A two-dimensional turntable high-precision stable-sighting tracking error correction method

Abstract

The application provides a two-dimensional rotary table high-precision stable-sighting tracking error correction method, relates to an optoelectronic tracking error correction method, and aims at solving the technical problem that the space-based rotary table cannot achieve the angle second level in stable-sighting tracking of a moving target in the prior art. The application realizes the error correction under different conditions of the static base rotary table and the dynamic base rotary table by performing coordinate conversion on the three-dimensional vector under the moving target simulator coordinate system and performing correction on the azimuth angle and the elevation angle under the two-dimensional rotary table coordinate system. When the two-dimensional rotary table performs long-time integration on a dark and weak moving target, the stable-sighting tracking precision can be improved to the angle second level through the error correction, so that the requirement for high-quality imaging in the shooting situation of long-time exposure is met.

Description

Technical Field

[0001] The present 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 space-based turntable's stable tracking accuracy are relatively high, usually reaching the arc-second level. Since the moving targets are relatively dim, a longer exposure time is required, generally 10s to 15s, or even longer. In order to ensure image quality, the turntable needs to maintain a high level of stable tracking accuracy within the integration time. In the existing technology, due to various random errors and systematic errors, the space-based turntable's stable tracking accuracy for darker moving targets is often difficult to achieve at the arc-second level. The vibration and movement of the satellite itself will cause tracking errors, and there will be axis errors during the turntable's rotation process, as well as target surface offsets when tracking moving targets. If the errors are not corrected, according to the theoretical calculation of the turntable's rotation angle based on the moving angle of the moving target, not only will it be impossible to achieve high-precision stable tracking, but it may even be impossible to capture the darker moving targets.

[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 the 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 systematic errors, the space-based turntable cannot achieve the stable tracking accuracy of dark moving targets at the order of arc seconds, and to provide a high-precision stable 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 high-precision stabilization tracking error correction method for a two-dimensional turntable is provided, which uses a satellite attitude simulator, a moving target simulator and a two-dimensional turntable. The method is special in 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 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 moving target simulator coordinate system 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, convert the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system 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 moving target simulator coordinate system into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system, and then convert the three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system;

[0014] 4) Based on the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3), calculate the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system 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 pitch angle Ez' in the two-dimensional turntable coordinate system:

[0018] a. When the satellite attitude simulator is a static base, measure the changes in the image point coordinates at different azimuths and elevations of the 2D turntable. Use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the changes in the image point coordinates. 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 changes in the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth angle increment dAz and elevation angle increment dEz caused by the changes in the image point coordinates;

[0020] Then measure the changes in the image point coordinates of the satellite attitude simulator at different azimuths and elevations, and use Fourier transform to fit the quadratic increments of azimuth and elevation caused by the changes in the 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, and 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, and 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, and Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz', and the corresponding transformation matrix is ​​Tylz;

[0028] 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 the three-dimensional vectors Lyz', Myz', and Nyz' in the initial two-dimensional turntable coordinate system;

[0029] A3) The initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz' is rotated counterclockwise about the Zyz' axis by an angle ay, and a zero-position transformation is performed to transform it into the two-dimensional turntable coordinate system Xz, Yz, and Zz, where ay = 120°; the corresponding transformation 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', and Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, and 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, and 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, and 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) 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;

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

[0043] B4) The standard two-dimensional turntable coordinate system Xz', Yz', and Zz' are rotated counterclockwise around the Zz' axis by an angle az to perform a zero-position transformation and converted into the two-dimensional turntable coordinate system Xz, Yz, and 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', and Nz' in the standard two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lz, Mz, and 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 systems Xyzl, Yyzl, and Zyzl are rotated clockwise around the Zyzl axis by an angle ay to transform them into coordinate systems Xyzl', Yyzl', and 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) Based on the transformation matrix Tza and the transformation matrix Tya, calculate 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' as follows:

[0053] Tylz=Tya*Tza;

