A star camera-based on-orbit turntable pointing error correction device and method

Abstract

The present invention provides an on-orbit turntable pointing error correction device and method based on a star camera, which are used to solve the technical problems existing in the existing installation error correction method based on stellar measurement and calibration, including large random errors in centroid extraction, incomplete coverage of the rotation range, low calibration efficiency, as well as the complex mathematical derivation process of the existing method for calculating the shafting error based on spherical trigonometric functions and the easy error in the rotation sequence of the rectangular coordinate conversion shafting error calculation method based on Euler angle conversion. The on-orbit turntable pointing error correction device based on the star camera of the present invention installs the star camera on the pitch axis of the on-orbit turntable, and according to the satellite attitude quaternion at different times, combines the least square method to fit and solve the installation matrix to be corrected, so as to realize the installation error correction and reduce the pointing error by more than one order of magnitude. At the same time, a space conversion method combining Euler angle conversion and quaternion conversion is adopted for shafting error correction, which greatly improves the calculation efficiency on the premise of ensuring the correction accuracy.

Description

Technical Field

[0001] The present invention relates to an error correction device and method for a spaceborne turntable, and particularly to an error correction device and method for a spaceborne turntable pointing error based on a star camera. Background Art

[0002] Spaceborne turntables are widely used in fields such as space debris monitoring, laser communication, and space debris tracking and measurement. After the spaceborne turntable is in orbit, due to the release of structural stress caused by the launch shock, and the alternating hot and cold of the satellite when entering and exiting the sunlight and shadow areas, it ultimately causes the pointing error of the spaceborne turntable. The pointing error is divided into external error and internal error according to the source. The external error is the error introduced by the structural deformation of the installation base of the spaceborne turntable, and the internal error is the error introduced by the non-perpendicularity and deformation between the moving axis systems of the spaceborne turntable, etc. Therefore, after the satellite is launched, it is necessary to correct the pointing error of the spaceborne turntable.

[0003] The structural deformation of the installation base of the spaceborne turntable describes the overall deformation of the installation base of the spaceborne turntable relative to the satellite body coordinate system, and the change can be described by the rotation matrix between Cartesian rectangular coordinate systems. The non-perpendicularity and deformation between the moving axis systems of the spaceborne turntable describe the non-orthogonal relationship of the internal structure of the spaceborne turntable. The deformation parameters can be converted into the pointing error of the spaceborne turntable by calculating with spherical trigonometric functions and adopting the axis system error correction method of small angle equivalence. For ground-based turntables, shipborne turntables or airborne turntables, the axis system error can be strictly calibrated and considered fixed. Although the spaceborne turntable can be adjusted and aligned with the satellite body coordinate system on the ground, after it is launched into orbit with the satellite, the structural deformation of the satellite and the spaceborne turntable is inevitable, and some deformation data is much larger than the axis system error, resulting in the inapplicability of the axis system error correction method of small angle equivalence on the ground. Therefore, the on-orbit error correction of the spaceborne turntable should include two steps: installation error correction and axis system error correction. The former corrects larger errors such as installation deformation, and the latter corrects the remaining smaller axis system errors.

[0004] Most of the existing installation error correction methods are based on stellar measurement and calibration. Multiple stars are imaged and processed in sequence, and correction information is obtained by processing the pointing errors of the spaceborne turntable pointing to each star. The disadvantages are as follows: (1) The calibration accuracy is limited by the absolute accuracy of the centroid extraction of a single star, and the imaging quality and image motion trailing of a single star lead to large random errors in centroid extraction; (2) The rotation range coverage is incomplete and the calibration efficiency is low. Due to the uneven distribution of stellar celestial bodies in the J2000 inertial celestial sphere, the limited rotation range of the spaceborne turntable, and the satellite orbital motion, etc., the observation angles and observation times of each observed star need to be strictly arranged, which is not easy to cover the entire rotation range of the spaceborne turntable, and it is usually difficult to complete the calibration within one satellite orbital period, resulting in low calibration efficiency. The existing axis system error correction methods include the method based on spherical trigonometric functions and the method of rectangular coordinate transformation based on Euler angle conversion. Although the axis system error calculation method based on spherical trigonometric functions is relatively intuitive, its mathematical derivation process is complex, and although the axis system error calculation method of rectangular coordinate transformation based on Euler angle conversion has a clear process, the rotation order is prone to errors. Summary of the Invention

[0005] The object of the present invention is to provide an apparatus and method for correcting the pointing error of a spaceborne turntable based on a star camera, aiming at the technical problems existing in the existing installation error correction method based on stellar measurement and calibration, such as large random errors in centroid extraction, incomplete rotation range coverage and low calibration efficiency, as well as the complex mathematical derivation process of the existing axis system error calculation method based on spherical trigonometric functions and the easy error in the rotation order of the axis system error calculation method of rectangular coordinate transformation based on Euler angle conversion.

