CN114280773B - Astronomical telescope calibration method and device - Google Patents
Astronomical telescope calibration method and device Download PDFInfo
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Abstract
The application relates to an astronomical telescope calibration method and device, the astronomical telescope calibration method includes defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope, obtaining a first coordinate of an observation star used for calibration in the ground plane coordinate system, carrying out coordinate conversion on the first coordinate in the ground plane coordinate system to obtain a second coordinate in the motor base coordinate system of the astronomical telescope, controlling a motor of the astronomical telescope to act according to the second coordinate so as to enable the astronomical telescope to accurately observe the observation star, reducing the manual intervention calibration process, realizing full-automatic calibration, reducing errors generated in the calibration process, and improving the calibration precision and speed.
Description
Technical Field
The application belongs to the technical field of astronomical observation, and particularly relates to an astronomical telescope calibration method and device.
Background
Astronomical testing methods collect information through observation, and astronomical telescopes are currently an important tool for observing astronomical objects. Due to the rotation of the earth, the stars observed on the earth rotate around the polar satellites at approximately the star speed. In addition, the larger the magnification of the astronomical telescope, the faster the astronomical telescope can move, and before observing the star, the polar axis mirror of the astronomical telescope needs to be aligned with the polar axis of the north, so that the rotation axis of the telescope is basically consistent with the polar axis of the south and north of the earth. The user can conveniently put the positive telescope, and search the star which the user wants to watch against the star map. The calibration mode belongs to manual adjustment, a user is required to manually dial codes to determine the current latitude, and then the alignment of the stars is carried out, so that the operation has great error, and even if the alignment is carried out to the stars, the alignment position is inevitably changed when the user observes the stars to carry out pitching and direction adjustment, thereby affecting star finding. In the related art, an electric following system is adopted to calibrate an astronomical telescope, that is, parameters such as the current longitude and latitude, world time zone and the like are manually input by a user, and a main lens is manually adjusted to align with the brightest star for calibration. In addition, whether the manual adjustment or the electric following system is used for calibrating the astronomical telescope, the astronomical telescope needs to be leveled in advance before the calibration, and when the tripod has a horizontal error, the calibration precision of the astronomical telescope is affected.
Disclosure of Invention
The application provides an astronomical telescope calibration method and device, which at least overcome the problems that the traditional astronomical telescope calibration method needs manual intervention to a certain extent and has errors to influence the calibration precision.
In a first aspect, the present application provides a method for calibrating an astronomical telescope, comprising:
defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
acquiring a first coordinate of an observation star used for calibration in the ground plane coordinate system;
Performing coordinate conversion on a first coordinate in the ground plane coordinate system to obtain a second coordinate in a motor base coordinate system of the astronomical telescope;
And controlling a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observation star.
Further, the positive directions of the coordinate axes of the ground plane coordinate system are the north direction, the east direction and the geocentric direction respectively;
The motor base coordinate system of the astronomical telescope is a space coordinate system established by taking the motor base as an origin, two coordinate axes in a plane where the motor base is located and a coordinate axis perpendicular to the plane where the motor base is located;
The relationship between the three coordinate directions of the ground plane coordinate system and the motor base coordinate system comprises: perpendicular to each other and any angular relationship.
Further, the coordinate conversion of the first coordinate in the ground plane coordinate system to obtain the second coordinate in the motor base coordinate system of the astronomical telescope includes:
Calculating a coarse calibration rotation matrix to obtain a primary conversion result from a first coordinate under a ground plane coordinate system to a motor base coordinate system of the astronomical telescope according to the coarse calibration rotation matrix;
calculating a fine calibration matrix, and carrying out recalibration on the primary conversion result to obtain a secondary conversion result;
performing iterative computation on the accurate calibration matrix;
And carrying out coordinate conversion on the first coordinate in the ground plane coordinate system by using the iteratively calculated accurate calibration matrix to obtain the second coordinate in the motor base coordinate system of the astronomical telescope.
