Universal air alignment method for cannon-guided ammunition navigation system
By using satellite navigation data and adaptive weighted filters to calculate rolling angle and attitude angle in the gunfire guided ammunition navigation system, the problems of poor aerial alignment accuracy and long convergence time in the prior art are solved, and a high-precision and rapid convergence air alignment effect is achieved.
Patent Information
- Application Number
- CN202411939889.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-26
- Publication Date
- 2025-04-08
- Estimated Expiration
- 2044-12-26
AI Technical Summary
In the prior art, when shooting guided ammunition, the air alignment method has problems such as poor alignment accuracy and long alignment convergence time, especially in the environment of strong magnetic interference and ballistic maneuverability, it is difficult to meet the requirements.
A general air alignment method for gunfire guided ammunition navigation system is adopted to obtain navigation data through satellite navigation receivers, calculate the roll angle in real time, and use an adaptive weighting filter to estimate the roll angle and attitude angle to achieve air alignment.
It improves the accuracy and convergence speed of air alignment, can adapt to various rotary guided ammunition and ballistics, reduces the impact of ballistic maneuver on alignment, and enhances the versatility and adaptability of alignment.
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Figure CN119779358A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a universal aerial alignment method for a gun-launched guided ammunition navigation system, belonging to the technical field of navigation. Background Art
[0002] When the shell is fired, there are harsh environments such as high rotation and high overload, which makes the alignment of the strapdown inertial navigation system on the ground static base invalid before the shell is fired, and aerial alignment is required. The traditional roll angle initial alignment in the air uses a geomagnetic sensor to measure the roll angle, but this method is easily interfered by the outside world and cannot work in a strong magnetic interference environment, resulting in the navigation information having no reference value. There is also a gyro signal modulation method to calculate the roll angle, but this method has weak observability, especially in the absence of boost after the ammunition is launched, the observability is extremely weak, the convergence speed is slow, the calculation error is large, and it is affected by the gyro cumulative error.
[0003] With the emergence of new guided ammunition, the firing rate continues to increase and the ballistic characteristics are diversified. The above-mentioned aerial alignment methods are difficult to meet the requirements in terms of alignment accuracy, alignment timeliness, ballistic adaptability and versatility. Summary of the invention
[0004] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to provide a universal aerial alignment method for a gun-launched guided munition navigation system, and to determine the initial attitude, position and speed of the navigation system.
[0005] The technical solution of the present invention is: a universal air alignment method for a gun-launched guided ammunition navigation system, comprising:
[0006] After the artillery-launched guided munition is fired from the gun, its satellite navigation receiver begins to receive satellite navigation data, obtains the position and speed of the navigation system as well as the pitch angle and heading angle, and calculates the roll angle of the guided munition in real time, and assigns the roll angle at the initial moment to the inertial navigation roll angle;
[0007] A filter is constructed, and the error terms in the non-observed variables of the pitch, heading and roll attitude angles of the guided munition are estimated based on the pitch angle, heading angle and roll angle of the navigation system and the satellite navigation data. When the estimation process converges for a certain period of time or the fluctuation of the state variable is less than a certain threshold, the error terms are compensated on the corresponding measured values to complete the air alignment, and then the navigation system enters the navigation stage.
[0008] Further, the calculating the rolling angle of the guided munition includes:
[0009] Acceleration modulation and demodulation of roll angle The roll angle is modulated and demodulated using the accelerometer measurement value of the inertial navigation system;
[0010] Angular velocity modulation and demodulation of the roll angle uses the angular velocity meter measurement value of the inertial navigation to modulate and demodulate the roll angle;
[0011] According to the polarity and amplitude of the axial overload of the ammunition, the roll angle demodulated by acceleration and the roll angle demodulated by angular velocity are fused to generate an adaptive estimated roll angle.
[0012] Furthermore, the acceleration modulation and demodulation of the roll angle is Among them, the gravity acceleration vector g' b =g b -f b , g b is the acceleration vector measured by the accelerometer in the body coordinate system, f b is the centrifugal force measured by the accelerometer in the body coordinate system, x, y, z represent the axial direction, corresponding to the front upper left coordinate axis respectively.
[0013] Furthermore, the angular velocity modulation and demodulation of the roll angle is Among them, ω b,y is the measured value of the left gyro angular velocity of the projectile, ω b,z is the measured value of the upward gyroscopic angular velocity of the projectile, is the heading angle change rate, θ is the pitch angle, is the pitch angle change rate.
