Equation-based precise solution of spatial azimuth of moving target

Abstract

This invention relates to an equation-based method for accurately solving the spatial azimuth angle of a moving target. In a given CPI (Central Impact Point), based on the platform's three-dimensional attitude angles and the servo's azimuth and elevation angles, a rotation transformation matrix is ​​obtained between the northeast-sky coordinate system, the carrier coordinate system, and the antenna coordinate system. The spatial azimuth angle of the target point is calculated using conventional methods and used for subsequent value removal. The spatial azimuth angle of the moving target point in the northeast-sky coordinate system is set as an unknown. The coordinates in the antenna coordinate system are obtained through coordinate rotation, while the azimuth angle of the moving target point in the antenna coordinate system is known. Based on this relationship, the spatial azimuth angle of the target point can be accurately solved by setting up equations. The results of the conventional method are then removed for value removal to obtain the accurate spatial azimuth angle of the target point. When there is no intersection point and no solution, the result of the conventional method is used as the final result.

Description

Technical Field

[0001] This invention belongs to the field of radar moving target detection technology, specifically relating to a method for accurately solving the spatial azimuth angle of a moving target based on equations. Background Technology

[0002] In modern radar, moving target detection is a crucial function. Modern radar moving target detection involves transmitting signals to the detection area, processing them using pulse Doppler to obtain the target point's slant range and azimuth relative to the aircraft's coordinate system, and combining this with the aircraft's instantaneous altitude to obtain the target point's spatial coordinates in a northeast-northeast celestial coordinate system with the aircraft as the origin. This can be considered a single observation of the target's spatial position. Combined with predicted values, adaptive filtering is used to track the target's spatial position. The target point's spatial coordinates in the northeast-northeast celestial coordinate system with the aircraft as the origin are typically represented in spherical coordinates and include slant range, spatial azimuth, and spatial elevation angles. As the initial input for adaptive filtering, the accuracy of the target point's spatial coordinates directly determines the tracking accuracy of the target's spatial position.

[0003] To improve the antenna beam cutoff capability and adjustment flexibility, phased array antennas are typically used. During moving target detection, the control antenna beam scans the observation area sequentially across each CPI (Cost Per Pixel). For the echo within each CPI, pulse Doppler processing is performed to obtain the target point's slant range and azimuth error angle. Based on the phased array antenna's beam angle, the servo's azimuth and elevation angles, and the aircraft's three-dimensional attitude angles, the target point's northeast-sky coordinates are further obtained. This is equivalent to obtaining a single measurement of the moving target's position. Then, based on a prediction model, a predicted value for the moving target's position in the next CPI is obtained. This predicted value is then used to obtain a weighted filtered result of the target point's position, and this process continues to track the target point.

[0004] Typically, when calculating the spatial azimuth of a moving target within a given CPI (Cost Per Target), the slant range and azimuth in the antenna coordinate system are obtained based on the radar's measured slant range, beam angle, and error angle reported by the signal receiver. The elevation angle is approximated as 0. The antenna coordinates of this target point are then transformed to the northeast-northeast coordinate system through coordinate rotation. The resulting spatial azimuth is then used as the spatial azimuth of the target point. This method is equivalent to projecting the target point's pointing vector onto the xy-plane in the antenna coordinate system, calculating the spatial azimuth of the projected vector in the northeast-northeast coordinate system through coordinate rotation, and using this spatial azimuth as the input to the tracking program. However, with increasing demands for moving target detection accuracy, specific requirements have been set for the magnitude and direction of the moving target's velocity in project comparison tests. Especially in many model projects, the goal is not merely to meet the standards, but to achieve even better results. Therefore, this approximation is insufficient, necessitating a more precise solution for the spatial azimuth of the moving target. Summary of the Invention

[0005] Technical problems to be solved

[0006] In moving target detection, it is necessary to determine the northeast-sky coordinates of the moving target point. In radar data processing, the target point's coordinates are typically represented in a spherical coordinate system, requiring the slant range, azimuth, and elevation angles. The slant range can be obtained through radar measurement, and the elevation angle can be calculated based on the platform height and slant range; only the azimuth angle remains unknown. The conventional method involves projecting the target point's antenna coordinates (i.e., the pointing vector) onto the xy-plane, rotating the coordinates, and calculating the azimuth angle of the projected vector in the northeast-sky coordinate system. This azimuth angle is then used as the input azimuth angle for the target point in the tracking program. However, this method becomes significantly inaccurate when the detection distance is long or the platform vibrates severely, failing to meet the requirements of comparative testing.