Further, the calculating the coarse calibration rotation matrix includes:
Acquiring inclined Euler angles of a plane where a motor base of the astronomical telescope is located, wherein the inclined Euler angles comprise a roll angle, a pitch angle and a heading angle which are gamma, theta and psi respectively;
Calculating an initial quaternion according to the roll, pitch and course of the inclined Euler angle
Calculating errors of the initial quaternion and the north, east and ground target quaternions
Wherein q_base= [ 1000 ], q_start -1 is the quaternion inverse;
Calculating a coarse calibration rotation matrix through q_diff, wherein q_diff= [ q 0,q1,q2,q3],q0,q1,q2,q3 ] is the imaginary part value in a quaternion complex expression;
further, the obtaining, according to the coarse calibration rotation matrix, a preliminary conversion result from a first coordinate in a ground plane coordinate system to a motor base coordinate system of the astronomical telescope includes:
calculating azimuth and elevation angles under a motor base coordinate system of the astronomical telescope through the coarse calibration rotation matrix;
Set the azimuth and elevation angle of the observation star under the ground plane coordinate system as The spherical coordinates corresponding to the observation star are/>
Decomposing the spherical coordinates into representations under the NED Cartesian coordinate system as
The representation of the preliminary conversion result vector in the motor base coordinate system is as follows
The preliminary conversion result vector under the motor base coordinate system is expressed as under the spherical coordinate system defined by the XY plane and the Z axis
Further, calculating the precision calibration matrix includes:
According to a coordinate conversion formula V 1＝RV2+Δ,V2, the data before the next point of the ground plane coordinate system is converted, V 1 is the data of the same point in the motor base coordinate system of the astronomical telescope after conversion, delta is a random error vector, R is a rotation matrix, and an initial matrix R 0 is a coarse calibration rotation matrix;
calculating parameter estimation values of all elements in the rotation matrix R;
Updating the estimated value of the rotation matrix R according to the obtained parameter estimated value of each element in the rotation matrix R;
and carrying out iterative computation on the rotation matrix R, and taking the rotation matrix R which reaches the iteration times or the secondary conversion result and meets the convergence condition as the accurate calibration matrix.
Further, the calculating the parameter estimation value of each element in the rotation matrix R includes:
constructing an error equation V=BX-L, wherein B is an n x u design matrix of the error equation, ln dimension constant vectors, and x is a u dimension parameter vector;
Constructing a constraint equation CX-W=0, wherein C is a [ s×u ] coefficient matrix of the constraint equation, W is an s-dimensional constant vector of the constraint equation, and 0 is an s-dimensional zero vector;
Assigning a value to the matrix B, L, C, W according to the input V 1,V2,R0;
and carrying out assignment of the matrix B, L, C and W into an error equation and a constraint equation for calculation, and obtaining a parameter estimated value.
Further, the number of the observation stars used for calibration is at least 2, and the method further comprises the following steps:
Obtaining a final accurate calibration matrix according to the accurate calibration matrix calculated by the at least 2 observation stars;
and carrying out coordinate conversion on the first coordinate in the ground plane coordinate system according to the final calibration matrix to obtain the second coordinate in the motor base coordinate system of the astronomical telescope.
In a second aspect, the present application provides an astronomical telescope calibration device comprising:
The definition module is used for defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
The acquisition module is used for acquiring a first coordinate of the observation star used for calibration in the ground plane coordinate system;
The conversion module is used for carrying out coordinate conversion on the first coordinate in the ground plane coordinate system to obtain the second coordinate in the motor base coordinate system of the astronomical telescope;
and the calibration module is used for controlling the motor of the astronomical telescope to act according to the second coordinate so as to enable the astronomical telescope to accurately observe the observed star.
