Inertial flight trajectory backstepping method and device

Abstract

The present invention discloses an inertial flight trajectory backstepping method and device, including acquiring trajectory data; determining projectile characteristic parameters and trajectory parameters; identifying the trajectory parameters according to the acquired trajectory data; performing backstepping calculation on the trajectory through a reduced-order rigid body trajectory equation based on the identified parameters to obtain the starting point of the flight trajectory. The longer the measurement length, the higher the calculation accuracy. When the projectile characteristic parameters are relatively accurate, the error of the backstepping result is the smallest, and the error of the back-calculated range is ≤3‰. When there are errors in the characteristic parameters, the accuracy is slightly worse, but it can still meet the usage requirements. This method can accurately perform trajectory back-calculation based on radar end data, has little dependence on the radar measurement length, and has a certain generality.

Description

Technical Field

[0001] The present invention relates to the technical field of ballistic backtracking of ballistic starting points, and specifically relates to an inertial flight ballistic backtracking method and device. Background Art

[0002] Ballistic backtracking refers to the process of obtaining the ballistic starting point through an algorithm using radar detection data. The ballistic backtracking algorithm is one of the key technologies of the artillery reconnaissance and calibration radar software system. Currently, the ballistic backtracking algorithms mainly include two categories. One is the estimation algorithm based on the ballistic model, and the other is the machine learning algorithm based on prior samples.

[0003] For the estimation algorithm based on the ballistic model, its principle is to perform ballistic integration from a certain point on the ballistic segment towards the ballistic starting point direction, and stop when the integrated ballistic height reaches a given value to obtain the result. The steps are as follows: 1. Obtain ballistic data through the radar; 2. Perform filtering processing using methods such as Kalman filtering to obtain the filtered ballistic data; 3. Use the particle ballistic model to estimate the ballistic parameters, generally only considering the ballistic coefficient; 4. Perform ballistic calculation.

[0004] Due to the limitation of the actual ballistic samples, the machine learning algorithm based on prior samples has low practicality of the extrapolation model.

[0005] In the traditional estimation algorithm based on the ballistic model, the particle ballistic model is used. This model is simple to calculate and requires fewer projectile parameters, but it depends on a large amount of radar observation data, and it is unable to effectively calculate the ballistic cross deviation. In the case of a short unknown ballistic (usually the extrapolation time is not more than 1 second), it can provide high accuracy. For the calculation of less radar observation data and a long unknown ballistic (extrapolation time greater than 1.5 seconds), the error of this method will be very large. Currently, the projectile concealment technology is constantly developing, and there will be more and more situations where sufficient radar data cannot be obtained. For the calculation with a small amount of test data, there is no systematic and effective application method, and it is difficult to obtain effective calculation results.

[0006] The present invention aims to solve the problem of how to effectively calculate the ballistic starting point when the radar measurement data is insufficient or even there is only a small amount of data. Summary of the Invention

[0007] The object of the present invention is to provide an inertial flight trajectory backstepping method, which belongs to an estimation algorithm based on a trajectory model. On the basis of traditional methods, a parameter identification step is added, and a more accurate reduced-order rigid body trajectory model is adopted, so that the calculation result is more accurate. Its basic principle is to identify the trajectory parameters through a small amount of trajectory measurement data on the basis of radar observation data, obtain relatively accurate trajectory parameters, and adopt an improved recursive average filtering algorithm to solve the divergence problem in the calculation, and finally obtain a more accurate result. The steps are as follows: obtaining insufficient observation data, determining the projectile and rocket characteristic parameters and trajectory parameters, parameter identification, trajectory backstepping calculation, and obtaining the result. Among them, in the parameter identification and trajectory backstepping calculation, an improved recursive average filtering algorithm is required to perform parameter filtering processing.

[0008] To solve the above technical problems, the present invention discloses an inertial flight trajectory backstepping method, including:

[0009] Obtaining trajectory data;

[0010] Determining the projectile and rocket characteristic parameters and trajectory parameters;

[0011] Identifying the trajectory parameters according to the obtained trajectory data;

[0012] According to the identified parameters, performing a backstepping calculation on the trajectory through a reduced-order rigid body trajectory equation to obtain the starting point of the flight trajectory.

[0013] Further, obtaining the trajectory data specifically includes:

[0014] Performing Kalman filtering processing on the obtained radar data,

[0015] wherein the radar data includes the three-dimensional spatial coordinates of the projectile, the projectile velocity (v x , v y , v z );

[0016] Making a preliminary judgment on the type of projectile and rocket through the radar observation signal.

