A method for supporting a team to control a weapon without a human

By using a squad-supported unmanned fire control method, and employing recursive least squares and string-cutting methods to calculate firing parameters, the problem of accuracy in combat operations affected by the experience of combat personnel has been solved, and high-precision strikes by unmanned firearms have been achieved.

CN116294808BActive Publication Date: 2026-02-17NANJING UNIV OF SCI & TECH
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Patent Information

Application Number
CN202111564348.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-12-20
Publication Date
2026-02-17
Estimated Expiration
2041-12-20

AI Technical Summary

Technical Problem

In existing technologies, the accuracy of striking small moving targets by relying on the experience of combat personnel is affected by personal factors, thus impacting the strike results.

Method used

By adopting a squad-supported unmanned fire control method, the fire control system delay time is calibrated, the target trajectory is filtered using the recursive least squares method, and the firing parameters are calculated by combining the secant method and fitting function, thus achieving precise aiming and firing of unmanned firearms.

Benefits of technology

It improves the accuracy of unmanned firearms in striking small moving targets, reduces the difficulty of firepower strikes, and has universal applicability.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

The application provides a method for supporting an unmanned gun fire control by a team, and the method comprises the following steps: obtaining a lag time of a fire control system after calibration; the lag time comprises an image processing lag time and a fire control calculation function calculation time; determining a target from objects entering a sighting area; the fire control system filters a target track by using a recursive least square method for the target in different motion modes; obtaining a position of the target after lag compensation according to the system lag time and the target track; calculating a future point of the target by using a chord cutting method and a fitting function on the basis of the target after lag compensation, and determining firing elements of a gun tower at the point; the firing elements comprise a gun sight azimuth angle and a corrected gun sight elevation angle. The method provided by the application provides an unmanned gun fire control implementation method for aiming and shooting, replaces a process in which combat personnel uses a gun to aim at a target and strikes the target, reduces a difficulty of gun fire striking, and improves a gun fire striking precision.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of weapon system control technology, in particular to a method for team supporting unmanned gun fire control. BACKGROUND

[0002] Looking forward to the future war, the unmanned battlefield evolves into a trend at a higher level. The traditional combat system constructed by human beings will be possibly overturned, and the future battlefield confrontation will be dominated by unmanned combat system. At present, there is no better weapon for striking the small target (target moving speed is 0-30km / h) moving at a distance of 20m-1200m, and the main method is still to rely on the experience of combat personnel to strike such targets.

[0003] This method highly depends on the experience of combat personnel, and the personal factors greatly interfere with the accuracy of target striking, affecting the final striking result. SUMMARY

[0004] The present application provides a method for team supporting unmanned gun fire control, which can be used to solve the technical problem that the method highly depends on the experience of combat personnel and the personal factors greatly interfere with the accuracy of target striking.

[0005] The present application provides a method for team supporting unmanned gun fire control, which comprises:

[0006] After calibration, the lag time of the fire control system is obtained; the lag time includes the lag time of image processing and the calculation time of the fire control calculation function;

[0007] From the objects entering the aiming area, the target is determined, and the recursive least squares method is used to filter the target track by the fire control system for the target under different motion modes;

[0008] According to the system lag time and the target track, the position of the target after lag compensation is obtained;

[0009] Using the string cutting method and the fitting function, the future point of the target is calculated on the basis of the target after lag compensation, and the firing elements of the gun tower at the point are determined; the firing elements include the gun-eye azimuth angle and the corrected gun-eye elevation angle.

[0010] Optionally, after calibration, the lag time of the fire control system is obtained, which includes:

[0011] The gun barrel is parallel to the intelligent scope, when the target is static, the aiming crosshair in the intelligent scope is pressed on the target, and the gun barrel is opposite to the target;

[0012] During the equipment test, the lag time of the image processing is obtained;

[0013] The time of the fire control solution is determined according to the time of the fire control solution and the time of the control servo turntable turning to the target future point;

[0014] The time lag of the fire control system is determined according to the time lag of the image processing and the time of the fire control solution.

