CN108759818B - Method for determining attitude of ultra-high-precision guide star sensor - Google Patents
Method for determining attitude of ultra-high-precision guide star sensor Download PDFInfo
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Abstract
The application relates to a method for determining the attitude of an ultra-high precision guide star sensor, which comprises the following steps: mapping the centroid position of the fixed star image point on the FGSCCD to a VT coordinate system; calculating attitude deviation in the directions of x, y and z in a VT coordinate system; calculating a relative attitude deviation quaternion; and calculating the absolute pose.
Description
Technical Field
The application relates to a space measurement and control method, in particular to a method for determining attitude of an ultrahigh-precision guide star sensor
Background
The star Sensor (Fine guide Sensor) is a high-precision and high-reliability attitude measurement component widely used in the current aerospace craft. The star sensor operates in a real-time dynamic measurement mode, which typically measures to an accuracy of about 3 arc seconds. However, in order to realize attitude determination of sub-arc second level, i.e. less than 1 arc second, the conventional star sensor cannot meet the measurement accuracy requirement.
In the prior art, a Fine guide Sensor (FGS for short) capable of realizing sub-angle-second measurement accuracy needs to be completed by calling a huge star table database pre-stored in the guide Sensor. Because the stars such as the celestial star height is higher than 18 and the like in hundreds of millions, a great amount of manpower and time are necessarily consumed for sorting the star catalogue and cutting data; meanwhile, the data volume of the star catalogue is often over 40G; if the attitude data is stored in the star guide sensor in advance, the star position is searched and matched in the huge database, and then the ultrahigh-precision attitude data is output, a complex star map matching algorithm is necessarily designed, and meanwhile, the extremely high processing capability requirement is put forward to a processor, so that not only is the algorithm complexity improved and the calculation time increased, but also the data updating rate is difficult to improve, and the requirements of high-precision, high-stability and high-frequency attitude information output of the current satellite cannot be met.
In order to meet the requirements of increasingly high attitude determination and attitude stability of a spacecraft, save satellite resources, avoid a star map matching complex algorithm and improve the data updating rate, a method for modeling and attitude determination of an ultrahigh-precision star guide sensor without prestoring a star map and star map matching algorithm is urgently needed in the field.
Disclosure of Invention
The application aims to provide a method for determining the attitude of an ultrahigh-precision star guide sensor.
In order to achieve the above object, the present application provides the following technical solutions.
The centroid position of a fixed star image point on the FGS CCD is mapped into a VT coordinate system; then calculating attitude deviation in the directions of x, y and z in a VT coordinate system; then calculating a relative attitude deviation quaternion; and finally calculating the absolute pose.
Compared with the prior art, the method has the beneficial effects that the method for modeling and determining the attitude of the ultra-high-precision star guide sensor without pre-storing the star catalogue and star map matching algorithm is provided.
Drawings
Fig. 1 is a schematic diagram of a CCD installation and corresponding coordinate system of the present application.
Figure 2 is a schematic diagram of the imaging spot of a star on a CCD.
Fig. 3 is a schematic diagram of the relationship of the spacecraft body system and the VT coordinate system.
Detailed Description
The technical solution of the present application will be clearly and completely described below with reference to the accompanying drawings and the embodiments of the present application.
As shown in fig. 1, a leading star sensor optical coupling Device detector 1(FGS CCD1) and a leading star sensor optical coupling Device detector 2(FGS CCD2) are respectively designed on the upper and lower sides of a Visible light Telescope (VT) optical coupling Device (CCD) detector (VT CCD).
VT coordinate system definition: the center of an optical telescope optical coupling device detector (VT CCD) is taken as an original point O, the row and column directions of the original point O are respectively the x-axis direction and the y-axis direction, and the z-axis direction is determined by a right-hand rule.
One Star Star forms an image point S on the FGS CCD1 through the optical lens1B, C are the image points S respectively1Mapping on x, y axes; the included angle between the vector pointing to the center O 'of the optical lens from B and the z axis is theta, and the included angle between the vector pointing to the center O' of the optical lens from C and the z axis is theta
The focal length f of the lens is OO'.
