Evaluation method for average ballistic difference of different cannonballs with same ammunition

Abstract

The invention belongs to the technical field of launching platforms, and particularly relates to a same-projectile different-shot average trajectory difference evaluation method which comprises the following steps: step 1, establishing a trajectory simulation model; 2, carrying out an average ballistic performance difference check test; 3, identifying a zero resistance coefficient; 4, coincidence calculation is carried out; step 5, determining equivalent distributed source parameter distribution characteristics; 6, equivalent current-day error source parameter distribution characteristics are determined; 7, estimating a system error; 8, evaluating the average ballistic difference of the non-test supporting points; step 9, reconstructing a trajectory; and step 10, evaluating the average ballistic difference of the test supporting points. Compared with the prior art, the method has the advantages that test supporting point average ballistic difference evaluation with low consumption, low false risk and high credibility can be realized; and non-test supporting point average ballistic performance difference evaluation information can be given, and comprehensive evaluation is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of launch platforms, and in particular relates to a method for evaluating the difference in average trajectories of the same projectile with different guns. Background Art

[0002] The same launch platform can launch different types of ammunition, and different launch platforms can also launch the same type of ammunition. Each type of gun and ammunition combination requires a corresponding firing table or a fire command and control ballistic calculation module developed based on the firing table. When the launch platform or ammunition changes, the firing table and the fire command and control ballistic calculation module should also be changed. The military has a wide variety of equipment and a huge number of effective gun and ammunition combinations, which poses a challenge to the development of firing tables, fire command and control ballistic calculation modules and their use by the troops. To address this issue, equipment demonstration units usually put forward ballistic consistency requirements for certain equipment with similar performance and the same caliber. When the same caliber and different types of launch platforms are adapted to the same type of ammunition, the most common ballistic performance indicator requirement is average trajectory consistency.

[0003] Only when the average ballistic performance of different launch platforms adapted to the same type of ammunition (same bullet, different gun) is consistent, can the two platforms share a firing table and fire command and control ballistic solution module, thereby reducing the cost of developing firing tables and improving fire command and control software, and avoiding the inconvenience caused by shooting.

[0004] The assessment of average trajectory differences between different guns and the same projectile is a common problem encountered in range assessment. Two methods are generally used to determine whether the average ballistic performance is consistent: trajectory consistency testing and firing table universality testing. The trajectory consistency test uses the T-test, while the firing table universality test uses the U-test.

[0005] The trajectory consistency test uses the T-test method. On the new research platform and the prototype platform, three groups of alternate firings are conducted, with 7-10 pairs in each group. The test results are statistically analyzed to obtain the mean difference of each pair of data. The average of the standard deviations of each pair of data The total number of paired samples is n, the degree of freedom is n-3, and the significance level is α (usually 5%). The limit value t of the t distribution is α / 2 .when If the two types of missiles have the same trajectory, then the trajectory is considered to be the same; otherwise, it is considered that there are obvious differences in the ballistic performance of the two types of missiles.

[0006] The U-test was used to test the universality of the shooting table. On the newly developed platform, three groups of 7-10 rounds were fired, or four groups of 5-8 rounds were fired. The test results were statistically analyzed to determine the range deviation as |ΔR| = (R T -R N ) / R T , R T is the range of the shooting table, R N Standardized range for inspection test; qualified range Probability error of shooting range Shooting table to check the probability error of the standardized range U α / 2 is the normal distribution limit value of the significance level α (usually 10%), where B R (take 0.45%) as the test range probability error, ε R (take 0.36%) as the standardized daily error, η R (take 0.2%) as the system error, N1 is the number of groups shot by the shooting table, n1 is the number of shots in each group shot by the shooting table, N2 is the number of groups checked by the shooting table, n2 is the number of shots in each group checked by the shooting table. When the inspection result satisfies |ΔR|≤ΔR max , then it is considered that the shooting table can be used universally; otherwise, it is considered that there are obvious differences in the ballistic performance of the two types of missiles and the shooting table cannot be used universally.

[0007] The current average trajectory difference assessment method, based on classic significance test theory and directly testing the ballistic parameters of interest (range), has guided equipment appraisal for over 50 years. However, it suffers from the following deficiencies:

[0008] (1) Ballistic consistency adopts T-test, which requires comparison shooting between the newly developed platform and the prototype platform. The test consumes a lot of energy, and one test point uses 42 rounds of ammunition. In addition, the prototype launch platform needs to participate in the test. As a companion test item, the allocation and coordination of the prototype launch platform is difficult. This is also the reason why the ballistic consistency test method is rarely used in range appraisal.

[0009] (2) The universality check of the firing table adopts the U-test. It only needs to test the newly developed platform and compare the ballistic characteristics information obtained with the firing table of the prototype platform. This can save some bullets. The amount of bullets used at one test point is 20 (or 21). However, the test false positive rate is high and the credibility of the assessment conclusion is poor. The false positive risk calculation shows that when there is a range difference Δ=σ between the two platforms, R (mean square error), the probability of false positives in the universal test of the shooting table is 0.6657.

[0010] (3) Whether it is a ballistic consistency test or a universal inspection of the firing table, a sampling test method is used. 42 or 20 rounds are fired at each test point. For single-charge, 2-3 test points are set up at different firing angles. For multiple charges, the charge number is selected at intervals for testing. If all the selected test points pass the inspection, it is considered that the average ballistics of the newly developed platform and the prototype platform are consistent, and the new equipment can use the prototype firing table. If there are test points that fail the inspection, it is considered that there is an average ballistic difference between the two types of equipment and the firing table cannot be shared. Considering the test cost, the number of test points is very limited. There is a risk in making a comprehensive affirmation or negation based on the conclusions of limited test points.

[0011] (4) U-test method for universal inspection of shooting tables. Its premise is that the probability error of the inspection object is known. For shooting tables, it is considered that the total intermediate error of the range is (Includes projectile dispersion E R 、Daily error ε R , system error η R The three factors are relatively certain when the initial velocity range and test sample are constant. However, in reality, it is difficult to say that the range dispersion and daily error of a specific weapon system are known. In the past, a large amount of statistical data was used to simply process the test results of different weapons, different charges, and different firing angles to calculate an average E. R , ε R , and in fact the E of different weapon systems R , ε R is different, even for the same weapon system, different charges, different firing angles E R , ε R It is also different. It is necessary to use a unified E R , ε R To check, it is inevitable that the qualified range will be sometimes too wide and sometimes too strict, which is unreasonable in itself. R , ε R ,η R It was obtained from statistics in the 1970s. It only represents the level of my country's weapons and equipment and testing technology before the mid-1970s. Now it is the 21st century. The accuracy of many weapon systems is much higher than the statistical values ​​at that time. Testing equipment and technology, test error control and data processing capabilities have made significant progress. Therefore, it is no longer appropriate to use it. Summary of the Invention

[0012] (1) Technical issues to be solved

[0013] The technical problems to be solved by the present invention are:

[0014] 1. Establish a new method for evaluating the difference in average ballistic trajectories between different guns and the same round, so as to achieve the goal of using no more rounds than a general inspection of a firing table, but with a risk of false positives equivalent to that of a ballistic consistency inspection;

[0015] 2. Establish a universal inspection method for the gun's full-range firing table, use limited sampling test data for calibration and simulation, and achieve the evaluation of the average trajectory difference of non-test support points;

[0016] 3. Establish an estimation method for the total intermediate error of range, and relate the total intermediate error of range to the characteristics of specific weapon and ammunition models, test levels and capabilities, and actual shooting conditions to achieve accurate and objective evaluation of ballistic simulation accuracy.

[0017] (2) Technical solution

[0018] In order to solve the above technical problems, the present invention provides a method for evaluating the average trajectory differences of the same projectile but different guns, the method comprising the following steps: step 1: establishing a trajectory simulation model; step 2: performing an average trajectory performance difference inspection test; step 3: identifying the zero drag coefficient; step 4: performing a coincidence calculation; step 5: determining the distribution characteristics of the equivalent dispersion source parameters; step 6: determining the distribution characteristics of the equivalent same-day error source parameters; step 7: estimating the system error; step 8: evaluating the average trajectory differences of non-test support points; step 9: trajectory reconstruction; step 10: evaluating the average trajectory differences of test support points.

[0019] (3) Beneficial effects

[0020] Compared with the existing technology, the present invention can realize the average ballistic difference assessment of test support points with low consumption, low risk of false positives and high credibility; it can provide the average ballistic performance difference assessment information of non-test support points to achieve comprehensive assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a diagram showing the idea of ​​evaluating the ballistic differences of support points in tests with the same bullet but different guns.

[0022] Figure 2 Schematic diagram of the principle for evaluating the ballistic differences of support points in tests with the same projectile but different guns.

[0023] Figure 3 This is a diagram for evaluating the ballistic differences of non-support points in the test.

[0024] Figure 4 This is a step diagram of the method for evaluating the difference in average ballistic trajectories of the same projectile but different guns according to the present invention.

[0025] Figure 5 This is the zero resistance coefficient identification result diagram. DETAILED DESCRIPTION

[0026] In order to make the purpose, content, and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0027] 1. Overall approach

[0028] 1.1 Analysis of the causes of high false positives in current table checks

[0029] The current firing chart verification method utilizes historical information (prototype platform firing charts) to answer whether there are differences in ballistic performance by comparing test results from two phases, using different launch platforms. Whether developing the firing charts on the prototype platform or verifying the firing charts on the newly developed platform, testing errors are inevitable. Furthermore, the errors in the two phases are inconsistent and cannot be eliminated. These errors accumulate and amplify into the constructed statistics (the difference between the table range and the test standardized range), contaminating or even overwhelming the information about the differences in launch platforms. This results in a high risk of false positives and poorly credible conclusions.

