First, fit the optimal trajectory using the measurement data within the sliding window, and then calculate the data values ​​at the discrete points of the pseudo-spectrum using the fitted trajectory;

[0012] An optimization algorithm is used to solve the discrete nonlinear programming problem, and the optimal local mean wind is finally obtained.

[0013] The significant advantages of this invention compared to existing technologies are:

[0014] (1) This invention expands and supplements the existing method for determining average wind. It no longer treats longitudinal and crosswinds as constants, but fully considers the variation characteristics of average wind with the distance of the trajectory. It can efficiently capture the variation law of average wind during the flight of the projectile and achieve a good approximation of the average wind under the condition of no actual measured high-altitude meteorology.

[0015] (2) This invention is mainly aimed at the closed-loop firing correction system of ground artillery. It focuses on the problem of communication data loss in the system and proposes a method for reconstructing the data transmitted back by the firing correction head based on the ballistic model, so as to minimize the adverse effects of wireless communication data loss on the solution of mean wind. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of ballistic data reconstruction.

[0017] Figure 2 Flowchart for reconstructing ballistic data. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0019] The technical solution of this invention can be described as follows: ① Prepare meteorological data; ② Conduct a comprehensive test of the closed-loop correction system and obtain test data; ③ Establish a set of ballistic motion equations including time-varying average wind; ④ Use time-varying average wind as a virtual control variable to establish a local average wind ballistic optimization model; ⑤ Discretize the local average wind ballistic optimization model; ⑥ Establish a method for reconstructing the measurement data of the correction head based on the ballistic model; ⑦ Use an optimization algorithm to solve the discretized nonlinear programming problem and finally obtain the optimal local average wind.

[0020] Step 1: Prepare meteorological data

[0021] Measure the local altitude, surface temperature and pressure values, and extrapolate the surface temperature and pressure values ​​to altitude according to standard meteorological laws to obtain the temperature and pressure values ​​at different altitudes.

[0022] Step 2: Conduct comprehensive testing of the closed-loop firing correction system

[0023] Conduct a comprehensive test of the closed-loop firing correction system. Record the following data:

[0024] a) Projectile structural parameters and aerodynamic parameters;

[0025] c) Measured bullet weight;

[0026] d) Actual angle and direction of fire;

[0027] e) Measured initial velocity;

[0028] f) Based on the satellite data of the projectile transmitted back by the calibration head, obtain the measured values ​​of the full trajectory data of the projectile in the ground coordinate system with the muzzle as the origin.

[0029] Step 3: Establish a set of ballistic motion equations including time-varying local mean wind.

[0030] Considering the requirements for computational accuracy and speed, a four-degree-of-freedom ballistic model is used as the ballistic calculation model. The state variables of the four-degree-of-freedom ballistic model are:

[0031]

[0032] In the formula, v x Let v be the horizontal velocity of the projectile. y v is the vertical velocity of the projectile. z Let x be the lateral velocity of the projectile, and let x, y, and z be the range, altitude, and lateral deflection, respectively. Let w be the angular velocity of the projectile's rotation along the longitudinal axis. x (t) and w z (t) represent the longitudinal and transverse winds as they change over time; these two parameters are the two variables that need to be determined. Considering the time-varying parameter w... x(t) and w z After (t), the state-space form of the four-degree-of-freedom ballistic model can be expressed as follows:

[0033]

[0034] In the formula, v r It is the relative velocity, and m is the projectile mass; ρ is the air density (calculated using air temperature and pressure; in this invention, only ground air temperature and pressure values ​​need to be measured, while high-altitude values ​​are extrapolated from ground data according to standard meteorological laws); t is time; S is the projectile reference area; l is the projectile length; d is the projectile diameter; C is the polar moment of inertia; g is the gravitational acceleration. The drag coefficient is zero angle of attack; c x2 c′ is the induced drag coefficient; y c″ is the derivative of the lift coefficient. z The derivative of the Magnus force coefficient; m′ xz α is the derivative of the polar damping moment coefficient; e α is the dynamic equilibrium angle of the projectile. ex ,α ey ,α ez These are the dynamic equilibrium angles α e The three components. Ignoring the damping term, the dynamic equilibrium angle α can be derived. e The three-component expression is (see Han Zipeng et al., External Ballistics of Projectiles and Arrows, Beijing Institute of Technology Press, 2014, page 196):

[0035]

[0036] In the formula:

[0037] x1 and x2 are both intermediate variables, and satisfy:

[0038]

[0039] a a a b All are intermediate variables, and satisfy the following:

[0040]

[0041] Where m″ y Let m′ be the derivative of the Magnus moment coefficient. z This is the derivative of the overturning moment coefficient. The above ballistic model (Equations (2) to (3)) considers the time-varying longitudinal wind w. x (t), Time-varying crosswinds w z (t).

