CN111578917A - Method for measuring earth orientation parameters by using three-field-of-view single-focal-plane optical telescope - Google Patents
Method for measuring earth orientation parameters by using three-field-of-view single-focal-plane optical telescope Download PDFInfo
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Abstract
The invention discloses a method for measuring earth orientation parameters by using a three-field-of-view single-focal-plane optical telescope, which comprises the following steps: (1) extracting the astrology; (2) separation of different fields of view; (4) calculating the direction; (5) and calculating the earth orientation parameters, including the pointing direction of the earth rotation axis, polar motion and UT1 calculation. The invention obtains fixed star images of three different fields of view simultaneously through the photographic observation of an optical telescope with three fields of view and a single focal plane; after the star images of different view fields are distinguished, the direction of each view field in an inertial space is solved, the direction of an instantaneous polar is obtained in an observation time period through continuous multi-frame images in a fitting mode, and the instantaneous polar reflects the nutation of the precision; acquiring polar shift information according to the change of longitude and latitude between different view field directions; based on the principle of equal height observation, the zenith directions of the telescope, namely right ascension and declination, are calculated, and the UT1 information of world time is obtained when the right ascension is a local fixed star.
Description
Technical Field
The invention belongs to the technical field of astronomical optical photography celestial body measurement, and relates to an astronomical observation data processing method.
Background
The earth orientation parameters (nutation, polar motion, universal time UT1) are used for describing the irregular change of the earth in the inertial space and are important parameters of space science and earth science. In the past, classical instruments (such as an altimeter, a zenith cylinder, a meridian ring and a celestial body instrument) need to be arranged in a wide-range networking mode, each instrument can only observe one visual field or one fixed star at a time, and finally, only average results of multi-day time resolution can be provided. A method for instantaneously measuring the orientation parameters of the earth can be realized by using an optical telescope with three view fields and a single focal plane. In order to realize two conditions of 'multi-view-field simultaneous observation' and 'angular distance fixation', the observation equipment is provided with a multi-surface reflector at the front end of the traditional optical telescope, the reflector is formed by cutting and processing a whole piece of glass, on one hand, the stability of an included angle is ensured, on the other hand, a plurality of fixed star light rays in different directions enter a telescope lens barrel after being reflected, and finally, the fixed star light rays are imaged on a focal plane detector terminal simultaneously. Different from the conventional astronomical observation image, in this case, a star image of a plurality of fields of view is mixed in one observation image at the same time, a special image processing method is required to obtain the pointing coordinate of each field of view, and then parameters such as the pointing direction of the earth rotation axis, polar motion, universal time UT1 and the like are solved.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a method for measuring earth orientation parameters by using a three-view-field single-focal-plane optical telescope, which solves the problems that only a single-view-field observation image can be processed and the earth orientation parameters cannot be measured by observing data through a single device in the existing data processing technology.
The technical scheme is as follows: the invention relates to a three-view field single focal plane optical telescope, which is characterized in that a reflector with three reflecting surfaces is arranged in front of the optical telescope, the included angle between every two three reflecting surfaces is 135 degrees, a single lens cone of the optical telescope receives light rays from three fixed stars in different sky areas and images the light rays on the same focal plane detector, and finally, fixed star images in three different view fields are simultaneously obtained, and the method for measuring the earth orientation parameters by using the three-view field single focal plane optical telescope is used for measuring the earth orientation parameters by processing the data of the fixed star images in the three different view fields, and specifically comprises the following steps:
(1) extracting the astrology; processing the acquired star images of three different fields of view by using an image processing technology, and extracting a star image from the star image;
(2) separation of different fields of view; for the separation of the star and star images in different sky areas in the observation image of the multi-view-field telescope, a method of correlating the observation images of adjacent frames is adopted, the association of the star and star images in the sky area is established through the speed by utilizing the motion rule of a target, and the star and star images meeting the speed association condition determine the sky area where the star and star images are located, so that the star images extracted in the step (1) are separated into star images of three view fields;
(3) matching fixed stars; carrying out star matching on the star images of the three fields of view respectively, and determining corresponding areas of the three fields of view;
(4) calculating the direction; respectively calculating the directions of the three fields of view according to the matched three fields of view;
(5) calculating the earth orientation parameters; including earth spin axis pointing, polar motion, and UT1 calculations.