[0030] 1.2 Analysis of factors affecting ballistic differences between the same projectile and different guns

[0031] Regardless of the launch platform, the same type of ammunition maintains the same structure and shape upon exiting the muzzle, and its aerodynamic characteristics are unique as it travels through the atmosphere. Any differences in ballistic performance can only be attributed to different initial conditions upon exiting the muzzle. As a rigid body, the initial muzzle parameters include the coordinates and velocity of the projectile's center of mass, its yaw (rotation) angle, and its angular velocity. Muzzle coordinate differences caused by gun vibration are minimal, and differences in the projectile's coordinates at the muzzle only result in similarly sized differences in impact point. Therefore, differences in the projectile's initial center of mass coordinates can be ignored. Differences in the projectile's center of mass velocity may cause significant differences in projectile impact point, but muzzle velocity is a key input parameter that can be adjusted and corrected both in firing table compilation and during firing. Therefore, the impact of initial center of mass velocity differences on ballistic performance can be disregarded. Differences in the direction of the projectile's center of mass velocity may cause significant differences in projectile impact point. The initial angle of attack is derived from the direction of the projectile's center of mass velocity and the projectile's yaw angle, and the projectile's yaw angular velocity is equivalent to the initial angle of attack velocity. After several nutation cycles of decay, the angle of attack and angular velocity approach zero. However, during this decay period, the angle of attack and angular velocity cause variations in the ballistic velocity, which in turn continues to affect the motion of the projectile's center of mass. The above analysis of influencing factors shows that the primary source of the average trajectory differences between identical projectiles and different guns is the initial perturbation.

[0032] 1.3 New ideas for evaluating the ballistic differences of test support points

[0033] When the same caliber ammunition is fired from different platforms, the projectile's shape and structural characteristics are identical, and the aerodynamic characteristics affecting its flight are the same. The only reason for the difference in ballistic performance is the difference in initial trajectory conditions caused by the different platforms. Therefore, assessing the ballistic differences between the same projectile and different artillery is essentially comparing the differences in the projectile's initial parameters (the starting point of the trajectory) or the resulting ballistic parameters (the end point of the trajectory) between the two launch platforms.

[0034] The error in the external ballistic test did not begin to accumulate at the muzzle. In theory, it is effective to answer whether there is a difference in ballistic performance by testing the consistency of the initial parameters of the projectiles of the two types of platforms. However, in engineering practice, the initial conditions of the projectile motion (initial velocity direction, swing angle direction and swing angular velocity) cannot be fully and accurately obtained, and this test method is not feasible.

[0035] Testing the consistency of the trajectory endpoint is highly operational, but the projectile takes a long time to fly in the air before reaching the endpoint. The interaction between the projectile and the air is highly random. With long-term accumulation, a large amount of errors are introduced into the test data, and the reliability of the evaluation conclusion is poor.

[0036] The ballistic data from the inspection test and the table firing data are homogenized, ensuring that the homogenized inspection test trajectory and the table firing trajectory have the same test error. This is similar to the alternating comparison shooting method. Through differential comparison, the test errors are canceled, reducing the contamination of the test error on the statistical data. A new approach to assessing the difference in test support point trajectories is to reconstruct the inspection test trajectory of the newly developed platform after the initial nutation decay period according to the table firing trajectory of the prototype platform. The reconstructed trajectory and the table firing trajectory are used to construct statistics, eliminating or reducing the influence of external ballistic meteorological errors on the impact point, reducing the variation in sample characteristics caused by test errors, and improving the reliability of the test.

[0037] From the hint Figure 2 As can be seen above, the current method's statistical quantities differ from the test error and the firing table error. The constructed statistics combine these two types of errors, contaminating the information about the difference between the new and original guns. The new method, however, reconstructs the inspection test trajectory, using the test trajectory before the end of nutation decay while retaining the initial perturbation information of the newly developed platform. After the nutation decay ends, the trajectory is calculated using the firing table model parameters to the impact point. This allows the error information for this section of the trajectory to be identical to the firing table error. By comparing the reconstructed trajectory with the firing table trajectory, the firing table error is canceled, improving the credibility of the assessment results.

[0038] 1.4 New Approach to Evaluating Trajectory Differences at Non-Test Support Points

[0039] The key to evaluating ballistic differences at non-test support points is determining the ballistic distribution characteristics of non-inspection test support points on the newly developed platform. Inspection test data demonstrates the ballistic distribution characteristics of the test support points. These test data also contain the source parameter information that causes these distribution characteristics. This source parameter information can be extracted through data processing techniques and then used to simulate trajectories at non-test support points, ultimately determining the ballistic distribution characteristics of the non-test support points.

[0040] Each shot data contains implicit projectile dispersion information. The shooting angle, zero-drag coefficient, etc. are selected as compliance parameters. Through shot-by-shot compliance calculation, the projectile dispersion information is transferred to the compliance parameters. The dispersion characteristics of each shot in each group of shooting, including the compliance parameters and the measured initial velocity, are statistically analyzed to obtain the distribution characteristics of the equivalent dispersion source parameters. Each group of standardized range data contains implicit error information for the day. Through group-by-group compliance calculation, the error information for the day is transferred to the compliance parameters. The dispersion characteristics of each group of compliance parameters are statistically analyzed to obtain the distribution characteristics of the equivalent error source parameters for the day.

[0041] By using the test support point data calibration simulation, combined with error synthesis and error propagation, the distribution characteristics of the ballistic performance parameters of the gun's entire firing range are determined, and compared with the prototype firing table information to achieve the universality evaluation of the multi-charge firing table for the entire firing range.

[0042] Example 1

[0043] This embodiment provides a method for evaluating the difference in average trajectory of the same bullet with different guns. Figure 4 As shown, the following steps are included:

[0044] Step 1: Establishment of ballistic simulation model;

[0045] According to the principles of flight dynamics, the projectile is regarded as a rigid body and a six-degree-of-freedom motion equation is established as the basis for trajectory simulation calculations.

[0046] Step 2: Average ballistic performance difference inspection test;

[0047] Reasonable test support points are selected, and exterior ballistic tests are conducted using a newly developed launch platform to obtain test data from the newly developed launch platform. This serves as the information basis for determining ballistic characteristic parameters and the distribution characteristics of test error sources.

[0048] Step 3: Identification of zero resistance coefficient;

[0049] Taking ballistic velocity data as original identification information, the continuously varying parameter overall identification technology is adopted to obtain the projectile zero-drag coefficient.

[0050] Step 4: Perform compliance calculations;

[0051] Using the coordinates and time of key trajectory feature points, such as the impact point, as the original coincidence information, the coincidence coefficients of key trajectory model parameters are determined according to the principle of maximum sensitivity mapping. The impact point dispersion information is transferred to the coincidence coefficient of each round through a shot-by-shot coincidence calculation; and the test day error (test group error) information is transferred to the coincidence coefficient of each group of rounds through a group-by-group coincidence calculation.

[0052] Step 5: Determine the distribution characteristics of the equivalent scattered source parameters;

[0053] Taking the coincidence coefficients of each group as input, the mean and mean square deviation of each coincidence coefficient group are calculated. The mean square deviation of the coincidence coefficients obtained is averaged to obtain the mean square deviation of the equivalent scatter source parameters. This allows the extraction of equivalent scatter source parameter information from the test data information.

[0054] Step 6: Determine the distribution characteristics of the equivalent daily error source parameters;

[0055] Using the compliance coefficients of each group at each support point as input, the mean and mean square error of the compliance coefficients of each group (operating condition) are calculated. This mean square error is the mean square error of the equivalent error source parameters for the day. This allows the extraction of equivalent error source parameter information from the test data.

[0056] Step 7: Estimation of systematic error;

[0057] Taking each system error source as input and considering the correction compensation of the compliance coefficient, a system error calculation model is constructed to realize the system error estimation under arbitrary shooting angles.

[0058] Step 8: Assessment of the average trajectory difference of non-test support points;

[0059] The model that meets the calibration criteria (after steps 1, 2, and 3) is used as the trajectory simulation model. Using the equivalent error source parameters obtained in steps 5 and 6 as input, calculate the range intermediate error and daily error at any firing angle based on the error synthesis principle. Combine this with the system error in step 7 to create the intermediate error for table preparation or the intermediate error for the standardized range of the inspection test. Use the U-test to determine the differences in average trajectory at non-test support points.

[0060] Step 9: Trajectory reconstruction;

[0061] The model that matches the calibration (after steps 1, 2, and 3) is used as the UKF prediction model. The test trajectory velocity or coordinate data before the end of the initial nutation decay is used as the measurement data. UKF filtering is performed to the end of the initial nutation decay, obtaining the parameters at the end of the initial nutation decay that contain the characteristics of the new launch platform. The prototype launch platform firing table model is then used to calculate the impact point, obtaining the impact point coordinates of the reconstructed trajectory. The reconstructed trajectory uses the same model as the original firing table trajectory after the end of the initial nutation decay, and has the same experimental error information.

[0062] Step 10: Evaluate the average ballistic difference of the test support points.

[0063] Using the reconstructed trajectory and the prototype launch platform's firing table trajectory as input, a U statistic is constructed to test and assess the differences in the average trajectory of the support points. The U statistic uses the difference between the reconstructed trajectory and the original firing table trajectory to cancel out any identical experimental errors.

[0064] The following describes each step in detail:

[0065] Step 1: Establishment of ballistic simulation model;

[0066] Based on the 6D rigid body ballistic equation, an equivalent average angle of attack calculation model is added to replace the influence of the initial disturbance on the trajectory. The specific derivation process can be found in the reference "Exterior Ballistics of Guns and Rockets". The trajectory simulation model is established as follows:

[0067]

[0068] α D =α D0 e ε

[0069] Where: V is the flight speed of the projectile, m / s;

[0070] V r ——the flight speed of the projectile relative to the wind, m / s;

[0071] V X ——x-axis component of the rocket's flight velocity in the ground coordinate system, m / s;

[0072] V Y ——The y-axis component of the rocket's flight velocity in the ground coordinate system, m / s;

[0073] V Z ——z-axis component of the rocket's flight velocity in the ground coordinate system, m / s;

[0074] X——x-axis component of the missile flight coordinate in the ground coordinate system, m;

[0075] Y - the y-axis component of the projectile's flight coordinates in the ground coordinate system, m;

[0076] Z - the z-axis component of the missile's flight coordinates in the ground coordinate system, m;

[0077] F X ——x-axis component of the force on the rocket during flight in the ground coordinate system, N;

[0078] F Y ——The y-axis component of the force on the rocket during flight in the ground coordinate system, N;

[0079] F Z ——z-axis component of the force on the rocket during flight in the ground coordinate system, N;

[0080] m——the flight mass of the projectile, kg;

[0081] ρ——air density, kg / m 3 ;

[0082] S——cross-sectional area of ​​the projectile, m 2 ;

[0083] C x ——air resistance coefficient;

[0084] δW X ——x-axis component of the disturbance wind speed in the ground coordinate system, m / s;

[0085] δW Y ——y-axis component of the disturbance wind speed in the ground coordinate system, m / s;