[0007] To avoid the shortcomings of existing technologies, this invention proposes an accurate solution method for the spatial azimuth of a target point by using rotational transformation and combining it with the concept of equations. This method can obtain the analytical solution for the spatial azimuth of the target point.

[0008] Technical solution

[0009] A method for accurately solving the spatial azimuth angle of a moving target based on equations, characterized by the following steps:

[0010] Step 1: In a given CPI, based on the platform's three-dimensional attitude angles α, β, γ and the servo's azimuth angle θ az Pitch angle θ el We obtain the rotation transformation matrix H between the northeast celestial coordinate system and the antenna coordinate system;

[0011] H=(H an2plat ) -1 (H plat2enu ) -1

[0012] H plat2enu =C(α)Y(β)R(γ)

[0013] H an2plat =C(θ) az -90)R(θ el )

[0014] Step 2: Based on the radio beam angle θ of the target point e and error angle θ σ Calculate the rectangular coordinates of the unit pointing vector of the moving target point B:

[0015] u an =[cos(-(θ)]e +θ σ )),sin(-(θ e +θ σ )),0] T

[0016] Calculate the unit pointing vector of the moving target point B in the northeast-northeast coordinate system based on the rotation transformation matrix H obtained in step 1:

[0017] u enu =H -1 u an

[0018] According to u enu Solving for the azimuth angle θ using the first component x′ and the second component y′ enu_0 =angle(y′+x′*j) / π*180;

[0019] Step 3: Let

[0020]

[0021]

[0022]

[0023]

[0024] θ'=θ e +θ σ

[0025] in The pitch angle;

[0026] Then a sinθ enu +b cosθ enu +c = 0;

[0027] Let x = sinθ enu y=cosθ enu The above problem is equivalent to:

[0028]

[0029] When 4a 2 c 2 -4(a 2 +b 2 (c) 2 -b 2 When )≥0, there is a solution.

[0030] but

[0031] Substitute x and y into x = sinθenu y=cosθ enu Two θ enu ; Choice with θ enu_0 Approximate θ enu As a final result;

[0032] No solution, use θ enu_0 As the final result.

[0033] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0034] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0035] Beneficial effects

[0036] This invention provides an accurate solution for the spatial azimuth of a target point. The northeast azimuth of the target point is set as an unknown. Equations are established based on the known azimuth of the target point in the antenna coordinate system, and then solved to obtain an analytical solution. Here, we will explain the meaning of "accurate." The solution for the spatial azimuth of the target point is based on measurements such as the platform's three-dimensional attitude, antenna azimuth and elevation angles, platform height, target slant range measured by radar, radio beam angle, and azimuth error angle reported by the signal receiver. The accuracy of this invention refers to the ability to obtain a mathematically analytical solution for the spatial azimuth of the target point using these measurements.

[0037] This invention first describes the various coordinate systems encountered in the problem and gives the rotational relationships between them. Then, it presents a conventional method for obtaining the spatial azimuth of the target point. Next, it elaborates and derives the exact solution in detail and gives the algorithm flow. Finally, it compares the experimental data results of the conventional method and the exact solution. The experimental data shows that the final tracking result obtained by the method of this invention is better than the tracking result of the conventional method. Attached Figure Description

[0038] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0039] Figure 1 Antenna coordinate system diagram;

[0040] Figure 2 A schematic diagram of the antenna coordinate system in the conventional method;

[0041] Figure 3 A comparison of spatial azimuth error curves between conventional methods and the precise solution of this invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0043] This invention proposes an accurate solution method to obtain the analytical solution for the spatial azimuth of all target points in the CPI. This invention sets the spatial azimuth of the moving target point in the northeast-northeast coordinate system as an unknown. The coordinates in the antenna coordinate system are obtained based on rotation relationships, while the azimuth of the moving target point in the antenna coordinate system is known. Based on this relationship, the spatial azimuth of the target point can be accurately solved by setting up equations. The specific steps are as follows:

[0044] 1) In a certain CPI, based on the platform's three-dimensional attitude angles and the servo's azimuth and pitch angles, the rotation transformation matrix between the northeast sky coordinate system, the carrier coordinate system, and the antenna coordinate system is obtained.