[0015] Optionally, the target is determined from the objects entering the aiming area, and the fire control system filters the target track by using the recursive least square method for the target in different motion modes, including:

[0016] After the current object is determined as the target, the fire control system receives a lock signal and controls the lock frame to lock the target;

[0017] The fire control system controls the execution module to perform coarse tracking on the target according to the position of the target in the scope;

[0018] After the execution module performs coarse tracking on the target, the motion form of the target is determined;

[0019] If the target is attacked, the target distance is obtained;

[0020] The target track is filtered by using the recursive least square method according to the target distance, the position of the target in the scope, and the motion form of the target.

[0021] Optionally, the position of the target after time lag compensation is obtained according to the time lag of the system and the target track, including:

[0022] The position of the target after time lag compensation is determined by using the following method:

[0023] (x t ,y t ,z t )=(v x ,v y ,v z )×Δt+(x0,y0,z0)

[0024] In the formula, (x0, y0, z0) is the position after filtering processing, (v x ,v y ,v z ) is the speed after filtering processing, Δt is the time lag of the system, and (x t ,y t ,z t ) is the position of the target after time lag compensation.

[0025] Optionally, the firing elements are determined according to the position of the target after time lag compensation by using the chord division method and the fitting function, including:

[0026] The independent variable is the gun sight distance and the dependent variable is the bullet flight time, and the fitting function is obtained by fitting the bullet firing table by the shooting table fitting method;

[0027] According to the position of the target after the delay compensation, the position of the gun tower, the filtered speed, and the fitting function of the bullet flight time, the position of the target future hit point is obtained by the chord cutting method;

[0028] According to the position relationship between the gun tower and the target future hit point, the gun sight elevation angle and the gun sight azimuth angle are obtained;

[0029] The independent variable is the gun sight distance and the dependent variable is the gun sight elevation compensation angle, and the fitting function is obtained by fitting the bullet firing table by the shooting table fitting method, and the gun sight elevation compensation angle of the target at the future hit point is obtained.

[0030] Optionally, the fitting function of the bullet flight time is determined by the following method:

[0031] t f =f tf (d F (T f ))=f tf (T f )

[0032] In the formula, t f is the flight time of the bullet from the position of the gun tower to the target after extrapolating T f time, f tf (·) is the bullet flight time shooting table fitting function, d F (T f ) is the gun sight distance;

[0033] Δα=f Δα (d F (T f ))=f Δα (T f )

[0034] In the formula, Δα is the gun sight elevation compensation angle, and f Δα (·) is the shooting table fitting function.

[0035] Optionally, the position of the target future hit point is determined by the following method:

[0036] T f∞ =f Tf (d F0 (p0,p m ),v0,f tf (T f ))

[0037] In the formula, T f∞is the time for the target to fly from the position after the delay compensation to the position of the future point of the target, f Tf is the secant iteration method function, d F0 is the distance function of the position of the gun tower and the target after the delay compensation, p0 is the position of the gun tower, p m is the position of the target after the delay compensation, v0 is the speed of the target after the filtering processing, f tf (T f ) is the fitting function of the bullet flight time table.

[0038] The position of the future hit point of the target is obtained according to the time for the target to fly from the position after the delay compensation to the position of the future point of the target, the position of the target after the delay compensation and the speed after the filtering processing.

[0039] The method provided by the application provides a set of unmanned gun fire control implementation method for shooting, replaces the process that the combat personnel uses the gun to aim at the target and attacks the target, reduces the difficulty of the gun fire attack, improves the gun fire attack precision, and the application has universality for various gun combat weapons. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The device schematic diagram for the team support unmanned gun fire control provided by the embodiment of the application is shown in the figure;

[0041] Figure 2 The intelligent sighting scope interface provided by the embodiment of the application is shown in the figure;

[0042] Figure 3 The flowchart of the method for the team support unmanned gun fire control provided by the embodiment of the application is shown in the figure;

[0043] Figure 4 The flowchart of the method for the team support unmanned gun fire control provided by the embodiment of the application is shown in the figure;

[0044] Figure 5 is a schematic principle flowchart provided by the embodiment of the application;

[0045] Figure 6 One of the simulation results provided by the embodiment of the application is shown in the figure;

[0046] Figure 7 The second simulation result provided by the embodiment of the application is shown in the figure;

[0047] Figure 8 The third simulation result provided by the embodiment of the application is shown in the figure;

[0048] Figure 9 The fourth simulation result provided by the embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the present application more clear, the embodiments of the present application will be described in further detail below with reference to the drawings.