The invention further preferably adopts the technical scheme that the specific steps of the starry elephant extraction in the step (1) are as follows:
step 1.1) segmenting a star point target in a star image and a star map background by a global threshold method;
step 1.2) highlighting star point pixels by a feature fusion method, wherein the used features are local gray maximum and local contrast mean contrast;
and step 1.3) extracting all pixels of the star point target to obtain a star image.
Preferably, the specific steps of separating the different fields of view in step (2) are:
step 2.1) selecting a bright star with the measurement coordinate of (x) near the center of the field of view of the kth frame image0,y0)k;
Step 2.2) in a certain range of the centre of the field of view of the (k + 1) th frame image, the range value is set according to the maximum and minimum movement distance of the star between the adjacent frame images, n star images exist, and the measurement coordinate of the star images is (x)i,yi)k+1,i=1,n;
Step 2.3) let x be 1 when i ═ 1i=x0,yi=y0Obtaining Δ x ═ xi-x0,Δy=yi-y0For all the stars in the (k + 1) th frame image, (x '═ x- Δ x, y' ═ y- Δ y) is performedk+1(ii) a Then the measured coordinates (x, y) of all the stars on the image of the k framekComparing one by one, and regarding the star association point pairs established with the difference value smaller than the threshold value, when the logarithm of the association points exceeds a preset number, considering that one day area is successfully screened and separated; otherwise, repeating the process until the screening and separation in one day zone are finished;
step 2.4) after separating the star image of an area of day, selecting a bright star from the rest star images near the center of the field of view of the kth frame image, and repeating the steps 2.1) to 2.3); until all screening and separation of the planetarium in other day areas are completed.
Preferably, the method for calculating the instantaneous rotation axis in the step (5) is as follows:
along with the rotation of the earth, in a certain observation period, the instantaneous optical axis of each view field direction points to a plane, the normal vector of the plane is the average instantaneous zenith direction in the period, and the direction of the instantaneous rotation shaft is calculated by using a method for calculating a plane equation; the observation equation is
Wherein (x, y, z) is the direction of the instantaneous optical axis in the international celestial sphere reference system [ GCRS ], and the calculation result is 3 normal vectors (A, B,1) common to the planes, which correspond to the direction of the instantaneous rotation axis in the [ GCRS ] in a certain period of time.
Preferably, the solution of the polar motion in step (5) is:
after the instantaneous celestial polar directions in a certain period of time are obtained, the latitude and longitude differences corresponding to the instantaneous optical axes in 3 directions are calculated, a certain observation epoch is designated as a reference epoch, and the latitude pointed by the optical axis of the No. 1 mirror is set as Longitude λ 100 as the starting point of longitude; meanwhile, the coordinate lambda of the optical axis of the No. 2 mirror pointing to the epoch is determined20Anddetermining the coordinate lambda of the optical axis of the No. 3 mirror pointing to the epoch30And
for other observation epochs t, the polar motion causes the optical axis pointing of the No. 1 mirror to change into
When lambda is10When the value is equal to 0, substituting the formula to obtain
The polar motion causes the optical axis direction of the No. 2 mirror and the No. 3 mirror to change into
To obtain
Wherein the longitudinal difference lambda of the mirror optical axis direction2(t)-λ1(t) and lambda3(t)-λ1(t), using the 'fixed angular distance' between the points, by observation calculation:
for the observation in three directions, the observation equation for resolving the polar motion is:
wherein the content of the first and second substances,
preferably, in the step (5), the method for calculating universal time UT1 is that the three-field telescope obtains local sidereal time S corresponding to a certain UTC time by adding equal-altitude observation modes, and further obtains UT 1.