[0006] To achieve the above object, the technical solution provided by the present invention is as follows:

[0007] An apparatus for correcting the pointing error of a spaceborne turntable based on a star camera, the spaceborne turntable includes an azimuth axis and a pitch axis arranged perpendicular to each other. The stator of the azimuth axis is installed on the satellite platform through the spaceborne turntable mounting base, and its rotor is connected to the stator of the pitch axis; an azimuth angle encoder is arranged on the azimuth axis, and a pitch angle encoder is arranged on the pitch axis; the special feature is that it includes a star camera, a star service computer, a turntable electric control box, and a star camera data processing unit;

[0008] The star camera is installed on the rotor of the pitch axis of the spaceborne turntable;

[0009] The star service computer is respectively communicatively connected to the turntable electric control box and the star camera data processing unit, and is used to respectively and real-time send time information, as well as power-on and power-off control instructions and working timing instructions of the spaceborne turntable and the star camera to the turntable electric control box and the star camera data processing unit. At the same time, the star service computer is also used to collect the satellite attitude quaternion and send it to the turntable electric control box;

[0010] The turntable electronic control box is used to drive the on - board turntable to adjust to the corresponding azimuth angle and pitch angle at different times according to the time information, on - board turntable power - on / off command and working timing command sent by the satellite mission computer, so that the star camera points to different airspaces;

[0011] The star camera data processing unit is used to control the star camera to capture star maps of different airspaces according to the time information, star camera power - on / off command and working timing command sent by the satellite mission computer, and perform real - time processing on the star maps captured by the star camera to obtain the right ascension angle and declination angle corresponding to the center of the star maps captured at different times in the inertial coordinate system;

[0012] The turntable electronic control box is also communicatively connected to the star camera data processing unit, the azimuth encoder and the pitch encoder of the on - board turntable respectively, and is used to calculate the installation error and the axis system error according to the right ascension angle and declination angle corresponding to the center of the star maps captured at different times in the inertial coordinate system, the time information sent by the satellite mission computer, the satellite attitude quaternion, and the azimuth angle and pitch angle at different times sent by the azimuth encoder and the pitch encoder.

[0013] Further, the field of view of the star camera is greater than or equal to 4°, the detection ability is greater than or equal to magnitude 6 stars, and the angle measurement accuracy is less than or equal to 30″.

[0014] Further, the rotation range of the azimuth axis of the on - board turntable is - 90° to + 90°, and the rotation range of the pitch axis is - 30° to + 60°.

[0015] In addition, the present invention also provides a method for correcting the pointing error of an on - board turntable based on a star camera, which is characterized by including the following steps:

[0016] Step 1, build the above - mentioned device for correcting the pointing error of an on - board turntable based on a star camera;

[0017] Step 2, when controlling the on - board turntable to rotate and point to different airspaces, use the star camera to capture corresponding star maps respectively;

[0018] Step 3, installation error correction;

[0019] Step 3.1, calculate the vectors of the star camera optical axis in the inertial coordinate system at the corresponding times respectively according to the right ascension angle and declination angle corresponding to the center of the star maps captured at different times in the inertial coordinate system, and record them as the star camera optical axis vectors;

[0020] Step 3.2, convert the corresponding star camera optical axis vectors to the satellite body coordinate system according to the satellite attitude quaternions at different times; convert the corresponding star camera optical axis vectors to the turntable reference coordinate system according to the azimuth angle and pitch angle of the on - board turntable at different times;

[0021] Step 3.3: Based on the star camera optical axis vectors in the satellite body coordinate system and the turntable reference coordinate system, use the least squares method to fit and obtain the installation matrix to be corrected.

[0022] Step 3.4: According to the installation matrix to be corrected and the star maps taken by the star camera at multiple different times, calculate the pointing errors of the azimuth angle and pitch angle of the spaceborne turntable respectively, and then obtain the residuals between the pointing angle of the spaceborne turntable and the theoretical angle; judge whether the residuals are less than the pointing error requirements. If so, update the installation matrix to the currently corrected installation matrix to complete the pointing error correction of the spaceborne turntable; otherwise, after updating the installation matrix to the currently corrected installation matrix, execute Step 4.

[0023] Step 4: Axis error correction.

[0024] Step 4.1: Use Euler angle conversion to calculate the rotation vector of the satellite attitude quaternion, and based on the relationship between the rotation vector of the satellite attitude quaternion and the rotation angle, obtain the axis error solution model based on quaternion vector rotation.

[0025] Step 4.2: Input the pointing errors of the azimuth angles of the spaceborne turntable obtained in Step 3.4 into the axis error solution model, and use the least squares method for fitting to calculate the axis errors of the spaceborne turntable; the axis errors of the spaceborne turntable include the pitch axis tilt and collimation error.

[0026] Step 4.3: When the spaceborne turntable points to a certain target, calculate the target vector in the turntable reference coordinate system and convert it into the azimuth angle and pitch angle in the turntable reference coordinate system; then, combined with the axis errors of the spaceborne turntable, calculate the azimuth angle and pitch angle after the pointing error correction of the spaceborne turntable to complete the pointing error correction of the spaceborne turntable.

[0027] Furthermore, in Step 3.3, the installation matrix to be corrected The expression is:

[0028]

[0029] In the above formula, , , , , are the three components of the star camera optical axis vector in the turntable reference coordinate system, , , are the three components of the star camera optical axis vector in the satellite body coordinate system, , n is the number of star maps taken by the star camera when calculating the vector of the star camera optical axis in the inertial coordinate system at the corresponding time, and T represents matrix transpose.

[0030] Further, in step 4.1, the shafting error solving model is as follows:

[0031]

[0032] In the above formula, is the azimuth pointing error, is the pitch pointing error, b is the pitch axis tilt amount, E is the pitch angle of the spaceborne turntable, c is the collimation error.

[0033] Further, in step 2, when controlling the spaceborne turntable to rotate and point to different airspaces, the azimuth rotation range is -90° to +90°, and the pitch rotation range is -30° to +60°; the number of airspaces pointed by the spaceborne turntable is greater than or equal to 30.

