Method for correcting high-precision sight-stabilizing tracking error of two-dimensional rotary table

Abstract

The invention provides a high-precision sight-stabilizing tracking error correction method for a two-dimensional rotary table, relates to a photoelectric tracking error correction method, and aims to solve the technical problem that sight-stabilizing tracking of a space-based rotary table on a moving target does not reach an arc second magnitude in the prior art. According to the method, the three-dimensional vector under the coordinate system of the moving target simulator is subjected to coordinate transformation, the azimuth angle and the pitch angle under the coordinate system of the two-dimensional rotary table are corrected, and error correction of the static base rotary table and the moving base rotary table under different conditions is achieved. When the two-dimensional rotary table carries out long-time integration on a dark moving target, by correcting the error, the sight-stabilizing tracking precision can be improved to an arc second magnitude, so that the requirement on high-quality imaging under a long-time exposure shooting situation is met.

Description

Technical Field

[0001] The invention relates to a photoelectric tracking error correction method, in particular to a two-dimensional turntable high-precision stabilization tracking error correction method. Background Art

[0002] When exploring low-brightness moving targets, the requirements for the stable tracking accuracy of the space-based turntable are relatively high, usually in the order of arc seconds. Since the moving target is dim, a longer exposure time is required, generally 10s to 15s, or even longer. In order to ensure the imaging quality, the turntable needs to ensure a high stable tracking accuracy within the integration time. In the prior art, due to various random errors and system errors, the stable tracking accuracy of the space-based turntable for darker moving targets is often difficult to reach the order of arc seconds. The vibration and movement of the satellite itself will cause tracking errors, there will be axis errors during the rotation of the turntable, and there will be target surface offset when tracking the moving target. If the error is not corrected, according to the movement angle of the moving target, the turntable rotation angle is calculated according to the theory, not only can high-precision stable tracking not be achieved, but it may even be impossible to capture the darker moving target.

[0003] In addition, in order to verify the high-precision stabilized tracking and error correction of the space-based turntable for dim moving targets, ground verification tests are usually adopted. A satellite attitude simulator is used to simulate the vibration and movement of the satellite, and a target motion simulator is used to simulate the target motion. The two-dimensional turntable is installed on the satellite attitude simulator to form a verification system, which realizes ground verification of the high-precision stabilized tracking of high-speed dim moving targets by the space-based turntable. Summary of the invention

[0004] The main purpose of the present invention is to solve the technical problem in the prior art that due to various random errors and system errors, the stable aiming and tracking accuracy of a space-based turntable for a darker moving target is difficult to reach the order of arc seconds, and to provide a high-precision stable aiming and tracking error correction method for a two-dimensional turntable.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A two-dimensional turntable high-precision stabilization tracking error correction method adopts a satellite attitude simulator, a moving target simulator and a two-dimensional turntable, and its special feature is that it includes the following steps:

[0007] 1) Establish a coordinate system:

[0008] The Xd, Yd, and Zd axes are defined as the coordinate system of the motion target simulator; the Xy, Yy, and Zy axes are defined as the coordinate system of the satellite attitude simulator; and the Xz, Yz, and Zz axes are defined as the coordinate system of the two-dimensional turntable;

[0009] 2) Calculate the three-dimensional vector in the moving target simulator coordinate system:

[0010] According to the azimuth angle Ad and the pitch angle Ed output by the moving target simulator, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are calculated;

[0011] 3) According to the motion state of the base of the satellite attitude simulator, select step A or step B to convert the three-dimensional vectors Ld, Md, and Nd in the coordinate system of the moving target simulator into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system:

[0012] Step A: When the satellite attitude simulator is a static base, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system;

[0013] Step B: When the satellite attitude simulator is a moving base, first convert the three-dimensional vectors Ld, Md, and Nd in the coordinate system of the moving target simulator into three-dimensional vectors Ly, My, and Ny in the coordinate system of the satellite attitude simulator, and then convert the three-dimensional vectors Ly, My, and Ny in the coordinate system of the satellite attitude simulator into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system;

[0014] 4) According to the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3), the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system are calculated as follows:

[0015] Az = atand(Mz / Lz);

[0016] Ez = asind(-Nz);

[0017] 5) According to the motion state of the base of the satellite attitude simulator, select step a or step b to perform error correction on the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system to obtain the corrected azimuth angle Az' and the pitch angle Ez' in the two-dimensional turntable coordinate system:

[0018] a. When the satellite attitude simulator is a static base, measure the change in the image point coordinates of the two-dimensional turntable at different azimuths and elevations, use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the change in the image point coordinates, and calculate the corrected azimuth Az' and elevation Ez', thus completing the correction of the stabilization tracking error;

[0019] b. When the satellite attitude simulator is a moving base, first measure the change in the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the change in the image point coordinates;

[0020] Then measure the change of image point coordinates at different azimuths and elevations of the satellite attitude simulator, and use Fourier transform to fit the quadratic increment of azimuth dAzy and the quadratic increment of elevation dEzy caused by the change of image point coordinates;

[0021] According to the azimuth angle increment dAz and the elevation angle increment dEz as well as the azimuth angle quadratic increment dAzy and the elevation angle quadratic increment dEzy, the corrected azimuth angle Az' and elevation angle Ez' are calculated, thus completing the correction of the stabilization tracking error.