[0086] δW Z ——z-axis component of the disturbance wind speed in the ground coordinate system, m / s;

[0087] ω ξ ——the ξ-axis component of the projectile's rotational velocity in the projectile's axis coordinate system, rad / s;

[0088] ω η ——η-axis component of the projectile's rotational velocity in the projectile axis coordinate system, rad / s;

[0089] ω ζ ——the ζ-axis component of the projectile's rotational velocity in the projectile's axis coordinate system, rad / s;

[0090] rad / s;

[0091] M ξ ——the ξ-axis component of the force and moment of the missile in flight in the missile axis coordinate system, Nm;

[0092] M η ——η-axis component of the force and moment of the missile in flight in the missile axis coordinate system, Nm;

[0093] M ξ ——the component of the force and moment of the missile in flight on the ζ axis in the missile axis coordinate system, Nm;

[0094] γ——rotation angle of the projectile around the ξ axis, rad;

[0095] φ1——the swing angle of the projectile around the ζ axis, rad;

[0096] φ2——the swing angle of the projectile around the η axis, rad;

[0097] A——equatorial moment of inertia of the projectile, kg.m 2 ;

[0098] C——Extreme moment of inertia of the projectile, kg.m 2 ;

[0099] α D0 ——initial nutation angle amplitude, rad;

[0100] α D——initial nutation angle, rad;

[0101] K zz ——Equatorial damping moment characteristic number;

[0102] b y ——lift characteristic number;

[0103] K xz ——Characteristic number of extreme damping moment;

[0104] K y ——Markov moment characteristic number;

[0105] K z ——characteristic number of pitching moment;

[0106] Γ——relative speed,

[0107] σ——σ=1-K z / Γ 2 .

[0108] Step 2: Average ballistic performance difference inspection test;

[0109] Carry out inspection shooting test; for single charge number ammunition, tests should be carried out at 2 / 3 of the maximum range, the maximum range angle and the maximum shooting angle. When there is no high shooting range, shooting should be carried out at 2 to 3 shooting angles. When there is a high shooting range, shooting should be carried out at 3 to 4 shooting angles. For multi-charge ammunition, charge numbers can be selected at intervals for testing, but the maximum charge number, the minimum charge number and the charge number with an initial velocity close to the speed of sound must be tested. In addition, except for the maximum range test point, other test points should try to avoid the support points of the prototype platform shooting table compilation test; the same test item shoots a group of shots every day , firing 4 groups of 5 rounds each; during the test, two muzzle velocity radars were used to measure the projectile's initial velocity (accuracy 0.1%), a ballistic velocity radar was used to measure the ballistic radial velocity (accuracy 0.1%), a ballistic radar or optical theodolite was used to measure the ballistic coordinates of the initial section of the muzzle (before the end point of nutation attenuation) (accuracy 1 meter), a high-speed video theodolite was used to precisely measure the ballistic coordinates of the end point of nutation attenuation (accuracy 0.5 meter), a satellite differential positioning system or total station was used to measure the coordinates of the impact point (accuracy 1 meter), and a satellite positioning sounding wind measurement system was used to detect high-altitude weather (temperature, air pressure, wind speed, and wind direction);

[0110] Step 3: Identification of zero resistance coefficient;

[0111] Based on the classical parameter differential correction algorithm and combined with spline fitting technology, a trajectory parameter overall identification method is established to expand the parameter identification range and improve the parameter identification accuracy. Starting from the global optimization of the estimated parameters and the residual variance of the original information, the trajectory parameter overall identification method overcomes the shortcomings of the piecewise constant algorithm, effectively utilizes the full trajectory velocity information, and identifies the drag characteristic parameters with high precision.

[0112] The independent variable is the flight Mach number M a The parameter to be identified is the projectile zero resistance coefficient C x0 (M a ), C x0 (M a ) Available N k +1 segment N o The order spline function is expressed as:

[0113]

[0114] B j (x) is N o The jth term of the B-spline function, α j is the jth coefficient, identify C x0 (M a ) is essentially about how to determine the coefficient α j . B j (x) is defined as: a ∈[M in ,M max ]Select N in the interval k internal nodes, dividing the interval into N k +1 copy, respectively, the 1st copy, the Nth copy k +1 part of the length is extended by N at both ends of the interval o segment, there are 2(N o +1)+N k Nodes M i ,i=1,2(N o +1)+N k ,but

[0115]

[0116] N t The residual sum of squares between the measured and calculated values ​​of the ballistic radial velocity is used as the objective function:

[0117]

[0118] V Rci is the parameter to be identified α j Function, in iterative identification, the current value Available previous value With the increment and representation:

[0119]

[0120] If SSR is minimized,

[0121]

[0122] Solving the differential correction equation can solve the correction amount Δα for each iteration j ;

[0123] The velocity components V in the three coordinate axis directions are directly obtained by calculating the trajectory in the ground coordinate system. X 、V Y 、V Z , the formula for converting to speed is:

[0124]

[0125] Among them, X0, Y0, and Z0 are the components of the ballistic velocity radar point coordinates in the ground coordinate system;

[0126] To find the sensitive factor in the differential correction equation, firstly transform the left side of the dynamic equation to α i Find the partial derivative and get the sensitivity factors of acceleration in three directions Sensitivity factors of speed in three directions Can be solved by The differential equation is obtained, and the sensitivity factors of the three directions of speed are synthesized to obtain the sensitivity factor of the sum speed. The synthesis formula is as follows:

[0127]

[0128] Step 4: Perform compliance calculations;

[0129] Select the angle of incidence coefficient K θ , deflection compliance coefficient K ψ , zero resistance compliance coefficient K R , the overturning moment complies with the coefficient K m To meet the parameters, the initial muzzle coordinate X S The corresponding Y S 、Z S and the impact point coordinate X c 、Z C In order to meet the object, the calculated muzzle initial segment and impact point coordinates are made to coincide with the measured values ​​by adjusting the matching parameters;

[0130] The raw data that meet the calculation requirements include: structural parameters of the gun and projectile; aerodynamic parameters of the projectile; actual firing angle and direction; measured projectile weight; measured initial velocity; meteorological parameters during the firing process; and the measured muzzle initial segment and impact coordinates in the ground coordinate system with the muzzle as the origin.

[0131] The calculation method for compliance is as follows:

[0132] a) Given K θ , K ψ , K R , K m The initial value of

[0133] b) Under actual conditions (initial velocity, firing angle are measured values, actual weather conditions and ballistic conditions, etc.), K θ , K ψ , K R and K m Substitute into the equations and solve. When the integral reaches the impact height, if formulas (1) to (4) are satisfied, the calculation is complete. Otherwise, adjust K according to c). θ , K ψ , K R , K m Recalculate the trajectory until it meets the requirements;

[0134] |Y Sc -Y St |≤ε θ (1)

[0135] |Z Sc -Z St |≤ε ψ (2)

[0136] |X Cc -X Ct |≤ε x (3)

[0137] |Z Cc -Z Ct |≤ε z (4)

[0138] Where: Y Sc 、Y St —— Muzzle initial segment X S Calculated and measured values ​​of the vertical coordinate at, m;

[0139] Z Sc 、Z St —— Muzzle initial segment X S Calculated and measured values ​​of the horizontal coordinate at , m;

[0140] X Cc 、x Ct ——the calculated or measured value of the vertical coordinate of the impact point, in m;

[0141] Z Cc 、Z Ct——the calculated or measured value of the abscissa of the impact point, in m;

[0142] ε θ ——The shooting angle meets the accuracy, generally taken as 0.01, m;

[0143] ε ψ ——Declination angle meets the accuracy, generally taken as 0.01, m;

[0144] ——Zero resistance meets the accuracy, generally 0.001%X Ct , m;

[0145] ——The turning moment meets the accuracy, generally 0.005%X Ct , m;

[0146] c) Adjust K θ , K ψ , K R , K m When K is calculated according to formulas (5) to (8), θ , K ψ , K R , K m increment;

[0147]

[0148] Where: ΔK θ - the increment of the angle of incidence coefficient;

[0149] ΔK ψ — increment of the deflection compliance coefficient;

[0150] ΔK R ——the increment of the zero resistance compliance coefficient;

[0151] ΔK m —Increment of the overturning moment compliance coefficient;

[0152] ΔY S —— Muzzle initial segment X S The difference between the calculated value and the measured value of the vertical coordinate at m;

[0153] ΔZ S —— Muzzle initial segment X S The difference between the calculated value and the measured value of the horizontal coordinate at m;

[0154] ΔX C ——the difference between the test value and the calculated result of the vertical coordinate of the impact point, in m;

[0155] ΔZ C ——the difference between the test value and the calculated result of the abscissa of the impact point, in m;

[0156] Generally, the average value of the zero-resistance compliance coefficient of each test point can be used to calculate the trajectory of each test shooting angle under actual conditions. If the difference between the calculated range and the actual range R is greater than 0.3% R, the compliance coefficients of all test shooting angles should be fitted to form K R ~θ curve, using K corresponding to each test angle R Calculate the actual trajectory. If the range error is less than 0.3%R, use the fitting result for simulation calculation. Otherwise, make additional shooting until the range error of all test points is less than 0.3%R. When checking the shooting table of multiple charge numbers, the K of the shooting charge number can be used. R Fit them separately, and then find the K of the untested charge number in the curve R value, for simulation calculation; K of the large elevation angle test point m Average, for ballistic simulation calculation; K should be considered when averaging m The nonlinear relationship between Z and K (the bias current Z and K expressed in degrees) m Construct a curve, and then use the average bias current to find K in the curve m the average value of

[0157] Use the determined compliance coefficient K θ , K ψ , K R , K m , given the initial conditions, termination conditions, and meteorological conditions of the shooting, the trajectory can be simulated and calculated to obtain the average trajectory under any conditions;

[0158] Step 5: Determine the distribution characteristics of the equivalent scattered source parameters;

[0159] Projectile density B R It is an important indicator for evaluating the ballistic performance of conventional projectiles and rockets, and is also a necessary parameter for calculating ballistic distribution characteristics. Live-fire shooting is usually used to determine the dispersion characteristics of model products. During development and appraisal, emphasis is placed on answering the density index at the maximum range. There are relatively more live-fire shooting samples at the maximum range, but there are very few live-fire shootings at other ranges, or even no data. Therefore, only the density statistics under a few specific working conditions such as the maximum range can be obtained. It is generally believed that the projectile dispersion caused by weapons and equipment is mainly caused by the dispersion of three factors: drag coefficient, initial velocity, and jump angle. Moreover, the dispersion characteristics of these three factors are not affected by the shooting conditions and can be regarded as constants. The dispersion characteristics of these three factors are obtained through experiments. Under different shooting conditions, the projectile dispersion caused by each factor alone is calculated through ballistic simulation and differential method, and the comprehensive projectile dispersion is obtained through error synthesis. The key to this processing method is to determine the distribution characteristics of the dispersion source parameters.