[0034] Further, in step 3.4, according to the installation matrix to be corrected and the star maps taken by the star camera at multiple different times, calculate the pointing errors of the azimuth and pitch angles of the spaceborne turntable, and then obtain the residuals between the pointing angle and the theoretical angle of the spaceborne turntable specifically as follows:

[0035] Step a, according to the installation matrix to be corrected, and the azimuth angle, pitch angle, right ascension angle, declination angle, and satellite attitude quaternion of the spaceborne turntable corresponding to the centers of the star maps taken by the star camera at multiple different times, calculate the optical axis vector of the star camera in the turntable reference coordinate system after correction, and convert the optical axis vector of the star camera in the turntable reference coordinate system into the azimuth and pitch angles of the spaceborne turntable;

[0036] Step b, subtract the azimuth and pitch angles obtained by converting the azimuth and pitch angles of the spaceborne turntable from the azimuth and pitch angles output by the azimuth encoder and pitch encoder corresponding to the center of the star map at different times, respectively, to obtain the azimuth pointing error and the pitch pointing error;

[0037] Step c, calculate the residual between the pointing angle and the theoretical angle of the spaceborne turntable through the following formula :

[0038]

[0039] In the above formula, is the azimuth pointing error, is the pitch pointing error, , m is the number of star maps taken by the star camera when calculating the pointing errors of the azimuth and pitch angles of the spaceborne turntable.

[0040] Further, in step a, the star maps captured by the star camera at multiple different times are the star maps captured by the star camera at different times in step 3.1, or the star maps captured by the star camera at other times.

[0041] Further, in step 3.4, the pointing error requirement is 0.05°.

[0042] The beneficial effects of the present invention compared with the prior art are as follows:

[0043] 1. Since the calibration accuracy is limited by the absolute accuracy of the centroid extraction of a single star, the on-orbit turntable pointing error correction device based on a star camera provided by the present invention installs the star camera on the rotor of the pitch axis of the on-orbit turntable. The star camera realizes high-precision astronomical positioning of the optical axis of the star camera based on the relative measurement of the centroid positioning of multiple stars in the field of view, is insensitive to small-range image motion trailing, has small measurement random error, and greatly improves the calibration accuracy of the present invention; at the same time, since the rotation range of the on-orbit turntable covers the whole, the present invention sequentially points to different celestial regions within the rotation range of the on-orbit turntable and captures star maps, without specifying the azimuth angle and pitch angle pointing angle sequences of the on-orbit turntable for different stars, greatly improving the calibration efficiency, and can be widely applied to the pointing error correction of high-precision on-orbit turntables for satellites or deep space applications.

[0044] 2. The on-orbit turntable pointing error correction method based on a star camera provided by the present invention combines the satellite attitude quaternions at different times and uses the least squares method to fit and solve the installation matrix to be corrected (i.e., the installation matrix with errors), and then performs installation error correction. This method reduces the pointing error by more than one order of magnitude; at the same time, the present invention uses a space conversion method combining Euler angle conversion and quaternion conversion for axis system error correction, greatly improving the calculation efficiency on the premise of ensuring the correction accuracy. Description of the Drawings

[0045] Figure 1 is a schematic structural diagram of an on-orbit turntable pointing error correction device based on a star camera of the present invention;

[0046] Figure 2 is a pointing error simulation diagram before error correction, where (a) is the azimuth angle error simulation diagram before error correction, and (b) is the pitch angle error simulation diagram before error correction;

[0047] Figure 3 is a pointing error simulation diagram after error correction using the existing pointing error correction method, where (a) is the azimuth angle error simulation diagram after error correction using the existing pointing error correction method, and (b) is the pitch angle error simulation diagram after error correction using the existing pointing error correction method;

[0048] Figure 4The figure shows the pointing error simulation diagram after error correction using the pointing error correction method of the present invention. Among them, (a) is the azimuth error simulation diagram after error correction using the pointing error correction method of the present invention, and (b) is the elevation angle error simulation diagram after error correction using the pointing error correction method of the present invention.

[0049] The specific reference numerals are as follows:

[0050] 0 - Spaceborne turntable; 1 - Star camera; 2 - Turntable electronic control box; 3 - Star camera data processing unit; 4 - Spaceborne turntable mounting base. Detailed implementation manners

[0051] To make the advantages and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] As Figure 1 shown, a spaceborne turntable pointing error correction device based on a star camera includes a star camera 1, a spacecraft computer, a turntable electronic control box 2, and a star camera data processing unit 3.

[0053] The spaceborne turntable 0 is carried on a satellite and includes two mutually perpendicular rotating shafts, namely an azimuth shaft (vertical shaft) and an elevation shaft (horizontal shaft). Both the azimuth shaft and the elevation shaft are composed of components such as a stator, a motor, an encoder, and a rotor. The stator of the azimuth shaft is fixedly installed on the satellite platform through the spaceborne turntable mounting base 4. The stator of the elevation shaft is fixedly connected to the rotor of the azimuth shaft. Therefore, the rotation of the azimuth shaft will drive the rotation of the elevation shaft; the motor is used to drive the corresponding rotor to rotate. The encoder is used to measure the angle of rotation of the rotor relative to the stator. That is, the encoder on the azimuth shaft is used to measure the azimuth angle, denoted as the azimuth angle encoder, and the encoder on the elevation shaft is used to measure the elevation angle, denoted as the elevation angle encoder.