[0017] Further, determining the projectile and rocket characteristic parameters and trajectory parameters specifically includes:

[0018] Obtaining the projectile and rocket characteristic parameters and the initial values of the trajectory calculation,

[0019] wherein the projectile and rocket characteristic parameters include the projectile diameter, projectile length, projectile weight, moment of inertia and aerodynamic parameters,

[0020] the trajectory parameters include the compliance coefficient and the parameters of the initial point in the trajectory,

[0021] the compliance coefficient includes the drag compliance coefficient KR and the overturning moment compliance coefficient Km,

[0022] The parameters of the initial point in the trajectory include velocity (v xc , v yc , v zc ), coordinates (X c , Y c , Z c ), the longitudinal component of the projectile swing angle the lateral component of the projectile swing angle rotation speed

[0023] Furthermore, based on the obtained trajectory data, identify the trajectory parameters, specifically including:

[0024] The identification object, which is the initial value of the reverse thrust and the compliance coefficients KR, Km;

[0025] The identification method, and the identification method is:

[0026]

[0027] where n is the number of observation points, N2 is the number of unknown initial conditions, N23 = N2 + N3, and N3 is the number of unknown parameters, is the observed value, y ji0 is the estimated value, a k is the parameter to be identified, and P jk is the sensitivity;

[0028] Trajectory parameter convergence processing.

[0029] Furthermore, based on the identified parameters, perform reverse calculation of the trajectory through the reduced-order rigid-body trajectory equation to obtain the starting point of the flight trajectory, specifically including:

[0030] Take a point on the trajectory segment as the initial point and use the Runge-Kutta method to perform trajectory integration in the direction of the trajectory starting point;

[0031] Stop when the integrated trajectory height reaches a given value to obtain the reverse calculation result;

[0032] Synchronously perform filtering processing using the recursive average filtering method.

[0033] Furthermore, for the Runge-Kutta method, directly obtain the function value of X n from the function value of the X n+1 point:

[0034] Assume the given differential equation:

[0035] Initial conditions: y(t n ) = y n ,

[0036] Accurate to h 4 The formula is as follows:

[0037]

[0038] K0 = h·f(t n , y n )

[0039] K1 = h·f(t n +0.5h, y n +0.5K0)

[0040] K2 = h·f(t n +0.5h, y n +0.5K1)

[0041] K3 = h·f(t n +h, y n +K2)

[0042] Where h is the integration step size (h = t n+1 - t n ),

[0043] X n+1 is the previous ballistic point of X n , and h is negative.

[0044] Furthermore, the recursive average filtering method specifically includes:

[0045] Calculate N consecutive values x1, x2... x n , and take the arithmetic mean of the N values Let Start from x n / 2 and continue to calculate N consecutive values x n / 2+1 , x n / 2+2 ... x n / 2+n , and take the arithmetic mean of the N values Let Repeat the above process until the calculation ends.

[0046] The present invention also discloses a terminal device, including:

[0047] A preprocessing module for obtaining ballistic data;

[0048] A parameter determination module for determining projectile characteristic parameters and ballistic parameters;

[0049] A parameter identification module for identifying ballistic parameters according to the obtained ballistic data;

[0050] A backstepping calculation module for performing backstepping calculation on the ballistic according to the identified parameters through a reduced-order rigid body ballistic equation to obtain the starting point of the flight trajectory.

[0051] The present invention discloses a storage medium storing a computer program which, after being loaded, can execute any of the above methods.

[0052] Beneficial effects:

[0053] The longer the measured length is, the higher the calculation accuracy is. When the characteristic parameters of the projectile are relatively accurate, the error of the inverse deduction result is the smallest, and the error of the calculated range is ≤ 3‰. When there are errors in the characteristic parameters, the accuracy is slightly worse, but it can still meet the usage requirements. This method can accurately perform ballistic inverse calculation based on the radar end data, has little dependence on the radar measurement length, and has a certain generality. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation to the present application. In the drawings:

[0055] Figure 1 is a schematic flow chart of the present application;

[0056] Figure 2 is a schematic diagram of the improved recursive average filtering algorithm of the present application;

[0057] Figure 3 is a schematic diagram of the ballistic inverse deduction principle of the present application;

[0058] Figure 4 is a schematic diagram of the comparison between the actual ballistic value and the inverse deduction value of the present application;

[0059] Figure 5 is a schematic diagram of the comparison between the actual value and the inverse deduction value of the ballistic rotation speed of the present application ;

[0060] Figure 6 is a schematic diagram of the comparison between the actual ballistic value and the inverse deduction value of the present application ;

[0061] Figure 7 is a schematic diagram of the comparison between the actual ballistic value and the inverse deduction value of the present application ;

[0062] Figure 8 is a schematic diagram of the structure of the device of the present application.