Preferably, the specific steps of the solving method of the universal time UT1 are as follows:
a. taking the 1 st reflecting surface as an example, t is obtained in sequence by rotating the telescope tube by 120 degrees step lengthi=1,2,3The instantaneous direction of the reflecting surface in the instantaneous equatorial coordinate system corresponds to the optical axis;
b. according to1iAnd tiα is corrected according to the angular velocity of the sidereal sunday movement1iConverting the observation of the optical axis at different times to t1Corresponding Chijing α 'at moment'1iI.e. by
α′11=α11
α′12=α12+k·cos12·(t1-t2)
α′13=α13+k·cos13·(t1-t3)
Similarly, for the 2 nd and 3 rd reflecting surfaces, there are
α′21=α21
α′22=α22+k·cos22·(t1-t2)
α′23=α23+k·cos23·(t1-t3)
α′31=α31
α′32=α32+k·cos32·(t1-t2)
α′33=α33+k·cos33·(t1-t3)
c、(α′1i,1i)、(α′1i,1i) And (α'1i,1i) Respectively distributed on 3 parallel planes, ideally, the normal vector of the plane corresponds to the zenith, so that the observation equation is established as
Wherein
The solution (A, B,1) is a common normal vector of the three planes, which is the zenith at t1Equatorial coordinate of time, wherein the right ascension is t1A corresponding local fixed star time S;
d. obtaining Greenwich mean sight constant star hour according to the instantaneous longitude lambda of the station, the ascension nutation of the observation time and the local sidereal time SAccording toUT1 is calculated.
Has the advantages that: the invention obtains fixed star images of three different fields of view simultaneously through the photographic observation of an optical telescope with three fields of view and a single focal plane; after the star images of different view fields are distinguished, the direction of each view field in an inertial space is solved, the direction of an instantaneous polar is obtained in an observation time period through continuous multi-frame images in a fitting mode, and the instantaneous polar reflects the nutation of the precision; acquiring polar shift information according to the change of longitude and latitude between different view field directions; based on the principle of equal height observation, the zenith directions of the telescope, namely right ascension and declination, are calculated, and the UT1 information of world time is obtained when the right ascension is a local fixed star.
Drawings
FIG. 1 is a schematic view of a three-field single focal plane optical telescope of the present invention;
FIG. 2 is a flow chart of the present invention for processing observed data for determining Earth orientation parameters;
FIG. 3 is a schematic view of the directions of movement of the star representation in different day zones;
FIG. 4 is a schematic diagram of star-star blending in three field-of-view sky regions;
FIG. 5 is a diagram illustrating the velocity vectors of stars in a field of view for three day regions;
FIG. 6 is a schematic diagram of a solution of the instant spinning shaft;
FIG. 7 is a schematic diagram of the calculation of the polar shift.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the embodiments.
Example 1: a method for measuring earth orientation parameters by using a three-field-of-view single-focal-plane optical telescope.
As shown in fig. 1, the three-view-field single-focal-plane optical telescope is formed by installing a reflector with three reflecting surfaces in front of the optical telescope, wherein the included angle between every two three reflecting surfaces is 135 degrees, a single lens barrel of the optical telescope receives light rays from three fixed stars in different sky areas and images the light rays on the same focal plane detector, and finally, fixed star images of three different view fields are obtained simultaneously.
The method for measuring the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as shown in figure 2 comprises the steps of star image extraction, separation of different fields of view, star matching, pointing calculation and earth orientation parameter calculation. The star image extraction, star matching and pointing calculation are all realized by using the existing method.
1. And (5) extracting the star image.
The star images of three different fields of view are processed and acquired by utilizing an image processing technology, and the star images are extracted from the star images. The method comprises the following specific steps:
step 1.1) segmenting a star point target in a star image and a star map background by a global threshold method;
step 1.2) highlighting star point pixels by a feature fusion method, wherein the used features are local gray maximum and local contrast mean contrast;
and step 1.3) extracting all pixels of the star point target to obtain a star image.
2. Separation of the different fields of view.
Under the influence of the autorotation of the earth, the fixed star has a day-to-day movement. The speed v of the diurnal movement of the star is related to the declination of the star, namely v is approximately equal to 15'/s & cos when seen on the ground station. The velocity direction is related to the direction of observation in which the stars are located. As shown in fig. 3, where P is the pole, N, W, S, E represents north, west, south and east, respectively, P is also the earth's pole of rotation, and the circle is the circle of celestial declination. For a multi-view field observation device fixed on the ground, stars in different directions can be observed at the same time, the stars in the sky area 1 are shown to move from north to west, the stars in the sky area 2 are shown to move from west to south, and the stars in the sky area 3 are shown to move from east to north. After reflection by the polygonal corner reflector, stars in different sky areas are imaged to a telescope focal plane terminal, as shown in fig. 4.
