A weather compensation method for trajectory calculation of large caliber artillery

Abstract

The application discloses a weather compensation method for trajectory calculation of a large-caliber artillery, and relates to the technical field of artillery trajectory. The application comprises the following steps: S1, atmospheric vertical profile data fusion; S2, dynamic modeling of a layered temperature gradient; S3, air density field reconstruction; S4, equation definition; S5, real-time correction of Kalman filtering; and S6, trajectory parameter output. The application can improve the trajectory calculation precision under complex weather conditions by constructing a segmented nonlinear temperature gradient function and combining dynamic correction. Specifically, the segmented nonlinear temperature gradient function can be used to dynamically adjust the temperature gradient parameters of different height layers according to real-time weather data, so that the vertical structure of the atmosphere can be more accurately described, the influence of complex weather phenomena, such as an inversion layer and a frontal passage, on air density can be better captured, and systematic errors in trajectory calculation can be effectively reduced.

Description

Technical Field

[0001] This invention belongs to the field of artillery ballistics technology, and in particular relates to a meteorological compensation method for calculating the trajectory of large-caliber artillery. Background Technology

[0002] In traditional artillery trajectory calculations, the influence of meteorological conditions on the trajectory is usually handled through simplified models, such as using a fixed temperature gradient (e.g., 6.5℃ / km) and a standard atmospheric model to calculate air density and drag. However, actual atmospheric conditions are often complex and variable, especially at high altitudes and in complex weather environments. Fixed gradient models can lead to significant errors in air density calculations, thus affecting the accuracy of trajectory predictions. Furthermore, traditional methods typically ignore the nonlinear characteristics of atmospheric stratification and changes in real-time meteorological data, resulting in further increases in trajectory calculation errors under special meteorological conditions such as temperature inversions and frontal processes.

[0003] To improve the accuracy of ballistic calculations, existing technologies have incorporated real-time data acquisition methods such as weather radar, weather balloons, and satellite remote sensing. However, the use of these data is often limited to simple interpolation or linear correction, failing to fully consider the dynamic changes and nonlinear characteristics of atmospheric stratification. To address these issues, the following solutions are proposed. Summary of the Invention

[0004] The purpose of this invention is to provide a meteorological compensation method for large-caliber artillery ballistic calculation. By constructing a piecewise nonlinear temperature gradient function and combining it with dynamic correction, the accuracy of drag calculation under complex meteorological conditions is significantly improved, and the problem of high-altitude air density calculation error caused by the use of a fixed temperature gradient in existing ballistic calculations is solved.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0006] This invention relates to a weather compensation method for calculating the trajectory of large-caliber artillery, comprising:

[0007] Step S1: Atmospheric vertical profile data fusion: Real-time temperature, air pressure, and humidity data of the launch site are obtained using weather radar, weather balloons, and satellite remote sensing.

[0008] Step S2, Dynamic Modeling of Layered Temperature Gradient: Based on real-time meteorological sounding data, piecewise gradient coefficients are obtained through least squares fitting, and an adaptive temperature gradient function is constructed.

[0009] Step S3: Air density field reconstruction: Calculate the air pressure distribution, obtain the air pressure values ​​at different altitudes, and reconstruct the air density field;

[0010] Step S4, Equation Definition: Considering the effect of air density variation with altitude on the trajectory, a compensation term is introduced to define the trajectory equation;

[0011] Step S5, Kalman filter real-time correction: Construct state vector and measurement equation, adjust gradient parameter confidence through covariance matrix, and correct ballistic parameters in real time;

[0012] Step S6, Ballistic Parameter Output: Perform iterative calculations at regular intervals to determine the temperature gradient, calculate the real-time air density, update the drag coefficient, and output the corrected firing angle and azimuth commands.

[0013] The adaptive temperature gradient function constructed in step S2, the dynamic modeling of layered temperature gradients, is specifically as follows:

[0014]

[0015] In the formula, Let h be the temperature gradient at height h, where h is the height, α1, α2, and α3 are the piecewise gradient coefficients for low, medium, and high altitudes, respectively, h1 and h2 are the dynamic boundary heights, and β1 and γ are nonlinear shape parameters.

[0016] By fitting real-time meteorological data, parameters such as α1, α2, and α3 are determined, making the model more closely resemble actual atmospheric conditions.