The technical scheme provided by the embodiment of the application can comprise the following beneficial effects:
The method and the device for calibrating the astronomical telescope provided by the embodiment of the invention comprise the steps of defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope, acquiring a first coordinate of an observation star used for calibration in the ground plane coordinate system, carrying out coordinate conversion on the first coordinate in the ground plane coordinate system to obtain a second coordinate in the motor base coordinate system of the astronomical telescope, and controlling a motor of the astronomical telescope to act according to the second coordinate so as to enable the astronomical telescope to accurately observe the observation star, thereby reducing the manual intervention calibration process, realizing full-automatic calibration, reducing errors generated in the calibration process, and improving the calibration precision and speed.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
Fig. 1 is a flowchart of an astronomical telescope calibration method according to an embodiment of the present application.
Fig. 2 is a flowchart of an astronomical telescope calibration method according to another embodiment of the present application.
Fig. 3 is a functional block diagram of an astronomical telescope calibration device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, based on the examples herein, which are within the scope of the application as defined by the claims, will be within the scope of the application as defined by the claims.
Fig. 1 is a flowchart of an astronomical telescope calibration method according to an embodiment of the present application, as shown in fig. 1, including:
s11: defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
S12: acquiring a first coordinate of an observation star used for calibration in the ground plane coordinate system;
S13: converting the first coordinate in the ground plane coordinate system into a second coordinate in a motor base coordinate system of the astronomical telescope;
s14: and controlling a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observed star.
The traditional astronomical telescope calibration method adopts an electric following system to calibrate the astronomical telescope, but the current longitude and latitude, world time zone and other parameters are manually input by a user, and the primary mirror is manually adjusted to be aligned to the brightest star for calibration. In addition, whether the manual adjustment or the electric following system is used for calibrating the astronomical telescope, the astronomical telescope needs to be leveled in advance before the calibration, and when the tripod has a horizontal error, the calibration precision of the astronomical telescope is affected.
In this embodiment, the calibration method of the astronomical telescope includes defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope, acquiring a first coordinate of an observation star used for calibration in the ground plane coordinate system, performing coordinate conversion on the first coordinate in the ground plane coordinate system to obtain a second coordinate in the motor base coordinate system of the astronomical telescope, and controlling a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observation star, thereby reducing human intervention calibration process, realizing full-automatic calibration, reducing errors generated in the calibration process, and improving calibration precision and speed.
Fig. 2 is a flowchart of an astronomical telescope calibration method according to another embodiment of the present application, and as shown in fig. 2, the astronomical telescope calibration method includes:
s21: coordinate axis directions of a motor base coordinate system of the astronomical telescope are respectively north, east and ground, and coordinate axis directions of a motor base are respectively front, right and lower of the motor base;
s22: acquiring a first coordinate of an observation star used for calibration in a ground plane coordinate system;
s23: calculating a coarse calibration rotation matrix to obtain a preliminary conversion result from a first coordinate under a ground plane coordinate system to a motor base coordinate system of the astronomical telescope according to the coarse calibration rotation matrix;
in this embodiment, calculating the coarse calibration rotation matrix includes:
s231: acquiring inclined Euler angles of a plane where a motor base of the astronomical telescope is located, wherein the inclined Euler angles comprise a roll angle, a pitch angle and a heading angle which are gamma, theta and psi respectively;