[0014] Furthermore, the adaptive estimated roll angle is in, The roll angle is modulated and demodulated for the angular velocity, is the roll angle k modulated by acceleration f is the adaptive coefficient, and the calculation formula is Where f b,x is the measured value of the axial accelerometer, f th To set the threshold parameters.
[0015] Furthermore, the filter observation variable is obtained by subtracting the inertial measurement vector composed of the three-dimensional attitude, three-dimensional position and three-dimensional velocity of the inertial navigation from the observation reference vector composed of the track pitch angle and track heading angle analyzed by the satellite navigation velocity, the roll angle calculated by the adaptive weighted coarse alignment method, the satellite navigation three-dimensional position and three-dimensional velocity, and is Z=[φ x φ y φ z δV E δV N δV U δP E δP N δP U ]; where the attitude error Speed error δV=V G -V INS , position error δP=P G -P INS, the state variables of the Kalman filter include the attitude error, velocity error, position error, gyroscope constant error, accelerometer constant error, angle of attack, and sideslip angle of the inertial navigation, that is,
[0016]
[0017] φ x ,φ y ,φ z are the attitude errors of inertial navigation, θ trace,G is the dead reckoning pitch angle of satellite navigation, θ INS is the inertial navigation pitch angle, To adaptively estimate the roll angle, γ INS is the inertial navigation roll angle, ψ trace,G is the dead reckoning heading angle of satellite navigation, ψ INS is the inertial navigation heading angle, V G Satellite navigation speed, V INS is the inertial navigation speed, P G is the satellite navigation position, P INS is the inertial navigation position, δV E is the eastward velocity error, δV N is the north velocity error, δV U is the celestial velocity error, δP E is the eastward position error, δP N is the north position error, δP U is the celestial position error, ε b,x is the forward gyro drift, ε b,y is the left gyro drift, ε b,z For upward gyro drift, For the forward addition table zero bias, It is the left direction plus zero bias. is the upward plus zero deviation, α is the angle of attack, and β is the sideslip angle.
[0018] Furthermore, the initial pitch angle and heading angle of the navigation system are provided by the track pitch angle and track heading angle resolved by satellite navigation velocity.
[0019] Furthermore, the initial position and speed of the navigation system are provided by the satellite navigation receiver after power-on or acquired through binding.
[0020] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of a universal air alignment method for a gun-launched guided munition navigation system are implemented.
[0021] A universal aerial alignment device for a gun-launched guided munition navigation system comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of a universal aerial alignment method for a gun-launched guided munition navigation system are implemented.
[0022] The advantages of the present invention compared with the prior art are:
[0023] (1) The present invention aims at the common problems of poor alignment accuracy and long alignment convergence time in the air alignment of the rotating and non-rotating guided munitions navigation system powered on after firing. An adaptive weighted roll angle estimation method is designed with the axial accelerometer measurement value as the independent variable, thereby realizing adaptive estimation of the roll angle. The method can adapt to various types of rotating guided munitions and various types of boosted or non-boosted trajectories, has the characteristics of good trajectory adaptability, and eliminates the influence and constraints of trajectory maneuvers on air alignment.
[0024] (2) The present invention adopts a two-step method for the general guided munition aerial alignment. The first step adopts an adaptive weighted coarse alignment method to calculate the initial roll angle of the guided munition. The second step adopts an extended dimension observation filtering fine alignment method to achieve roll angle estimation and attitude alignment. Compared with the traditional alignment method, more error terms such as the instrument zero position error after overload can be estimated, and it has the advantages of high accuracy and short alignment convergence time. BRIEF DESCRIPTION OF THE DRAWINGS
[0025] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:
[0026] Figure 1 The present invention provides a block diagram of the general aerial alignment method.
[0027] Figure 2 A flow chart of a general aerial alignment method is proposed for the present invention. DETAILED DESCRIPTION
[0028] In order to better understand the above technical scheme, the technical scheme of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical scheme of the present invention, rather than limitations on the technical scheme of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.
[0029] The following is a further detailed description of a general air alignment method for a gun-launched guided munition navigation system provided by an embodiment of the present invention in conjunction with the accompanying drawings. Figure 1 , the specific implementation methods may include:
[0030] The first step uses an adaptive weighted coarse alignment method to calculate the initial roll angle of the guided munition, which includes the following specific steps:
[0031] 1) The initial position and speed of the navigation system are provided by the satellite navigation receiver after power-on or obtained through binding;
[0032] 2) The initial pitch angle and heading angle of the navigation system are provided by the track pitch angle and track heading angle resolved by the satellite navigation velocity, or the initial shooting angle and shooting direction are obtained by binding;
[0033] 3) The initial roll angle of the navigation system is provided by an adaptive weighted roll angle estimation algorithm.