[0054] A24) Based on 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 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, and Zyl is rotated clockwise around the Zyl axis by an angle ay and converted to the coordinate system Xyl', Yyl', and Zyl'. The corresponding transformation matrix Tzb is:

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

[0059] B22) The coordinate systems Xyl', Yyl', and Zyl' are rotated clockwise around the Yyl' axis by an angle by to 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, 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:

[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) Based on the conversion matrix Tyz, 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 standard two-dimensional turntable coordinate system according to the following formula:

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

[0073] Furthermore, step a in step 5) is specifically as follows:

[0074] a1) Measure the changes in the coordinates of the image points at different azimuth and elevation angles on the 2D turntable. 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] Wherein, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes at different azimuth and elevation angles of the two-dimensional turntable, ω is the period of the fitted trigonometric function, and t is time;

[0078] a2) Calculate the corrected azimuth angle Az' and elevation angle Ez' based on the azimuth angle increment dAz and the elevation angle increment dEZ. The formula is as follows:

[0079] Az'=Az+dAz;

[0080] Ez'=Ez+dEz.

[0081] Furthermore, step b in step 5) is specifically as follows:

[0082] b1) Measure the change in the coordinates of the image points at different azimuth and elevation angles of the 2D turntable, and use Fourier transform to fit the azimuth angle increment dAz and elevation angle 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 in the coordinates of the image points of the satellite attitude simulator at different azimuths and elevations, and use Fourier transform to fit the quadratic increments of azimuth and elevation caused by the change in the coordinates of the image points. 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) Based on the azimuth angle increment dAz, the elevation angle increment dEz, and the azimuth angle quadratic increment dAzy, and the elevation angle quadratic increment dEzy, calculate the corrected azimuth angle Az' and elevation angle Ez' according to the following formula:

[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 present method transforms the three-dimensional vectors in the moving target simulator coordinate system and corrects the azimuth and elevation angles in the two-dimensional turntable coordinate system, achieving error correction for both static and dynamic turntables. When the two-dimensional turntable performs long-term integration on a faint moving target, this error correction improves stabilized tracking accuracy to the arc-second level, thus meeting the high-quality imaging requirements required for long-exposure photography.

[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 a moving target by a space-based two-dimensional turntable in the method of the present invention can be fully verified in ground tests, so that key technologies can be fully verified in the early stages, reducing the time for on-orbit verification and lowering costs.

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

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

[0098] Figure 2 The process of the present invention is 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 according to 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 according to the present invention;

[0101] Figure 5 This is a schematic diagram of the satellite attitude simulator coordinate system in a two-dimensional turntable high-precision stabilization tracking error correction method of the present invention. 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] Example 1: When the satellite attitude simulator is a stationary 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 motion of the moving target and the brightness of the moving target. A satellite attitude simulator is used to simulate the motion and vibration of the satellite. The 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 the 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, the following three steps are performed:

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

[0115] First, the ideal two-dimensional turntable coordinate systems Xyzl, Yyzl, and Zyzl are rotated clockwise around the Zyzl axis by an angle ay, where ay = 120°, and converted to the coordinate systems 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, the coordinate systems Xyzl', Yyzl', and Zyzl' are rotated 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 the 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 azimuth axis zero position of the initial two-dimensional turntable coordinate system starts at 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 counterclockwise around the Zyz' axis by 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', and Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system as follows:

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

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

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

[0129] Ez=asind(-Nz).

[0130] 5) According to the azimuth angle Az and 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', completing the stable aiming and tracking error correction. Specifically:

[0131] 5.1) Measure the change in the coordinates of the image points at different azimuth and elevation angles of the 2D turntable. 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] Wherein, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes at different azimuth and elevation angles of the two-dimensional turntable, ω is the period of the fitted trigonometric function, and t is time;

[0135] 5.2) Based on the azimuth angle increment dAz and the elevation angle increment dEZ, calculate the corrected azimuth angle Az' and elevation angle Ez' using the following formula:

[0136] Az'=Az+dAz;

[0137] Ez'=Ez+dEz.