[0022] Furthermore, step A is specifically as follows:

[0023] A1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Yd axis by an angle ayd to transform it into the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl, where ayd = +180°; the corresponding transformation matrix Tdyzl is:

[0024] Tdyzl=[cosd(ayd)0-sind(ayd); 0 1 0; sind(ayd)0cosd(ayd)]

[0025] According to the conversion matrix Tdyzl, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lyzl, Myzl, and Nyzl in the ideal two-dimensional turntable coordinate system as follows:

[0026] [Lyzl;Myzl;Nyzl]=Tdyzl*[Ld;Md;Nd];

[0027] A2) converting the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz', and the corresponding transformation matrix is ​​Tylz;

[0028] According to the transformation matrix Tylz, the three-dimensional vectors Lyzl, Myzl, Nyzl in the ideal two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system;

[0029] A3) The initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz' is rotated counterclockwise around the Zyz' axis by an angle ay, and a zero position conversion is performed to convert it into a two-dimensional turntable coordinate system Xz, Yz, Zz, where ay = 120°; the corresponding conversion matrix Tyz0 is:

[0030] Tyz0=[cosd(-ay)sind(-ay)0;-sind(-ay)cosd(-ay)0;0 0 1];

[0031] According to the transformation matrix Tyz0, the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows:

[0032] [Lz;Mz;Nz]=Tyz0*[Lyz';Myz';Nyz'].

[0033] Furthermore, step B is specifically as follows:

[0034] B1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Zd axis by an angle azd to transform it into the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl, where azd = +180°; the corresponding transformation matrix Tdyl is:

[0035] Tdyl=[cosd(azd)sind(azd)0; -sind(azd)cosd(azd)0; 0 0 1];

[0036] According to the conversion matrix Tdyl, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lyl, Myl, and Nyl in the ideal satellite attitude simulator coordinate system as follows:

[0037] [Lyl; Myl; Nyl]=Tdyl*[Ld; Md; Nd];

[0038] B2) converting the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl into the satellite attitude simulator coordinate system Xy, Yy, Zy, and the corresponding conversion matrix is ​​Tyly;

[0039] According to the conversion matrix Tyly, the three-dimensional vectors Lyl, Myl, and Nyl in the ideal satellite attitude simulator coordinate system are converted into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system as follows:

[0040] [Ly;My;Ny]=Tyly*[Lyl;Myl;Nyl];

[0041] B3) converting the satellite attitude simulator coordinate system Xy, Yy, Zy into the standard two-dimensional turntable coordinate system Xz', Yz', Zz', and the corresponding conversion matrix is ​​Tyz;

[0042] According to the conversion matrix Tyz, the three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system;

[0043] B4) The standard two-dimensional turntable coordinate system Xz', Yz', Zz' is rotated counterclockwise around the Zz' axis by an angle az to perform a zero position transformation and converted into a two-dimensional turntable coordinate system Xz, Yz, Zz, where az = 120°; the corresponding transformation matrix Tyz0 is:

[0044] Tyz0=[cosd(-az)sind(-az)0; -sind(-az)cosd(-az)0; 0 0 1];

[0045] According to the transformation matrix Tyz0, the three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows:

[0046] [Lz;Mz;Nz]=Tyz0*[Lz';Mz';Nz'].

[0047] Furthermore, step A2 is specifically as follows:

[0048] A21) The ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl is rotated clockwise around the Zyzl axis by an angle ay and converted to the coordinate system Xyzl', Yyzl', Zyzl'. The corresponding transformation matrix Tza is:

[0049] Tza=[cosd(ay)sind(ay)0;-sind(ay)cosd(ay)0;0 0 1];

[0050] A22) The coordinate systems Xyzl', Yyzl', and Zyzl' are rotated clockwise around the Yyzl' axis by an angle by to transform them into the initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz', where by = 120°; the corresponding transformation matrix Tya is:

[0051] Tya=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)];

[0052] A23) According to the transformation matrix Tza and the transformation matrix Tya, the transformation matrix Tylz of the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz' is calculated as follows:

[0053] Tylz=Tya*Tza;

[0054] A24) According to the transformation matrix Tylz, the three-dimensional vectors Lyzl, Myzl, Nyzl in the ideal two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system as follows:

[0055] [Lyz';Myz';Nyz']=Tylz*[Lyzl;Myzl;Nyzl].