[0054] In the present invention, the star camera 1 is fixedly installed on the rotor of the pitching axis and is used to follow the rotation of the on-board turntable 0 to photograph star charts of different airspaces. The satellite computer is installed inside the satellite and is communicatively connected to the turntable electronic control box 2. It is used to send time information, power-on and power-off control instructions, and working timing instructions of the on-board turntable 0 to the turntable electronic control box 2 in real time. At the same time, it collects the satellite attitude quaternion in real time and sends it to the turntable electronic control box 2. The satellite computer is also communicatively connected to the star camera data processing unit 3 and is used to send time information, power-on and power-off control instructions, and working timing instructions of the star camera 1 to the star camera data processing unit 3 in real time. The turntable electronic control box 2 is used to drive the on-board turntable 0 to adjust to the corresponding azimuth angle and pitching angle at different times according to the time information, power-on and power-off instructions of the on-board turntable 0, and working timing instructions sent by the satellite computer, so that the star camera 1 points to different airspaces. The star camera data processing unit 3 is used to control the star camera 1 to photograph star charts of different airspaces according to the time information, power-on and power-off instructions of the star camera 1, and working timing instructions sent by the satellite computer, and to perform real-time processing on the star charts photographed by the star camera 1 to obtain the right ascension angle and declination angle corresponding to the center of the star charts photographed at different times in the inertial coordinate system. The turntable electronic control box 2 is also communicatively connected to the star camera data processing unit 3, the azimuth encoder, and the pitching angle encoder of the on-board turntable 0 respectively, and is used to calculate the installation error and shafting error according to the right ascension angle and declination angle corresponding to the center of the star charts photographed at different times in the inertial coordinate system sent by the star camera data processing unit 3, the time information sent by the satellite computer, the satellite attitude quaternion, and the azimuth angle and pitching angle at different times sent by the azimuth encoder and the pitching angle encoder.

[0055] The specific working process is as follows: When the on-board turntable 0 works in the area gazing mode and the optical axis of the star camera points to the predetermined airspace, after the star camera 1 collects more than 5 photos in the same airspace, the on-board turntable 0 drives the star camera 1 to the next airspace for collection. The star camera data processing unit 3 outputs the right ascension angle and declination angle corresponding to the center of the star charts photographed by the star camera 1 at different times in the inertial coordinate system to the turntable electronic control box 2 in real time; the turntable electronic control box 2 receives the right ascension angle and declination angle corresponding to the center of the star charts photographed in different airspaces, and combines the time information sent by the satellite computer, the satellite attitude quaternion, and the azimuth angle and pitching angle at different times sent by the azimuth encoder and the pitching angle encoder to calculate the installation error and shafting error, and updates them in the software program of the turntable electronic control box 2 to complete the pointing error correction.

[0056] Preferably, the field of view of the star camera 1 is greater than or equal to 4°, the detection ability is greater than or equal to magnitude 6 stars, and the angle measurement accuracy is less than or equal to 30″.

[0057] The present invention also provides a method for correcting the pointing error of an on-board turntable based on a star camera, which specifically includes the following steps:

[0058] Step 1, set up the above-mentioned star-mounted turntable pointing error correction device based on a star camera, and establish an inertial coordinate system, a satellite centroid orbital coordinate system, a satellite body coordinate system, a turntable reference coordinate system, a star-mounted turntable measurement coordinate system, and a star camera coordinate system.

[0059] Establish an inertial coordinate system , whose coordinate origin is located at the center of the earth, the z-axis points to the north pole of the earth at 0:0:0 UTC on January 1, 2000, the x-axis points to the vernal equinox position at 0:0:0 UTC on January 1, 2000, the y-axis is in the earth's equatorial plane at 0:0:0 UTC on January 1, 2000, and forms a right-handed orthogonal system with and .

[0060] Establish a satellite centroid orbital coordinate system , whose coordinate origin is located at the satellite centroid, and the Z o -axis points from the satellite centroid to the center of the earth, the x-axis is perpendicular to the -axis in the satellite orbit plane and along the satellite's velocity direction, the y-axis forms a right-handed orthogonal system with and , pointing to the negative normal direction of the satellite orbit plane.

[0061] Establish a satellite body coordinate system , whose coordinate origin is located at the satellite centroid, and the three coordinate axes are respectively parallel to the three inertial principal axes of the satellite. The satellite attitude quaternion rotation matrix represents the rotation relationship between the satellite body coordinate system and the satellite centroid orbital coordinate system .

[0062] Establish a turntable reference coordinate system , whose coordinate origin is located at the center of the mounting base 4 of the star-mounted turntable, and the line connecting the center of the azimuth axis encoder and the 0° scale of the azimuth axis encoder is parallel to the -axis, and the normal of the turntable mounting surface is defined as the -axis, the y-axis is in the turntable mounting surface and forms a right-handed coordinate system with the -axis. The mounting matrix of the star-mounted turntable 0 is used to describe the mounting relationship between the turntable reference coordinate system and the satellite body coordinate system. When this mounting matrix is a third-order identity matrix, the turntable reference coordinate system and the satellite body coordinate system are parallel to each other.

[0063] Establish a star-mounted turntable measurement coordinate system , whose origin is located at the intersection of the 0 azimuth axis and the pitch axis of the spaceborne turntable, The axis is parallel to the azimuth axis and points from the origin to the origin of the turntable reference coordinate system . The axis is parallel to the pitch axis, The axis and The axis form a right-handed coordinate system. The measurement coordinate system of the spaceborne turntable Rotates with the rotation of the azimuth angle and pitch angle of the spaceborne turntable. When the azimuth angle and pitch angle of the spaceborne turntable 0 are 0°, the measurement coordinate system of the spaceborne turntable and the turntable reference coordinate system are parallel.

[0064] Establish the star camera coordinate system , whose origin is located at the center of the target surface of the detector of star camera 1, The axis is along the optical axis direction of star camera 1, The axes respectively correspond to the rows and columns of the detector of star camera 1. The installation matrix of star camera 1 is used to describe the conversion relationship between the star camera coordinate system and the measurement coordinate system of the spaceborne turntable , and this conversion relationship is related to the azimuth angle and pitch angle of the turntable.

[0065] Step 2, when controlling the spaceborne turntable 0 to rotate and point to different airspaces, take corresponding star maps through star camera 1 respectively.