[0160] The flight of projectiles and arrows is affected by a variety of random factors, including random variations in the parameters of the projectile, gun, and ammunition system; changes in environmental conditions such as weather and geography; and changes in human factors such as gun mounting, ammunition loading, gun aiming, and firing control. If the moment the projectile leaves the muzzle is recorded as zero time, then the position of the projectile at a given moment is determined by factors such as weapon equipment, initial conditions, and weather conditions.

[0161] As the main factors affecting ballistics, weapons and equipment, initial conditions, and meteorological conditions can undergo systematic changes and also have random components. When the influencing factors undergo systematic changes during the test, the data obtained is heterogeneous data. Heterogeneous data come from different matrices and cannot be directly used for density calculation. When the influencing factors undergo only random changes during the test, the test data obtained come from the same matrices and can be directly used for density calculation.

[0162] The heterogeneous data encountered in engineering practice mainly refers to test data under conditions of systematic changes in launch position, elevation angle, firing direction, and meteorological conditions. Heterogeneous data come from different matrices and cannot be directly mixed for computational density. However, the heterogeneous data still contain information on the distribution characteristics of dispersion source parameters that affect the trajectory. It is generally believed that the distribution characteristics of dispersion source parameters that affect the trajectory will not change due to initial conditions and meteorological conditions such as launch position, elevation angle, firing direction, etc. For example, a certain type of artillery and ammunition fired 7 rounds under working condition 1 (20° elevation angle, meteorological condition 1) and 3 rounds under working condition 2 (45° elevation angle, meteorological condition 2). Obviously, the test data under the two working conditions cannot be directly mixed for statistics, especially under working condition 2, where the sample size is too small and the density cannot be determined. Although meteorological conditions 1 and 2 are different, the fluctuation characteristics of the meteorological conditions have not changed in essence. The launch elevation angle is different, but the hop angle dispersion characteristics remain unchanged. If the distribution characteristics of the dispersion source parameters that affect the trajectory are extracted from the test data, the projectile dispersion under any shooting conditions can be obtained through ballistic simulation, solving the problem of comprehensive acquisition of projectile dispersion.

[0163] Normalized simulation methods can be used to unify heterogeneous data to the same launch conditions or meteorological conditions without losing random information. Normalized simulation is essentially a process of ballistic calibration simulation. The overall idea is to use a certain test condition data to adjust the model parameters that have a significant impact on the trajectory, so that the ballistic simulation calculation results are consistent with the test results, and then use the corrected model simulation to calculate the trajectory under a certain launch condition or meteorological condition. Through ballistic calibration, the distribution characteristics of the ballistic dispersion source parameters implicit in the test data are extracted. There are many factors affecting the trajectory, and it is unrealistic to mine the distribution characteristics of all dispersion source parameters only from the test data. It is necessary to determine the main key ballistic influencing factors based on the specific ballistic characteristics, and transform and merge other minor influencing factors into the main influencing factors to extract the equivalent dispersion source parameter distribution characteristics. The projectile dispersion calculated according to the equivalent dispersion source distribution characteristics can be consistent with the test statistical results.

[0164] For artillery-launched grenades, the equivalent dispersion source parameters can be taken as initial velocity, firing angle, firing direction, zero-drag coefficient, and overturning moment coefficient. Dispersion source parameters that can be directly measured, such as initial velocity, can be determined through field measurements. For dispersion source parameters that cannot be directly measured, the equivalent dispersion source parameters need to be extracted through ballistic modeling methods. The influence of random factors such as wind on the trajectory is incorporated into the zero-drag coefficient.

[0165] A certain type of missile has N β Equivalent scatter source parameter β i (i=1,2,…,N β ), in the test condition j (j = 1, 2, ..., M) shoot L j For the kth launch, the equivalent dispersion source parameters can be determined The equivalent dispersion source parameters not only include the random components that affect the projectile dispersion, but also the systematic errors under each working condition and the systematic errors of the ballistic model used for extraction. These systematic components should be eliminated when determining the parameter distribution characteristics. In order to eliminate the systematic errors, the projectile amount L in each working condition is j ≥3;

[0166] Mean value of equivalent scattered source parameters under working condition j:

[0167]

[0168] The deviation of the equivalent scattered source parameters under working condition j is:

[0169]

[0170] The intermediate error of the i-th equivalent scatter source parameter:

[0171]

[0172] By using normalized simulation methods to unify heterogeneous data under the same launch or meteorological conditions, random ballistic characteristics in the data are extracted and utilized, achieving comprehensive utilization of multi-source test data, increasing the sample size under specific working conditions, and improving the accuracy of statistical results.

[0173] Step 6: Determine the distribution characteristics of the equivalent daily error source parameters;

[0174] The error on the day of the test is also called the group error. It is mainly caused by the high-altitude meteorological error during each shooting group, the gun adjustment error due to the uneven support of the gun, etc. The equivalent error source parameters of the day's error are obtained by using the equivalent scattered source parameter extraction method for the test results of different groups under the same parameters.

[0175] A certain type of missile has N ε Equivalent intraday error source parameter ε i (i=1,2,…,N ε ), in the test condition j (j = 1, 2, ..., M) shoot L j For the jth working condition, the equivalent error source parameters of the day can be determined The equivalent day error source parameters mainly include the systematic components that affect the shooting error of each working condition; the random components of projectile dispersion are reduced by about L j times;

[0176] Equivalent mean of error source parameters on the same day:

[0177]

[0178] Equivalent daily error source parameter deviation from the mean:

[0179]

[0180] The intermediate error of the i-th equivalent error source on the same day:

[0181]

[0182] By using the distribution characteristics of the equivalent day error source parameters, the day error under any shooting conditions can be obtained through ballistic simulation;

[0183] Step 7: Estimation of systematic error;

[0184] Systematic error refers to the error that is unrelated to the number of shooting groups and rounds, and is the error caused by non-repeatable factors in the preparation of the firing table; the test process mainly involves artillery batch errors and ammunition batch errors, and model errors are involved in data processing and firing table calculations; the batches of weapons and ammunition used in firing table tests are limited, and are usually tested with one artillery piece and one batch of ammunition. Obviously, one artillery piece and one batch of ammunition cannot well represent the parent characteristics of this type of equipment. For example, the curvature of the barrel will affect the initial disturbance, the zero-drag coefficient error caused by the rifling state on the belt cutting, and the influence of the projectile shape and mass distribution on the aerodynamic characteristics; the ballistic simulation calculation adopts the rigid body motion equation, and the equation itself more accurately reflects the spatial motion law of the projectile; the error caused solely by the motion equation is already very small and can be ignored; the difference between the calculated trajectory and the actual trajectory is mainly caused by the inaccuracy of some original data in the motion equation, and the errors in these original data constitute the main error source of the simulation model system error;

[0185] The main error sources of the ground artillery grenade firing table test system error include: p , take η p =0.1%R; rifling inconsistency error η g , take η g =0.1%R;

[0186] The error sources of the simulation model system error mainly include: Δθ0 jump angle error, taking the corresponding equivalent dispersion characteristic parameter value; Δα D0 The initial nutation amplitude error is taken as 1°; Initial speed error, take Induced drag coefficient error, take Δc x0 Zero lift drag coefficient error, take the corresponding equivalent dispersion characteristic parameter value; Δc' y Lift coefficient derivative error, take 5% c' y ;Δm' z The derivative error of the overturning moment coefficient is 5% m' z ;Δc” z The derivative error of the Martensitic force coefficient is 20% c" z ;Δm” y The derivative error of the Marginal moment coefficient is 20% m" y ;Δm' xd Roll damping moment coefficient derivative error, take 20% m' xd ;Δm' zd The derivative error of the swing damping torque coefficient is 20% m' zd ;

[0187] System error source c i The corresponding equivalent scattered source parameter β is caused at the incident angle θ0j Response object error After the coincidence calculation, it is included in the coincidence coefficient, so the system error of the trajectory simulation at the shooting angle θ0 is zero; k ≠θ0, And then it is transferred to other angles through the coincidence coefficient; system error The error in the compliance coefficient caused by Any angle of incidence θ k The systematic error at can be calculated using the following formula:

[0188]

[0189] Where: c i — each system error source;

[0190] ——Angle θ k System error at , m;

[0191] ——Error source c i At the incident angle θ k Range error caused by, m;

[0192] ——Error source c i The jth coincidence coefficient error is caused at the incident angle θ0;

[0193] ——Error source c i The jth response object error is caused at the incident angle θ0, m;

[0194] In the above system error calculation formula, the error caused by each error source is The trajectory is calculated under standard conditions, but in the actual shooting table compilation, the systematic error of the support angle is It is included in the compliance coefficient when the calculation is performed under actual conditions. Therefore, the premise for the above formula to be valid is that at the angle θ0, the change in the compliance coefficient caused by each error source under actual conditions is equal to the change in the compliance coefficient caused under standard conditions, that is,

[0195]

[0196] Using the data of a certain grenade, taking the firing angle of 45°, calculate the zero resistance coincidence coefficient K caused by each error source under different conditions. R Changes, calculation results are shown in Table 1;

[0197] Table 1 Changes in the compliance coefficient caused by error sources under different conditions

[0198]

[0199] The unit of the variation of the compliance coefficient in Table 1 is K R / 100; it can be seen that the maximum difference in the change of the compliance coefficient is only 1.48×10 -6 K R , which is three orders of magnitude lower than the variation of the coincidence coefficient, and the range error caused is only 10 -2 For a range of more than ten kilometers, the relative error is only 10 -6 Therefore, it can be considered that the change in the compliance coefficient caused by each error source under actual conditions is equal to the change in the compliance coefficient caused under standard conditions;

[0200] Step 8: Assessment of the average trajectory difference of non-test support points;