[0034] 4) The roll angle estimation algorithm of the rolling projectile with adaptive weighting includes three parts: acceleration modulation and demodulation of the roll angle, angular velocity modulation and demodulation of the roll angle, and adaptive weighting algorithm. The acceleration modulation and demodulation of the roll angle uses the measured value of the accelerometer of the inertial navigation system to modulate and demodulate the roll angle, and the angular velocity modulation and demodulation of the roll angle uses the measured value of the angular velocity meter of the inertial navigation system to modulate and demodulate the roll angle. The adaptive weighting algorithm uses an adaptive calculation formula according to the polarity and amplitude of the axial overload of the ammunition to fuse the acceleration demodulation roll angle and the angular velocity demodulation roll angle to generate an adaptive estimated roll angle. This adaptive weighted calculation method can ensure that the guided ammunition can obtain a good roll angle estimation accuracy in the extended range boost phase or the non-boost phase after launch, and weaken the influence of the ballistic maneuver on the roll angle estimation accuracy.
[0035] The second step uses the extended-dimensional observation filtering precision alignment method to accurately estimate the three-way attitude angle alignment error, gyroscope constant error, and accelerometer constant error of the guided munition, which specifically includes the following steps:
[0036] 5) The expanded-dimensional observation filtering precise alignment method uses a Kalman filter to estimate non-observed variables such as three-way attitude angle alignment error, gyroscope constant error, and accelerometer constant error. The observation variables of the Kalman filter are the observation reference vector composed of the track pitch angle and track heading angle analyzed by satellite navigation velocity, the roll angle calculated by the adaptive weighted coarse alignment method, the three-dimensional position of the satellite navigation, and the three-dimensional velocity, minus the inertial measurement vector composed of the three-dimensional attitude, three-dimensional position, and three-dimensional velocity of the inertial navigation. The state variables of the Kalman filter include the attitude error, velocity error, position error, angle of attack, and sideslip angle of the inertial navigation. The rapid and accurate estimation of the error terms in the non-observed variables is achieved by expanding the dimension of the attitude observation variables.
[0037] In the solution provided in the embodiment of the present invention, Figure 2 , including the following steps:
[0038] 1) After the artillery-launched guided ammunition is fired from the artillery, the navigation system is powered on, and the inertial navigation measurement unit, satellite navigation receiver and other components inside the navigation system start working.
[0039] 2) After a few seconds of startup, the satellite navigation receiver begins to receive satellite navigation data, which includes the three-dimensional position vector P measured by the satellite navigation. G =[P GE P GN P GU ] and the three-dimensional velocity vector V G =[V GE V GN V GU ].
[0040] 3) The first step of air alignment, adaptive weighted coarse alignment, is started.
[0041] 4) The initial position and speed of the navigation system are provided by the satellite navigation receiver after power-on or obtained through binding. The initial position P of the inertial navigation INS =P G , initial velocity V INS =V G .
[0042] 5) The initial pitch angle and heading angle of the navigation system are provided by the track pitch angle and track heading angle analyzed by the satellite navigation velocity. The initial pitch angle of the inertial navigation is Inertial navigation initial heading angle The track pitch angle or the initial shooting angle can also be obtained by binding.
[0043] 6) The initial roll angle of the navigation system is provided by an adaptive weighted roll angle estimation algorithm.
[0044] 7) The roll angle adaptive estimation algorithm of the rolling projectile includes three parts: acceleration modulation and demodulation of the roll angle, angular velocity modulation and demodulation of the roll angle, and an adaptive weighting algorithm. The acceleration modulation and demodulation of the roll angle utilizes the accelerometer measurement value of the inertial navigation to modulate and demodulate the roll angle, and the angular velocity modulation and demodulation of the roll angle utilizes the angular velocity meter measurement value of the inertial navigation to modulate and demodulate the roll angle. The adaptive weighting algorithm uses an adaptive calculation formula according to the polarity and amplitude of the axial overload of the ammunition to fuse the acceleration demodulation roll angle and the angular velocity demodulation roll angle to generate an adaptive estimated roll angle.
[0045] The above three parts run in parallel. The algorithm implementation of the three parts is introduced in detail below.