[0050] As shown in Figure 1 , it is a schematic diagram of a device for team supporting unmanned gun fire control provided by the embodiments of the present application.

[0051] Figure 1 The device comprises an intelligent sighting scope 1, a gun rack 2, a high-low direction rotating table 3, an azimuth direction rotating table 4 and a carrier base 5. The intelligent sighting scope 1 has the functions of large and small field of view switching, infrared ranging and target locking. The gun rack 2 is used for placing various guns. The intelligent sighting scope 1 and the gun rack 2 are fixed together. The high-low direction rotating table 3 is responsible for controlling the angle transformation of the intelligent sighting scope and the gun rack in the high-low direction. The azimuth direction rotating table 4 is responsible for controlling the angle transformation of the intelligent sighting scope and the gun rack in the azimuth direction. The carrier base 5 can be an unmanned vehicle or a triangular support frame.

[0052] As shown in Figure 2 , it is an intelligent sighting scope interface provided by the embodiments of the present application. 21 in the figure is the central cross of the intelligent sighting scope, which is fixed and does not move. 22 (cross circle) is the ranging cross of the intelligent sighting scope, and the center position of the circle is the center of the ranging infrared. 23 is a target locking frame. 24 is a sighting cross division, that is, in actual use, when the target enters the center position of the sighting cross division, the fire can hit the target. 25 is the position of the target in the intelligent sighting scope.

[0053] As shown in Figure 3 , it is a flowchart of a method for team supporting unmanned gun fire control provided by the embodiments of the present application.

[0054] In step S301, the hysteresis time of the fire control system is obtained after calibration.

[0055] The hysteresis time comprises the hysteresis time of image processing and the calculation time of the fire control calculation function.

[0056] Specifically, the gun barrel is parallel to the intelligent sighting scope, when the target is stationary, the sighting cross division in the intelligent sighting scope presses the target, and the gun barrel is opposite to the target.

[0057] In the device test process, the hysteresis time of image processing is obtained.

[0058] The calculation time of the fire control calculation function is determined according to the calculation time of the fire control and the time of controlling the servo rotating table to rotate to the future point of the target.

[0059] The hysteresis time of the fire control system is determined according to the hysteresis time of image processing and the calculation time of the fire control calculation function.

[0060] It should be noted that the lag time of image processing refers to the time required for the intelligent scope to acquire the target and perform image analysis, which will cause the position of the target displayed in the intelligent scope to lag behind the actual position of the target. This lag time is generally between 60-100 ms. The fire control calculation time and the time for the rear control servo turret to turn to the target future point are accumulated within a calculation period as the fire control calculation function calculation time (fire control calculation is performed every 20 ms), wherein the fire control calculation time is very small, generally between 5-10 ms. The lag time of image processing can be obtained during testing of the device. Generally, the lag time of image processing and the fire control calculation function calculation time are taken as the lag time Δt of the gun fire control system during operation.

[0061] In step S302, the target is determined from the objects entering the aiming area, and the fire control system uses the recursive least squares method to filter the target track for the target in different motion modes.

[0062] Specifically, after the current object is determined as a target, the fire control system receives a locking signal and controls the locking frame to lock the target.

[0063] The fire control system controls the execution module to perform coarse tracking on the target according to the position of the target in the scope.

[0064] After the execution module performs coarse tracking on the target, the motion form of the target is determined.

[0065] If the target is to be attacked, the target distance is obtained.

[0066] According to the target distance, the position of the target in the scope, and the motion form of the target, the recursive least squares method is used to filter the target track.