FGS CCD1 coordinate system definition: with the center of the FGS CCD1 as the origin O1Its row and column directions are respectively x1And y1Axial direction, z1The axial direction is determined by the right hand rule. O is1The coordinate in the VT coordinate system is (L)x1,Ly10), coordinate axis y1At an angle gamma to the axis y1。
FGS CCD2 coordinate system definition: with the center of the FGS CCD2 as the origin O2Its row and column directions are respectively x2And y2Axial direction, z2The axial direction is determined by the right hand rule. O is2The coordinate in the VT coordinate system is, the coordinate axis y2At an angle gamma to the axis y2。
And (3) attitude resolving process:
(1) mapping the centroid position of the fixed star image point on the FGS CCD into the VT coordinate system
The coordinate of the centroid position of the fixed star image point on the FGS CCD1 in the FGS CCD1 coordinate system is set as S1(xFGS1,yFGS1) The coordinate of the centroid position of the fixed star image point on the FGS CCD2 in the FGS CCD2 coordinate system is S2(xFGS2,yFGS2) Wherein 1 and 2 denote CCD1 and CCD 2.
Definition of S'1(xVT1,yVT1) And S'2(xVT2,yVT2) Respectively is a fixed star image point S on the FGS CCD1(xFGS1,yFGS1) AndS2(xFGS2,yFGS2) And (3) projection in the VT coordinate system, converting the centroid position of the fixed star image point on the FGS CCD into the VT coordinate system by using the following formula:
wherein lxpixelIs the length of the star image point region in the x direction, lypixelThe length of the fixed star image point area in the y direction;
(2) calculating the attitude deviation of the x, y and z three-axis directions under the VT coordinate system
The position coordinates of the image point of the fixed star frame 1 are marked by a superscript 1, and the position coordinates of the image point of the nth frame are marked by a superscript n.
The position of the image point of the n frame of the star and the position of the image point of the 1 st frame have the following relation on the x-axis and y-axis coordinates of the VT coordinate system:
wherein Δ Ψ is an attitude deviation in the z-axis direction in the VT coordinate system, and the calculation formula is as follows:
wherein (x)VTi,yVTi) i is 1, and 2 is the coordinate of two fixed star image points in the VT coordinate system, which is obtained by the conversion of formula 1;
where the superscript T represents the transpose of the matrix.
Matrix transpose definition: let a be an m × n matrix, the element in the ith row and the jth column is a (i, j), i.e., a ═ a (i, j), the transpose of a is defined as an n × m matrix B, and B ═ a (j, i) is satisfied, and is denoted as aT＝B。
From the above formula 2, the calculation formula of the displacement between the image point of the n-th frame of the star and the image point of the 1 st frame is as follows:
where the superscript T represents the transpose of the matrix.
The calculation formula of the attitude deviation in the x-axis direction and the y-axis direction under the VT coordinate system is as follows:
And its matrix transposition in VT coordinate system
Then the attitude deviation angle at three axes of the VT coordinate system xyz. The error between the true and measured values of the attitude deviation angle calculated by the above formula can be as small as 0.3 arc second (determined by FGS hardware performance).
(3) Calculating relative attitude deviation quaternion
The corresponding attitude deviation quaternion dQ is calculated by rotating the Euler angle to the quaternion by 3-1-2FGS；
"3-1-2" rotational Euler angle to quaternion formula:
spacecraft body coordinate system definition: taking the centroid of the spacecraft as an origin Ob, Xb is vertical to the bottom plate and faces upwards, Zb is parallel to the bottom plate and points to H01 from the origin Ob, and Yb is determined by a right-hand rule.
The relationship between the VT coordinate system and the spacecraft body coordinate system is shown in fig. 3.
Calculating the quaternion of the attitude deviation of the lower guide star of the spacecraft system by using the following formula
Denoted by superscript b:
wherein A isVTIs the mounting matrix of the VT on the spacecraft,
Q(AVT) Is AVTCorresponding installation quaternion, Q (A)VT)＝[-0.5 -0.5 -0.5 0.5]T。
Calculation from the installation matrix to the installation quaternion:
is provided with a mounting matrix of
Mounting quaternion Q ═ Q1 q2 q3 q4]T
Then
Q is determined by the following formula1，q2，q3Symbol of
let q be [ q ]1,q2,q3,q4]T，q'＝[q1',q2',q3',q4']TThen, then
(4) Absolute attitude calculation
Absolute attitude of nth frame based on FGS output
Is obtained by the following formula:
wherein the content of the first and second substances,
the absolute quaternion is obtained by measuring the 1 st frame of the star sensor, and the error between the measured value and the actual value is about 3 arc seconds;
for conversion between FGS and star sensor, i.e. quaternion
The algorithm only uses the 1 st frame data of the star sensor as the basis of the absolute attitude, the error is in the angular second magnitude and can be deducted when the relative stability is calculated, so the attitude determination error level is determined by FGS and can be improved by one magnitude compared with the star sensor to reach 0.3 angular second (3 sigma). Meanwhile, star map matching is not used in the design, so that the algorithm and the operation amount are greatly simplified, and the method is suitable for the spacecraft with loose absolute pointing requirement and extremely high relative stability requirement.