[0046] The formula for calculating the roll angle by acceleration modulation and demodulation is: where g' b =[g' b,x g' b,y g' b,z ] is the periodic variation part of the acceleration vector measured by the accelerometer in the body coordinate system, which shows the characteristics of periodic variation. The calculation formula is g' b =g b -f b , gb is the acceleration vector measured by the accelerometer in the body coordinate system, f b is the centrifugal force measured by the accelerometer in the body coordinate system. x, y, z represent the axial direction, corresponding to the front upper left coordinate axis respectively.
[0047] The roll angle calculation formula of angular velocity modulation and demodulation is: This formula is derived from the Euler equation, where ω b =[ω b,x ω b,x ω b,x ] is the angular velocity vector measured by the gyroscope in the body coordinate system.
[0048] The formula for calculating the roll angle using the adaptive weighted algorithm is: Where k f is the adaptive coefficient, and the calculation formula is Where f b,x is the measured value of the axial accelerometer, f th In order to set the threshold parameters, the adaptive weighted calculation method can ensure that the guided munition can obtain better roll angle estimation accuracy in the extended-range boost phase or the non-boost phase after launch, and weaken the influence of the roll angle estimation accuracy of ballistic maneuvers.
[0049] 8) After the adaptive weighted estimated roll angle is obtained, it is assigned to the inertial navigation roll angle, and the adaptive weighted coarse alignment algorithm continues to execute, but the calculated roll angle is no longer assigned to the inertial navigation roll angle.
[0050] 9) The second step of aerial alignment, the expanded-dimensional observation filtering and precise alignment algorithm, is started.
[0051] 10) The extended-dimensional observation filtering fine alignment method uses a Kalman filter to estimate non-observed variables such as the three-way attitude angle alignment error, the gyroscope constant error, and the accelerometer constant error. The observed variables of the Kalman filter are the observation reference vector composed of the track pitch angle and track heading angle analyzed by the satellite navigation velocity, the roll angle calculated by the adaptive weighted coarse alignment method, the satellite navigation three-dimensional position, and the three-dimensional velocity, minus the inertial measurement vector composed of the three-dimensional attitude, three-dimensional position, and three-dimensional velocity of the inertial navigation, that is, the observed variable Z = [φ x φ y φ z δV EδV N δV U δP E δP N δP U ], where the attitude error Speed error δV=V G -V INS , position error δP=P G -P INS , the state variables of the Kalman filter include the attitude error, velocity error, position error, gyroscope constant error, accelerometer constant error, angle of attack, and sideslip angle of the inertial navigation, that is, The Kalman filter used can adopt an open-loop design or a closed-loop design to realize the correction of the accumulated error of inertial navigation. Through the expansion of the above-mentioned observed variables, the error terms in the non-observed variables can be estimated quickly and accurately.
[0052] 11) When the fine alignment algorithm converges for a certain period of time or the fluctuation of the state variable is less than a certain threshold, the fine alignment three-way attitude angle alignment error, gyroscope constant error and accelerometer constant error are compensated on the inertial navigation attitude angle, gyroscope measurement value and accelerometer measurement value respectively.
[0053] 12) The expanded-dimensional observation filtering precise alignment algorithm is completed, and the entire aerial alignment process is completed, after which the navigation system enters the navigation phase.
[0054] The invention discloses a universal air alignment method for a gun-launched guided munition navigation system, wherein the adaptive weighted algorithm roll angle estimation algorithm in the adaptive weighted coarse alignment, f th The threshold parameter can be set to [0.1g, g] according to the ballistic characteristics, where g is the local gravity acceleration. Compared with the traditional aerial alignment method, the universal aerial alignment method proposed in this patent has more advantages in alignment accuracy, alignment timeliness, ballistic adaptability, and versatility, and can overcome the problems existing in the traditional aerial alignment method.
[0055] The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are executed on a computer, the computer executes Figure 2 The method described.
[0056] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.
[0057] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0058] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.
[0059] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.
[0060] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
[0061] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.
Claims
1. A universal aerial alignment method for a guided munitions navigation system, characterized in that: include: After the artillery-launched guided munition is fired from the gun, its satellite navigation receiver begins to receive satellite navigation data, obtains the position and speed of the navigation system as well as the pitch angle and heading angle, and calculates the roll angle of the guided munition in real time, and assigns the roll angle at the initial moment to the inertial navigation roll angle; Construct a filter and estimate the error terms in the non-observed variables of the pitch, heading and roll attitude angles of the guided munition based on the pitch, heading and roll angles of the navigation system and the satellite navigation data; When the estimation process converges for a certain period of time or the fluctuation of the state variable is less than a certain threshold, the error terms are compensated on the corresponding measurement values, the air alignment is completed, and then the navigation system enters the navigation stage.