in some embodiments, after the telescope is powered on, acquiring a roll angle, a pitch angle and a heading angle through an inertial sensor, a dual-antenna satellite direction finding system, a pitch and heading encoder and a roll positioner;
s232: calculating an initial quaternion according to the roll, pitch and course of the inclined Euler angle
S233: calculating errors of the initial quaternion and the north, east and ground target quaternions;
wherein q_base= [ 1000 ], q_start-1 is the quaternion inverse result;
The calculation process is that
Let q _ base= [ 1000 ],
The quaternion inversion has the following formula
Where q * is the conjugated quaternion of q, i q is the norm of q,
If q=q 0+q1·i+q2·j+q3. K
Then
q*＝q0-q1·i-q2·j-q3·k
The cross-multiplication calculation of the quaternion has the following formula
S234: the coarse calibration rotation matrix is calculated by q_diff, where q_diff= [ q 0,q1,q2,q3 ],
In this embodiment, obtaining a preliminary conversion result from a first coordinate in a ground plane coordinate system to a motor base coordinate system of an astronomical telescope according to a coarse calibration rotation matrix includes:
calculating azimuth and elevation angles of the astronomical telescope under a motor base coordinate system through the coarse calibration rotation matrix;
Set the azimuth and elevation angle of the observation star under the ground plane coordinate system as The spherical coordinates corresponding to the observation star are/>
Decomposing the spherical coordinates into representations under the NED Cartesian coordinate system as
The representation of the preliminary conversion result vector in the motor base coordinate system is as follows
The preliminary conversion result vector under the motor base coordinate system is expressed as under the spherical coordinate system defined by the XY plane and the Z axis
S24: calculating a precise calibration matrix, and carrying out recalibration on the primary conversion result to obtain a secondary conversion result;
In this embodiment, calculating the precision calibration matrix includes:
S241: according to a coordinate conversion formula V 1＝RV2+Δ,V2, the data before the next point of the ground plane coordinate system is converted, V 1 is the data of the same point in the motor base coordinate system of the astronomical telescope after conversion, delta is a random error vector, R is a rotation matrix, and an initial matrix R 0 is a coarse calibration rotation matrix;
controlling the rotation of the pitching and heading motors to lead the lens barrel to point And the azimuth is controlled, and the roll motor is controlled to roll the lens barrel to 0.
In this embodiment, the coarse calibration rotation matrix is used as the initial matrix, so that convergence of the iterative process can be accelerated, and the calibration speed can be improved.
S242: calculating parameter estimation values of all elements in the rotation matrix R;
in this embodiment, the calculation of the parameter estimation of each element in the rotation matrix R includes:
constructing an error equation V=BX-L, wherein B is an n x u design matrix of the error equation, ln dimension constant vectors, and x is a u dimension parameter vector;
Constructing a constraint equation CX-W=0, wherein C is a [ s×u ] coefficient matrix of the constraint equation, W is an s-dimensional constant vector of the constraint equation, and 0 is an s-dimensional zero vector;
Assigning a value to the matrix B, L, C, W according to the input V 1,V2,R0;
and carrying out assignment of the matrix B, L, C and W into an error equation and a constraint equation for calculation, and obtaining a parameter estimated value.
The specific calculation process is as follows:
Is provided with
Wherein the rotation matrix r=r ZRYRX, and
The lengths of V 1 and V 2 should be [ l×3,1], where l is the number of data sets involved in the operation. For example, the coordinate points [X1;Y1;Z1],[X2;Y2;Z2],[X3;Y3;Z3] before conversion and the coordinate points [I1;J1;K1],[I2;J2;K2],[I3;J3;K3], after conversion are added to participate in the operation
V1＝[X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3]T
V2＝[I1 J1 K1 I2 J2 K2 I3 J3 K3]T
Since V 1 and V 2 are both observations, errors need to be taken into account, i.e
V1＝RV2+Δ
Where Δ is the random error vector. In the existing application scene of measurement fitting, the best estimation values of 9 elements in the rotation matrix R are respectively obtained by a least square method through a series of observation data V 1 and V 2. And directly taking 9 elements in the rotation matrix as parameters, linearizing a nonlinear relation containing a large rotation angle through Taylor series under the constraint of an orthogonal matrix, constructing a parameter model, and obtaining a result by adopting an indirect adjustment method with a limiting condition.