Different sky areas show different motion characteristics (speed magnitude and direction) on the terminal of the focal plane of the telescope, and as shown in fig. 5, arrows indicate the motion direction and speed magnitude of the star stars in the field of view.
Therefore, for the separation of the fixed star and the star in different sky areas in the observation image of the multi-view telescope, the association method of the observation images of adjacent frames is adopted, the association of the fixed star and the star in the sky area is established through the speed by utilizing the motion rule of the target, the fixed star and the star meeting the speed association condition can determine the sky area where the fixed star and the star are located, and the specific steps are as follows:
step 2.1) selecting a bright star with the measurement coordinate of (x) near the center of the field of view of the kth frame image0,y0)k;
Step 2.2) in a certain range of the centre of the field of view of the (k + 1) th frame image, the range value is set according to the maximum and minimum movement distance of the star between the adjacent frame images, n star images exist, and the measurement coordinate of the star images is (x)i,yi)k+1,i=1,n;
Step 2.3) let x be 1 when i ═ 1i=x0,yi=y0Obtaining Δ x ═ xi-x0,Δy=yi-y0For all the stars in the (k + 1) th frame image, (x '═ x- Δ x, y' ═ y- Δ y) is performedk+1(ii) a Then the measured coordinates (x, y) of all the stars on the image of the k framekComparing one by one, and regarding the star association point pairs established with the difference value smaller than the threshold value, when the logarithm of the association points exceeds a preset number, considering that one day area is successfully screened and separated; otherwise, repeating the process until the screening and separation in one day zone are finished;
step 2.4) after separating the star image of an area of day, selecting a bright star from the rest star images near the center of the field of view of the kth frame image, and repeating the steps 2.1) to 2.3); until all screening and separation of the planetarium in other day areas are completed.
3. Star matching
And respectively carrying out star matching on the star images of the three fields of view to determine corresponding areas of the three fields of view. This step uses existing processing methods.
4. Direction calculation
And respectively calculating the directions of the three fields according to the matched three fields. This step uses existing processing methods.
5. Earth orientation parameter calculation
(1) The method for resolving the instantaneous rotation shaft comprises the following steps:
as shown in fig. 6, with the rotation of the earth, in a certain observation period, the instantaneous optical axis of each field direction points on a plane, the normal vector of the plane is the average instantaneous polar direction in the period, and the direction of the instantaneous rotation axis is calculated by using a method of solving a plane equation; the observation equation is
Wherein (x, y, z) is the direction of the instantaneous optical axis in the international celestial sphere reference system [ GCRS ], and the calculation result is 3 normal vectors (A, B,1) common to the planes, which correspond to the direction of the instantaneous rotation axis in the [ GCRS ] in a certain period of time.
(2) The method for resolving the polar motion comprises the following steps:
as shown in fig. 7, the transient within a certain period of time is obtainedCalculating the latitude and longitude differences corresponding to the instantaneous optical axes in 3 directions after the time-pole direction, designating a certain observation epoch as a reference epoch, and setting the latitude pointed by the optical axis of the No. 1 mirror as Longitude λ 100 as the starting point of longitude; meanwhile, the coordinate lambda of the optical axis of the No. 2 mirror pointing to the epoch is determined20Anddetermining the coordinate lambda of the optical axis of the No. 3 mirror pointing to the epoch30And
for other observation epochs t, the polar motion causes the optical axis pointing of the No. 1 mirror to change into
When lambda is10When the value is equal to 0, substituting the formula to obtain
The polar motion causes the optical axis direction of the No. 2 mirror and the No. 3 mirror to change into
To obtain
Wherein the longitudinal difference lambda of the mirror optical axis direction2(t)-λ1(t) and lambda3(t)-λ1(t), using the 'fixed angular distance' between the points, by observation calculation:
for the observation in three directions, the observation equation for resolving the polar motion is:
wherein the content of the first and second substances,
(3) solving method of universal time UT1
The three-field telescope obtains local fixed star time S corresponding to a certain UTC time by increasing equal-altitude observation modes, and further obtains UT, wherein the specific mode is as follows:
a. rotating the telescope tube by 120 degree step length to 1 st inverseTaking a shot surface as an example, sequentially obtaining ti=1,2,3Instantaneous (UTC instant), the reflecting surface corresponding to the orientation of the optical axis in the instantaneous equatorial coordinate system;