[0045] 2) The spatial azimuth of the target point is calculated using the conventional solution method and used for subsequent de-rotation.

[0046] 3) Set the spatial azimuth of the moving target point in the northeast-northeast coordinate system as an unknown. Obtain the coordinates in the antenna coordinate system through coordinate rotation. The azimuth of the moving target point in the antenna coordinate system is known. Based on this relationship, the spatial azimuth of the target point can be accurately solved by setting up equations. Through derivation, the final equation can be equivalent to solving the problem of finding the intersection point of a straight line and a unit circle. Since there are often two intersection points, two spatial azimuth results can be obtained.

[0047] 4) Based on the result of the conventional method in step (2), remove the bad values ​​and obtain the accurate result of the spatial azimuth of the target point; when there is no intersection point and no solution, use the result of the conventional method as the final result.

[0048] 1. Three coordinate systems and rotation matrices

[0049] This invention involves three coordinate systems: the antenna coordinate system, the carrier aircraft coordinate system, and the northeast-sky coordinate system, which will be described one by one below.

[0050] The technical terms involved in this invention are: enu is an abbreviation of east, north, and up, representing the northeastern sky; plat represents a platform or carrier aircraft; and an is taken from the first two letters of antenna, representing an antenna.

[0051] Antenna Coordinate System: Modern radar typically uses phased array antennas, where the antenna beam scans along the azimuth of the antenna surface. The antenna coordinate system is defined with the center of the antenna surface as the origin, the normal direction as the x-axis, and the upward direction as the z-axis. According to the right-hand rule, the y-axis is located to the left of the antenna surface, as shown below. Figure 1 As shown.

[0052] Aircraft Coordinate System: For an aircraft platform, the fuselage center is the origin, the nose direction is the y-axis, and the top of the aircraft is the z-axis. According to the right-hand rule, the right side of the aircraft is the x-axis. This definition is because it's generally necessary to measure the platform's three-dimensional attitude angles using an inertial navigation system (INS). The INS itself has a coordinate system, and the heading angle measured by the INS is essentially the heading angle represented by the y-axis of the INS coordinate system. However, in practical applications, the heading angle in the nose direction needs to be measured. Therefore, when installing the INS on the aircraft platform, the y-axis of the INS is generally oriented towards the nose, and the z-axis towards the top of the aircraft. Naturally, the right side of the aircraft is the x-axis of the INS. The aircraft coordinate system is defined similarly, and the rotational relationship between the aircraft coordinate system and the north-south coordinate system can be directly determined using the three-dimensional attitude angles measured by the INS.

[0053] Northeast-Northeast coordinate system: East is the x-axis, North is the y-axis, and the sky is the z-axis.

[0054] In this invention, the spherical coordinates of a certain coordinate system are represented by slope distance, azimuth, and elevation angle. The azimuth angle is defined with 0° on the y-axis and rotation towards the x-axis as positive. The elevation angle is defined with the xy-plane as 0° and upward as positive. For example, the azimuth angle can be calculated using the first and second components of a three-dimensional vector. Let the three-dimensional vector be [xyz], then its azimuth angle θ = angle(y + x*j) / π*180, where angle() is a function in MATLAB for calculating the complex argument. The range of the angle() function is -180° to 180°. If needed, the azimuth angle can be further converted to a range of 0-360°. Here, the definition of azimuth angle differs from the definition of azimuth angle in spherical coordinates as commonly found in mathematics textbooks.