[0042] Step 4: Establish a local mean wind trajectory optimization model

[0043] The main objective of this invention is to determine the parameter w that varies with the projectile's flight time based on measured ballistic data. x (t) and w z (t), the problem can be reduced to the following: Under actual firing conditions, based on a series of measured flight coordinates of the projectile... in m s =0,1,...,N m , indicates the sampling time, N m Find the optimal w for the index corresponding to the last sampling time. x (t) and w z The variation law of (t) makes the flight coordinate values ​​(x) calculated by the ballistic model (Equations (2) to (3)) c (t ms ),y c (t ms ),z c (t ms )) and measured value The residuals between them are extremely small. Therefore, this invention utilizes the solution approach of the optimal control problem to address the time-varying longitudinal wind speed w. x (t), Time-varying crosswinds w z (t) is treated as a virtual control input, and a virtual control variable u is introduced. w (t)=[w x (t),w z (t)] T By seeking the optimal control variable u w To minimize the objective function J, the following ballistic optimization model is constructed:

[0044]

[0045] Step 5: Discretize the local average wind trajectory optimization model.

[0046] Equation (4) is a continuous ballistic optimization model. This section uses the Radau pseudospectral method to discretize the model for subsequent solution. First, variables are introduced. Perform time-domain transformation, changing the time interval in model (4) Converted to [-1,1], model (4) is converted to:

[0047]

[0048] In the formula Sampling time The corresponding new variable after transformation. Within the transformed interval [-1, 1], select an nth-order LGR (i.e., Legendre-Gauss-Radau) point τ. k (k = 1, 2, ..., N) and τ0 = -1 are nodes, where N is the number of discrete points. Using the Lagrange interpolation polynomial as basis functions to approximate the state variables and the virtual control variables respectively, we obtain:

[0049]

[0050]

[0051] In the formula, L i (τ) is the i-th Lagrange interpolation basis function.

[0052] Differentiating the approximate state variable (as shown in Equation (6)) yields the state variable at the discrete point τ. k The derivative at is

[0053]

[0054] In the formula, D ki Let L be the element in the k-th row and i-th column of the differential matrix, and let L be the element in the differential matrix obtained by using the interpolation basis function L. i (τ) is obtained through offline calculation. Substituting equation (8) into equation (2), we obtain the algebraic constraints for the transformation of the differential equation as follows:

[0055]

[0056] In the formula F k This represents the residual after constraint discretization.

[0057] Through the above transformation, the continuous form of the dynamic equation in equation (5) is constrained at node τ. k The constraints on (k = 1, 2, ..., N) are transformed into algebraic constraints (Equation (9)). After the above processing, the calculated flight coordinates will only be within τ. k There is a value above, therefore the objective function J in equation (5) depends on the node τ. k The values ​​on (k = 1, 2, ..., N) are used to reconstruct a new objective function J′ as follows:

[0058]

[0059] After the above transformation, the continuous ballistic optimization model is discretized into the following nonlinear programming problem:

[0060]

[0061] Step 6: Reconstruct the measurement data of the calibration head

[0062] The continuous ballistic optimization problem (5) is discretized into a nonlinear programming problem (11) at the discrete point τ. k The measurements were performed on (k = 1, 2, ..., N), while the ballistic measurement data were taken at time points. The measurement above, generally τ k and They are not the same. Furthermore, the ballistic measurement data for closed-loop firing correction missiles is obtained through backhaul, and the data reception quality largely depends on the communication quality. When the communication quality is poor (e.g., due to interference, obstruction, etc.), a segment of measurement data will be lost (called the communication loss segment). To address the above problem, in order to solve the nonlinear programming problem (11), it is necessary to... k For the trajectory (k = 1, 2, ..., N), the ballistic data is reconstructed. The main idea is to first fit the optimal trajectory using the measurement data within a sliding window, and then use the fitted trajectory to calculate the data values ​​at the discrete points of the pseudospectral. The specific reconstruction method is as follows:

[0063] 1) Set the length L of the sliding window w This length needs to be greater than the length of the lost communication data segment, such as... Figure 1 As shown.

[0064] 2) Using the current pseudospectral discrete point τ k Expand L to the left and right from the center point. w Using data of length / 2, construct the current sliding window for ballistic fitting. For processing data at both ends, when the data length is less than the given window length, extend one side by L. w Length data, construct a sliding window.

[0065] 3) Fit the trajectory using least squares within the sliding window, as follows:

[0066] a) Use the starting point of the sliding window as the initial value and give a default drag coefficient value;

[0067] b) Integrate the ballistic equations of the particle until the end of the window;

[0068] c) Calculate the residual between the ballistic data obtained by integration and the measured ballistic data;

[0069] d) Determine if the residual value has reached the minimum value. If not, readjust the drag coefficient value and repeat steps b) to d). If the minimum value has been reached, end the calculation.

[0070] 4) After obtaining the best-fit trajectory, calculate τ on the fitted trajectory. k The data value corresponding to the given time is used as the reconstructed value of the measurement data.

[0071] 5) Traverse all pseudospectral discrete points τ k Repeat steps 2) to 4).

[0072] The above-mentioned process for reconstructing the measurement data of the calibration head is as follows: Figure 2 As shown.