[0017] Furthermore, the formula for calculating the air pressure distribution in step S3, air density field reconstruction, is as follows:

[0018]

[0019] In the formula, P(h) is the air pressure at height h, P0 is the air pressure at the initial height, and g is the acceleration due to gravity (≈9.81 m / s²). 2 M is the molar mass of dry air (≈0.029 kg / mol), R * Here, is the universal gas constant (≈8.314 J / (mol·K)), h is the altitude, T(h′) is the temperature at altitude h′, and e(h′) is the water vapor pressure at altitude h′, calculated from temperature and humidity.

[0020] The formula calculates the change in air pressure with altitude by integration, taking into account the effects of temperature and humidity.

[0021] Furthermore, the formula for calculating the water vapor pressure e is:

[0022]

[0023] In the formula, e(h) is the water vapor pressure at height h, T(h) is the temperature at height h, and H(h) is the relative humidity at height h.

[0024] Furthermore, in step S4, the ballistic equation in the equation definition is:

[0025]

[0026] In the formula, For the acceleration of the projectile, Let be the velocity vector of the projectile. Let C be the gravitational acceleration vector, ρ(h) be the air density at height h, and C be the velocity vector. D The drag coefficient is given by (related to Mach number Ma and air density), where A is the projectile's frontal area and m is the projectile's mass. For the magnitude of the projectile velocity, This is a compensating force caused by the density gradient, used to correct the influence of air density changes that are ignored in traditional ballistic equations.

[0027] Furthermore, the compensating force The calculation formula is:

[0028]

[0029] In the formula, ρ is the air density, h is the altitude, t is the time, A is the frontal area of ​​the projectile, and C is the air density. D Where m is the drag coefficient and m is the mass of the projectile. δt is the square of the magnitude of the projectile's velocity vector, and δt is the time interval.

[0030] Furthermore, the state vector constructed in step S5, the real-time correction of the Kalman filter, is as follows:

[0031] X = [x, y, z, v] x v y v z [α1, α2, α3] T ;

[0032] Where X is the state vector, x, y, z represent the position coordinates of the projectile in three-dimensional space, and v x v y v z Let α1, α2, and α3 represent the velocity components of the projectile in the x, y, and z directions, respectively, and let α1, α2, and α3 be the temperature gradient parameters. T This is for the transpose operation.

[0033] Furthermore, the measurement equation constructed in step S5, the real-time correction of the Kalman filter, is as follows:

[0034] Z k =HX k +v k ;

[0035] In the formula, Z kLet H be the measured value at time k (e.g., the position of a projectile measured by radar), H be the observation matrix, and X be the state vector mapped to the measurement space. k Let v be the state vector at time k. k The measurement noise at time k;

[0036] Kalman filtering corrects ballistic prediction errors in real time by dynamically adjusting the state vector.

[0037] The present invention has the following beneficial effects:

[0038] 1. This invention improves the accuracy of ballistic calculation under complex meteorological conditions by constructing a piecewise nonlinear temperature gradient function and combining it with dynamic correction. Specifically, by constructing a piecewise nonlinear temperature gradient function, the temperature gradient parameters of different altitude layers can be dynamically adjusted according to real-time meteorological data, thereby more accurately describing the vertical structure of the atmosphere and better capturing the influence of complex meteorological phenomena such as temperature inversion layers and frontal passages on air density, effectively reducing systematic errors in ballistic calculation.

[0039] 2. This invention achieves real-time correction of ballistic parameters through Kalman filtering technology. Kalman filtering can not only dynamically adjust the state vector, but also fuse real-time measurement data from sensors such as radar with the predicted trajectory through measurement equations, further improving the robustness and real-time performance of the ballistic solution. This dynamic correction mechanism enables the ballistic solution to adapt to complex and ever-changing weather conditions, improving the accuracy of artillery in actual combat environments. At the same time, by optimizing the algorithm structure and introducing efficient numerical calculation methods, it can meet the timeliness requirements of real-time ballistic solution while ensuring accuracy.

[0040] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart illustrating a meteorological compensation method for large-caliber artillery trajectory calculation according to the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] Please see Figure 1 As shown, this invention is a weather compensation method for calculating the trajectory of large-caliber artillery, comprising:

[0045] Step S1: Atmospheric vertical profile data fusion: Real-time temperature, air pressure, and humidity data of the launch site are obtained using weather radar, weather balloons, and satellite remote sensing.

[0046] Step S2, Dynamic Modeling of Layered Temperature Gradient: Based on real-time meteorological sounding data, piecewise gradient coefficients are obtained through least squares fitting, and an adaptive temperature gradient function is constructed.