[0063] Legend: 1. Device; 11. Pretreatment module; 12. Parameter determination module; 13. Parameter identification module; 14. Inverse deduction calculation module. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0064] To make the objectives, technical solutions and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments of this application and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of this application, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without creative efforts belong to the scope of protection of this application.

[0065] As Figure 1 shown, the present invention discloses an inertial flight trajectory reverse thrust method, which specifically includes the following steps:

[0066] S100: Obtain trajectory data.

[0067] Furthermore, obtaining trajectory data specifically includes:

[0068] Based on the reduced-order rigid body trajectory model, perform Kalman filtering on the obtained insufficient radar data.

[0069] Among them, the radar data includes the three-dimensional spatial coordinates of the projectile, the projectile velocity (v x , v y , v z ).

[0070] Through the radar observation signal, initially judge the type of projectile, such as a grenade or a rocket.

[0071] S200: Determine the projectile characteristic parameters and trajectory parameters.

[0072] The trajectory model of the present invention adopts a reduced-order rigid body trajectory equation, which has a good degree of coincidence with the actual flight state of the projectile, relatively fast calculation speed, and high calculation accuracy.

[0073] Furthermore, determining the projectile characteristic parameters and trajectory parameters specifically includes:

[0074] The calculation of this model requires obtaining the projectile characteristic parameters and the initial values of the trajectory calculation.

[0075] Among them, the projectile characteristic parameters include the projectile diameter, projectile length, projectile weight, moment of inertia, and aerodynamic parameters.

[0076] The trajectory parameters include the compliance coefficient and the parameters of the initial point (a certain point) for reverse thrust calculation in the trajectory.

[0077] The compliance coefficient includes the drag compliance coefficient KR and the overturning moment compliance coefficient Km.

[0078] The parameters of the initial point in the trajectory include the velocity (v xc , v yc , v zc ), coordinates (X c, Y c , Z c ), the longitudinal component of the projectile swing angle The transverse component of the projectile swing angle Rotational speed

[0079] The projectile shape characteristics and ballistic characteristics of each type of projectile and rocket have certain similarities. During the inverse calculation process, the projectile diameter, projectile length, projectile weight, moment of inertia, and aerodynamic parameters can be replaced by the parameters of typical projectiles and rockets, v xc , v yc , v zc , Y c can be obtained through radar measurement data, X c , Z c can take the coordinate value relative to one's own position or take 0, KR and Km cannot be effectively measured and need to be obtained during the parameter identification process.

[0080] S300: Identify the ballistic parameters based on the obtained ballistic data.

[0081] Furthermore, identify the ballistic parameters based on the obtained ballistic data, specifically including:

[0082] Identification object, the identification object is the inverse initial value and the compliance coefficients KR and Km.

[0083] Identification method, the identification method is:

[0084] Then the identification criterion can be written as:

[0085]

[0086] Among them, n is the number of observation points, N2 is the number of unknown initial conditions, N23 = N2 + N3, and N3 is the number of unknown parameters. is the observed value, y ji0 is the estimated value, a k is the parameter to be identified, P jk is the sensitivity.

[0087]

[0088] In this way, the problem of projectile and rocket parameter identification is transformed into an extreme value problem of seeking the parameter to be identified a k = a k0 + Δa k to minimize the criterion function ε. To find Δa k , only need to solve the system of equations

[0089]

[0090] After arrangement, we get

[0091] AB = C

[0092] where

[0093]

[0094]

[0095] Solving the above equation can obtain Δa k , for the Δa calculated in each step of iteration k , correct the original identification parameter a k = a k0 + Δa k , when ε is the smallest, the iteration terminates, and the identification parameter obtained at this time is used as the required parameter. The sensitivity P jk can be obtained from the sensitivity equation set or by engineering methods.

[0096] Ballistic parameter convergence processing, specifically:

[0097] The value has a great influence on the stability of the inverse ballistic trajectory and even causes the calculation result to diverge. If its error from the true value is large, it will diverge in a short time, while the estimation of usually has a large error before the identification iteration, which may cause divergence during the identification process, making the identification process unable to proceed. Even if the relatively accurate initial value obtained after identification is used, it cannot meet the requirement of the inverse calculation accuracy, and it may also diverge after a long flight time.