[0055] Combining the three-dimensional attitude angles of the inertial navigation system and the azimuth and elevation angles of the antenna servo, the rotational relationships between the northeast sky coordinate system and the carrier coordinate system, and between the carrier coordinate system and the antenna coordinate system, are given.

[0056] Let the aircraft heading angle, pitch angle, and roll angle measured by inertial navigation be α, β, and γ, respectively, and the corresponding rotation matrices be C(α), Y(β), and R(γ).

[0057]

[0058]

[0059]

[0060] Since C(α), Y(β), and R(γ) are all rotation matrices, their respective inverse matrices satisfy the following relationship: (C(α)) -1 =C(-α),(Y(β)) -1 =Y(-β),(R(γ)) -1 =R(-γ).

[0061] Suppose that the coordinates of the same vector in the northeast celestial coordinate system and the aircraft coordinate system are z and z respectively. enu and z plat Based on the definitions of rotation matrices and three-dimensional attitude angles in matrix theory, we can conclude that:

[0062] z enu =C(α)Y(β)R(γ)z plat (4)

[0063] Let H plat2enu =C(α)Y(β)R(γ) (5)

[0064] Then z enu =H plat2enu z plat (6)

[0065] According to the theory of inverse matrices, we can obtain:

[0066] z plat =R(-γ)Y(-β)C(-α)z enu (7)

[0067] Assume the azimuth angle of the servo is θ. az With the machine head as 0°, looking down from above, clockwise is the positive direction. The servo's pitch angle is θ. el With the horizontal direction as 0° and downward as positive.

[0068] Suppose that the coordinates of the same vector in the aircraft coordinate system and the antenna coordinate system are z and z respectively. plat and z an Based on the definitions of rotation matrices and three-dimensional attitude angles in matrix theory, we can conclude that:

[0069] z plat =C(θ) az -90)R(θ el )z an (8)

[0070] Let H an2plat =C(θ) az -90)R(θ el (9)

[0071] Then z plat =H an2plat z an

[0072] Because θ az =0° is the direction of the machine head, and turning to the right is positive. When θ az When θ = 90°, the aircraft coordinate system and the antenna coordinate system coincide. When all input angles in the rotation matrix are 0, the aircraft coordinate system and the antenna coordinate system coincide, so θ in equation (8) is equal to 0. az 90° needs to be subtracted.

[0073] 2. Conventional methods

[0074] like Figure 2 As shown, the rectangular coordinate system is the antenna coordinate system, the elliptical region is the area on the ground illuminated by the antenna beam, ray OA is the direction of the antenna beam center, and point A is the intersection of the beam center direction and the ground. Since the phased array antenna scans along the azimuth of the antenna surface, point A lies in the xy plane of the antenna coordinate system. Assuming point A is in spherical coordinates... Where R is obtained by radar measurement, Assuming the antenna surface normal direction is 0°, and scanning to the right is the positive direction, the positive direction of the error angle θ is related to θ'. e If they are consistent, then θ an The radio beam angle θ of the phased array antenna e Error angle θ obtained by Doppler processing of the signal source σ The sum is obtained. Point B is another point in the antenna illumination area. The slant range of point B is different from that of point A. In the spherical coordinates of point B, the slant range is known, θ. an This is obtained from the current CPI beam angle and the error angle at point B. If the xy plane of the antenna coordinate system is exactly parallel to the horizontal plane, and the z-axis points upwards, it can be calculated using the slant range and platform height. However, due to factors such as airflow and vibration, the xy plane of the antenna coordinate system is often not parallel to the horizontal plane, therefore It is unknown.

[0075] The conventional approach involves using radar measurements of the slant range and the radio beam angle θ to determine the location of a moving target at different distances. e Error angle θ obtained from the signal source σ To obtain R and θ an It is approximately considered that All are 0, and this is used as the antenna coordinate system pointing vector of the target point. This is equivalent to projecting the coordinates of the antenna coordinate system of the moving target point onto the xy plane, rotating and transforming the projection vector to the northeast-sky coordinate system, and obtaining the spatial azimuth angle of the projection vector in the northeast-sky coordinate system spherical coordinates. This is used as the spatial azimuth angle of the target point input into the tracking program.