The embodiments described above are intended to facilitate the understanding and appreciation of the application by those skilled in the art. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present application is not limited to the embodiments herein, and those skilled in the art who have the benefit of this disclosure will appreciate that many modifications and variations are possible within the scope of the present application without departing from the scope and spirit of the present application.
Claims (6)
1. A method for determining the attitude of an ultra-high precision guide star sensor is characterized by comprising the following steps:
(1) the centroid position of the star image point on the FGS CCD is mapped into a VT coordinate system, wherein the coordinate of the centroid position of the star image point on the FGS CCD1 in the coordinate system of the FGS CCD1 is S1(xFGS1,yFGS1) The coordinate of the centroid position of the fixed star image point on the FGS CCD2 in the FGS CCD2 coordinate system is S2(xFGS2,yFGS2) Wherein 1,2 denote CCD1 and CCD2, wherein the calculation formula of the mapping of step (1) is as follows:
wherein lxpixelIs the length of the star image point region in the x direction, lypixelThe length of the fixed star image point area in the y direction; l isxiAnd LyiRespectively are x-axis coordinates and y-axis coordinates of the central origin O of the FGS CCD coordinate system in the VT coordinate system; gamma rayiIs the included angle between the y axis of the FGS CCD coordinate system and the y axis of the VT coordinate system;
(2) calculating attitude deviations in three directions of x, y and z in a VT coordinate system, wherein the step (2) comprises the steps of:
a) assuming that the coordinates of the position of the image point of the 1 st frame are marked by a superscript 1, and the coordinates of the position of the image point of the nth frame are marked by a superscript n, the following relationship exists between the position of the image point of the nth frame of the sidereal and the position of the image point of the 1 st frame on the x-axis and y-axis coordinates of the VT coordinate system:
wherein Δ Ψ is an attitude deviation in the z-axis direction in the VT coordinate system, and the calculation formula is as follows:
wherein，(xVTi,yVTi) i is 1, and 2 is the coordinate of two fixed star image points in the VT coordinate system, which is obtained by the conversion of formula 1;
wherein, superscript T represents the transpose of the matrix;
b) the formula for calculating the displacement between the image point of the n-th frame and the image point of the 1 st frame derived from the above formula 2 is as follows:
wherein, superscript T represents the transpose of the matrix;
c) and calculating the attitude deviation of the X-axis direction and the Y-axis direction under the VT coordinate system according to the following calculation formula:
d) matrix transposition of the attitude deviation in a VT coordinate system
Then is the attitude deviation angle under the three axes x, y and z of the VT coordinate system;
(3) calculating a relative attitude deviation quaternion; and
(4) the absolute pose is calculated.
2. The method of claim 1, wherein the calculating step of step (3) is as follows:
a) the corresponding attitude deviation quaternion dQ is calculated by rotating the Euler angle to the quaternion by 3-1-2FGS(ii) a And
b) calculating the quaternion of the attitude deviation of the lower guide star of the spacecraft system by using the following formula
Wherein A isVTIs a VT installation matrix; q (A)VT) Is AVTCorresponding installation quaternion;
is a quaternion multiplication.
3. The method of claim 2, wherein the method is as set forth in claim 2
And said
4. The method of claim 2, wherein quaternion multiplication
Is defined as follows: let q be [ q ]1,q2,q3,q4]T，q′＝[q1′,q2′,q3′,q4′]TThen, then
5. The method of claim 1, wherein the calculating step of step (4) is as follows:
a) calculating the absolute attitude of the nth frame based on the FGS output by the following formula
Wherein the content of the first and second substances,
obtaining an absolute quaternion measured for the 1 st frame of the star sensor;
is a conversion quaternion between the FGS and the star sensor.
6. The method of claim 5, wherein the method is performed in a batch process
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