The indirect adjustment model can be expressed as:
Error equation v=bx-L
Constraint equation CX-w=0
Wherein V is an n-dimensional observation error vector, B is an n-dimensional design matrix of an error equation, X is a u-dimensional parameter vector, L is an n-dimensional constant vector, C is an s-dimensional constant vector of a constraint equation, W is an s-dimensional constant vector of the constraint equation, and 0 is an s-dimensional zero vector. According to the principle of the least squares method, let
VTPV+2KT(CX-W)＝0
Where K is a coefficient vector corresponding to the constraint equation, and the normal equation can be obtained by biasing x and making it equal to zero:
BTPBX-BTPL+CTK＝0
let N＝BTPB,M＝BTPL,N'bb＝N+CTC,N'cc＝CN'bb -1CT, solve:
X＝(N′bb -1-N′bb -1CTN′cc -1CN′bb -1)M+N′bb -1CTN′cc -1W
the method comprises the steps of constructing an error equation coefficient matrix B, an error equation constant vector L, a constraint equation coefficient matrix C and a constraint equation constant vector W, wherein the specific process comprises the following steps of:
Expanding the three-dimensional rotation formula by Taylor series to ensure that R=R 0 +DeltaR is brought into the Taylor expansion, wherein the three-dimensional rotation formula comprises
Collated into a format conforming to the error equation v=bx-L, for each set of corresponding V 1 and V 2, there is
xi＝[Δa1 Δa2 Δa3 Δb1 Δb2 Δb3 Δc1 Δc2 Δc3]T
The data for operation share I group, and then the error equation coefficient matrix B and the error equation constant vector L are respectively
Since the rotation matrices R are the result of sequentially multiplying rotation matrices in three directions, i.e., r=r ZRYRX, each rotation matrix has strict orthogonality characteristics, satisfying the orthogonality condition R TR＝RRT =e, the rotation matrix R is also an orthogonal matrix, and the same holds true for R 0. Thus, the following relationship exists:
a1 2+a2 2+a3 2＝1
b1 2+b2 2+b3 2＝1
c1 2+c2 2+c3 2＝1
a1a2+b1b2+c1c2＝0
a1a3+b1b3+c1c3＝0
a2a3+b2b3+c2c3＝0
The above equations are combined and organized, and constraint equation Cx-w=0 can be listed, and constraint equation coefficient matrix C and constraint equation constant vector W are respectively:
x＝[Δa1 Δa2 Δa3 Δb1 Δb2 Δb3 Δc1 Δc2 Δc3]T
It should be noted that when a value greater than 1 occurs in the R 0 matrix, i.e., the R 0 matrix is wrong, the initial R 0 matrix may cause the iterative process to diverge. Therefore, before performing the calculation, it is first determined whether a value greater than 1 appears in the R 0 matrix, if so, it is determined that the calculation is abnormal, otherwise, it enters a normal calculation process.
S243: updating the estimated value of the rotation matrix R according to the obtained parameter estimated value of each element in the rotation matrix R;
Calculating R=R 0 +x according to the solved x, and updating an estimated value of R;
s244: and taking the rotation matrix R which reaches the iteration times or the secondary conversion result and meets the convergence condition as a precise calibration matrix.
S25: performing iterative computation on the accurate calibration matrix until the number of iterations is met or the secondary conversion result meets the convergence condition;
S26: and performing coordinate conversion on the first coordinate in the ground plane coordinate system by using the accurate calibration matrix to obtain the second coordinate in the motor base coordinate system of the astronomical telescope.
In some embodiments, the number of viewing stars used for calibration is at least 2, further comprising:
obtaining a final accurate calibration matrix according to the accurate calibration matrix calculated by at least 2 observation stars;
And carrying out coordinate conversion on the first coordinate in the ground plane coordinate system according to the final calibration matrix to obtain the second coordinate in the motor base coordinate system of the astronomical telescope.
However, since the rotation angular velocity of the earth is small, newly generated observation points can be concentrated in a certain direction of the airspace in a short time, and in order to prevent the transformation matrix from being tidied and biased, a plurality of star observations are needed in the calculation process.
S27: and controlling a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observed star.
And controlling the pitching, heading and rolling motors to rotate so that the lens barrel points to the second coordinate direction.
In the related art, an automatic star finding method relying on inertial measurement sensors, GPS and visual correction is provided. However, the method is severely dependent on a visual algorithm when in satellite, and the precision is not suitable for long-time exposure shooting of a main mirror.