[0076] The following example illustrates the conventional method. Assume that the moving target point B is any point within the antenna illumination area, and its spherical coordinates in the antenna coordinate system are... It is approximated that its spherical coordinates are [R, θ] e +σ,0], now let's perform coordinate rotation. Because what we need to find is [R,θ] e The spatial azimuth angle of the vector after rotation to the northeast-central coordinate system [+σ,0] is given. Therefore, during the rotation, only the direction of the target point needs to be considered; that is, only the unit vector needs to be used for rotation, and the R information is not required. The rectangular coordinates of the unit pointing vector of point B are:

[0077] u an =[cos(-(θ)] e +θ σ )),sin(-(θ e +θ σ )),0] T

[0078] Then, the unit pointing vector u of point B in the northeast celestial coordinate system. enu =H plat2enu H an2plat u an , by u enu The first and second components can be used to calculate the required spatial azimuth angle θ. enu .

[0079] 3. Precise solution for the spatial azimuth of a moving target

[0080] As can be seen from the above description, the conventional method has certain approximations for each target point.

[0081] Since the slant range and elevation angle of the target point's northeast celestial coordinates are known, we only need to calculate the spatial azimuth angle to obtain the target point's northeast celestial coordinates. In the target point's antenna coordinate system spherical coordinates, the slant range and azimuth angle are known, but the elevation angle is unknown. Therefore, we can assume that the spatial azimuth angle of the target point's northeast celestial coordinates is unknown, calculate the target point's northeast celestial coordinates, obtain the target point's antenna coordinate system spherical coordinates through coordinate rotation, and solve the equations based on the known azimuth angle in these spherical coordinates. This is the core idea of ​​the exact solution method of this invention.

[0082] Let θ be the spatial azimuth angle of the target point in the northeast celestial sphere. enuThe pitch angle is obtained from the slant range and the aircraft altitude. Let u be the unit pointing vector of the target point in the northeast celestial sphere and the antenna coordinate system. enu u an ,but

[0083]

[0084] u enu =H plat2enu H an2plat u an

[0085] Here, we need to explain equation (10). In mathematics textbooks, the argument is usually defined with the x-axis as 0 and counterclockwise as the positive direction. Therefore, for a vector with amplitude R and argument θ, the rectangular coordinates are [R cosθ, R sinθ]. However, in equation (10), the amplitude... The sine component is the x-component, and the cosine component is the y-component. This is because, as emphasized earlier, the definition of azimuth in the coordinate system of this invention is different from the definition of argument in ordinary mathematics books.

[0086] That is (H) an2plat ) -1 (H plat2enu ) -1 u enu =u an

[0087] Let H = (H an2plat ) -1 (H plat2enu ) -1 (11)

[0088] Then Hu enu =u an

[0089] make

[0090] In practice, the components of H above are calculated through programming. For a given CPI, H is the same for all target points and only needs to be calculated once.

[0091] but

[0092] According to u an The spherical coordinate azimuth angle is θ e +θ σ For simplicity, let θ' = θ e +θ σ ,but Where sinθ enu cosθ enuFor the unknown variable, and the others known, we can simplify to get...

[0093]

[0094] make

[0095]

[0096] Then a sinθ enu +b cosθ enu +c=0

[0097] Let x = sinθ enu y=cosθ enu The above problem is equivalent to:

[0098]

[0099] In other words, we need to find the two intersection points of the unit circle and the straight line. The angle between the two intersection point vectors, with the y-axis as 0 and clockwise as positive, is the required θ. enu Of course, only one solution is consistent with the actual situation, which can be determined by the results of conventional solutions.

[0100] make Substitute x 2 +y 2 =1, and simplifying, we get

[0101] (a 2 +b 2 )x 2 +2acx+(c 2 -b 2 ) = 0

[0102] When 4a 2 c 2 -4(a 2 +b 2 (c) 2 -b 2 When )≥0, there is a solution.

[0103] but

[0104] Then, based on ax + by + c = 0, calculate the corresponding y, and then you can calculate θ. enu For cases where there is no solution, the result of the conventional method can be directly used.