[0047] Step S3: Air density field reconstruction: Calculate the air pressure distribution, obtain the air pressure values ​​at different altitudes, and reconstruct the air density field;

[0048] Step S4, Equation Definition: Considering the effect of air density variation with altitude on the trajectory, a compensation term is introduced to define the trajectory equation;

[0049] Step S5, Kalman filter real-time correction: Construct state vector and measurement equation, adjust gradient parameter confidence through covariance matrix, and correct ballistic parameters in real time;

[0050] Step S6, Ballistic Parameter Output: Perform iterative calculations at regular intervals to determine the temperature gradient, calculate the real-time air density, update the drag coefficient, and output the corrected firing angle and azimuth commands.

[0051] The adaptive temperature gradient function constructed in step S2, the dynamic modeling of layered temperature gradients, is specifically as follows:

[0052]

[0053] In the formula, Let h be the temperature gradient at height h, where h is the height, α1, α2, and α3 are the piecewise gradient coefficients for low, medium, and high altitudes, respectively, h1 and h2 are the dynamic boundary heights, and β1 and γ are nonlinear shape parameters.

[0054] By fitting real-time meteorological data, parameters such as α1, α2, and α3 are determined, making the model more closely resemble actual atmospheric conditions.

[0055] Furthermore, the formula for calculating the air pressure distribution in step S3, air density field reconstruction, is as follows:

[0056]

[0057] In the formula, P(h) is the air pressure at height h, P0 is the air pressure at the initial height, and g is the acceleration due to gravity (≈9.81 m / s²). 2 M is the molar mass of dry air (≈0.029 kg / mol), R * is the universal gas constant (≈8.314 J / (mol·K)), h is the height, T(h′) is the temperature at height h′, and e(h′) is the water vapor pressure at height h′, which is calculated from temperature and humidity;

[0058] The formula calculates the change in air pressure with altitude by integration, taking into account the effects of temperature and humidity.

[0059] Furthermore, the formula for calculating the water vapor pressure e is:

[0060]

[0061] In the formula, e(h) is the water vapor pressure at height h, T(h) is the temperature at height h, and H(h) is the relative humidity at height h.

[0062] Furthermore, in step S4, the ballistic equation in the equation definition is:

[0063]

[0064] In the formula, For the acceleration of the projectile, Let be the velocity vector of the projectile. Let C be the gravitational acceleration vector, ρ(h) be the air density at height h, and C be the velocity vector. D The drag coefficient is given by (related to Mach number Ma and air density), where A is the projectile's frontal area and m is the projectile's mass. For the magnitude of the projectile velocity, This is a compensating force caused by the density gradient, used to correct the influence of air density changes that are ignored in traditional ballistic equations.

[0065] Furthermore, the compensating force The calculation formula is:

[0066]

[0067] In the formula, ρ is the air density, h is the altitude, t is the time, A is the frontal area of ​​the projectile, and C is the air density. D Where m is the drag coefficient and m is the mass of the projectile. δt is the square of the magnitude of the projectile's velocity vector, and δt is the time interval.

[0068] Furthermore, the state vector constructed in step S5, the real-time correction of the Kalman filter, is as follows:

[0069] 1 = [x, y, z, v] x v y v z [α1, α2, α3] T ;

[0070] Where X is the state vector, x, y, z represent the position coordinates of the projectile in three-dimensional space, and v x v y v z Let α1, α2, and α3 represent the velocity components of the projectile in the x, y, and z directions, respectively, and let α1, α2, and α3 be the temperature gradient parameters. T This is for the transpose operation.

[0071] Furthermore, the measurement equation constructed in step S5, the real-time correction of the Kalman filter, is as follows:

[0072] Z k =HX k +v k ;

[0073] In the formula, Z k Let H be the measured value at time k (e.g., the position of a projectile measured by radar), H be the observation matrix, and X be the state vector mapped to the measurement space. k Let v be the state vector at time k. k The measurement noise at time k;

[0074] Kalman filtering corrects ballistic prediction errors in real time by dynamically adjusting the state vector.

[0075] One specific application of this embodiment is:

[0076] Step S1: Atmospheric Vertical Profile Data Fusion: In practical application scenarios, weather radar, sounding balloons, and satellite remote sensing equipment are first activated to continuously acquire real-time meteorological data from the battlefield. This data includes temperature sampling points at different altitudes: T0(h0), T1(h1), ..., T n (h n ), air pressure sampling points P0(h0), P1(h1), ..., P n (h n and humidity sampling points H0(h0), H1(h1), ..., H n (h n This data is then transmitted to the ballistic calculation system in real time.