[0138] Example 2: When the satellite attitude simulator is a moving base, a two-dimensional turntable high-precision stabilization tracking error correction method is provided. Steps 1 and 2 refer to Example 1. Step 3 is specifically 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, and 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, and 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 systems Xyl, Yyl, and Zyl are rotated clockwise around the Zyl axis by an angle ay to transform them into coordinate systems Xyl', Yyl', and 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 to transform them into 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 to the standard two-dimensional turntable coordinate system Xz', Yz', Zz'. The corresponding transformation 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. 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, and Ny in the satellite attitude simulator coordinate system are converted into three-dimensional vectors Lz', Mz', and Nz' in the standard two-dimensional turntable coordinate system according to the following formula:

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

[0162] 3.4) The standard two-dimensional turntable coordinate system Xz', Yz', and Zz' are rotated counterclockwise around the Zz' axis by an angle az to perform a zero-position transformation, transforming it into the two-dimensional turntable coordinate system Xz, Yz, and 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', and Nz' in the standard two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lz, Mz, and 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 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 in the coordinates of the image points at different azimuth and elevation angles of the 2D turntable. Use Fourier transform to fit the azimuth angle increment dAz and elevation angle 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] Wherein, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes at different azimuth and elevation angles of the two-dimensional turntable, ω is the period of the fitted trigonometric function, and t is time;

[0174] 5.2) Measure the change in the coordinates of the image points of the satellite attitude simulator at different azimuths and elevations. Use Fourier transform to fit the quadratic increments of azimuth and elevation caused by the change in the coordinates of the image points. 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 at different azimuths and elevations of the satellite attitude simulator, ω is the period of the fitted trigonometric function, and t is time;

[0178] 5.3) Based on the azimuth angle increment dAz, the elevation angle increment dEz, and 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:

[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 Examples 1 and 2 are finally integrated into the guidance algorithm of the two-dimensional turntable. The two-dimensional turntable follows the moving target according to the corrected guidance instructions to achieve an accuracy of the order 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 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 moving target simulator coordinate system 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, convert the three-dimensional vectors Ld, Md, and Nd in the moving target simulator coordinate system 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 moving target simulator coordinate system into three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system, and then convert the three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system; 4) Based on the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system obtained in step 3), calculate the azimuth angle Az and the pitch angle Ez in the two-dimensional turntable coordinate system 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 pitch angle Ez' in the two-dimensional turntable coordinate system: a. When the satellite attitude simulator is a static base, measure the changes in the image point coordinates at different azimuths and elevations of the 2D turntable. Use Fourier transform to fit the azimuth increment dAz and elevation increment dEz caused by the changes in the image point coordinates. 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 changes in the image point coordinates at different azimuths and elevations of the two-dimensional turntable, and use Fourier transform to fit the azimuth angle increment dAz and elevation angle increment dEz caused by the changes in the image point coordinates; Then measure the changes in the image point coordinates of the satellite attitude simulator at different azimuths and elevations, and use Fourier transform to fit the quadratic increments of azimuth and elevation caused by the changes in the 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, and 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, and 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, and Zyzl into the initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz', and the corresponding transformation matrix is ​​Tylz; 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 the three-dimensional vectors Lyz', Myz', and Nyz' in the initial two-dimensional turntable coordinate system; A3) The initial two-dimensional turntable coordinate system Xyz', Yyz', and Zyz' is rotated counterclockwise about the Zyz' axis by an angle ay, and a zero-position transformation is performed to transform it into the two-dimensional turntable coordinate system Xz, Yz, and Zz, where ay = 120°; the corresponding transformation 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', and Nyz' in the initial two-dimensional turntable coordinate system are transformed into three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system as follows: [Lz;Mz;Nz]=Tyz0*[Lyz';Myz';Nyz'].