[0105] The following are the steps for accurately solving the spatial azimuth angle of a target point in the northeast-north-sky coordinate system:

[0106] 1) In a given CPI, the current three-dimensional attitude angles α, β, γ of the aircraft platform and the azimuth angle θ of the servo. az and pitch angle θel Calculate H and H according to equations (5), (9), and (11). -1 ;

[0107] 2) Based on the target point's beam angle and error angle, and H... -1 Calculate H -1 [cos(-(θ e +θ σ )),sin(-(θ e +θ σ )),0] T The result is then used to obtain the result θ from the conventional solution based on the first and second components of the result. enu_0 ;

[0108] 3) Calculate a, b, and c according to equation (12), then calculate x according to equation (14), then calculate y, and finally calculate the two θ values. enu If equation (14) is less than 0, there is no solution, and θ is used. enu_0 As a final result;

[0109] 4) Choose with θ enu_0 Approximate θ enu As the final result.

[0110] In the above method, for all points in a given CPI, H and H -1 It is the same, and only needs to be calculated once. That is to say, step (1) only needs to be calculated once for all points.

[0111] 4. Verification using measured data

[0112] The following verification is performed using measured data. Forty consecutive tracking cycles are selected. Based on the GPS values ​​provided by the test vehicle during the field test and the GPS values ​​of the carrier aircraft at the same time, the true value of the spatial azimuth of the test vehicle at that moment can be calculated. Then, based on the GPS value estimated from the output test vehicle track point, combined with the carrier aircraft's GPS value, the estimated spatial azimuth of the test vehicle is calculated. Subtracting the estimated spatial azimuth from the true spatial azimuth values ​​for each cycle yields the following result: Figure 3The spatial azimuth error curves for each cycle are shown. Statistically, the mean of the spatial azimuth error curve obtained by the conventional method is 0.021 degrees, and the variance is 0.089 degrees. The mean of the spatial azimuth error curve obtained by the exact solution method is 0.006 degrees, and the variance is 0.041 degrees. In the field comparison test of moving target detection in the project, it is generally required that the distance difference between the true position of the test vehicle and the output position of the track point at the same moment, i.e., the position accuracy, should not exceed tens of meters. Assuming the position accuracy requirement is less than 40 meters, and the moving target detection distance is generally tens of kilometers, let's assume it's 20 km. Since this position error is mainly caused by the spatial azimuth error of the final track point output, when the position accuracy requirement is 40 meters and the slant distance is 20 km, the corresponding angle deviation is 0.11 degrees. That is, when the angle deviation of a certain cycle is greater than 0.11 degrees, the result of that cycle is unacceptable. Statistical analysis showed that the conventional method failed to meet the standard in 9 out of 40 cycles, while the precise solution method only failed in one out of 40 cycles. Furthermore, many results obtained using the conventional method, while meeting the standard, were within the critical range, as can be seen from the variance of the two methods analyzed above. The comparison of actual measurement data clearly demonstrates that the final tracking result obtained using the precise solution method is superior to that obtained using the conventional method.

[0113] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for accurately solving the spatial azimuth angle of a moving target based on equations, characterized in that... The steps are as follows: Step 1: Within a given CPI, based on the platform's three-dimensional attitude angles And the azimuth angle of the servo Pitch angle The rotation transformation matrix between the northeast celestial coordinate system and the antenna coordinate system is obtained. ; in, These are the rotation matrices corresponding to the aircraft's heading angle, pitch angle, and roll angle, respectively. Step 2: Based on the beam angle of the target point and error angle Calculate the rectangular coordinates of the unit pointing vector of the moving target point B: Based on the rotation transformation matrix obtained in step 1 Calculate the unit pointing vector of the moving target point B in the northeast-northeast coordinate system: according to First component Second component Solve for azimuth angle ; Step 3: Let in The pitch angle; but ; in It is the spatial azimuth angle; make The above problem is equivalent to: when Sometimes, there is a solution. but , Will Substitute them separately Get two Choice and Close As a final result; No solution, use As the final result.

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

Images