[0077] Step S2, Dynamic Modeling of Layered Temperature Gradients: After receiving the data, the system processes and analyzes it, uses the least squares fitting algorithm to calculate the piecewise gradient coefficients in the adaptive temperature gradient function, and constructs a layered temperature gradient model that conforms to the current site meteorological conditions based on these coefficients, preset nonlinear shape parameters, and dynamic boundary height.

[0078]

[0079] In the formula, Let h be the temperature gradient at height h, where h is the height, α1, α2, and α3 are the piecewise gradient coefficients obtained by fitting real-time data with least squares, h1 and h2 are the dynamic boundary heights, and β1 and γ are nonlinear shape parameters.

[0080] Step S3, Air Density Field Reconstruction: Combining the collected temperature, humidity, and air pressure data, calculate the air pressure distribution at different altitudes, and then reconstruct the air density field. The air pressure distribution calculation formula is as follows:

[0081]

[0082] In the formula, P(h) is the air pressure at height h, P0 is the air pressure at the initial height, and g is the acceleration due to gravity (≈9.81 m / s²). 2 M is the molar mass of dry air (≈0.029 kg / mol), R * Here, is the universal gas constant (≈8.314 J / (mol·K)), h is the altitude, T(h′) is the temperature at altitude h′, and e(h′) is the water vapor pressure at altitude h′, calculated from temperature and humidity.

[0083] The above integral equation is numerically solved by the fourth-order Runge-Kutta method to obtain the air pressure value P(h) at different altitudes h. The air pressure value is a key parameter for calculating air density. Accurate calculation of air pressure distribution helps to reconstruct the air density field more accurately and provide more accurate air density data for subsequent ballistic calculations.

[0084] The formula calculates the change in air pressure with altitude by integration, taking into account the effects of temperature and humidity;

[0085] The formula for calculating water vapor pressure e is:

[0086]

[0087] In the formula, e(h) is the water vapor pressure at height h, T(h) is the temperature at height h, and H(h) is the relative humidity at height h;

[0088] Step S4, Equation Definition: Considering the effect of air density variation with altitude on the trajectory, a compensation term is introduced.

[0089]

[0090] In the formula, ρ is the air density, h is the altitude, t is the time, A is the frontal area of ​​the projectile, and C is the air density. D Where m is the drag coefficient and m is the mass of the projectile. δt is the square of the magnitude of the projectile's velocity vector, and δt is the time interval;

[0091] This compensation term takes into account the change in air density with altitude and the effect of altitude change on drag during projectile motion. By introducing this dynamic density compensation term, the ballistic equation can be adaptively adjusted according to real-time meteorological conditions and projectile motion state, thereby improving the accuracy of ballistic calculation in complex meteorological environments.

[0092] Substituting the reconstructed air density field data into the ballistic equations that include dynamic density compensation terms, the projectile's trajectory is calculated based on its real-time motion. The ballistic equations are as follows:

[0093]

[0094] In the formula, For the acceleration of the projectile, Let be the velocity vector of the projectile. Let C be the gravitational acceleration vector, ρ(h) be the air density at height h, and C be the velocity vector. D The drag coefficient is given by (related to Mach number Ma and air density), where A is the projectile's frontal area and m is the projectile's mass. For the magnitude of the projectile velocity, It is a compensating force caused by the density gradient, used to correct the influence of air density changes that are ignored in traditional ballistic equations;

[0095] Step S5, Kalman Filter Real-time Correction: The state vector and measurement equation are processed using the Kalman filter algorithm. Based on the difference between the radar measurement position and the predicted trajectory, the confidence level of the gradient parameters is dynamically adjusted to correct the trajectory parameters in real time. The constructed state vector is: X = [x, y, z, v] x v y v z [α1, α2, α3] T Where X is the state vector, x, y, z represent the position coordinates of the projectile in three-dimensional space, and v x v y v z Let α1, α2, and α3 represent the velocity components of the projectile in the x, y, and z directions, respectively, and let α1, α2, and α3 be the temperature gradient parameters. T This is a transpose operation;

[0096] The measurement equation is:

[0097] Z k =HX k +v k ;

[0098] In the formula, Z k Let H be the measured value at time k (e.g., the position of a projectile measured by radar), H be the observation matrix, and X be the state vector mapped to the measurement space. k Let v be the state vector at time k. k The measurement noise at time k;

[0099] The Kalman filtering algorithm can effectively process measurement data containing noise, correct ballistic parameters in real time, and enable the system to quickly adapt to changes in weather conditions and projectile motion, further improving the real-time performance and accuracy of ballistic calculation.