b. according to1iAnd tiα is corrected according to the angular velocity of the sidereal sunday movement1iConverting the observation of the optical axis at different times to t1Corresponding Chijing α 'at moment'1iI.e. by
α′11=α11
α′12=α12+k·cos12·(t1-t2)
α′13=α13+k·cos13·(t1-t3)
Similarly, for the 2 nd and 3 rd reflecting surfaces, there are
α′21=α21
α′22=α22+k·cos22·(t1-t2)
α′23=α23+k·cos23·(t1-t3)
α′31=α31
α′32=α32+k·cos32·(t1-t2)
α′33=α33+k·cos33·(t1-t3)
c、(α′1i,1i)、(α′1i,1i) And (α'1i,1i) Respectively distributed on 3 parallel planes, ideally, the normal vector of the plane corresponds to the zenith, so that the observation equation is established as
Wherein
The solution (A, B,1) is a common normal vector of the three planes, which is the zenith at t1Equatorial coordinate of time, wherein the right ascension is t1A corresponding local fixed star time S;
d. obtaining Greenwich mean sight constant star hour according to the instantaneous longitude lambda of the station, the ascension nutation of the observation time and the local sidereal time SAccording toUT1 is calculated. WhereinThe method can be calculated by the existing theoretical formula for observing the fixed star at the time 0 in the world.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A method for measuring the earth orientation parameters by using a three-field-of-view single-focal-plane optical telescope is characterized in that a reflector with three reflecting surfaces is arranged in front of the optical telescope, the included angle between every two three reflecting surfaces is 135 degrees, a single lens cone of the optical telescope receives light rays from three fixed stars in different sky areas and images the light rays on the same focal plane detector, finally, fixed star images in three different fields of view are obtained simultaneously, and data processing is carried out on the fixed star images in the three different fields of view to measure the earth orientation parameters, and the method specifically comprises the following steps:
(1) extracting the astrology; processing the acquired star images of three different fields of view by using an image processing technology, and extracting a star image from the star image;
(2) separation of different fields of view; for the separation of the star and star images in different sky areas in the observation image of the multi-view-field telescope, a method of correlating the observation images of adjacent frames is adopted, the association of the star and star images in the sky area is established through the speed by utilizing the motion rule of a target, and the star and star images meeting the speed association condition determine the sky area where the star and star images are located, so that the star images extracted in the step (1) are separated into star images of three view fields;
(3) matching fixed stars; carrying out star matching on the star images of the three fields of view respectively, and determining corresponding areas of the three fields of view;
(4) calculating the direction; respectively calculating the directions of the three fields of view according to the matched three fields of view;
(5) calculating the earth orientation parameters; including earth spin axis pointing, polar motion, and UT1 calculations.
2. The method for measuring the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as claimed in claim 1, wherein the star image extraction in the step (1) comprises the following specific steps:
step 1.1) segmenting a star point target in a star image and a star map background by a global threshold method;
step 1.2) highlighting star point pixels by a feature fusion method, wherein the used features are local gray maximum and local contrast mean contrast;
and step 1.3) extracting all pixels of the star point target to obtain a star image.
3. The method for determining the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as claimed in claim 1, wherein the step (2) of separating different fields of view comprises the following specific steps:
step 2.1) selecting a bright star with the measurement coordinate of (x) near the center of the field of view of the kth frame image0,y0)k;
Step 2.2) in a certain range of the centre of the field of view of the (k + 1) th frame image, the range value is set according to the maximum and minimum movement distance of the star between the adjacent frame images, n star images exist, and the measurement coordinate of the star images is (x)i,yi)k+1,i=1,n;
Step 2.3) let x be 1 when i ═ 1i=x0,yi=y0Obtaining Δ x ═ xi-x0,Δy=yi-y0For all the stars in the (k + 1) th frame image, (x '═ x- Δ x, y' ═ y- Δ y) is performedk+1(ii) a Then the measured coordinates (x, y) of all the stars on the image of the k framekComparing one by one, and regarding the star association point pairs established with the difference value smaller than the threshold value, when the logarithm of the association points exceeds a preset number, considering that one day area is successfully screened and separated; otherwise, repeating the process until the screening and separation in one day zone are finished;
step 2.4) after separating the star image of an area of day, selecting a bright star from the rest star images near the center of the field of view of the kth frame image, and repeating the steps 2.1) to 2.3); until all screening and separation of the planetarium in other day areas are completed.