[0098] The errors of all cause divergence by affecting Ultimately, so only the divergence problem of during the inverse process needs to be solved. diverges around its actual value and has a certain periodicity. can be regarded as having a periodic disturbance effect on the actual value. During the identification process, a filtering algorithm can be used to process to avoid divergence and complete the ballistic calculation process.

[0099] During the ballistic inverse calculation process, filtering needs to be carried out synchronously while calculating. It can be improved on the traditional recursive average filtering method, as shown in Figure 2 . First, calculate N consecutive values x1, x2…x n , and take the arithmetic mean of the N values Let From x n / 2Start from here and continue to calculate N consecutive values x n / 2+1 , x n / 2+2 … x n / 2 +n, and take the arithmetic mean of the N values Let Repeat the above process until the calculation ends. This method can effectively solve the divergence problem in the calculation process.

[0100] S400: According to the identified parameters, perform backtracking calculation on the ballistic trajectory through the reduced-order rigid-body ballistic equation to obtain the starting point of the flight ballistic trajectory.

[0101] Furthermore, according to the identified parameters, perform backtracking calculation on the ballistic trajectory through the reduced-order rigid-body ballistic equation, specifically including:

[0102] As Figure 3 shown, adopt the reduced-order rigid-body ballistic equation, perform ballistic integration from a certain point on the ballistic segment towards the starting point of the ballistic trajectory, and stop when the integrated ballistic height reaches a given value, thereby obtaining the backtracking result. The integration uses the Runge-Kutta method, and this process needs to be synchronously filtered using the above improved recursive average filtering method.

[0103] The Runge-Kutta method directly obtains the function value of X n from the function value at point X n+1 .

[0104] Assume the given differential equation:[[]]

[0105] Initial condition: y(t n ) = y n

[0106] Accurate to h 4 The formula is:[[]]

[0107]

[0108] K0 = h · f(t n , y n )

[0109] K1 = h · f(t n +0.5h, y n +0.5K0)

[0110] K2 = h · f(t n +0.5h, y n +0.5K1)

[0111] K3 = h · f(t n +h, y n +K2)

[0112] In the formula: h - is the integration step size (h = tn+1 -t n )

[0113] Since it is a reverse calculation, the calculated X n+1 is the previous ballistic point of X, and h is negative. n

[0114] Example 1

[0115] Taking the relevant parameters of a 155 mm howitzer shell as the ballistic inverse calculation characteristic parameters, the relative coordinates and velocities of a section of the ballistic trajectory at the end of the trajectory have been obtained. Taking the velocities v x , v y , v z as the observables, selecting and the compliance coefficients KR and Km as the identification parameters, and using the ballistic inverse calculation method based on the end measurement data for calculation, the calculation results are as follows:

[0116] Inverse calculation results (see Table 1):

[0117]

[0118] Table 1

[0119] It can be seen from the results that by using this method, the ballistic inverse calculation of this type of ammunition can be accurately carried out, and the relevant projectile and rocket characteristic parameters remain unchanged. Other projectiles and rockets can also be calculated. The calculation results of other types of ammunition are as follows:

[0120] Example 2

[0121] Inverse calculation results of 130 mm howitzer shell (see Table 2):

[0122]

[0123] Table 2

[0124] Example 3

[0125] Inverse calculation results of 122 mm howitzer shell (see Table 3):

[0126]

[0127] Table 3

[0128] Example 4

[0129] Inverse calculation results of 100 mm howitzer shell (see Table 4):

[0130]

[0131]

[0132] Table 4

[0133] ​As can be seen from the calculation results, the longer the measured length, the higher the calculation accuracy. When the characteristic parameters of the projectile are relatively accurate, the error of the inverse calculation result is the smallest, and the error of the inverse calculated range is ≤3‰. When there are errors in the characteristic parameters, the accuracy is slightly worse, but it can still meet the usage requirements. This method can accurately perform ballistic inverse calculation based on the radar end data, has little dependence on the radar measurement length, and has a certain generality. The comparison between the inverse value and the actual value of the ballistic trajectory is shown in Figures 4 - 7 , under the condition of insufficient measurement data, by adopting a reduced-order rigid-body ballistic model, the parameter identification step is added, and the improved recursive average filtering method is used for filtering processing synchronously during the parameter identification process and the ballistic inverse calculation process. The error of the result obtained by the inverse calculation is small. The above is an inertial flight ballistic inverse calculation method provided by an embodiment of the present application. Based on the same idea, an embodiment of the present application also provides an inertial flight ballistic inverse calculation device 1, as

[0134] shown. Figure 8 shown.