[0100] Step S6, Ballistic Parameter Output: An iterative calculation is performed every 0.1 seconds. First, based on the current projectile height h, the corresponding temperature gradient is determined using the previously constructed temperature gradient function. Then, the real-time air density ρ(h) is calculated based on the reconstructed air density field. Finally, the drag coefficient C is updated based on the real-time air density ρ and Mach number Ma. D (ρ, Ma); Finally, the corrected firing angle / azimuth command is output, providing precise parameter guidance for the actual firing of large-caliber artillery and effectively improving the firing accuracy of the artillery.

[0101] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0102] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A meteorological compensation method for calculating the trajectory of large-caliber artillery, characterized in that, Includes the following steps: Step S1: Atmospheric vertical profile data fusion: Real-time temperature, air pressure, and humidity data of the launch site are obtained using weather radar, weather balloons, and satellite remote sensing. Step S2, Dynamic Modeling of Layered Temperature Gradient: Based on real-time meteorological sounding data, piecewise gradient coefficients are obtained through least squares fitting, and an adaptive temperature gradient function is constructed. Step S3: Air density field reconstruction: Calculate the air pressure distribution, obtain the air pressure values ​​at different altitudes, and reconstruct the air density field; Step S4, Equation Definition: Considering the effect of air density variation with altitude on the trajectory, a compensation term is introduced to define the trajectory equation; Step S5, Kalman filter real-time correction: Construct state vector and measurement equation, adjust gradient parameter confidence through covariance matrix, and correct ballistic parameters in real time; Step S6, Ballistic Parameter Output: Perform iterative calculations at regular intervals to determine the temperature gradient, calculate the real-time air density, update the drag coefficient, and output the corrected firing angle and azimuth commands. The adaptive temperature gradient function constructed in step S2, the dynamic modeling of layered temperature gradients, is specifically as follows: In the formula, Let h be the temperature gradient at height h, where h is the height, α1, α2, and α3 are the piecewise gradient coefficients obtained by fitting real-time data using least squares, h1 and h2 are the dynamic boundary heights, and β1 and γ are the nonlinear shape parameters.

2. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 1, characterized in that, The formula for calculating the air pressure distribution in step S3, air density field reconstruction, is as follows: In the formula, P(h) is the air pressure at height h, P0 is the air pressure at the initial height, g is the acceleration due to gravity, M is the molar mass of dry air, and R... * Let be the universal gas constant, h be the altitude, T(h′) be the temperature at altitude h′, and e(h′) be the vapor pressure at altitude h′.

3. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 2, characterized in that, The formula for calculating the water vapor pressure e is: In the formula, e(h) is the water vapor pressure at height h, T(h) is the temperature at height h, and H(h) is the relative humidity at height h.

4. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 1, characterized in that, The ballistic equation in step S4, the equation definition, is as follows: In the formula, For the acceleration of the projectile, Let be the velocity vector of the projectile. Let C be the gravitational acceleration vector, ρ(h) be the air density at height h, and C be the velocity vector. D Where A is the drag coefficient, A is the projectile's frontal area, and m is the projectile's mass. For the magnitude of the projectile velocity, This is the compensating force caused by the density gradient.

5. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 4, characterized in that, The compensating force The calculation formula is: In the formula, ρ is the air density, h is the altitude, t is the time, A is the frontal area of ​​the projectile, and C is the air density. D Where m is the drag coefficient and m is the mass of the projectile. δ is the square of the magnitude of the projectile's velocity vector. t For time intervals.

6. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 1, characterized in that, The state vector constructed in step S5, Kalman filter real-time correction, is: X=[x,y,z,v x ,v y ,v z ,α1,α2,α3] T ; Where X is the state vector, x, y, z represent the position coordinates of the projectile in three-dimensional space, and v x v y v z Let α1, α2, and α3 represent the velocity components of the projectile in the x, y, and z directions, respectively, and let α1, α2, and α3 be the temperature gradient parameters. T This is for the transpose operation.

7. The meteorological compensation method for large-caliber artillery trajectory calculation according to claim 1, characterized in that, The measurement equation constructed in step S5, Kalman filter real-time correction, is as follows: Z k =HX k +v k ; In the formula, Z k Let H be the measurement value at time k, H be the observation matrix, and X be the measurement value. k Let v be the state vector at time k. k Let be the measurement noise at time k.

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