[0056] Furthermore, step B2 is specifically as follows:

[0057] B21) The ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl is rotated clockwise around the Zyl axis by an angle ay and converted to the coordinate system Xyl', Yyl', Zyl'. The corresponding transformation matrix Tzb is:

[0058] Tzb=[cosd(ay)sind(ay)0; -sind(ay)cosd(ay)0; 0 0 1];

[0059] B22) Rotate the coordinate systems Xyl', Yyl', and Zyl' clockwise around the Yyl' axis by an angle by and transform them into the satellite attitude simulator coordinate systems Xy, Yy, and Zy. The corresponding transformation matrix Tyb is:

[0060] Tyb=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)];

[0061] According to the transformation matrix Tzb and the transformation matrix Tyb, the transformation matrix Tyly from the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows:

[0062] Tyly=Tyb*Tzb;

[0063] B23) According to the conversion matrix Tyly, the three-dimensional vectors Lyl, Myl, Nyl in the ideal satellite attitude simulator coordinate system are converted into three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system as follows:

[0064] [Ly;My;Ny]=Tyly*[Lyl;Myl;Nyl].

[0065] Furthermore, step B3 is specifically as follows:

[0066] B31) According to step B1 and step B2, the conversion matrix Tdy from the moving target simulator coordinate system Xd, Yd, Zd to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows:

[0067] Tdy=Tyly*Tdyl;

[0068] B32) converting the moving target simulator coordinate system Xd, Yd, Zd into the two-dimensional turntable coordinate system Xz, Yz, Zz, and the corresponding conversion matrix is ​​Tdz;

[0069] According to the conversion matrix Tdz of the moving target simulator coordinate system Xd, Yd, Zd into the two-dimensional turntable coordinate system Xz, Yz, Zz and the conversion matrix Tdy of the moving target simulator coordinate system Xd, Yd, Zd into the satellite attitude simulator coordinate system Xy, Yy, Zy, the conversion matrix Tyz of the satellite attitude simulator coordinate system Xy, Yy, Zy into the two-dimensional turntable coordinate system Xz, Yz, Zz is calculated as follows:

[0070] Tyz = Tdz*inv(Tdy);

[0071] B33) According to the conversion matrix Tyz, the three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system according to the following formula:

[0072] [Lz';Mz';Nz']=Tyz*[Ly;My;Ny].

[0073] Further, step a in step 5) is specifically:

[0074] a1) Measure the change of the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows:

[0075] dAz=aa+cos(ωt+ba)+ca;

[0076] dEz=ae+cos(ωt+be)+ce;

[0077] Among them, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes of the two-dimensional turntable at different azimuth angles and different pitch angles, ω is the period of the fitted trigonometric function, and t is time;

[0078] a2) According to the azimuth angle increment dAz and the elevation angle increment dEZ, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows:

[0079] Az'=Az+dAz;

[0080] Ez'=Ez+dEz.

[0081] Further, step b in step 5) is specifically:

[0082] b1) Measure the change of the image point coordinates at different azimuth and elevation angles of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows:

[0083] dAz=aa+cos(ωt+ba)+ca、

[0084] dEz=ae+cos(ωt+be)+ce;

[0085] b2) Measure the change of image point coordinates at different azimuths and elevations of the satellite attitude simulator, and use Fourier transform to fit the quadratic increment of azimuth dAzy and the quadratic increment of elevation dEzy caused by the change of image point coordinates. The formula is as follows:

[0086] dAzy=ay+cos(ωt+by)+cy、

[0087] dEzy=aey+cos(ωt+bey)+cey;

[0088] Among them, ay, by, cy and aey, bey, cey are the parameters of the trigonometric function fitted by measuring the image point changes of the satellite attitude simulator at different azimuth angles and different pitch angles;

[0089] b3) According to the azimuth angle increment dAz and the elevation angle increment dEz as well as the azimuth angle quadratic increment dAzy and the elevation angle quadratic increment dEzy, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows:

[0090] Az'=Az+dAz+dAzy;

[0091] Ez'=Ez+dEz+dEzy.

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] 1. The method of the present invention corrects the azimuth and elevation angles in the two-dimensional turntable coordinate system by performing coordinate conversion on the three-dimensional vector in the moving target simulator coordinate system, thereby realizing error correction in different situations of the static base turntable and the dynamic base turntable. When the two-dimensional turntable performs long-term integration on a dim moving target, the error correction can improve the stabilization tracking accuracy to the arc second level, thereby meeting the requirements for high-quality imaging in long-time exposure shooting scenarios.

[0094] 2. The method of the present invention can not only correct the tracking error caused by satellite vibration and movement, but also correct the stabilization tracking error caused by target surface offset, axis system error, etc.

[0095] 3. The tracking and aiming of the moving target by the space-based two-dimensional turntable in the method of the present invention can be fully verified in ground tests, so that the key technology can be fully verified in the early stage, reducing the time of on-orbit verification and reducing the cost.