[0066] When the spaceborne turntable 0 performs pointing error correction, no less than 30 airspaces are evenly selected within the entire rotation range of its azimuth angle and pitch angle for star map shooting. In this embodiment, taking the azimuth angle rotation range of -90° to +90° and the pitch angle rotation range of -30° to +60° as an example, 39 specified airspaces as shown in Table 1 are evenly selected within the rotation range for star map shooting.

[0067] Table 1 Angle pointing of the spaceborne turntable corresponding to 39 specified airspaces

[0068]

[0069] The spaceborne turntable 0 stays at each angular pointing position for 5 seconds for the star camera 1 to take pictures, and then uses 30 seconds to rotate to the next angle. It takes a total of 28 minutes to complete the star map shooting at all angular pointings. Among them, 21 groups of right ascension angle and declination angle data corresponding to azimuth angles of -90°, -60°, -30°, 0°, 30°, 60°, and 90° are used to calculate the installation error of the spaceborne turntable 0, and 18 groups of right ascension angle and declination angle data corresponding to the remaining azimuth angles are used to verify the correctness of the installation error of the spaceborne turntable and the correction accuracy. In other embodiments of the present invention, 21 groups of data for calculating the installation error of the spaceborne turntable can also be used to verify the correctness of the installation error of the spaceborne turntable and the correction accuracy.

[0070] The pointing error of the spaceborne turntable 0 includes installation error and shafting error. The parameters required for the turntable electronic control box 2 to calculate the pointing error of the spaceborne turntable 0 are shown in Table 2.

[0071] Table 2 Parameters required for the turntable electronic control box to calculate the pointing error of the spaceborne turntable

[0072]

[0073] Among them, the time information and satellite attitude quaternion are from the on-board computer, the turntable angles (azimuth angle and pitch angle) are from the azimuth encoder and pitch encoder of the spaceborne turntable 0, and the star map center coordinates (right ascension angle and declination angle) are from the star camera data processing unit 3.

[0074] Step 3, installation error correction.

[0075] The turntable electronic control box 2 calculates according to the right ascension angle and declination angle corresponding to the center of a certain star map taken by the star camera 1 at time in the inertial coordinate system, and calculates the vector of the star camera optical axis (spaceborne turntable sighting axis) in the inertial coordinate system at

[0076] (1)

[0077] Among them, n represents the number of star maps taken by the star camera 1 when calculating the vector of the star camera optical axis in the inertial coordinate system at the corresponding time. In this embodiment, n = 21.

[0078] Denote the vector of the star camera optical axis in the inertial coordinate system as the star camera optical axis vector, and convert the star camera optical axis vector to the satellite body coordinate system through the satellite attitude matrix. Specifically: The turntable electronic control box 2 calculates according to the satellite attitude quaternion at , calculate the current satellite attitude matrix , that is, the transformation matrix of the satellite body coordinate system relative to the inertial coordinate system:

[0079] (2)

[0080] The turntable electric control box 2 combines the current satellite attitude matrix , and transforms the star camera optical axis vector into the satellite body coordinate system. The expression is as follows:

[0081] (3)

[0082] Among them, represents the three components of the star camera optical axis vector in the satellite body coordinate system , , .

[0083] When the azimuth angle and pitch angle of the spaceborne turntable are both 0°, the star camera optical axis vector is parallel to the axis of the spaceborne turntable measurement coordinate system , that is, the star camera optical axis vector is . At the same time, At time Az i and pitch angle El i , the spaceborne turntable 0 rotates to the azimuth angle

[0084] (4)

[0085] Among them, represents the three components of the star camera optical axis vector in the turntable reference coordinate system , , .

[0086] The star camera optical axis vector in the satellite body coordinate system is transformed to the star camera optical axis vector in the turntable reference coordinate system through the installation matrix of the spaceborne turntable 0, that is:

[0087] (5)

[0088] Combine the right ascension angle, declination angle, and satellite attitude quaternion in the inertial coordinate system corresponding to the centers of multiple star maps taken at different times ( i = 1, 2, 3,... n), and calculate the star camera optical axis vector in the satellite body coordinate system by combining equations (1) to (3), and form a matrix Y:

[0089] (6)

[0090] At different times ( i = 1, 2, 3, …… n), the azimuth and elevation angles of the star carrier turntable 0 corresponding to the centers of multiple star maps taken are combined with Equation (4) to calculate the optical axis vector of the star camera in the turntable reference coordinate system, and a matrix X is formed:

[0091] (7)

[0092] Comparing with Equation (5), let , and the least squares method is used to fit and calculate the optimal estimate of the actual installation matrix, which is the installation matrix to be corrected , and the calculation formula is as follows:

[0093] (8)

[0094] Obtain the installation matrix to be corrected After that, the installation matrix to be corrected , and the azimuth, elevation, right ascension, declination, and satellite attitude quaternion of the star carrier turntable corresponding to the remaining 18 groups of star map centers are substituted into Equation (9) to calculate the optical axis vector of the star camera of the 18 groups of star maps in the turntable reference coordinate system:

[0095] (9)

[0096] Among them, is the vector of the optical axis of the star camera at time m in the inertial coordinate system, is the number of star maps taken by star camera 1 when calculating the pointing errors of the azimuth and elevation angles of the star carrier turntable ( m time), and in this embodiment

[0097] = 18. The optical axis vector of the star camera in the turntable reference coordinate system is converted into the azimuth

[0098] and elevation angle of the star carrier turntable 0 through Equation (10):

[0099] and elevation angle output by the azimuth encoder and elevation encoder corresponding to the centers of the 18 groups of star maps respectively, and the pointing error of the azimuth Pointing error of pitch angle :

[0100] (11)

[0101] Calculate the residual after correction by the installation matrix to be quasi-corrected, that is, calculate the residual between the pointing angle of the on-board turntable 0 and the theoretical angle, and determine whether the pointing error correction of the on-board turntable 0 is completed according to the magnitude of the residual. In the present invention, when calculating the residual between the pointing angle of the on-board turntable 0 and the theoretical angle, the maximum value of the deviation is taken, that is, by calculate the residual between the pointing angle of the on-board turntable 0 and the theoretical angle, .