In the embodiment, the problem that human intervention is needed in the process of calibrating the astronomical telescope base is solved, the rotation matrix between the motor coordinate system and the horizon coordinate system is estimated by means of the sensor in the telescope and the machine vision method, full-automatic calibration is further achieved, the precision is high, real-time conversion can be achieved, and the method is suitable for long-time exposure shooting of a primary mirror.
The embodiment of the invention provides an astronomical telescope calibrating device, which is shown in a functional structure diagram in fig. 3, and comprises:
a definition module 31 for defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
An acquisition module 32 for acquiring a first coordinate of the observed star for calibration in a ground plane coordinate system;
The conversion module 33 is configured to coordinate-convert a first coordinate in a ground plane coordinate system to obtain a second coordinate in a motor base coordinate system of the astronomical telescope;
the calibration module 34 is configured to control the motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observed star.
In this embodiment, a definition module defines a ground plane coordinate system and a motor base coordinate system of the astronomical telescope, an acquisition module acquires a first coordinate of an observation star used for calibration in the ground plane coordinate system, a conversion module converts the first coordinate in the ground plane coordinate system into a second coordinate in the motor base coordinate system of the astronomical telescope, and a calibration module controls a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observation star; the manual intervention calibration process is reduced, full-automatic calibration is realized, errors generated in the calibration process can be reduced, and the calibration precision and speed are improved.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
It should be noted that in the description of the present application, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Furthermore, in the description of the present application, unless otherwise indicated, the meaning of "plurality" means at least two.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the application.
It should be noted that the present application is not limited to the above-mentioned preferred embodiments, and those skilled in the art can obtain other products in various forms without departing from the scope of the present application, however, any changes in shape or structure of the present application, and all technical solutions that are the same or similar to the present application, fall within the scope of the present application.
Claims (4)
1. An astronomical telescope calibration method, comprising:
defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
acquiring a first coordinate of an observation star used for calibration in the ground plane coordinate system;
Performing coordinate conversion on a first coordinate in the ground plane coordinate system to obtain a second coordinate in a motor base coordinate system of the astronomical telescope;
Controlling a motor of the astronomical telescope to act according to the second coordinate so that the astronomical telescope accurately observes the observation star;
The positive directions of coordinate axes of the ground plane coordinate system are north, east and geocentric directions respectively; the motor base coordinate system of the astronomical telescope is a space coordinate system established by taking the motor base as an origin, two coordinate axes in a plane where the motor base is located and a coordinate axis perpendicular to the plane where the motor base is located; any angular relation which is not equal to 0 is formed between the three coordinate directions of the ground plane coordinate system and the motor base coordinate system;
the coordinate conversion of the first coordinate in the ground plane coordinate system to obtain the second coordinate in the motor base coordinate system of the astronomical telescope includes:
Calculating a coarse calibration rotation matrix to obtain a primary conversion result from a first coordinate under a ground plane coordinate system to a motor base coordinate system of the astronomical telescope according to the coarse calibration rotation matrix;
calculating a fine calibration matrix, and carrying out recalibration on the primary conversion result to obtain a secondary conversion result;
performing iterative computation on the accurate calibration matrix;
Performing coordinate conversion on a first coordinate in the ground plane coordinate system by using the iteratively calculated accurate calibration matrix to obtain a second coordinate in a motor base coordinate system of the astronomical telescope;
Wherein said calculating a coarse calibration rotation matrix comprises:
Acquiring inclined Euler angles of a plane where a motor base of the astronomical telescope is located, wherein the inclined Euler angles comprise a roll angle, a pitch angle and a heading angle which are gamma, theta and psi respectively;
Calculating an initial quaternion according to the roll, pitch and course of the inclined Euler angle
Calculating errors of the initial quaternion and the north, east and ground target quaternions
Wherein/>，/>Taking the inverse result for the quaternion;
by passing through Calculating a coarse calibration rotation matrix, wherein q_diff= [ q 0,q1,q2,q3],q0,q1,q2,q3 ] is the imaginary part value in the quaternion complex expression,
；
The calculating a precision calibration matrix includes:
According to the coordinate conversion formula ，/>For the data before the next point conversion of the ground plane coordinate system,For converting data of the same point in the motor base coordinate system of the rear astronomical telescope,/>The random error vector is represented by R, which is a rotation matrix, and the initial matrix R 0 of the rotation matrix R is the coarse calibration rotation matrix;
calculating parameter estimation values of all elements in the rotation matrix R;
Updating the estimated value of the rotation matrix R according to the obtained parameter estimated value of each element in the rotation matrix R;
and carrying out iterative computation on the rotation matrix R, and taking the rotation matrix R which reaches the iteration times or the secondary conversion result and meets the convergence condition as the accurate calibration matrix.