[0096] 4. The final calculation accuracy of the method of the present invention is close to the measurement accuracy of sensors used in moving target simulators, satellite attitude simulators, and components in two-dimensional turntables, further illustrating that the present invention can be close to correcting the errors generated during actual operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 The present invention is a process flow of a two-dimensional turntable high-precision stabilization tracking error correction method Figure 1 ;

[0098] Figure 2 The present invention is a process flow of a two-dimensional turntable high-precision stabilization tracking error correction method Figure 2 ;

[0099] Figure 3 A schematic diagram of a moving target simulator coordinate system in a two-dimensional turntable high-precision stabilization tracking error correction method of the present invention;

[0100] Figure 4 A schematic diagram of a two-dimensional turntable coordinate system in a two-dimensional turntable high-precision stabilization tracking error correction method of the present invention;

[0101] Figure 5 The present invention is a schematic diagram of a satellite attitude simulator coordinate system in a two-dimensional turntable high-precision stabilization tracking error correction method. DETAILED DESCRIPTION

[0102] The technical solution of the present invention will be further described below in conjunction with the embodiments and drawings of the present invention. Figure 1 and Figure 2 Together they constitute a complete flow chart of the present invention.

[0103] Embodiment 1: When the satellite attitude simulator is a static base, a two-dimensional turntable high-precision stabilization tracking error correction method is used, such as Figure 1 and Figure 2 As shown, in this embodiment, a moving target simulator is used to simulate the movement of the moving target and the brightness of the moving target, and a satellite attitude simulator is used to simulate the movement and vibration of the satellite, and a two-dimensional turntable is installed on the satellite attitude simulator. The following steps are included:

[0104] 1) According to their respective coordinate system definitions, coordinate systems are established for the moving target simulator, satellite attitude simulator and two-dimensional turntable, such as Figure 3 As shown, the Xd, Yd, and Zd axes are defined as the motion target simulator coordinate system; Figure 4 As shown, the Xy, Yy, and Zy axes are defined as the satellite attitude simulator coordinate system; Figure 5 As shown, the Xz, Yz, and Zz axes are defined as a two-dimensional turntable coordinate system;

[0105] 2) According to the azimuth angle Ad and pitch angle Ed output by the moving target simulator, calculate the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system:

[0106] Ld=cos(Ed)*cos(Ad),

[0107] Md=cos(Ed)*sin(Ad),

[0108] Nd = sin(Ed);

[0109] 3) The three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system, specifically in the following three steps:

[0110] 3.1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Yd axis by an angle ayd, ayd = +180°, and converted to the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl. The corresponding transformation matrix Tdyzl is:

[0111] Tdyzl=[cosd(ayd)0-sind(ayd); 0 1 0; sind(ayd)0cosd(ayd)];

[0112] According to the transformation matrix Tdyzl, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are transformed into three-dimensional vectors Lyzl, Myzl, and Nyzl in the ideal two-dimensional turntable coordinate system:

[0113] [Lyzl;Myzl;Nyzl]=Tdyzl*[Ld;Md;Nd];

[0114] 3.2) Convert the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl to the initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz', and the corresponding transformation matrix is ​​Tylz:

[0115] First, the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, and Zyzl are rotated clockwise around the Zyzl axis by an angle ay, where ay = 120°, and converted to the coordinate system Xyzl', Yyzl', and Zyzl', where ay is the tilt direction of the Zyzl axis. The corresponding transformation matrix Tza is:

[0116] Tza=[cosd(ay)sind(ay)0;-sind(ay)cosd(ay)0;0 0 1];

[0117] Then rotate the coordinate systems Xyzl', Yyzl', and Zyzl' clockwise around the Yyzl' axis by an angle by to transform them into the ideal two-dimensional turntable coordinate systems Xyzl, Yyzl, and Zyzl, where by is the tilt of the Zyzl' axis, and by = 120°; the corresponding transformation matrix Tya is:

[0118] Tya=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)];

[0119] According to the transformation matrix Tza and the transformation matrix Tya, the transformation matrix Tylz from the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl to the initial two-dimensional turntable coordinate system Xyz, Yyz, Zyz is calculated as follows:

[0120] Tylz=Tya*Tza;

[0121] According to the transformation matrix Tylz, the three-dimensional vectors Lyzl, Myzl, and Nyzl in the ideal two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lyz', Myz', and Nyz' in the initial two-dimensional turntable coordinate system:

[0122] [Lyz';Myz';Nyz']=Tylz*[Lyzl;Myzl;Nyzl];

[0123] 3.3) The zero position of the azimuth axis of the initial two-dimensional turntable coordinate system starts from the angle ay. In fact, the zero position of the two-dimensional turntable coordinate system is consistent with the zero position of the moving target coordinate system. Therefore, the initial two-dimensional turntable coordinate system needs to be rotated around the Zyz' axis in the counterclockwise direction by an angle ay, that is, rotated -ay, to become the two-dimensional turntable coordinate system Xz, Yz, Zz. The corresponding transformation matrix Tyz0 is:

[0124] Tyz0=[cosd(-ay)sind(-ay)0;-sind(-ay)cosd(-ay)0;0 0 1];

[0125] According to the transformation matrix Tyz0, the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows:

[0126] [Lz;Mz;Nz]=Tyz0*[Lyz';Myz';Nyz'].