[0102] When the residual is less than the pointing error requirement, update the installation matrix in the software program of the turntable electronic control box 2 to , and the pointing error correction of the on-board turntable 0 ends. When the residual is greater than or equal to the pointing error requirement, after updating the installation matrix in the software program of the turntable electronic control box 2 to , continue to carry out the shafting error correction inside the on-board turntable 0. In this embodiment, the pointing error requirement is 0.05°.

[0103] Step 4, perform shafting error correction based on Euler angle conversion and quaternion conversion.

[0104] When the on-board turntable 0 points to the target, it actually rotates the azimuth angle and pitch angle around the azimuth axis and pitch axis with shafting errors respectively. For the same space target, the pointing angles obtained by rotating around the azimuth axis and pitch axis of the on-board turntable without errors are definitely different from those obtained by rotating around the azimuth axis and pitch axis with shafting errors. After the installation error correction, the deviation between the two is mainly caused by the shafting error of the on-board turntable 0 and its deformation, including the pitch axis tilt amount and collimation error.

[0105] The present invention proposes a space conversion method combining Euler angle conversion and quaternion conversion for shafting error correction. Among them, Euler angle conversion is used to calculate the rotation vector of the satellite attitude quaternion, and then based on the rotation vector of the satellite attitude quaternion and the rotation angle relationship, a shafting error solution model based on quaternion vector rotation is deduced. Its advantage is that using quaternion conversion to realize the rotation process only requires knowing the space vector of the rotation axis, the space vector to be rotated, and the angle of rotation of the space vector around the rotation axis, regardless of the rotation order. When using Euler angle conversion to solve the space vector of the rotation axis and the space vector to be rotated, each step of the 3×3 matrix operation only needs to calculate one row or one column of the matrix, with less computational complexity. The following is an example:[[]]

[0106] Define the coordinate axes X, Y, and Z. They respectively represent the unit vectors in the directions of the coordinate axes X, Y, and Z. Assume a certain spatial rotation process, where the spatial vector of the rotation axis is the X-axis, that is , and the spatial vector to be rotated is , and the angle of rotation around the spatial vector of the rotation axis is A. Then, the expression of the spatial vector to be rotated after rotation calculated using quaternion transformation is:

[0107] (12)

[0108] According to the operation relationship of quaternion transformation , and by combining with the sum and difference formulas of trigonometric functions, equation (12) can be simplified to .

[0109] The process of calculating the expression of the star camera optical axis vector in the turntable reference coordinate system after the spaceborne turntable without axis system error rotates by the azimuth angle A and the pitch angle E using the quaternion transformation method is as follows:

[0110] The spatial vector to be rotated rotates around the X-axis, that is, the spatial vector of the rotation axis by the azimuth angle A, and the new optical axis vector is:

[0111] (13)

[0112] Similarly, at this time, the pitch axis in the measurement coordinate system of the spaceborne turntable is:

[0113] (14)

[0114] According to equation (12), rotate the star camera optical axis vector around the pitch axis by the angle E, and the final optical axis vector is:

[0115] (15)

[0116] From the above calculation process, it can be seen that although the principle of using quaternion transformation to solve the rotation process is simple, after multiple rotations, the expressions of the spatial vector to be rotated and the spatial vector of the rotation axis become longer and longer, and the calculation process is rather cumbersome. If the Euler angle transformation is completely used, the rotation axis cannot be directly specified, and only the rotation axis of the next step can be obtained by rotating step by step from the initial coordinate axes X, Y, and Z, and the calculation process of the spatial vector of the rotation axis is closely related to the rotation sequence and is prone to errors. Therefore, the present invention adopts a spatial transformation method combining Euler angle transformation and quaternion transformation for axis system error correction.

[0117] It is known that the initial optical axis vector is parallel to the axis in the turntable reference coordinate system, and this vector can be expressed as . Since the x-component and y-component of this vector are 0 respectively, the calculation processes of formulas (13) to (15) can adopt Euler angle conversion and only use the third column of the calculation matrix, and then the rotated optical axis vector can be directly obtained.

[0118] When the spaceborne turntable 0 points to a certain airspace, the azimuth angle is A and the pitch angle is E. Considering that there is no pointing error in the azimuth axis and pitch axis of the spaceborne turntable 0, the rotated optical axis vector is:

[0119] (16)

[0120] That is , which is exactly the same as formula (15). Therefore, the spatial conversion method combining Euler angle conversion and quaternion conversion adopted by the present invention for axis system error correction can greatly reduce the calculation amount.