2. The method according to claim 1, wherein obtaining the preliminary conversion result from the first coordinate in the ground plane coordinate system to the motor base coordinate system of the astronomical telescope according to the coarse calibration rotation matrix comprises:
calculating azimuth and elevation angles under a motor base coordinate system of the astronomical telescope through the coarse calibration rotation matrix;
Set the azimuth and elevation angle of the observation star under the ground plane coordinate system as The spherical coordinates corresponding to the observed stars are/>；
Decomposing the spherical coordinates into representations under the NED Cartesian coordinate system as
；
The representation of the preliminary conversion result vector in the motor base coordinate system is as follows
；
The preliminary conversion result vector under the motor base coordinate system is expressed as under the spherical coordinate system defined by the XY plane and the Z axis，
。
3. The method of calibrating an astronomical telescope according to claim 1, wherein the number of observation stars used for calibration is at least 2, further comprising:
Obtaining a final accurate calibration matrix according to the accurate calibration matrix calculated by the at least 2 observation stars;
and carrying out coordinate conversion on the first coordinate in the ground plane coordinate system according to the final calibration matrix to obtain the second coordinate in the motor base coordinate system of the astronomical telescope.
4. An astronomical telescope calibration device, characterized in that it is used for performing the astronomical telescope calibration method according to any one of claims 1-3, comprising:
The definition module is used for defining a ground plane coordinate system and a motor base coordinate system of the astronomical telescope;
The acquisition module is used for acquiring a first coordinate of the observation star used for calibration in the ground plane coordinate system;
The conversion module is used for carrying out coordinate conversion on the first coordinate in the ground plane coordinate system to obtain the second coordinate in the motor base coordinate system of the astronomical telescope;
and the calibration module is used for controlling the motor of the astronomical telescope to act according to the second coordinate so as to enable the astronomical telescope to accurately observe the observed star.
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| CN200944152Y (en) * | 2006-07-04 | 2007-09-05 | 苏州信达光电科技有限公司 | Theodolite cradle type telescope system capable of automatic tracking celestial object |
| US8477419B1 (en) * | 2010-12-31 | 2013-07-02 | Celestron, Llc | System and method for automatically aligning a telescope without requiring user intervention |
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| CN112964238A (en) * | 2021-03-03 | 2021-06-15 | 中国科学院紫金山天文台 | Device and method for improving pointing accuracy of optical telescope auxiliary radio telescope |
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| WO2004107012A1 (en) * | 2003-05-30 | 2004-12-09 | Vixen Co., Ltd. | Automatic introduction system of celestial body |
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| CN200944152Y (en) * | 2006-07-04 | 2007-09-05 | 苏州信达光电科技有限公司 | Theodolite cradle type telescope system capable of automatic tracking celestial object |
| US8477419B1 (en) * | 2010-12-31 | 2013-07-02 | Celestron, Llc | System and method for automatically aligning a telescope without requiring user intervention |
| CN110471338A (en) * | 2019-08-12 | 2019-11-19 | 南通斯密特森光电科技有限公司 | A kind of astronomical telescope system of more host controls |
| CN111879298A (en) * | 2020-08-17 | 2020-11-03 | 中国科学院上海天文台 | Automatic star pointing method for moon unattended telescope |
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