[0067] For example, when an object enters the aiming area, the combat personnel determine whether it is a target. If it is a target, a locking signal is sent to the fire control system, and the fire control system controls the locking frame to lock the target. Then the fire control system controls the servo, i.e., the execution module, to perform coarse tracking on the target according to the position [α, β] of the target in the scope, and controls the servo to rotate the gun barrel (scope) so that the target is near the center position of the aiming (wherein α is the azimuth angle of the target and β is the elevation angle of the target). After the servo performs coarse tracking on the target, the combat personnel determine the motion form of the target (typical motion forms include static, uniform linear motion, and uniform circular motion). Then the combat personnel determine whether to attack, and if the target is to be attacked, the fire control system controls the range finder to measure the distance to the target, obtaining the target distance D. Then, according to the position [α, β] of the target in the scope and the assumption of the target motion made by the combat personnel, the target motion is estimated, i.e., the motion form of the target is determined.

[0068] Assuming that the target motion is uniform linear motion, the weighted least square method is used to filter the uniform linear motion to obtain the position (x, y, z) and velocity (v x ,v y ,v z ) of the filtered target in the earth coordinate system.

[0069] In step S303, the position of the target after time delay compensation is obtained according to the system time delay and the target track.

[0070] The position of the target after time delay compensation is determined by the following method:

[0071] (x t ,y t ,z t )=(v x ,v y ,v z )×Δt+(x0,y0,z0)

[0072] In the formula, (x0, y0, z0) is the position after filtering, (v x ,v y ,v z ) is the velocity (flight speed of the target) after filtering, Δt is the system time delay, and (x t ,y t ,z t ) is the position of the target after time delay compensation.

[0073] In step S304, the future point of the target is calculated based on the position of the target after time delay compensation by using the secant method and the fitting function, and the firing elements of the gun tower at the point are determined.

[0074] The firing elements include the gun azimuth and the corrected gun elevation.

[0075] Specifically, the fitting function of the independent variable (gun distance, the distance between the gun tower and the target point) and the dependent variable (bullet flight time, the flight time of the bullet from the gun tower to the target point) is obtained by fitting the firing table of the bullet by the firing table fitting method.

[0076] In the embodiment of the application, the fitting function of the bullet flight time is determined by the following method:

[0077] t f =f tf (d F (T f ))=f tf (T f )

[0078] In the formula, t f is the flight time of the bullet from the gun tower to the target extrapolated Tf Flight time after time, f tf (·) is the trajectory table fitting function for the projectile flight time, d F (T f () is the gun-to-eye distance.

[0079] Δα=f Δα (d F (T f ))=f Δα (T f )

[0080] In the formula, Δα is the gun sight elevation compensation angle, and f Δα (·) is the scatter table fitting function.

[0081] The future impact point of the target is obtained by fitting a function of the target's position after hysteresis compensation, the turret's position, the target's flight speed, and the ejection time, using the chord-cutting method.

[0082] like Figure 4 The diagram shown is a flowchart illustrating the process of determining the future hit point position using the chord-cutting method provided in this embodiment of the application.

[0083] Solving for the target future point is when f tf (T f )-T f When = 0(1), calculate the target extrapolation T. f The position after time. Because f tf (T f If is a curve function, then equation (1) is a curve equation. The method of secant is used to solve this curve equation.

[0084] Specifically, the secant method is derived from Newton's iteration method by approximating the derivative of the function using the slope of the chord. It assumes that the curve equation f(x) = 0 has a unique root on [a, b], and f(x1), f(x2), ..., f(x... n+1 If all ) are within [a, b], then the iterative formula for the secant method is:

[0085]

[0086] After a finite number of iterations, f(x) n → 0.

[0087] From (1) and (2), we can obtain:

[0088]

[0089] (3) Conditions for establishment

[0090] t f (n)-t f (n-1)+Tf (n-1)-T f (n)≠0,n=1,2,... (4)

[0091] where, T f (n) represents the time that the target travels from the current point at the n th iteration, t f (n) = f tf (T f (n)). T f (n), T f (n-1) represent two different initial values of the independent variable in the n th iteration, respectively.

[0092] When using the secant method to solve the future hit point, the steps are as follows:

[0093] a step: using the secant method to iterate the future hit point, first need to input four initial values, namely the four initial values when the iteration step number n = 1: T f (n), T f (n-1), t f (n), t f (n-1). Among them, T f (0) = 0, T f (1) = 0.001, then calculate t f (0), t f (1).