3. The method for correcting high-precision stabilization tracking errors of a two-dimensional turntable according to claim 1, characterized in that: The step B is specifically as follows: B1) The moving target simulator coordinate system Xd, Yd, and 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, and 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 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: [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) 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; According to the transformation matrix Tyz, the three-dimensional vectors Ly, My, and Ny in the satellite attitude simulator coordinate system are transformed into three-dimensional vectors Lz', Mz', and Nz' in the standard two-dimensional turntable coordinate system; B4) The standard two-dimensional turntable coordinate system Xz', Yz', and Zz' are rotated counterclockwise around the Zz' axis by an angle az to perform a zero-position transformation and converted into the two-dimensional turntable coordinate system Xz, Yz, and 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', and Nz' in the standard two-dimensional turntable coordinate system are transformed into the three-dimensional vectors Lz, Mz, and Nz in the two-dimensional turntable coordinate system as follows: [Lz;Mz;Nz]=Tyz0*[Lz';Mz';Nz'].

4. The method for correcting high-precision stabilization tracking errors of a two-dimensional turntable according to claim 2, characterized in that: The step A2 is specifically as follows: A21) The ideal two-dimensional turntable coordinate systems Xyzl, Yyzl, and Zyzl are rotated clockwise around the Zyzl axis by an angle ay to transform them into coordinate systems Xyzl', Yyzl', and 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) Based on the transformation matrix Tza and the transformation matrix Tya, calculate 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' as follows: Tylz=Tya*Tza; A24) Based on 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 as follows: [Lyz';Myz';Nyz']=Tylz*[Lyzl;Myzl;Nyzl].

5. The method for correcting high-precision stabilization tracking errors of a two-dimensional turntable according to claim 3, characterized in that: The step B2 is specifically as follows: B21) The ideal satellite attitude simulator coordinate system Xyl, Yyl, and Zyl is rotated clockwise around the Zyl axis by an angle ay and converted to the coordinate system Xyl', Yyl', and Zyl'. The corresponding transformation matrix Tzb is: Tzb=[cosd(ay)sind(ay)0; -sind(ay)cosd(ay)0; 0 0 1]; B22) The coordinate systems Xyl', Yyl', and Zyl' are rotated clockwise around the Yyl' axis by an angle by to 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, 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].

6. The method for correcting high-precision stabilization tracking errors of a two-dimensional turntable 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 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: Tyz=Tdz*inv(Tdy); B33) Based on the conversion matrix Tyz, 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 standard two-dimensional turntable coordinate system according to the following formula: [Lz';Mz';Nz']=Tyz*[Ly;My;Ny].

7. A method for correcting high-precision stabilization and tracking errors of a two-dimensional turntable according to any one of claims 1 to 6, characterized in that: Step a in step 5) is specifically: a1) Measure the changes in the coordinates of the image points at different azimuth and elevation angles on the 2D turntable. 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; Wherein, aa, ba, ca and ae, be, ce are the parameters of the trigonometric function fitted by measuring the image point changes at different azimuth and elevation angles of the two-dimensional turntable, ω is the period of the fitted trigonometric function, and t is time; a2) Calculate the corrected azimuth angle Az' and elevation angle Ez' based on the azimuth angle increment dAz and the elevation angle increment dEZ. The formula is 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 in the coordinates of the image points at different azimuth and elevation angles of the 2D turntable, and use Fourier transform to fit the azimuth angle increment dAz and elevation angle 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 in the coordinates of the image points of the satellite attitude simulator at different azimuths and elevations, and use Fourier transform to fit the quadratic increments of azimuth and elevation caused by the change in the coordinates of the image points. 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) Based on the azimuth angle increment dAz, the elevation angle increment dEz, and the azimuth angle quadratic increment dAzy, and the elevation angle quadratic increment dEzy, calculate the corrected azimuth angle Az' and elevation angle Ez' according to the following formula: Az'=Az+dAz+dAzy; Ez'=Ez+dEz+dEzy.

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