[0073] Step 7: Numerical solution of the local mean wind optimization problem

[0074] After discretization using the Radau pseudospectral method and reconstruction of the ballistic measurement data, the nonlinear programming problem (11) can be solved to obtain the values ​​of the virtual control quantities at each discrete node, and thus the longitudinal wind speed w. x (t) and crosswind w z (t) The variation of projectile flight time. The solution of nonlinear programming problems is also relatively mature, and many algorithms can solve this problem, such as the interior point method and the sequential quadratic programming algorithm. This invention selects the interior point method to solve the nonlinear programming problem (11). This algorithm is a mature algorithm. For the specific principle, please refer to the literature (Forsgren, A.; Gill, PE Interior Methods for Nonlinear Optimization. SIAM Rev.44, 2022). The details of this invention will not be repeated.

Claims

1. A method for rapidly determining the local battlefield mean wind based on a closed-loop fire correction system, characterized in that, Includes the following steps: Establish a set of ballistic motion equations that include time-varying local mean wind: (This is related to the longitudinal wind...) and crosswind Treating it as a variable that changes with the projectile's flight time, a four-degree-of-freedom ballistic model is established as the local battlefield mean wind calculation model. Establish a local mean wind trajectory optimization model: This incorporates time-varying longitudinal winds. , changing crosswinds As a virtual control input, virtual control variables are introduced. By seeking the optimal control variables to minimize the objective function, a ballistic optimization model is constructed. in Let be the objective function. Indicates the sampling time. , This is the index corresponding to the last sampling time. The measured coordinates of the projectile's flight path. To calculate the projectile's flight coordinates, Here, t represents the state variables of a four-degree-of-freedom ballistic model. These are virtual control variables; Discretize the local average wind trajectory optimization model; Reconstructing the measurement data of the calibration head: First, fit the optimal trajectory using the measurement data within the sliding window, and then calculate the data values ​​at the discrete points of the pseudo-spectrum using the fitted trajectory; An optimization algorithm is used to solve the discrete nonlinear programming problem, and the optimal local mean wind is finally obtained.

2. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 1, characterized in that, The following model is established using a four-degree-of-freedom ballistic model as the local battlefield mean wind calculation model: In the formula, The relative velocity is m, and the mass of the projectile is m. Let be the air density, and t be the time. denoted as the projectile's reference area; l as the projectile length; d as the projectile diameter; C as the polar moment of inertia; g as the acceleration due to gravity. The drag coefficient is zero angle of attack. This is the induced drag coefficient; The derivative of the lift coefficient; The derivative of the Magnus force coefficient; The derivative of the polar damping moment coefficient; The dynamic equilibrium angle of the projectile; , , These are the dynamic balance angles. The three components, The horizontal velocity of the projectile, The vertical velocity of the projectile. The lateral velocity of the projectile. and These represent the longitudinal and transverse winds that change over time. Let be the angular velocity of the projectile's rotation along the longitudinal axis.

3. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 2, characterized in that, relative speed for: 。 4. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 1, characterized in that, The model was discretized using the Radau pseudospectral method.

5. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 4, characterized in that, Discretizing the local average wind trajectory optimization model yields the following nonlinear programming problem: in The objective function J is based on the discrete points of the independent variable. Reconstruct a new objective function based on the values ​​on the above. N is the number of discrete points; For the terminal time, At the starting time, for The projectile position measurement value at that moment. for The calculated position of the projectile at that moment. This represents the residual after constraint discretization.

6. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 5, characterized in that, Constrained discretized residuals: Let be the element in the k-th row and i-th column of the differential matrix. for The state variables of the four-degree-of-freedom ballistic model at time t. for The state constraint equations corresponding to each time step.

7. The method for rapidly determining the local battlefield average wind based on a closed-loop fire correction system according to claim 1, characterized in that, The specific reconstruction method is as follows: 1) Set the length L of the sliding window w This length is greater than the length of the lost communication data segment. 2) Using the current pseudospectral discrete points Expand L to the left and right from the center point. w Using data of length / 2, construct the current sliding window for ballistic fitting; for processing data at both ends, when the data length is less than the given window length, expand unilaterally by L. w Length data, construct a sliding window; 3) Fit the trajectory using least squares within the sliding window, as follows: 4) After obtaining the best-fit trajectory, calculate the trajectory... The data value corresponding to the given time point will be used as the reconstructed value of the measurement data. 5) Traverse all pseudospectral discrete points Repeat steps 2) to 4).

8. The method for rapidly determining the local battlefield mean wind based on a closed-loop fire correction system according to claim 1, characterized in that, The specific method for fitting the ballistic trajectory is as follows: a) Use the starting point of the sliding window as the initial value and give a default drag coefficient value; b) Integrate the ballistic equations of the particle until the end of the window; c) Calculate the residual between the ballistic data obtained by integration and the measured ballistic data; d) Determine if the residual value has reached the minimum value. If not, readjust the drag coefficient value and repeat steps b) to d). If the minimum value has been reached, the calculation ends.

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