[0121] Assume that the tilt amount of the pitch axis of the spaceborne turntable 0 is b . Considering the physical effect of the pitch axis tilt amount, rotate the pitch axis around the new optical axis vector by b angle to obtain the actual pitch axis. At this time, the spatial vector to be rotated is the Y axis, that is . Adopting Euler angle conversion only needs to calculate the second column to obtain the actual pitch axis vector as:

[0122] (17)

[0123] Then rotate the optical axis vector around the tilted pitch axis vector by the pitch angle E to obtain the final spatial pointing of the optical axis. At this time, the spatial vector of the known rotation axis is , the spatial vector to be rotated is and the rotation angle is E. Directly adopt the quaternion conversion method to calculate the actual star camera optical axis vector as:

[0124] (18)

[0125] Similarly, calculate the pointing of the spaceborne turntable with collimation error c . Considering the physical effect of the collimation error, that is, rotate the optical axis vector around the azimuth axis by c angle to obtain the actual optical axis. When the collimation error is known, the spatial vector to be rotated is the optical axis vector without error That is the spatial vector to be rotated, and the spatial vector of the rotation axis is , and the rotation angle is c . The calculation results directly using Euler angle conversion and quaternion conversion are as follows:

[0126] (19)

[0127] By simultaneously solving equations (18) and (16), the pitch axis tilt b is obtained. The influence on the pointing error is:

[0128] (20)

[0129] In the above formula, is the pitch angle pointing error, is the azimuth angle pointing error, . Therefore has nothing to do with the pointing error, .

[0130] By simultaneously solving equations (19) and (16), the collimation error c is obtained. The influence on the pointing error is:

[0131] (21)

[0132] Similarly, . Therefore has nothing to do with the pointing error, .

[0133] Two kinds of axis system errors of the spaceborne turntable 0 (i.e., the pitch axis tilt b and the collimation error c ) exist simultaneously. Therefore, the influence of the axis system error on the azimuth angle and the pitch angle is expressed as:

[0134] (22)

[0135] Formula (22) is the axis system error solution model of the present invention.

[0136] Substitute the 18 groups of pointing errors of the azimuth angle calculated by formula (11) into the axis system error solution model of formula (22), and use the least squares method for fitting to calculate and obtain the pitch axis tilt b of the spaceborne turntable 0 and the collimation error c , that is:

[0137] (23)

[0138] Finally, according to the pitch axis tilt bAnd the collimation error c is used to correct the axis system error. First, when the spaceborne turntable 0 points to a certain target T, the right ascension angle of the target is known and the declination angle . The turntable electronic control box 2 combines the current satellite attitude quaternion and calculates the target vector in the turntable reference coordinate system according to Equation (24):

[0139] (24)

[0140] Secondly, the target vector in the turntable reference coordinate system is converted into the azimuth angle and the pitch angle in the turntable reference coordinate system:

[0141] (25)

[0142] Then, combining the pitch axis tilt amount b of the spaceborne turntable 0 and the collimation error c, calculate the target pointing angle after correcting the pointing error of the spaceborne turntable, that is, the azimuth angle and the pitch angle :

[0143] (26)

[0144] In the above formula, .

[0145] Finally, the turntable electronic control box 2 drives the motor of the spaceborne turntable 0 to rotate according to this target pointing angle to point to the target.

[0146] The technical effects of the present invention are verified through specific experiments below. As Figures 2 - 4 shown, they are successively the pointing error simulation diagram without error correction (when the installation error is set to 0.5° and the axis system error is 3″ according to engineering experience), the pointing error simulation diagram after error correction using the existing pointing error correction method, and the pointing error simulation diagram after error correction using the pointing error correction method of the present invention. Figures 2 - 4 In (a) of are the corresponding azimuth angle error simulation diagrams, and in (b) are the corresponding pitch angle error simulation diagrams. It can be seen that the pointing error using the present invention is reduced by more than one order of magnitude.

[0147] The above is only used to illustrate the technical solution of the present invention and is not a limitation thereof. For those of ordinary skill in the art, the specific technical solution recorded in the above embodiments can be modified, or some technical features can be equivalently replaced, and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the scope of the technical solution protected by the present invention.

Claims

1. A star - on - board turntable pointing error correction device based on a star camera. The star - on - board turntable (0) includes an azimuth axis and a pitch axis which are perpendicular to each other. The stator of the azimuth axis is installed on the satellite platform through the star - on - board turntable mounting base (4), and its rotor is connected to the stator of the pitch axis. An azimuth encoder is arranged on the azimuth axis, and a pitch encoder is arranged on the pitch axis. It is characterized in that: It includes a star camera (1), a satellite mission computer, a turntable electronic control box (2), and a star camera data processing unit (3); The star camera (1) is installed on the rotor of the pitch axis of the star - on - board turntable (0); The satellite mission computer is communicatively connected to the turntable electronic control box (2) and the star camera data processing unit (3) respectively, and is used to respectively and real - time send time information, as well as power - on / off control instructions and working timing instructions for the star - on - board turntable (0) and the star camera (1), collect the satellite attitude quaternion and send it to the turntable electronic control box (2); The turntable electronic control box (2) is used to drive the star - on - board turntable (0) to adjust to the corresponding azimuth angle and pitch angle at different times according to the time information, power - on / off instructions and working timing instructions of the star - on - board turntable (0) sent by the satellite mission computer, so that the star camera (1) points to different airspaces; The star camera data processing unit (3) is used to control the star camera (1) to capture star maps of different airspaces according to the time information, power - on / off instructions and working timing instructions of the star camera (1) sent by the satellite mission computer, and perform real - time processing on the star maps captured by the star camera (1) to obtain the right ascension angle and declination angle corresponding to the center of the star maps captured at different times in the inertial coordinate system; The turntable electronic control box (2) is also communicatively connected to the star camera data processing unit (3), as well as the azimuth encoder and pitch encoder of the star - on - board turntable (0), and is used to calculate the installation error and axis system error according to the right ascension angle and declination angle corresponding to the center of the star maps captured at different times in the inertial coordinate system, the time information sent by the satellite mission computer, the satellite attitude quaternion, and the azimuth angle and pitch angle at different times sent by the azimuth encoder and pitch encoder.

2. The star - on - board turntable pointing error correction device based on a star camera according to claim 1, characterized in that: The field of view of the star camera (1) is greater than or equal to 4°, the detection ability is greater than or equal to magnitude 6 stars, and the angle measurement accuracy is less than or equal to 30″.