[0094] b step: T f (n-1), T f (n), t f (n-1), t f (n), n = 1,2,... are brought into formula (4) to judge whether the condition of formula (3) is established, if it is satisfied, then bring into formula (3) to calculate T f (n+1). If it is not satisfied, t f (n-1) = t f (n-1) + 0.001, n = 1,2,... are brought into formula (4).

[0095] c step: according to T f (n+1) obtained in b step, the corresponding t f (n+1) is calculated by table fitting.

[0096] d step: let Δt f = T f (n+1) - t f (n+1), if | Δt f | > T set , it is explained that the precision has not been reached, then let T f (n-1) = Tf (n), T f (n) = T f (n+1), t f (n-1) = t f (n), t f (n) = t f (n+1) is brought back to b, c step in turn to calculate the next T f (n+1) and t f (n+1) and calculate Δt f , repeat c step judgment, when |Δt f | < T set out of iteration, get the time T f (n+1) required for the target to hit the future point, then get the future hit point, and then according to the position relationship between the gun tower and the future hit point, combined with the high and low compensation angle calculated by bringing T f (n+1) into the firing table fitting function, obtain the firing elements of the gun tower.

[0097] In the embodiment of the application, the position of the target future hit point is determined by the following method:

[0098] T f∞ = f Tf (d F0 (p0, p m ), v0, f tf (T f ))

[0099] In the formula, T f∞ is the time for the target to fly from the position after the delay compensation to the position of the target future point, f Tf (·) is the secant iteration method function, d F0 is the distance function between the gun tower and the target after the delay compensation, p0 is the position of the gun tower, p m is the position of the target after the delay compensation, v0 is the speed of the target after the filtering processing, and f tf (T f ) is the projectile flight time firing table fitting function.

[0100] According to the time for the target to fly from the position after the delay compensation to the position of the target future point, the position of the target after the delay compensation, and the speed after the filtering processing, the position of the target future hit point is obtained.

[0101] According to the position relationship between the gun tower and the target future hit point, the gun-eye high and low angle and the gun-eye azimuth angle are obtained.

[0102] The independent variable is the gun sight distance and the dependent variable is the gun sight height compensation angle, and the gun sight height compensation angle of the target at the future hit point is obtained by fitting the gun sight table by the gun table fitting method.

[0103] As shown in Fig. 5, it is a principle schematic flow chart provided by the embodiment of the application. Wherein, Figure 5.1 The target enters the aiming area, and the coarse tracking stage is performed. Figure 5.2 The laser ranging measures the target in the coarse tracking mode, the fire instruction is allowed to be obtained, and the fine tracking stage is started. Figure 5.3 The target future point is aimed at, and the attack stage is started.

[0104] The method provided by the application is described below in combination with the embodiments. It is assumed that the initial speed of the bullet is 800 m / s, T set = 0.0001 s. It is assumed that the image lag time of the target 1 and the target 2 is 100 ms, the fire control calculation time of the fire control system and the servo control gun muzzle rotation time is less than 40 ms. It is assumed that the target 1 is 500 m away from the unmanned gun fire control weapon station and moves at a speed of 10 km / h and 30 km / h respectively, and the target track is 50 m away from the weapon station. It is assumed that the target 2 is 300 m away from the unmanned gun fire control weapon station and moves at a speed of 10 km / h and 30 km / h respectively, and the target track is 70 m away from the weapon station. The simulation results are as follows:

[0105] The target 1 moves at a speed of 10 km / h, and the simulation results are as shown in Fig. Figure 6 .

[0106] The target 1 moves at a speed of 30 km / h, and the simulation results are as shown in Fig. Figure 7 .

[0107] The target 2 moves at a speed of 30 km / h, and the simulation results are as shown in Fig. Figure 8 .

[0108] The target 2 moves at a speed of 10 km / h, and the simulation results are as shown in Fig. Figure 9 .

[0109] The method provided by the application provides a set of aiming and shooting unmanned gun fire control implementation method, which replaces the process of using the gun by the combat personnel to aim at the target and attack the target, reduces the difficulty of the gun fire attack, improves the gun fire attack precision, and the application has universality for various gun combat weapons.