[0135] An inertial flight ballistic inverse calculation device 1 includes:

[0136] A preprocessing module 11 for obtaining ballistic data;

[0137] A parameter determination module 12 for determining the characteristic parameters and ballistic parameters of the projectile;

[0138] A parameter identification module 13 for identifying the ballistic parameters according to the obtained ballistic data;

[0139] An inverse calculation module 14 for performing an inverse calculation of the ballistic trajectory through a reduced-order rigid-body ballistic equation according to the identified parameters to obtain the starting point of the flight ballistic trajectory.

[0140] A specific application of the inertial flight ballistic inverse calculation device 1 here can be understood as a virtual device, such as a software product similar to a browser. A specific application of the preprocessing module 11, the parameter determination module 12, the parameter identification module 13, and the inverse calculation module 14 can be understood as functional functions that can be independently encapsulated.

[0141] Furthermore, in an embodiment provided by the present application, the preprocessing module 11 is used to obtain ballistic data, specifically for:

[0142] Performing Kalman filtering processing on the obtained radar data,

[0143] wherein the radar data includes the three-dimensional spatial coordinates of the projectile and the projectile velocity (v x , v y , v z );

[0144] Making a preliminary judgment on the type of the projectile through the radar observation signal.

[0145] Further, in an embodiment provided by the present application, the parameter determination module 12 is used to determine the projectile characteristic parameters and the ballistic parameters, specifically:

[0146] Obtain the projectile characteristic parameters and the initial values of ballistic calculation,

[0147] Among them, the projectile characteristic parameters include the projectile diameter, projectile length, projectile weight, moment of inertia, and aerodynamic parameters,

[0148] The ballistic parameters include the conformity coefficient and the parameters of the initial point in the ballistic,

[0149] The conformity coefficient includes the drag conformity coefficient KR and the overturning moment conformity coefficient Km,

[0150] The parameters of the initial point in the ballistic include the velocity (v xc , v yc , v zc ), coordinates (X c , Y c , Z c ), the longitudinal component of the projectile swing angle The lateral component of the projectile swing angle Rotational speed

[0151] Further, in an embodiment provided by the present application, the parameter identification module 13 is used to identify the ballistic parameters according to the obtained ballistic data, specifically:

[0152] Identification object, the identification object is the initial value of the reverse thrust And the conformity coefficients KR and Km;

[0153] Identification method, the identification method is:

[0154]

[0155] Among them, n is the number of observation points, N2 is the number of unknown initial conditions, N23 = N2 + N3, and N3 is the number of unknown parameters, is the observed value, y ji0 is the estimated value, a k is the parameter to be identified, P jk is the sensitivity;

[0156] Ballistic parameter convergence processing.

[0157] Further, in an embodiment provided by the present application, the reverse thrust calculation module 14 is used to perform reverse thrust calculation on the ballistic according to the identified parameters through the reduced-order rigid body ballistic equation to obtain the starting point of the flight trajectory, specifically:

[0158] Take a certain point on the ballistic segment as the initial point, and use the Runge-Kutta method to perform ballistic integration in the direction of the ballistic starting point;

[0159] Stop when the integrated ballistic height reaches a given value to obtain the backstepping result;

[0160] Synchronously perform filtering processing using the recursive average filtering method

[0161] The embodiment of the present application also provides a storage medium, the storage medium stores a computer program, and after the computer program is loaded, the following steps can be executed:

[0162] Obtain ballistic data;

[0163] Determine the projectile characteristics parameters and ballistic parameters;

[0164] According to the obtained ballistic data, identify the ballistic parameters;

[0165] According to the identified parameters, perform backstepping calculation on the ballistic by using the reduced-order rigid body ballistic equation to obtain the starting point of the flight ballistic.

[0166] In a typical configuration, a computing device includes one or more processors (CPUs), an input / output interface, a network interface, and a memory.

[0167] The memory may include non-permanent memory in the computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of, for example, read-only memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.

[0168] Computer-readable media includes permanent and non-permanent, removable and non-removable media and can be implemented by any method or technology for information storage. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media such as modulated data signals and carrier waves.

[0169] It should also be noted that the term "comprise", "include" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, commodity or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, commodity or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, commodity or device comprising said element.