[0127] 4) According to the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3.3), the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system are calculated as follows;

[0128] Az = atand(Mz / Lz);

[0129] Ez=asind(-Nz).

[0130] 5) According to the azimuth angle Az and the elevation angle Ez in the two-dimensional turntable coordinate system, the two-axis difference and the sighting error are corrected to obtain the corrected elevation angle Az' and azimuth angle Ez', and the stable aiming and tracking error correction is completed, specifically:

[0131] 5.1) Measure the change of the image point coordinates at different azimuth and elevation angles of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows:

[0132] dAz=aa+cos(ωt+ba)+ca;

[0133] dEz=ae+cos(ωt+be)+ce;

[0134] Among them, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes of the two-dimensional turntable at different azimuth and elevation angles, ω is the period of the fitted trigonometric function, and t is the time;

[0135] 5.2) According to the azimuth angle increment dAz and the elevation angle increment dEZ, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows:

[0136] Az'=Az+dAz;

[0137] Ez'=Ez+dEz.

[0138] Embodiment 2: When the satellite attitude simulator is a moving base, a two-dimensional turntable high-precision stabilization tracking error correction method, step 1 and step 2 refer to embodiment 1. Step 3 is as follows:

[0139] 3) First, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system, and then the three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system, including the following steps:

[0140] 3.1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Zd axis by an angle azd and converted to the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl, where azd = +180°; the corresponding transformation matrix Tdyl is:

[0141] Tdyl=[cosd(azd)sind(azd)0; -sind(azd)cosd(azd)0; 0 0 1]

[0142] According to the conversion matrix Tdyl, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lyl, Myl, and Nyl in the ideal satellite attitude simulator coordinate system as follows:

[0143] [Lyl; Myl; Nyl]=Tdyl*[Ld; Md; Nd];

[0144] 3.2) Convert the ideal satellite attitude simulator coordinate system Xyl, Yyl, and Zyl to the satellite attitude simulator coordinate system Xy, Yy, and Zy. The corresponding conversion matrix is ​​Tyly. The conversion process is as follows:

[0145] The ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl is rotated clockwise around the Zyl axis by an angle ay and converted to the coordinate system Xyl', Yyl', Zyl', where ay = 120°; the corresponding transformation matrix Tzb is:

[0146] Tzb=[cosd(ay)sind(ay)0; -sind(ay)cosd(ay)0; 0 0 1];

[0147] The coordinate systems Xyl', Yyl', and Zyl' are rotated clockwise around the Yyl' axis by an angle by and converted to the satellite attitude simulator coordinate systems Xy, Yy, and Zy. The corresponding transformation matrix Tyb is:

[0148] Tyb=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)];

[0149] According to the transformation matrix Tzb and the transformation matrix Tyb, the transformation matrix Tyly from the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows:

[0150] Tyly=Tyb*Tzb;

[0151] According to the conversion matrix Tyly, the three-dimensional vectors Lyl, Myl, and Nyl in the ideal satellite attitude simulator coordinate system are converted into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system as follows:

[0152] [Ly;My;Ny]=Tyly*[Lyl;Myl;Nyl].

[0153] 3.3) Convert the satellite attitude simulator coordinate system Xy, Yy, Zy into the standard two-dimensional turntable coordinate system Xz', Yz', Zz', and the corresponding conversion matrix is ​​Tyz;

[0154] According to the conversion matrix Tdyl in step 3.1 and the conversion matrix Tyly in step 3.2, the conversion matrix Tdy from the moving target simulator coordinate system Xd, Yd, Zd to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows:

[0155] Tdy=Tyly*Tdyl;

[0156] The moving target simulator coordinate system Xd, Yd, Zd is converted to the two-dimensional turntable coordinate system Xz, Yz, Zz, and the corresponding conversion matrix is ​​Tdz. Referring to the conversion matrices Tdyzl, Tylz and Tyz0 calculated in step 3 of Example 1, Tdz is calculated as follows:

[0157] Tdz=Tyz0*Tylz*Tdyzl;

[0158] According to the conversion matrix Tdz of the moving target simulator coordinate system Xd, Yd, Zd to the two-dimensional turntable coordinate system Xz, Yz, Zz and the conversion matrix Tdy of the moving target simulator coordinate system Xd, Yd, Zd to the satellite attitude simulator coordinate system Xy, Yy, Zy, the conversion matrix Tyz of the satellite attitude simulator coordinate system Xy, Yy, Zy to the two-dimensional turntable coordinate system Xz, Yz, Zz is calculated as follows:

[0159] Tyz = Tdz*inv(Tdy);

[0160] According to the conversion matrix Tyz, the three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system as follows:

[0161] [Lz';Mz';Nz']=Tyz*[Ly;My;Ny];

[0162] 3.4) The standard two-dimensional turntable coordinate system Xz', Yz', Zz' is rotated counterclockwise around the Zz' axis by an angle az to perform a zero-position transformation, and becomes a two-dimensional turntable coordinate system Xz, Yz, Zz, where az = 120°; the corresponding transformation matrix Tyz0 is:

[0163] Tyz0=[cosd(-az)sind(-az)0; -sind(-az)cosd(-az)0; 0 0 1];

[0164] According to the transformation matrix Tyz0, the three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows:

[0165] [Lz;Mz;Nz]=Tyz0*[Lz';Mz';Nz'].

[0166] 4) Convert the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3 into the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system:

[0167] Az = atand(Mz / Lz);

[0168] Ez=asind(-Nz).

[0169] 5) According to the azimuth angle Az and the elevation angle Ez in the two-dimensional turntable coordinate system, the two-axis difference and the sighting error are corrected to obtain the corrected elevation angle Az' and azimuth angle Ez', which are specifically:

[0170] 5.1) First, measure the change of the image point coordinates at different azimuth and elevation angles of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows:

[0171] dAz=aa+cos(ωt+ba)+ca;

[0172] dEz=ae+cos(ωt+be)+ce;

[0173] Among them, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes of the two-dimensional turntable at different azimuth and elevation angles, ω is the period of the fitted trigonometric function, and t is the time;

[0174] 5.2) Measure the change of image point coordinates at different azimuths and elevations of the satellite attitude simulator, and use Fourier transform to fit the quadratic increment of azimuth dAzy and the quadratic increment of elevation dEzy caused by the change of image point coordinates. The formula is as follows:

[0175] dAzy=ay+cos(ωt+by)+cy;

[0176] dEzy=aey+cos(ωt+bey)+cey;

[0177] Among them, ay, by, cy and aey, bey, cey are the parameters of the trigonometric function fitted by measuring the change of the image point coordinates of the satellite attitude simulator at different azimuths and different pitch angles, ω is the period of the fitted trigonometric function, and t is the time;

[0178] 5.3) According to the azimuth angle increment dAz and the elevation angle increment dEz as well as the azimuth angle secondary increment dAzy and the elevation angle secondary increment dEzy, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows:

[0179] Az'=Az+dAz+dAzy;

[0180] Ez'=Ez+dEz+dEzy.

[0181] In the method of the present invention, the two-dimensional turntable is used as the control object. The correction values ​​calculated in Example 1 and Example 2 are finally integrated into the guidance algorithm of the two-dimensional turntable. The two-dimensional turntable tracks the moving target according to the corrected guidance instructions to achieve an accuracy of arc seconds. At the same time, the camera on the optical axis of the two-dimensional turntable images the luminous target simulated by the moving target simulator.

Claims

1. A high-precision stabilization tracking error correction method for a two-dimensional turntable, using a satellite attitude simulator, a moving target simulator and a two-dimensional turntable, characterized in that: The following steps are involved: 1) Establish a coordinate system: The Xd, Yd, and Zd axes are defined as the coordinate system of the motion target simulator; the Xy, Yy, and Zy axes are defined as the coordinate system of the satellite attitude simulator; and the Xz, Yz, and Zz axes are defined as the coordinate system of the two-dimensional turntable; 2) Calculate the three-dimensional vector in the moving target simulator coordinate system: According to the azimuth angle Ad and the pitch angle Ed output by the moving target simulator, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are calculated; 3) According to the motion state of the base of the satellite attitude simulator, select step A or step B to convert the three-dimensional vectors Ld, Md, and Nd in the coordinate system of the moving target simulator into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system: Step A: When the satellite attitude simulator is a static base, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system; Step B: When the satellite attitude simulator is a moving base, first convert the three-dimensional vectors Ld, Md, and Nd in the coordinate system of the moving target simulator into three-dimensional vectors Ly, My, and Ny in the coordinate system of the satellite attitude simulator, and then convert the three-dimensional vectors Ly, My, and Ny in the coordinate system of the satellite attitude simulator into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system; 4) According to the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3), the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system are calculated as follows: Az = atand(Mz / Lz); Ez = asind(-Nz); 5) According to the motion state of the base of the satellite attitude simulator, select step a or step b to perform error correction on the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system to obtain the corrected azimuth angle Az' and the pitch angle Ez' in the two-dimensional turntable coordinate system: a. When the satellite attitude simulator is a static base, measure the change in the image point coordinates of the two-dimensional turntable at different azimuths and elevations, use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the change in the image point coordinates, and calculate the corrected azimuth Az' and elevation Ez', thus completing the correction of the stabilization tracking error; b. When the satellite attitude simulator is a moving base, first measure the change in the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the change in the image point coordinates; Then measure the change of image point coordinates at different azimuths and elevations of the satellite attitude simulator, and use Fourier transform to fit the quadratic increment of azimuth dAzy and the quadratic increment of elevation dEzy caused by the change of image point coordinates; According to the azimuth angle increment dAz and the elevation angle increment dEz as well as the azimuth angle quadratic increment dAzy and the elevation angle quadratic increment dEzy, the corrected azimuth angle Az' and elevation angle Ez' are calculated, thus completing the correction of the stabilization tracking error.

2. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 1, characterized in that: The step A is specifically as follows: A1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Yd axis by an angle ayd to transform it into the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl, where ayd = 180°; the corresponding transformation matrix Tdyzl is: Tdyzl=[cosd(ayd)0-sind(ayd); 0 1 0; sind(ayd)0cosd(ayd)] According to the conversion matrix Tdyzl, the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system are converted into three-dimensional vectors Lyzl, Myzl, and Nyzl in the ideal two-dimensional turntable coordinate system as follows: [Lyzl;Myzl;Nyzl]=Tdyzl*[Ld;Md;Nd]; A2) converting the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz', and the corresponding transformation matrix is ​​Tylz; According to the transformation matrix Tylz, the three-dimensional vectors Lyzl, Myzl, Nyzl in the ideal two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system; A3) The initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz' is rotated counterclockwise around the Zyz' axis by an angle ay, and a zero position conversion is performed to convert it into a two-dimensional turntable coordinate system Xz, Yz, Zz, where ay = 120°; the corresponding conversion matrix Tyz0 is: Tyz0=[cosd(-ay)sind(-ay)0; -sind(-ay)cosd(-ay)0; 0 0 1]; According to the transformation matrix Tyz0, the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows: [Lz;Mz;Nz]=Tyz0*[Lyz';Myz';Nyz'].

3. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 1, characterized in that: The step B is specifically as follows: B1) The moving target simulator coordinate system Xd, Yd, Zd is rotated clockwise around the Zd axis by an angle azd to transform it into the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl, where azd = 180°; the corresponding transformation matrix Tdyl is: Tdyl=[cosd(azd)sind(azd)0; -sind(azd)cosd(azd)0; 0 0 1]; According to the conversion matrix Tdyl, the three-dimensional vectors Ld, Md, and Nd in the coordinate system of the moving target simulator are converted into three-dimensional vectors Lyl, Myl, and Nyl in the coordinate system of the ideal satellite attitude simulator as follows: [Lyl; Myl; Nyl]=Tdyl*[Ld; Md; Nd]; B2) converting the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl into the satellite attitude simulator coordinate system Xy, Yy, Zy, and the corresponding conversion matrix is ​​Tyly; According to the conversion matrix Tyly, the three-dimensional vectors Lyl, Myl, and Nyl in the ideal satellite attitude simulator coordinate system are converted into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system as follows: [Ly;My;Ny]=Tyly*[Lyl;Myl;Nyl]; B3) converting the satellite attitude simulator coordinate system Xy, Yy, Zy into the standard two-dimensional turntable coordinate system Xz', Yz', Zz', and the corresponding conversion matrix is ​​Tyz; According to the conversion matrix Tyz, the three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system; B4) The standard two-dimensional turntable coordinate system Xz', Yz', Zz' is rotated counterclockwise around the Zz' axis by an angle az to perform a zero position transformation and converted into a two-dimensional turntable coordinate system Xz, Yz, Zz, where az = 120°; the corresponding transformation matrix Tyz0 is: Tyz0=[cosd(-az)sind(-az)0; -sind(-az)cosd(-az)0; 0 0 1]; According to the transformation matrix Tyz0, the three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, Nz in the two-dimensional turntable coordinate system as follows: [Lz;Mz;Nz]=Tyz0*[Lz';Mz';Nz'].

4. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 2, characterized in that: The step A2 is specifically as follows: A21) The ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl is rotated clockwise around the Zyzl axis by an angle ay and converted to the coordinate system Xyzl', Yyzl', Zyzl'. The corresponding transformation matrix Tza is: Tza=[cosd(ay)sind(ay)0;-sind(ay)cosd(ay)0;0 0 1]; A22) The coordinate systems Xyzl', Yyzl', and Zyzl' are rotated clockwise around the Yyzl' axis by an angle by to transform them into the initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz', where by = 120°; the corresponding transformation matrix Tya is: Tya=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)]; A23) According to the transformation matrix Tza and the transformation matrix Tya, the transformation matrix Tylz of the ideal two-dimensional turntable coordinate system Xyzl, Yyzl, Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', Zyz' is calculated as follows: Tylz=Tya*Tza; A24) According to the transformation matrix Tylz, the three-dimensional vectors Lyzl, Myzl, Nyzl in the ideal two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lyz', Myz', Nyz' in the initial two-dimensional turntable coordinate system as follows: [Lyz';Myz';Nyz']=Tylz*[Lyzl;Myzl;Nyzl].

5. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 3, characterized in that: The step B2 is specifically as follows: B21) The ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl is rotated clockwise around the Zyl axis by an angle ay and converted to the coordinate system Xyl', Yyl', Zyl'. The corresponding transformation matrix Tzb is: Tzb=[cosd(ay)sind(ay)0; -sind(ay)cosd(ay)0; 0 0 1]; B22) Rotate the coordinate systems Xyl', Yyl', and Zyl' clockwise around the Yyl' axis by an angle by and transform them into the satellite attitude simulator coordinate systems Xy, Yy, and Zy. The corresponding transformation matrix Tyb is: Tyb=[cosd(by)0-sind(by); 0 1 0; sind(by)0cosd(by)]; According to the transformation matrix Tzb and the transformation matrix Tyb, the transformation matrix Tyly from the ideal satellite attitude simulator coordinate system Xyl, Yyl, Zyl to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows: Tyly=Tyb*Tzb; B23) According to the conversion matrix Tyly, the three-dimensional vectors Lyl, Myl, Nyl in the ideal satellite attitude simulator coordinate system are converted into three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system as follows: [Ly;My;Ny]=Tyly*[Lyl;Myl;Nyl].

6. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 3, characterized in that: The step B3 is specifically as follows: B31) According to step B1 and step B2, the conversion matrix Tdy from the moving target simulator coordinate system Xd, Yd, Zd to the satellite attitude simulator coordinate system Xy, Yy, Zy is calculated as follows: Tdy=Tyly*Tdyl; B32) converting the moving target simulator coordinate system Xd, Yd, Zd into the two-dimensional turntable coordinate system Xz, Yz, Zz, and the corresponding conversion matrix is ​​Tdz; According to the conversion matrix Tdz of the moving target simulator coordinate system Xd, Yd, Zd into the two-dimensional turntable coordinate system Xz, Yz, Zz and the conversion matrix Tdy of the moving target simulator coordinate system Xd, Yd, Zd into the satellite attitude simulator coordinate system Xy, Yy, Zy, the conversion matrix Tyz of the satellite attitude simulator coordinate system Xy, Yy, Zy into the two-dimensional turntable coordinate system Xz, Yz, Zz is calculated as follows: Tyz=Tdz*inv(Tdy); B33) According to the conversion matrix Tyz, the three-dimensional vectors Ly, My, Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', Nz' in the standard two-dimensional turntable coordinate system according to the following formula: [Lz';Mz';Nz']=Tyz*[Ly;My;Ny].

7. A two-dimensional turntable high-precision stabilization tracking error correction method according to any one of claims 1 to 6, characterized in that: Step a in step 5) is specifically: a1) Measure the change of the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows: dAz=aa+cos(ωt+ba)+ca; dEz=ae+cos(ωt+be)+ce; Among them, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes of the two-dimensional turntable at different azimuth angles and different pitch angles, ω is the period of the fitted trigonometric function, and t is the time; a2) According to the azimuth angle increment dAz and the elevation angle increment dEZ, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows: Az'=Az+dAz; Ez'=Ez+dEz.

8. A two-dimensional turntable high-precision stabilization tracking error correction method according to claim 7, characterized in that: Step b in step 5) is specifically: b1) Measure the change of the image point coordinates at different azimuth and elevation angles of the two-dimensional turntable, and use Fourier transform to fit the azimuth increment dAz and elevation increment dEZ caused by this change. The formula is as follows: dAz=aa+cos(ωt+ba)+ca、 dEz=ae+cos(ωt+be)+ce; b2) Measure the change of image point coordinates at different azimuths and elevations of the satellite attitude simulator, and use Fourier transform to fit the quadratic increment of azimuth dAzy and the quadratic increment of elevation dEzy caused by the change of image point coordinates. The formula is as follows: dAzy=ay+cos(ωt+by)+cy、 dEzy=aey+cos(ωt+bey)+cey; Among them, ay, by, cy and aey, bey, cey are the parameters of the trigonometric function fitted by measuring the image point changes of the satellite attitude simulator at different azimuth angles and different pitch angles; b3) According to the azimuth angle increment dAz and the elevation angle increment dEz as well as the azimuth angle quadratic increment dAzy and the elevation angle quadratic increment dEzy, the corrected azimuth angle Az' and elevation angle Ez' are calculated as follows: Az'=Az+dAz+dAzy; Ez'=Ez+dEz+dEzy.

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