[0110] Those skilled in the art can clearly understand that the technical solution in the embodiments of the present application can be realized by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution in the embodiments of the present application can be embodied in the form of a software product in essence or in the form of a part of the prior art that makes a contribution. The computer software product can be stored in a storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the method described in each embodiment or some part of the embodiments of the present application.

[0111] The same or similar parts among the various embodiments in the specification can be referred to each other. In particular, for the service building device and the service loading device embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the description in the method embodiments.

[0112] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A method of team supporting an unmanned gun fire control, characterized in that, The method comprises: After calibration, the hysteresis time of the fire control system is obtained; the hysteresis time comprises the hysteresis time of image processing and the calculation time of a fire control calculation function; A target is determined from objects entering a sighting area, and the fire control system filters a target track by using a recursive least square method for the target in different motion modes; According to the hysteresis time of the system and the target track, a position of the target after hysteresis compensation is obtained; By using a chord cutting method and a fitting function, a future point of the target is calculated on the basis of the position of the target after hysteresis compensation, and firing elements of a gun turret and the point are determined; the firing elements comprise a gun sight azimuth angle and a gun sight elevation angle after correction; By using a chord cutting method and a fitting function, the firing elements are determined according to the position of the target after hysteresis compensation, and comprise: A fitting function with a gun sight distance as an independent variable and a bullet flight time as a dependent variable is obtained by fitting a bullet firing table by using a firing table fitting method; A position of a future hit point of the target is obtained by using a chord cutting method according to the position of the target after hysteresis compensation, a position of the gun turret, a filtered speed, and the fitting function of the bullet flight time; A gun sight elevation angle and a gun sight azimuth angle are obtained according to a positional relationship between the gun turret and the future hit point of the target; A fitting function with a gun sight distance as an independent variable and a gun sight elevation compensation angle as a dependent variable is obtained by fitting a bullet firing table by using a firing table fitting method, and a gun sight elevation compensation angle of the target at the future hit point is obtained. The fitting function of the bullet flight time is determined by the following method: ; wherein Tf is the time of flight of the projectile from the location of the gun turret to the target, is the time of flight of the projectile from the location of the gun turret to the target, is the gun-target distance; ; wherein is the gun elevation angle, is the firing table fitting function; The position of the future hit point of the target is determined by the following method: ; wherein, is the time for the target to fly from the position after the delay compensation to the position where the target future point is located, is the secant iteration method function, is the distance function of the gun turret and the position of the target after the delay compensation, is the position of the gun turret, is the position of the target after the delay compensation, is the speed of the target after the filtering processing, is the projectile flight time table fitting function; According to a time for the target to fly from the position after hysteresis compensation to the position of the future hit point, the position after hysteresis compensation of the target, and the filtered speed, the position of the future hit point of the target is obtained.

2. The method of claim 1, wherein, After calibration, the hysteresis time of the fire control system is obtained, comprising: The gun muzzle is parallel to the intelligent sighting scope, and when the target is stationary, the intelligent sighting scope is pressed on the target by the sighting cross division, and the gun muzzle is opposite to the target; During the device test, the hysteresis time of image processing is obtained; The calculation time of the fire control calculation function is determined according to the calculation time of the fire control and the time for the control servo turntable to turn to the future hit point of the target; The hysteresis time of the fire control system is determined according to the hysteresis time of image processing and the calculation time of the fire control calculation function.

3. The method of claim 1, wherein, A target is determined from objects entering a sighting area, and the fire control system filters a target track by using a recursive least square method for the target in different motion modes, comprising: After the current object is determined as a target, the fire control system receives a locking signal and controls a locking frame to lock the target; The fire control system controls an execution module to perform coarse tracking on the target according to a position of the target in the sighting scope; After the execution module performs coarse tracking on the target, a motion form of the target is determined; If the target is attacked, a target distance is obtained; According to the target distance, the position of the target in the sighting scope, and the motion form of the target, a target track is filtered by using a recursive least square method.

4. The method of claim 1, wherein, According to the hysteresis time of the system and the target track, a position of the target after hysteresis compensation is obtained, comprising: The position of the target after hysteresis compensation is determined by the following method: ; In the formula, is the position after filtering processing, is the velocity after filtering processing, is the system time delay, is the target position after time delay compensation.