[0201] After performing the coincidence calculation according to step 4, substitute the coincidence coefficients into the ballistic model and calculate the arbitrary firing angle θ under the standard artillery conditions. k trajectory, and obtain the standardized range R T , compared with the table value R N Calculate the deviation:

[0202] |ΔR|=|R T -R N |

[0203] Use the U test method to determine the qualified limit:

[0204]

[0205] Determine the intermediate error of the equivalent scattered source parameters according to step 5 and calculate the incident angle θ k Error in the middle of the range:

[0206]

[0207] Determine the intermediate error of the equivalent error source parameters according to step 6 and calculate the angle θ k Error on the day:

[0208] Intermediate error in shooting table compilation:

[0209]

[0210]

[0211] Average Ballistic Performance Difference Check Standardized Range Middle Error:

[0212]

[0213] Where: ΔR - deviation of the standardized range during the shooting table inspection;

[0214] ΔR max- qualified limit of the radiometer inspection;

[0215] E T - Intermediate error in the compilation of the shooting table;

[0216] E N - Intermediate error of the shooting table inspection;

[0217] N1, n1 - the number of groups and the number of rounds in each group required for the shooting test;

[0218] N2, n2 - the shooting table checks the number of groups and the number of rounds in each group of the shooting test;

[0219] U0 - Inspection limit: 2.44 for one inspection shot, 2.91 for two or more inspection shots;

[0220] When ΔR≤ΔR max When ΔR>ΔR max When it is found that there is something wrong with the shooting table;

[0221] Step 9: Trajectory reconstruction;

[0222] The initial nutation of a stable flying projectile is constantly decaying. Assuming that at time t k , the initial nutation decays, then the difference in the subsequent trajectory parameters is mainly due to the velocity at that moment and displacement Determine; analyze the initial nutation attenuation period of the projectile and clearly reconstruct the trajectory demarcation point; use the measured data of trajectory velocity and trajectory coordinates, select the initial disturbance and other parameters to be optimized, use the UKF filter optimization method to reconstruct the trajectory, and determine the time t k of t k Then the trajectory is calculated using the basic parameters calculated in the original firing table to complete the inspection test trajectory reconstruction;

[0223] The UKF algorithm is obtained by replacing the linear approximation of the statistical characteristic propagation method in the EKF algorithm with the UT transform method. Since the system state equation and / or measurement equation are nonlinear systems, the main problem solved by nonlinear filtering is the propagation of random quantities along the nonlinear system. The UKF algorithm uses a set of deterministic sampling points to approximate the state distribution. The transformed sampling points obtained through the UT transform are used to approximate the mean and variance of the state, completing the propagation of the state along the nonlinear function. The distribution of the Gauss noise transform sampling points can be approximated to the true mean and variance with third-order accuracy.

[0224] The discrete nonlinear state equation and measurement equation can be expressed as:

[0225] Θ K+1 =f(Θ K )+W K

[0226] Z K+1 =h(X K+1 )+V K

[0227] Where: Θ K ——state vector;

[0228] Z K+1 ——measurement vector;

[0229] W K , Q K ——Gaussian white noise and variance matrix of dynamic system process;

[0230] V K 、R K ——Measure Gaussian white noise and variance matrix;

[0231] Since the state equation and measurement equation contain noise terms, it is necessary to expand the dimension of the filtered state variables, let Θ a =[Θ T W T V T ] T ,The specific algorithm steps are described as follows;

[0232] initialization:

[0233]

[0234] For the initial state Add the noise term to get the initial state vector after dimension expansion

[0235]

[0236] For the state vector Perform Sigma point sampling, and the vector after sampling is

[0237]

[0238] Among them, n x is the dimension of the state vector; k is a proportional parameter used to adjust the Sigma point and The distance between the two moments is affected, and only affects the deviation caused by the higher-order moments after the second-order moment. k is generally set to 0. is the ith row or ith column of the square root of the matrix, i = 1, 2, ..., n x ;

[0239] Prediction equation:

[0240]

[0241] in, It is the weight of the impact on expectation and variance;

[0242] Update equation:

[0243]

[0244]

[0245] P ΘΘ (k+1|k+1)=P ΘΘ (k+1|k)-K(k+1)P YY (k+1|k)K T (k+1)

[0246] The reconstructed trajectory model is consistent with the trajectory simulation model in step 1; the Kalman filter measurement equation mainly includes the trajectory velocity equation and the trajectory coordinate equation;

[0247] Ballistic radial velocity model:

[0248]

[0249] Model for measuring coordinates using the spatial polar coordinate method:

[0250]

[0251] Model for measuring coordinates using the spatial angle intersection method:

[0252]

[0253] Step 10: Evaluation of the average ballistic difference of the test support points;

[0254] Use the new research platform to carry out N2 group and each group n2 emission table inspection test at a certain support point, Reconstruct the trajectory and range for the j-th test of the i-th group; Under the new platform inspection test conditions, the trajectory is calculated using the basic parameters of the prototype platform shooting table to obtain the shooting table trajectory. is the range of the jth firing table trajectory of the i-th group; the statistical value |ΔR|=|R is constructed by comparing the firing table trajectory with the inspection test trajectory. T -R N | / R T If there is no significant difference in the trajectory of the two platforms, then ΔR obeys Distribution; Based on the principles and processes of shooting table compilation and trajectory reconstruction, analyze the error composition and statistically calculate the distribution characteristics of statistical quantities;

[0255] in:

[0256]

[0257] Where: R T ——The range corresponding to the trajectory of the shooting table, m;

[0258] R N ——Corresponding range of the reconstructed trajectory during the inspection test, m;

[0259] B T ——Probability error of the ballistic range of the shooting table, %;

[0260] B N ——Probability error of the ballistic range reconstructed by checking the shooting, %;

[0261] - Random error of firing angle related to the number of shots fired, taking 0.3mil or the test statistical result;

[0262] - Random error in muzzle velocity related to the number of rounds fired, taking 0.1% of V0 or the statistical result of the test;

[0263] - Shooting angle error related to the number of shooting groups, take 0.3mil or the test statistical results;

[0264] ——The initial nutation amplitude error caused by the batch error of artillery ammunition is taken as 1°;

[0265] ——The systematic error of the trajectory inclination angle of the trajectory reconstruction is taken as 0.5mil;

[0266] ——The error of the trajectory reconstruction initial velocity system is 0.1% V0;

[0267] The first part of the range probability error is related to the number of groups and rounds fired, which should be determined by the shooting angle error. Initial velocity error Drag coefficient error The meteorological error and the random component of the initial disturbance are caused. Due to the ballistic reconstruction, the drag coefficient error and meteorological error on the vast majority of the ballistics are offset and should not be taken into account in the calculation of the qualified limit. The impact of the initial disturbance on the trajectory before the end of the nutation decay is mainly reflected in the velocity magnitude and direction. Changes in the velocity magnitude and direction will cause a large change in the trajectory landing point. The velocity magnitude error caused by the random component of the initial disturbance is merged into the initial velocity error, and the velocity direction error is merged into the shooting angle error, and its impact on the range is comprehensively calculated. The initial disturbance has an impact on the trajectory coordinates and velocity during the nutation decay period. Because the action time is short, the coordinate change in this section of the trajectory is very small compared to the entire range, and this coordinate change will not be amplified in the subsequent flight of the projectile. It is only a linear superposition on the original trajectory landing point, so it can be ignored. The second part of the range probability error is related to the number of shooting groups. Also because of the ballistic reconstruction, the drag coefficient error and meteorological error on the vast majority of the ballistics are offset, leaving only the shooting angle error. This refers to the initial disturbance differences caused by batch errors of artillery ammunition due to factors such as processing technology, material properties, and quality control. For example, there are differences in barrel curvature, rifling processing, and initial disturbance differences caused by batch differences between two stages of test ammunition. However, this does not include gun adjustment errors. For a single gun or a single batch of ammunition, this error is a systematic error. It is the systematic error in the velocity magnitude and direction of the end point of the initial nutation decay caused by the trajectory reconstruction method and model errors;

[0268] Use U-test assessment to determine the acceptance limit of the inspection (U α / 2 The significance level α=10% normal distribution limit value is 2.91). When the inspection result satisfies |ΔR|≤ΔR max , then it is considered that the shooting table can be used universally; otherwise, it is considered that there are obvious differences in the ballistic performance of the two platforms and the shooting table cannot be used universally.

[0269] Example 2

[0270] Evaluation of the differences in average ballistic performance of a certain type of howitzer with the same projectile but different guns.

[0271] Taking the low-range firing range of a lethal explosive projectile on a vehicle-mounted platform and a tracked platform as an example, the difference in average ballistic performance was assessed. When compiling the low-range firing table for the tracked platform lethal explosive projectile, tests were conducted at two support points, 51° and 29°, with four groups of five valid rounds fired at each support point. The average of the two support points' conformity coefficients was used as the calibration parameter. To verify the consistency of the ballistic performance of the newly developed vehicle-mounted lethal explosive projectile with that of a tracked platform, a test was conducted on the vehicle-mounted platform. Two support points, 51° and 30°, were selected, with four groups of five valid rounds fired at each support point. Test data was obtained by performing the test as described in Step 2.

[0272] 1. Zero resistance coefficient identification

[0273] Using the ballistic model in step 1, identify the zero drag coefficient according to the method in step 3. The identification results are shown in Figure 5 .

[0274] 2. Check the model to ensure it is consistent with the calculation

[0275] Perform the shot-by-shot coincidence calculation according to the method in step 4. The calculation results for the 51° shooting angle are shown in Tables 2 to 5, and the calculation results for the 30° shooting angle are shown in Tables 6 to 9.

[0276] Table 2. Calculation results of the first group of shots at a 51° firing angle.

[0277]

[0278]

[0279] Table 3. Calculation results of the second group of shots at a 51° firing angle.

[0280]

[0281] Table 4. Calculation results of the third group of shots at a 51° firing angle.

[0282]

[0283] Table 5. Calculation results of the fourth group of shots at a firing angle of 51°

[0284]

[0285] Table 6. Calculation results of the first group of shots at a 30° firing angle.

[0286]

[0287] Table 7. Calculation results of the second group of shots at a 30° firing angle.

[0288]

[0289] Table 8. Calculation results of the first group of shots at a 30° firing angle.

[0290]

[0291] Table 9. Calculation results of the fourth group of shots at a 30° firing angle.

[0292]

[0293] Using the mean of each group of test data, the compliance calculation was performed group by group according to the method in step 4. The calculation results are shown in Tables 10 and 11.