4. The method for measuring the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as claimed in claim 1, wherein the solution method of the instantaneous rotation axis in the step (5) is as follows:
along with the rotation of the earth, in a certain observation period, the instantaneous optical axis of each view field direction points to a plane, the normal vector of the plane is the average instantaneous zenith direction in the period, and the direction of the instantaneous rotation shaft is calculated by using a method for calculating a plane equation; the observation equation is
Wherein (x, y, z) is the direction of the instantaneous optical axis in the international celestial sphere reference system [ GCRS ], and the calculation result is 3 normal vectors (A, B,1) common to the planes, which correspond to the direction of the instantaneous rotation axis in the [ GCRS ] in a certain period of time.
5. The method for measuring the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope according to claim 4, wherein the solution of polar motion in the step (5) is as follows:
after the instantaneous celestial polar directions in a certain period of time are obtained, the latitude and longitude differences corresponding to the instantaneous optical axes in 3 directions are calculated, a certain observation epoch is designated as a reference epoch, and the latitude pointed by the optical axis of the No. 1 mirror is set asLongitude λ100 as the starting point of longitude; meanwhile, the coordinate lambda of the optical axis of the No. 2 mirror pointing to the epoch is determined20Anddetermining the coordinate lambda of the optical axis of the No. 3 mirror pointing to the epoch30And
for other observation epochs t, the polar motion causes the optical axis pointing of the No. 1 mirror to change into
When lambda is10When the value is equal to 0, substituting the formula to obtain
The polar motion causes the optical axis direction of the No. 2 mirror and the No. 3 mirror to change into
To obtain
Wherein the longitudinal difference lambda of the mirror optical axis direction2(t)-λ1(t) and lambda3(t)-λ1(t), using the 'fixed angular distance' between the points, by observation calculation:
for the observation in three directions, the observation equation for resolving the polar motion is:
wherein the content of the first and second substances,
6. the method for determining the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as claimed in claim 5, wherein the solving method of the universal time UT1 in the step (5) is that the three-field-of-view telescope obtains the local sidereal time S corresponding to a certain UTC time by increasing the equal-altitude observation mode, and further obtains the UT 1.
7. The method for measuring the earth orientation parameters by using the three-field-of-view single-focal-plane optical telescope as claimed in claim 6, wherein the solving method of the universal time UT1 comprises the following specific steps:
a. taking the 1 st reflecting surface as an example, t is obtained in sequence by rotating the telescope tube by 120 degrees step lengthi=1,2,3The instantaneous direction of the reflecting surface in the instantaneous equatorial coordinate system corresponds to the optical axis;
b. according to1iAnd tiα is corrected according to the angular velocity of the sidereal sunday movement1iConverting the observation of the optical axis at different times to t1Corresponding Chijing α 'at moment'1iI.e. by
α′11=α11
α′12=α12+k·cos12·(t1-t2)
α′13=α13+k·cos13·(t1-t3)
Similarly, for the 2 nd and 3 rd reflecting surfaces, there are
α′21=α21
α′22=α22+k·cos22·(t1-t2)
α′23=α23+k·cos23·(t1-t3)
α′31=α31
α′32=α32+k·cos32·(t1-t2)
α′33=α33+k·cos33·(t1-t3)
c、(α′1i,1i)、(α′1i,1i) And (α'1i,1i) Respectively distributed on 3 parallel planes, ideally, the normal vector of the plane corresponds to the zenith, so that the observation equation is established as
Ax1i+By1i+z1i+C1=0
Ax2i+By2i+z2i+C2=0 i=1,2,3
Ax3i+By3i+z3i+C3=0
Wherein
xki=cosα′kicoski
yki=sinα′kicoskik=1,2,3;i=1,2,3
zki=sinki
The solution (A, B,1) is a common normal vector of the three planes, which is the zenith at t1Equatorial coordinate of time, wherein the right ascension is t1A corresponding local fixed star time S;
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