2. A universal aerial alignment method for a gun-launched guided munition navigation system according to claim 1, characterized in that: The calculation of the rolling angle of the guided munition comprises: Acceleration modulation and demodulation of roll angle The roll angle is modulated and demodulated using the accelerometer measurement value of the inertial navigation system; Angular velocity modulation and demodulation of the roll angle uses the angular velocity meter measurement value of the inertial navigation to modulate and demodulate the roll angle; According to the polarity and amplitude of the axial overload of the ammunition, the roll angle demodulated by acceleration and the roll angle demodulated by angular velocity are fused to generate an adaptive estimated roll angle.
3. A universal aerial alignment method for a gun-launched guided munition navigation system according to claim 2, characterized in that: The acceleration modulation and demodulation roll angle is Among them, the gravity acceleration vector g' b =g b -f b , g b is the acceleration vector measured by the accelerometer in the body coordinate system, f b is the centrifugal force measured by the accelerometer in the body coordinate system, x, y, z represent the axial direction, corresponding to the front upper left coordinate axis respectively.
4. The universal aerial alignment method for a gun-launched guided munition navigation system according to claim 2, characterized in that: The angular velocity modulation and demodulation roll angle is Among them, ω b,y is the measured value of the left gyro angular velocity of the projectile, ω b,z is the measured value of the upward gyroscopic angular velocity of the projectile, is the heading angle change rate, θ is the pitch angle, is the pitch angle change rate.
5. The universal aerial alignment method for a gun-launched guided munition navigation system according to claim 2, characterized in that: The adaptive estimated roll angle is in, The roll angle is modulated and demodulated for the angular velocity, is the roll angle k modulated by acceleration f is the adaptive coefficient, and the calculation formula is Where f b,x is the measured value of the axial accelerometer, f th To set the threshold parameters.
6. The universal aerial alignment method for a gun-launched guided munition navigation system according to claim 1, characterized in that: The filter observation variable is obtained by subtracting the inertial measurement vector composed of the three-dimensional attitude, three-dimensional position and three-dimensional velocity of the inertial navigation from the observation reference vector composed of the track pitch angle and track heading angle analyzed by the satellite navigation velocity, the roll angle calculated by the adaptive weighted coarse alignment method, the satellite navigation three-dimensional position and three-dimensional velocity, and the inertial measurement vector composed of the three-dimensional attitude, three-dimensional position and three-dimensional velocity of the inertial navigation, which is Z=[φ x φ y φ z δV E δV N δV U δP E δP N δP U ]; where the attitude error Speed error δV=V G -V INS , position error δP=P G -P INS , the state variables of the Kalman filter include the attitude error, velocity error, position error, gyroscope constant error, accelerometer constant error, angle of attack, and sideslip angle of the inertial navigation, that is, φ x ,φ y ,φ z are the attitude errors of inertial navigation, θ trace,G is the dead reckoning pitch angle of satellite navigation, θ INS is the inertial navigation pitch angle, To adaptively estimate the roll angle, γ INS is the inertial navigation roll angle, ψ trace,G is the dead reckoning heading angle of satellite navigation, ψ INS is the inertial navigation heading angle, V G Satellite navigation speed, V INS is the inertial navigation speed, P G is the satellite navigation position, P INS is the inertial navigation position, δV E is the eastward velocity error, δV N is the north velocity error, δV U is the celestial velocity error, δP E is the eastward position error, δP N is the north position error, δP U is the celestial position error, ε b,x is the forward gyro drift, ε b,y is the left gyro drift, ε b,z For upward gyro drift, For the forward addition table zero bias, It is the left direction plus zero bias. is the upward plus zero deviation, α is the angle of attack, and β is the sideslip angle.
7. The universal aerial alignment method for a gun-launched guided munition navigation system according to claim 1, characterized in that: The initial pitch angle and heading angle of the navigation system are provided by the track pitch angle and track heading angle resolved by satellite navigation velocity.
8. The universal aerial alignment method for a gun-launched guided munition navigation system according to claim 1, characterized in that: The initial position and speed of the navigation system are provided by the satellite navigation receiver after power-on or acquired through binding.
9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.
10. A universal aerial alignment device for a gun-launched guided munition navigation system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.
Citation Information
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