[0294] Table 10. Calculation results for each group of 51° angles

[0295]

[0296] Table 11. Calculation results for each group at 30° angle

[0297]

[0298] 3. Determination of distribution characteristics of equivalent scattered source parameters

[0299] According to the method in step 5, the distribution characteristics of the equivalent scattered source parameters are calculated. The results are shown in Table 12.

[0300] Table 12. Intermediate errors of equivalent scattered source parameters

[0301]

[0302]

[0303] 4. Determination of the distribution characteristics of the equivalent daily error source parameters

[0304] According to the method in step 6, the distribution characteristics of the equivalent daily error source parameters are calculated. The results are shown in Table 13.

[0305] Table 13. Equivalent intraday error source intermediate error

[0306] Support Point Angle of incidence (°) Deflection angle (°) Zero resistance% Turning torque% 51° 0.0068 0.0050 0.18 6.16 30° 0.0099 0.0045 0.23 7.01 average 0.0085 0.0047 0.21 6.60

[0307] 5.Sensitive factor simulation calculation

[0308] The average values ​​of the coincidence coefficients for the 51° and 30° angles were taken as calibration parameters, which were 0.0577, 0.0335, 0.9994, and 0.9343, respectively. The sensitivity factors of the range to each error source at different angles were calculated, and the results are shown in Tables 14-1 and 14-2.

[0309] Table 14-1 Sensitivity factors of range to various error sources at different shooting angles

[0310]

[0311] Table 14-2 Sensitivity factors of range to various error sources at different shooting angles

[0312]

[0313]

[0314] 6. Evaluation of the difference in average ballistic performance of support points

[0315] Reconstruct the trajectory using the method in step 9, and compare the range deviation between the table trajectory and the reconstructed trajectory shot by shot. The calculation results are shown in Tables 15-24.

[0316] Table 15. Trajectory reconstruction and deviation results of the first group at a 51° shooting angle

[0317]

[0318] Table 16. Trajectory reconstruction and deviation results for the second group at a 51° shooting angle

[0319]

[0320] Table 17. Trajectory reconstruction and deviation results of the third group at a 51° shooting angle

[0321]

[0322] Table 18. Trajectory reconstruction and deviation results of the fourth group at a 51° shooting angle

[0323]

[0324]

[0325] Table 19. 51° trajectory reconstruction and deviation results

[0326]

[0327] Table 20.30° shooting angle first group trajectory reconstruction and deviation results

[0328]

[0329] Table 21. Trajectory reconstruction and deviation results for the second group at a 30° shooting angle

[0330]

[0331] Table 22. Trajectory reconstruction and deviation results of the third group at a 30° shooting angle

[0332]

[0333] Table 23. Trajectory reconstruction and deviation results of the fourth group at a 30° shooting angle

[0334]

[0335]

[0336] Table 24. 30° shooting angle trajectory reconstruction and deviation results

[0337]

[0338] Determine the value of the support point inspection statistic error source, including the initial velocity error related to the number of rounds Vertical jump angle error Shooting angle error related to the number of shooting groups Initial nutation amplitude error caused by batch error of artillery ammunition Systematic error of trajectory inclination in trajectory reconstruction Trajectory reconstruction initial velocity system error The calculation results of the range error caused by each error source are shown in Table 25. The support point inspection statistics and qualified limits are calculated according to the method in Step 10, and the assessment conclusion is obtained. The results are shown in Table 26.

[0339] Table 25. Calculation results of error components of support point check statistics

[0340]

[0341] Table 26. Results of the evaluation of the difference in trajectory of support points

[0342]

[0343] 6. Evaluation of the difference in average ballistic performance at non-support points

[0344] Calculate the systematic error at each firing angle using the method in step 7. Calculate the range mid-range error, daily error, and acceptance limit using the method in step 8. Calculate the range deviation using the table range and the standardized range to obtain the test results. The calculation results are shown in Table 27.

[0345] Table 27. Evaluation results of the difference in average trajectory of the two types of platform-based explosive bombs

[0346]

[0347]

[0348] The non-support point average ballistic performance difference evaluation method was used to evaluate and calculate the support points at shooting angles of 51° and 30°. The test results were consistent with those obtained using the support point average ballistic performance difference evaluation method. However, since the support point inspection method achieves test error cancellation through ballistic reconstruction, the range deviation and the acceptance margin are smaller, the risk of false inspection is reduced, and the effectiveness is improved.

[0349] Comparison of this method with existing methods

[0350] Based on the data of Example 2, the effectiveness of the technical solution method of the present invention is analyzed.

[0351] The existing firing table inspection method can only give an assessment conclusion for the inspection test support point, and cannot give assessment information for non-inspection test points. According to the existing ground artillery grenade firing table inspection method, the range mid-range error BR Take 0.45% and the standardized intraday error ε R Take 0.36%, the system error η R Take 0.2%, the number of shooting groups N1 = 4, the number of shots in each group n1 = 5, the number of inspection test groups N2 = 4, the number of shots in each group n2 = 5, when the inspection test point is the support point of the shooting table, the qualified limit ΔR max =0.85%, when the inspection test point is not the support point of the test in the shooting table, the qualified limit ΔR max =1.03%. Compared with the statistical error components in Example 2 in Table 28, the error sources in Example 2 are determined based on the specific model and test conditions, which better reflects the characteristics of the equipment model and the level of control over test errors. Furthermore, each error component is smaller than the given value of the current method, which also reduces the risk of false assessment and increases the reliability of the assessment conclusion.

[0352] Table 28. Calculation results of error components of non-support point inspection statistics

[0353]

[0354] For the inspection test support point, the data processing method of trajectory reconstruction is used, and the shooting angle is 51° Take σ R =0.45% / 0.6745.

[0355]

[0356]

[0357] When the average range difference between the new platform and the prototype platform is Δ=γσ R When , there is a pseudo probability:

[0358]

[0359] Calculate the difference in range Δ=γσ R The change in the probability of false positives when the ranges vary is shown in Table 29. As can be seen, with the same sample size, this method has a lower probability of false positives than the current firing table inspection method. In particular, when the range difference exceeds 1 times the mean square error, the probability of false positives becomes very small, greatly improving the test validity. Compared with the trajectory consistency test using 3 groups and 7 pairs at a significance level of 0.05, the false positive risk is comparable.

[0360] Table 29. Comparison of acceptance limits and false positive probability of different test methods

[0361] γ 0.01 0.2 0.4 0.6 0.8 1.0 1.25 2.40 Qualified % Amount of ammunition This method 0.8999 0.8534 0.7197 0.5256 0.3225 0.1619 0.0500 0.0000 0.50 20 Shooting table inspection method 0.9000 0.8901 0.8605 0.8119 0.7460 0.6657 0.5514 0.1036 0.85 20 Ballistic consistency 0.9499 0.9117 0.7827 0.5610 0.3145 0.1347 0.0335 0.0000 0.29 42

[0362] Verification shows that this method uses the same amount of ammunition as the current firing table inspection method, and the risk of false positives is greatly reduced. It is equivalent to the risk of false positives in ballistic consistency inspection, but the amount of ammunition used is only 50%, which fully demonstrates the effectiveness of the method.

[0363] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for evaluating the difference in average trajectories of the same projectile with different guns, characterized in that: The method comprises the following steps: Step 1: Establishment of ballistic simulation model; Step 2: Average ballistic performance difference inspection test; Step 3: Identification of zero resistance coefficient; Step 4: Perform compliance calculations; Step 5: Determine the distribution characteristics of the equivalent scattered source parameters; Step 6: Determine the distribution characteristics of the equivalent daily error source parameters; Step 7: Estimation of systematic error; Step 8: Assessment of the average trajectory difference of non-test support points; Step 9: Trajectory reconstruction; Step 10: Evaluate the average ballistic difference of the test support points.

2. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 1, wherein: In the step 1, a trajectory simulation model is established; Based on the 6D rigid body trajectory equation, an equivalent average angle of attack calculation model is added to replace the influence of the initial disturbance on the trajectory; the trajectory simulation model is established as follows: α D ＝α D0 e ε Where: V is the flight speed of the projectile, m / s; V r ——the flight speed of the projectile relative to the wind, m / s; V X ——x-axis component of the rocket's flight velocity in the ground coordinate system, m / s; V Y ——The y-axis component of the rocket's flight velocity in the ground coordinate system, m / s; V Z ——z-axis component of the rocket's flight velocity in the ground coordinate system, m / s; X——x-axis component of the missile flight coordinate in the ground coordinate system, m; Y - the y-axis component of the projectile's flight coordinates in the ground coordinate system, m; Z - the z-axis component of the missile's flight coordinates in the ground coordinate system, m; F X ——x-axis component of the force on the rocket during flight in the ground coordinate system, N; F Y ——The y-axis component of the force on the rocket during flight in the ground coordinate system, N; F Z ——z-axis component of the force on the rocket during flight in the ground coordinate system, N; m——the flight mass of the projectile, kg; ρ——air density, kg / m 3 ; S——cross-sectional area of ​​the projectile, m 2 ; C x ——air resistance coefficient; δW X ——x-axis component of the disturbance wind speed in the ground coordinate system, m / s; δW Y ——y-axis component of the disturbance wind speed in the ground coordinate system, m / s; δW Z ——z-axis component of the disturbance wind speed in the ground coordinate system, m / s; ω ξ ——the ξ-axis component of the projectile's rotational velocity in the projectile's axis coordinate system, rad / s; ω η ——η-axis component of the projectile's rotational velocity in the projectile axis coordinate system, rad / s; ω ξ ——the ζ-axis component of the projectile's rotational velocity in the projectile's axis coordinate system, rad / s; —— rad / s; M ξ ——the ξ-axis component of the moment acting on the projectile in flight in the projectile axis coordinate system, Nm; M η ——the η-axis component of the moment acting on the projectile in flight in the projectile axis coordinate system, Nm; M ζ ——the component of the moment acting on the missile in flight along the ζ axis in the missile axis coordinate system, in Nm; γ——rotation angle of the projectile around the ξ axis, rad; φ1——the swing angle of the projectile around the ζ axis, rad; φ2——the swing angle of the projectile around the η axis, rad; A——equatorial moment of inertia of the projectile, kg.m 2 ; C——Extreme moment of inertia of the projectile, kg.m 2 ; α D0 ——initial nutation angle amplitude, rad; α D ——initial nutation angle, rad; K zz ——Equatorial damping moment characteristic number; b y ——lift characteristic number; K xz ——Characteristic number of extreme damping moment; K y ——Markov moment characteristic number; K z ——characteristic number of pitching moment; Γ——relative speed, σ——σ=1-K z / C 2 。 3. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 2, wherein: In step 2, an average ballistic performance difference inspection test is performed; For single charge number ammunition, tests should be conducted at 2 / 3 of the maximum range, the maximum range angle, and the maximum firing angle. If there is no high firing range, two to three firing angles should be tested. If there is a high firing range, three to four firing angles should be tested. For multi-charge ammunition, charge numbers are selected at intervals for testing, but the largest charge number, the smallest charge number, and the charge number with an initial velocity close to the speed of sound must be tested; In addition, except for the test point of maximum range, other test points avoid the support points of the prototype platform shooting table compilation test; The same test item was shot in one group every day, with 4 groups of 5 shots in each group; During the test, the projectile's initial velocity was measured by two initial velocity radars, the ballistic radial velocity was measured by a ballistic velocity radar, the ballistic coordinates of the initial section of the muzzle were measured by a ballistic radar or an optical theodolite, the ballistic coordinates of the starting nutation attenuation end point were accurately measured by a high-speed video theodolite, the coordinates of the impact point were measured by a satellite differential positioning system or a total station, and the high-altitude weather was detected by a satellite positioning sounding wind measurement system.

4. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 3, wherein: In the step 3, the zero resistance coefficient is identified; Define the independent variable as the flight Mach number M a The parameter to be identified is the projectile zero resistance coefficient C x0 (M a ), C x0 (M a ) Available N k +1 segment N o The order spline function is expressed as: B j (x) is N o The jth term of the B-spline function, α j is the jth coefficient, identify C x0 (M a ) is essentially about how to determine the coefficient α j ; B j (x) is defined as: a ∈[M min ,M max ]Select N in the interval k internal nodes, dividing the interval into N k +1 part, respectively extending N at both ends of the interval with the length of the 1st part and the Nk+1th part o segment, there are 2(N o +1)+N k Nodes M i ,i=1,2(N o +1)+N k ,but N t The residual sum of squares between the measured and calculated values ​​of the ballistic radial velocity is used as the objective function: V Rci is the parameter to be identified α j Function, in iterative identification, the current value Available previous value With the increment and representation: If SSR is minimized, Solving the differential correction equation can solve the correction amount Δα for each iteration j ; The velocity components V in the three coordinate axis directions are directly obtained by calculating the trajectory in the ground coordinate system. X 、V Y 、V Z , the formula for converting to speed is: Among them, X0, Y0, and Z0 are the components of the ballistic velocity radar point coordinates in the ground coordinate system; To find the sensitive factor in the differential correction equation, firstly transform the left side of the dynamic equation to α i Find the partial derivative and get the sensitivity factors of acceleration in three directions Sensitivity factors of speed in three directions Can be solved by The differential equation is obtained, and the sensitivity factors of the three directions of speed are synthesized to obtain the sensitivity factor of the sum speed; the synthesis formula is as follows:

5. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 4, wherein: In the step 4, a compliance calculation is performed; Select the angle of incidence coefficient K θ , deflection compliance coefficient K ψ , zero resistance compliance coefficient K R , the overturning moment complies with the coefficient K m To meet the parameters, the initial muzzle coordinate X S The corresponding Y S 、Z S and the impact point coordinate X c 、Z C In order to meet the object, the calculated muzzle initial segment and impact point coordinates are made to coincide with the measured values ​​by adjusting the matching parameters; The raw data that meet the calculation requirements include: structural parameters of the gun and projectile; aerodynamic parameters of the projectile; actual firing angle and direction; measured projectile weight; measured initial velocity; meteorological parameters during the firing process; and the measured muzzle initial segment and impact coordinates in the ground coordinate system with the muzzle as the origin. The calculation method for compliance is as follows: a) Given K θ , K ψ , K R , K m The initial value of b) Under the actual conditions of measured initial velocity, measured firing angle, actual meteorological conditions and ballistic conditions, K θ , K ψ , K R and K m Substitute into the equations and solve. When the integral reaches the impact height, if formulas (1) to (4) are satisfied, the calculation is complete. Otherwise, adjust K according to c). θ , K ψ , K R , K m Recalculate the trajectory until it meets the requirements; |And Sc -AND st |≤ε θ (1) |Z Sc -WITH St |≤ε ψ (2) |X Cc -X Ct |≤ε x (3) |Z Cc -WITH Ct |≤ε z (4) Where: Y Sc 、Y St —— Muzzle initial segment X S Calculated and measured values ​​of the vertical coordinate at, m; Z Sc 、Z St —— Muzzle initial segment X S Calculated and measured values ​​of the horizontal coordinate at , m; X Cc 、X Ct ——the calculated or measured value of the vertical coordinate of the impact point, in m; Z Cc 、Z Ct ——the calculated or measured value of the abscissa of the impact point, in m; ε θ ——The shooting angle meets the accuracy, generally taken as 0.01, m; ε ψ ——Declination angle meets the accuracy, generally taken as 0.01, m; ——Zero resistance meets the accuracy, generally 0.001%X Ct , m; ——The turning moment meets the accuracy, generally 0.005%X Ct , m; c) Adjust K θ , K ψ , K R , K m When K is calculated according to formulas (5) to (8) θ , K ψ , K R , K m the increment; Where: ΔK θ - the increment of the angle of incidence coefficient; ΔK ψ — increment of the deflection compliance coefficient; ΔK R ——the increment of the zero resistance compliance coefficient; ΔK m —Increment of the overturning moment compliance coefficient; ΔY S —— Muzzle initial segment X S The difference between the calculated value and the measured value of the vertical coordinate at m; ΔZ S —— Muzzle initial segment X S The difference between the calculated value and the measured value of the horizontal coordinate at m; ΔX C ——the difference between the test value and the calculated result of the vertical coordinate of the impact point, in m; ΔZ C ——the difference between the test value and the calculated result of the abscissa of the impact point, in m; The trajectory of each test angle is calculated under actual conditions using the average value of the zero-resistance compliance coefficient of each test point. If the difference between the calculated range and the actual range R is greater than 0.3% R, the compliance coefficients of all test angles should be fitted to form K. R ~θ curve, using K corresponding to each test angle R Calculate the actual trajectory. If the range error is less than 0.3%R, use the fitting result for simulation calculation. Otherwise, make additional shooting until the range error of all test points is less than 0.3%R. When checking the shooting table of multiple charge numbers, the K of the shooting charge number can be used. R Fit them separately, and then find the K of the untested charge number in the curve R value, for simulation calculation; K of the large elevation angle test point m Average, for ballistic simulation calculation; consider K when averaging m The nonlinear relationship between Z and K is expressed as an angle. m Construct a curve, and then use the average bias current to find K in the curve m The average value of Use the determined compliance coefficient K θ , K ψ , K R , K m , given the initial conditions, termination conditions, and meteorological conditions of the shooting, the trajectory can be simulated and calculated to obtain the average trajectory under any conditions.

6. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 5, characterized in that: In the step 5, the distribution characteristics of the equivalent scattered source parameters are determined; Projectile density B R It is an important indicator for evaluating the ballistic performance of conventional projectiles and is also a necessary parameter for calculating ballistic distribution characteristics. The projectile dispersion caused by weapons and equipment is mainly caused by the dispersion of three factors: drag coefficient, initial velocity, and bounce angle. Moreover, the dispersion characteristics of these three factors are not affected by shooting conditions and can be regarded as constants. The dispersion characteristics of these three factors are obtained through experiments. Under different shooting conditions, the projectile dispersion caused by each factor alone is calculated through ballistic simulation and differential methods. The comprehensive projectile dispersion is obtained through error synthesis. The key to this processing method is to determine the distribution characteristics of the dispersion source parameters. For the equivalent dispersion source parameters of artillery-launched grenades, the initial velocity, firing angle, firing direction, zero-drag coefficient, and overturning moment coefficient are taken; for dispersion source parameters such as initial velocity that can be directly measured, they are determined through actual measurement; for dispersion source parameters that cannot be directly measured, the equivalent dispersion source parameters are extracted through the ballistic modeling method; the influence of meteorological conditions on the trajectory is incorporated into the zero-drag coefficient; A certain type of missile has N β Equivalent scatter source parameter β i , i=1,2,…,N β , in the test condition j, j = 1, 2, ..., M shoots L j For the kth launch, the equivalent dispersion source parameters can be determined The equivalent dispersion source parameters not only include the random components that affect the projectile dispersion, but also the systematic errors under each working condition and the systematic errors of the ballistic model used for extraction. These systematic components should be eliminated when determining the parameter distribution characteristics. In order to eliminate the systematic errors, the projectile amount L in each working condition is j ≥3; Mean value of equivalent scattered source parameters under working condition j: The deviation of the equivalent scattered source parameters under working condition j is: The intermediate error of the i-th equivalent scatter source parameter: Through the normalized simulation method, heterogeneous data are unified under the same launch conditions or meteorological conditions, and the random ballistic characteristic information in the data is extracted and utilized to achieve the comprehensive utilization of multi-source test data, increase the sample size under specific working conditions, and improve the accuracy of statistical results.

7. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 6, wherein: In step 6, the distribution characteristics of the error source parameters of the equivalent day are determined; The error on the day of the test, also known as the group error, is caused by the high-altitude meteorological error during each group of shooting and the gun adjustment error caused by the uneven support of the gun. The equivalent error source parameters of the day's error are obtained by using the equivalent scattered source parameter extraction method for the test results of different groups under the same parameters. A certain type of missile has N ε Equivalent daily error source parameter ε i , i=1,2,…,N ε , in the test condition j, j = 1, 2, ..., M shoots L j For the jth working condition, the equivalent error source parameters of the day can be determined The equivalent day error source parameters mainly include the systematic components that affect the shooting error of each working condition; the random components of projectile dispersion are reduced by about L j times; Equivalent mean of error source parameters on the same day: Equivalent daily error source parameter deviation from the mean: The intermediate error of the i-th equivalent error source on the same day: By utilizing the parameter distribution characteristics of the equivalent day error source, the day error under any shooting conditions can be obtained through ballistic simulation.

8. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 7, wherein: In the step 7, the system error is estimated; Systematic error refers to errors that are unrelated to the number of firing groups and rounds, and are errors caused by non-repeatability factors in the preparation of the firing table. The test process involves artillery batch errors and ammunition batch errors, and model errors are involved in data processing and firing table calculations. The batches of weapons and ammunition used in firing table tests are limited. Testing is conducted with one artillery piece and one batch of ammunition. Obviously, one artillery piece and one batch of ammunition cannot well represent the characteristics of the parent equipment of this type. The ballistic simulation calculation uses the rigid body motion equation, which itself accurately reflects the spatial motion law of the projectile. The error caused solely by the motion equation is already very small and can be ignored. The difference between the calculated trajectory and the actual trajectory is caused by the inaccuracy of some raw data in the motion equation. The errors in these raw data constitute the main error source of the simulation model system error. The error sources that constitute the system error of the ground artillery grenade firing table test include: p , take η p =0.1%R; rifling inconsistency error η g , take η g =0.1%R; The error sources of the simulation model system error include: Δθ0 jump angle error, taking the corresponding equivalent dispersion characteristic parameter value; Δα D0 The initial nutation amplitude error is taken as 1°; Initial speed error, take Induced drag coefficient error, take Δc x0 Zero lift drag coefficient error, take the corresponding equivalent dispersion characteristic parameter value; Δc' y Lift coefficient derivative error, take 5% c' y ;Δm' z The derivative error of the overturning moment coefficient is 5% m' z ;Δc” z The derivative error of the Martensitic force coefficient is 20% c" z ;Δm” y The derivative error of the Marginal moment coefficient is 20% m" y ;Δm' xd Roll damping moment coefficient derivative error, take 20% m' xd ;Δm' zd The derivative error of the swing damping torque coefficient is 20% m' zd ; System error source c i The corresponding equivalent scattered source parameter β is caused at the incident angle θ0 j Response object error After the coincidence calculation, it is included in the coincidence coefficient, so the system error of the trajectory simulation at the shooting angle θ0 is zero; k ≠θ0, And then it is transferred to other angles through the coincidence coefficient; system error The error in the compliance coefficient caused by Any angle of incidence θ k The systematic error at is calculated using the following formula: Where: c i — each system error source; ——Angle θ k System error at , m; ——Error source c i At the incident angle θ k Range error caused by, m; ——Error source c i The jth coincidence coefficient error is caused at the incident angle θ0; ——Error source c i The jth response object error is caused at the incident angle θ0, m; In the above system error calculation formula, the error caused by each error source is The trajectory is calculated under standard conditions, but in the actual shooting table compilation, the systematic error of the support angle is It is included in the compliance coefficient when the calculation is performed under actual conditions. Therefore, the premise for the above formula to be valid is that at the angle θ0, the change in the compliance coefficient caused by each error source under actual conditions is equal to the change in the compliance coefficient caused under standard conditions, that is, 9. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 8, wherein: In step 8, an average trajectory difference assessment of non-test support points is performed; After performing the coincidence calculation according to step 4, substitute the coincidence coefficients into the ballistic model and calculate the arbitrary firing angle θ under the standard artillery conditions. k trajectory, and obtain the standardized range R T , compared with the table value R N Calculate the deviation: |ΔR|=|R T -R N | Use the U test method to determine the qualified limit: Determine the intermediate error of the equivalent scattered source parameters according to step 5 and calculate the incident angle θ k Error in the middle of the range: Determine the intermediate error of the equivalent error source parameters according to step 6 and calculate the angle θ k Error on the day: Intermediate error in shooting table compilation: Average Ballistic Performance Difference Check Standardized Range Middle Error: Where: ΔR - deviation of the standardized range during the shooting table inspection; ΔR max - qualified limit of the radiometer inspection; E T - Intermediate error in the compilation of the shooting table; E N - Intermediate error of the shooting table inspection; N1, n1 - the number of groups and the number of rounds in each group required for the shooting test; N2, n2 - the shooting table checks the number of groups and the number of rounds in each group of the shooting test; U0 - Inspection limit: 2.44 for one inspection shot, 2.91 for two or more inspection shots; When ΔR≤ΔR max When ΔR>ΔR max When the meter is turned on, it is considered that there is a problem with the meter.

10. The method for evaluating the difference in average trajectories of the same projectile with different guns as claimed in claim 9, wherein: In step 9, trajectory reconstruction is performed; The initial nutation of a stable flying projectile is constantly decaying. Assuming that at time t k , the initial nutation decays, then the difference in the subsequent trajectory parameters is mainly due to the velocity at that moment and displacement Determine; analyze the initial nutation attenuation period of the projectile and clearly reconstruct the trajectory demarcation point; use the measured data of trajectory velocity and trajectory coordinates, select the initial disturbance as the parameter to be optimized, and use the UKF filter optimization method to reconstruct the trajectory and determine the time t k of t k Then the trajectory is calculated using the basic parameters calculated in the original firing table to complete the inspection test trajectory reconstruction; The UKF algorithm is obtained by replacing the linear approximation of the statistical characteristic propagation method in the EKF algorithm with the UT transform method. Since the system state equation and / or measurement equation are nonlinear systems, the main problem solved by nonlinear filtering is the propagation of random quantities along the nonlinear system. The UKF algorithm uses a set of deterministic sampling points to approximate the state distribution. The transformed sampling points obtained through the UT transform are used to approximate the mean and variance of the state, completing the propagation of the state along the nonlinear function. The distribution of the Gauss noise transform sampling points can be approximated to the true mean and variance with third-order accuracy. The discrete nonlinear state equation and measurement equation are expressed as: Where: Θ K ——state vector; Z K+1 ——measurement vector; W K , Q K ——Gaussian white noise and variance matrix of dynamic system process; V K 、R K ——Measure Gaussian white noise and variance matrix; Since the state equation and measurement equation contain noise terms, it is necessary to expand the dimension of the filtered state variables, let Θ a =[Θ T W T V T ] T , the specific steps are as follows; initialization: For the initial state Add the noise term to get the initial state vector after dimension expansion For the state vector Perform Sigma point sampling, and the vector after sampling is Among them, n x is the dimension of the state vector; κ is a proportional parameter used to adjust the Sigma point and The distance between the two moments is 0, and it only affects the deviation caused by the higher-order moments after the second-order moment. κ is generally taken as 0. is the ith row or ith column of the matrix square root, i = 1, 2, ..., n x ; Prediction equation: in, It is the weight of the impact on expectation and variance; Update equation: P ΘΘ (k+1|k+1)=P ΘΘ (k+1|k)-K(k+1)P YY (k+1|k)K T (k+1) The reconstructed trajectory model is consistent with the trajectory simulation model in step 1; the Kalman filter measurement equation mainly includes the trajectory velocity equation and the trajectory coordinate equation; Ballistic radial velocity model: Model for measuring coordinates using the spatial polar coordinate method: Model for measuring coordinates using the spatial angle intersection method: In step 10, an average trajectory difference assessment of the test support points is performed; Use the new research platform to carry out N2 group and each group n2 emission table inspection test at a certain support point, Reconstruct the trajectory and range for the j-th test of the i-th group; Under the new platform inspection test conditions, the trajectory is calculated using the basic parameters of the prototype platform shooting table to obtain the shooting table trajectory. is the range of the jth firing table trajectory of the i-th group; the statistical value |ΔR|=|R is constructed by comparing the firing table trajectory with the inspection test trajectory. T -R N | / R T If there is no significant difference in the trajectory of the two platforms, then ΔR obeys Distribution; Based on the principles and processes of shooting table compilation and trajectory reconstruction, analyze the error composition and statistically calculate the distribution characteristics of statistical quantities; in: Where: R T ——The range corresponding to the trajectory of the shooting table, m; R N ——Corresponding range of the reconstructed trajectory during the inspection test, m; B T ——Probability error of the ballistic range of the shooting table, %; B N ——Probability error of the ballistic range reconstructed by checking the shooting, %; - Random error of firing angle related to the number of shots fired, taking 0.3mil or the test statistical result; - Random error in muzzle velocity related to the number of rounds fired, taking 0.1% of V0 or the statistical result of the test; - Shooting angle error related to the number of shooting groups, take 0.3mil or the test statistical results; ——The initial nutation amplitude error caused by the batch error of artillery ammunition is taken as 1°; ——The systematic error of the trajectory inclination angle of the trajectory reconstruction is taken as 0.5mil; ——The error of the trajectory reconstruction initial velocity system is 0.1% V0; The first part of the range probability error is related to the number of groups and rounds fired, which should be determined by the shooting angle error. Initial velocity error Drag coefficient error The meteorological error and the random component of the initial disturbance are caused. Due to the ballistic reconstruction, the drag coefficient error and meteorological error on the vast majority of the ballistics are offset and should not be taken into account in the calculation of the qualified limit. The impact of the initial disturbance on the trajectory before the end of the nutation decay is mainly reflected in the velocity magnitude and direction. Changes in the velocity magnitude and direction will cause a large change in the trajectory landing point. The velocity magnitude error caused by the random component of the initial disturbance is merged into the initial velocity error, and the velocity direction error is merged into the shooting angle error, and its impact on the range is comprehensively calculated. The initial disturbance has an impact on the trajectory coordinates and velocity during the nutation decay period. Because the action time is short, the coordinate change in this section of the trajectory is very small compared to the entire range, and this coordinate change will not be amplified in the subsequent flight of the projectile. It is only a linear superposition on the original trajectory landing point, so it can be ignored. The second part of the range probability error is related to the number of shooting groups. Also because of the ballistic reconstruction, the drag coefficient error and meteorological error on the vast majority of the ballistics are offset, leaving only the shooting angle error. This refers to the initial disturbance differences caused by batch errors of artillery ammunition due to factors such as processing technology, material properties, and quality control. For example, there are differences in barrel curvature, rifling processing, and initial disturbance differences caused by batch differences between two stages of test ammunition. However, this does not include gun adjustment errors. For a single gun or a single batch of ammunition, this error is a systematic error. It is the systematic error in the velocity magnitude and direction of the end point of the initial nutation decay caused by the trajectory reconstruction method and model errors; Use U-test assessment to determine the acceptance limit of the inspection (U α / 2 The significance level α=10% normal distribution limit value is 2.91). When the inspection result satisfies |ΔR|≤ΔR max , then it is considered that the shooting table can be used universally; otherwise, it is considered that there are obvious differences in the ballistic performance of the two platforms and the shooting table cannot be used universally.

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