[0170] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0171] The above are only the embodiments of the present application and are not intended to limit the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the scope of the claims of the present application.

Claims

1. An inertial flight trajectory reverse thrust method, characterized in that, Including: Obtain ballistic data; Determine the projectile characteristic parameters and ballistic parameters; According to the obtained ballistic data, identify the ballistic parameters; According to the identified parameters, perform backward calculation on the trajectory through the reduced-order rigid-body trajectory equation to obtain the starting point of the flight trajectory; According to the identified parameters, perform backward calculation on the trajectory through the reduced-order rigid-body trajectory equation to obtain the starting point of the flight trajectory, specifically including: Take a point on the ballistic segment as the initial point, and use the Runge-Kutta method to perform ballistic integration in the direction of the ballistic starting point; Stop when the integrated ballistic height reaches a given value to obtain the backward calculation result; Synchronously perform filtering processing using the improved recursive average filtering method; The Runge-Kutta method directly obtains the function value of X from the function value at point X n : n+1 The function value of Given the differential equation: Initial condition: y(t n ) = y n , Accurate to h 4 The formula is: K0 = h·f(t n ,y n ) K1 = h·f(t n + 0.5h, y n + 0.5K0) K2 = h·f(t n + 0.5h, y n + 0.5K1) K3 = h·f(t n +h,y n +K2) where h is the integration step size, h = t n+1 - t n , X n+1 is the previous ballistic point of X n and h is negative; The improved recursive average filtering method specifically includes: Calculate consecutive N values x1, x2…x n , and take the arithmetic mean of the N values Let Starting from x n / 2 , continue to calculate consecutive N values x n / 2+1 , x n / 2+2 …x n / 2+n , and take the arithmetic mean of the N values Let Repeat the above process until the calculation ends; Determine the projectile characteristic parameters and ballistic parameters, specifically including: Obtain the projectile characteristic parameters and the initial values of ballistic calculation, wherein the projectile characteristic parameters include projectile diameter, projectile length, projectile weight, moment of inertia, and aerodynamic parameters, the ballistic parameters include the conformity coefficient and the parameters of the initial point in the trajectory, the conformity coefficient includes the drag conformity coefficient KR and the overturning moment conformity coefficient Km, The parameters of the initial point in the trajectory include velocity (v xc , v yc , v zc ), coordinates (X c , Y c , Z c ), the longitudinal component of the projectile swing angle the lateral component of the projectile swing angle rotation speed The identifying the ballistic parameters according to the obtained ballistic data specifically includes: Object to be identified, where the object to be identified is the initial value of reverse thrust and coincidence coefficients KR, Km; The identification criterion is written as: where n is the number of observation points, N2 is the number of unknown initial conditions, N23 = N2 + N3, and N3 is the number of unknown parameters. is the observed value, y ji0 is the estimated value, a k is the parameter to be identified, P jk is the sensitivity; In this way, the problem of missile and rocket parameter identification is transformed into an extreme value problem of seeking the parameter \(a\) to be identified k = \(a\) k0 + \(\Delta a\) k such that the criterion function \(\varepsilon\) reaches the minimum. To find \(\Delta a\) k , it is only necessary to solve the system of equations After arrangement, we get ΑΒ = C where Solving the above equation can obtain △a k , for the △a calculated in each step of iteration k , correct the original identification parameter a k = a k0 + △a k , when ε is the smallest, the iteration terminates, and the identification parameter obtained at this time is used as the parameter to be found. During the identification process, an improved recursive average filtering method is adopted to perform ballistic parameter convergence processing.

2. The inertial flight trajectory backstepping method according to claim 1, wherein Obtain ballistic data, specifically including: Perform Kalman filtering on the obtained radar data, Among them, the radar data includes the three-dimensional spatial coordinates of the projectile and the projectile velocity (v x , v y , v z ). Make a preliminary judgment on the type of projectile through the radar observation signal.

3. A terminal device for performing the method according to claim 1, characterized in that, Including: A preprocessing module for obtaining ballistic data; A parameter determination module for determining the projectile characteristic parameters and ballistic parameters; A parameter identification module for identifying the ballistic parameters according to the obtained ballistic data; A backward calculation module for performing backward calculation on the trajectory through the reduced-order rigid-body trajectory equation according to the identified parameters to obtain the starting point of the flight trajectory.

4. A storage medium, characterized in that, The storage medium stores a computer program, and after the computer program is loaded, the method described in any one of claims 1 to 2 can be executed.

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