3. The star - on - board turntable pointing error correction device based on a star camera according to claim 1, characterized in that: The rotation range of the azimuth axis of the star - on - board turntable (0) is - 90° to + 90°, and the rotation range of the pitch axis is - 30° to + 60°.

4. A method for correcting the pointing error of a spaceborne turntable based on a star camera, characterized in that, It includes the following steps: Step 1, build the star - on - board turntable pointing error correction device based on a star camera according to any one of claims 1 - 3; Step 2, when controlling the star - on - board turntable (0) to rotate and point to different airspaces, capture the corresponding star maps through the star camera (1) respectively; Step 3, install error correction; Step 3.1: According to the right ascension angle and declination angle in the inertial coordinate system corresponding to the center of the star maps taken at different times, calculate the vectors of the star camera optical axis in the inertial coordinate system at the corresponding times, and denote them as the star camera optical axis vectors. Step 3.2: According to the satellite attitude quaternions at different times, convert the corresponding star camera optical axis vectors to the satellite body coordinate system; according to the azimuth angle and pitch angle of the on-board turntable (0) at different times, convert the corresponding star camera optical axis vectors to the turntable reference coordinate system. Step 3.3: Based on the star camera optical axis vectors in the satellite body coordinate system and the turntable reference coordinate system, use the least squares method to fit and obtain the installation matrix to be corrected. Step 3.4: According to the installation matrix to be corrected and the star maps taken by the star camera (1) at multiple different times, calculate the pointing errors of the azimuth angle and pitch angle of the on-board turntable (0) respectively, and then obtain the residuals between the pointing angle of the on-board turntable (0) and the theoretical angle; judge whether the residuals are less than the pointing error requirement. If so, update the installation matrix to the currently corrected installation matrix to complete the pointing error correction of the on-board turntable (0); otherwise, after updating the installation matrix to the currently corrected installation matrix, execute Step 4. Step 4: Axis system error correction. Step 4.1: Calculate the rotation vector of the satellite attitude quaternion by using Euler angle conversion, and obtain the axis system error solution model based on the relationship between the rotation vector of the satellite attitude quaternion and the rotation angle. Step 4.2: Input the multiple groups of pointing errors of the azimuth angle of the on-board turntable (0) obtained in Step 3.4 into the axis system error solution model, and use the least squares method for fitting to calculate the axis system error of the on-board turntable (0); the axis system error of the on-board turntable (0) includes the pitch axis tilt amount and the collimation error. Step 4.3: When the on-board turntable (0) points to a certain target, calculate the target vector in the turntable reference coordinate system and convert it to the azimuth angle and pitch angle in the turntable reference coordinate system; then, combined with the axis system error of the on-board turntable (0), calculate the azimuth angle and pitch angle after the pointing error correction of the on-board turntable (0) to complete the pointing error correction of the on-board turntable (0).

5. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 4, wherein: In Step 3.3, the installation matrix to be corrected The expression is: ； In the above formula, , , 、 、 are the three components of the star camera optical axis vector in the turntable reference coordinate system, 、 、 are the three components of the star camera optical axis vector in the satellite body coordinate system, , n is the number of star maps captured by the star camera (1) when calculating the vector of the star camera optical axis in the inertial coordinate system at the corresponding moment, and T represents matrix transpose.

6. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 4 or 5, wherein: In Step 4.1, the axis system error solution model is: ； In the above formula, is the azimuth pointing error, is the elevation pointing error, b is the elevation axis tilt amount, E is the elevation angle of the spaceborne turntable (0), c is the collimation error.

7. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 6, wherein: In Step 2, when controlling the on-board turntable (0) to rotate and point to different airspaces, the azimuth angle rotation range is -90° to +90°, and the pitch angle rotation range is -30° to +60°; the number of airspaces pointed to by the on-board turntable (0) is greater than or equal to 30.

8. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 7, wherein: In step 3.4, according to the installation matrix to be corrected and the star maps captured by the star camera (1) at multiple different times, calculate the pointing errors of the azimuth and elevation angles of the on-board turntable (0), and further obtain the residuals between the pointing angle of the on-board turntable (0) and the theoretical angle, specifically as follows: Step a: According to the installation matrix to be corrected, as well as the azimuth angle, elevation angle, right ascension angle, declination angle, and satellite attitude quaternion of the on-board turntable (0) corresponding to the centers of the star maps captured by the star camera (1) at multiple different times, calculate the optical axis vector of the star camera in the turntable reference coordinate system corresponding to the corrected star map, and convert the optical axis vector of the star camera in the turntable reference coordinate system into the azimuth and elevation angles of the on-board turntable (0); Step b: Subtract the azimuth and elevation angles obtained by conversion of the on-board turntable (0) from the azimuth and elevation angles output by the azimuth encoder and elevation encoder corresponding to the centers of the star maps at different times respectively to obtain the pointing error of the azimuth angle and the pointing error of the elevation angle; Step c, calculate the residual between the pointing angle of the spaceborne turntable (0) and the theoretical angle by the following formula : ； In the above formula, is the pointing error of the azimuth angle, is the pointing error of the elevation angle, , m is the number of star maps captured by the star camera (1) when calculating the pointing errors of the azimuth angle and elevation angle of the spaceborne turntable (0).

9. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 8, wherein: In step a, the star maps captured by the star camera (1) at multiple different times are the star maps captured by the star camera (1) at different times in step 3.1, or the star maps captured by the star camera (1) at other times.

10. The method for correcting the pointing error of an on-board turntable based on a star camera according to claim 4, wherein: In step 3.4, the requirement for the pointing error is 0.05°.

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