CN110068312B - Digital zenith instrument positioning method based on spherical triangle - Google Patents

Digital zenith instrument positioning method based on spherical triangle Download PDF

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CN110068312B
CN110068312B CN201910380589.5A CN201910380589A CN110068312B CN 110068312 B CN110068312 B CN 110068312B CN 201910380589 A CN201910380589 A CN 201910380589A CN 110068312 B CN110068312 B CN 110068312B
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周召发
张志利
刘先一
常振军
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Rocket Force University of Engineering of PLA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C15/00—Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations

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Abstract

The invention relates to a digital zenith instrument positioning method based on spherical triangles, which is carried out on a general digital zenith instrument, has a star map and an identification program, and is characterized in that: extracting inclination angle data of a double-shaft inclinometer arranged on a zenith instrument; constructing an inclination correction model of the biaxial inclinometer; resolving an astronomical coordinate; compensating a biaxial inclinometer shafting; and acquiring astronomical coordinates of the survey station. Compared with the prior art, the method is not easily influenced by the coarse value when the mode is adopted for positioning, the factors directly influencing the precision of the positioning result can be eliminated, and the test data analysis shows that the longitude and latitude difference between the finally solved measuring station position and the actual position is within 0.3 ″, so that the influence of partial coarse values on the positioning result is effectively overcome. High-precision positioning of the station to be measured is realized.

Description

Digital zenith instrument positioning method based on spherical triangle
Technical Field
The invention belongs to the technical field of geodetic astronomical measurement, relates to a digital zenith instrument positioning method, and particularly relates to a high-precision digital zenith instrument positioning method based on a spherical triangle.
Background
The digital zenith instrument is a high-precision astronomical positioning instrument, can be used for acquiring astronomical coordinates of a station to be measured, and has the characteristics of high automation degree, small influence of human factors and the like. The research on the digital zenith instrument is firstly carried out in Germany, and then, the research units such as the university of Zurich in Switzerland and the like successively carry out related researches. In China, units such as Chinese academy of sciences and Shandong science and technology university develop a digital zenith instrument prototype. At present, when the units are positioned by adopting a digital zenith instrument, celestial coordinates of celestial tangent planes are mainly obtained through astronomical coordinates of fixed stars, the astronomical coordinates pointed by a rotating shaft are solved by establishing a corresponding relation between image coordinates of the fixed stars and the celestial tangent plane coordinates, and finally, the inclination angle compensation and the average value calculation are carried out to complete the positioning of a station. When the mode is adopted for positioning, the influence of a rough value is easy to occur, and the precision of a positioning result is directly influenced. Although the construction of the spherical triangle is involved in the article "image processing of digital zenith camera" published by greater aspiration and Xiong et al in 2004 in "Photonic newspapers" 33, 2 nd and the application of the spherical triangle method in digital zenith camera "published by Liu Xian et al in 2015 in geodetic survey and Earth dynamics" 35, 4 th, 35 th, the application of the spherical triangle in image processing and iterative operation of star points is mainly discussed, the inclination of the instrument and the axis system error of the instrument are not analyzed, and the high-precision positioning of the instrument cannot be realized. In the digital zenith instrument rotation axis solution (invention patent application number: 201110406263.9) applied by zhanghuawei et al, star maps shot in different directions are adopted, and a specific solution is provided for the rotation axis coordinates of the digital zenith instrument, but no specific research is carried out on the positioning method.
Disclosure of Invention
In view of the above-mentioned state of the art, the present invention aims to: the method for positioning the digital zenith instrument based on the spherical triangle is provided, so that the influence of a coarse value on a positioning result is reduced, and the positioning precision of the instrument is improved.
The concept and technical solution of the present invention will now be described as follows:
the basic concept of the invention is as follows: when the digital zenith instrument is positioned, firstly, a double-shaft inclinometer arranged on the zenith instrument is used for measuring an inclination angle, the inclination is corrected, a star point image coordinate is corrected to be in a horizontal state, then a spherical triangle is constructed, a theoretical value of the star point image coordinate is calculated, iterative operation is carried out through a difference value between the star point image coordinate theoretical value and the correction value to obtain an astronomical coordinate pointed by an optical axis of the instrument, and finally, shafting compensation is carried out in a least square circle fitting mode to realize high-precision positioning of a station to be measured.
The invention relates to a digital zenith instrument positioning method based on spherical triangles, which is carried out on a general digital zenith instrument, is provided with a star map and an identification program, and is characterized in that: the method comprises five steps of extracting inclination angle data of a double-shaft inclinometer installed on a zenith instrument, constructing an inclination correction model, resolving astronomical coordinates and compensating a shafting, and specifically comprises the following steps:
step 1: extracting tilt angle data of a dual axis inclinometer mounted on a zenith gauge
Extracting star point image coordinates in the star map and inclination angle data u and v recorded in the star map by adopting a gray-scale weighting method;
step 2: tilt correction model for constructing biaxial inclinometer
Step 2.1: the installation angle of the double-shaft tilt angle sensor is beta, the angle measured by the double-shaft tilt angle sensor is small, and the included angle theta between two directions of the CCD image sensor and the horizontal plane can be obtained1And theta2Comprises the following steps:
Figure BDA0002053244940000021
step 2.2: the focal coordinates of the biaxial inclinometer are (0,0, f), and the image coordinates of the star point in the inclined state are (x)0,y00), the image coordinate value when the star point image coordinate is corrected to the horizontal state is (x, y,0):
Figure BDA0002053244940000022
step 2.3: the fixed star light is parallel light at infinity, the directions of star light vectors are parallel, and the coordinates of the corrected star point image are as follows:
Figure BDA0002053244940000023
Figure BDA0002053244940000024
step 3; solution of astronomical coordinates
Step 3.1: a spherical triangle is formed by a north pole P of a celestial sphere, an approximate position (alpha ', delta') pointed by an optical axis of a biaxial inclinometer and any star (alpha, delta), and theoretical coordinates (x ', y') of the acquirable star (alpha, delta) in an image coordinate system are as follows:
Figure BDA0002053244940000031
the error equation of the image coordinate of any star is as follows:
V＝BΔX+f (5)
the following can be obtained:
ΔX＝-(BTB)-1BTf (6)
in the formula
Figure BDA0002053244940000032
Step 3.2: the deviation value DeltaX is added to the initial value to carry out 3 to 5 times of iterative calculation, and the astronomical coordinate (alpha) pointed by the optical axis can be solvedi,δi) Resolving astronomical coordinates of the shot plurality of star maps to obtain a group of data;
and 4, step 4: compensation of biaxial inclinometer shafting
Step 4.1: when the biaxial inclinometer rotates to shoot a star chart, an optical axis forms a conical surface around a rotating shaft, a circle is drawn on a celestial sphere, and in order to eliminate shafting errors and overcome the influence of a coarse value on a positioning result, a least square fitting circle algorithm is adopted to point to a coordinate (alpha) of the optical axisi,δi) Performing circle fitting to compensate shafting error between the optical axis and the rotating shaft, wherein the circle center coordinate, namely the astronomical coordinate of the measuring station represented by the rotating shaft direction is (alpha)0,δ0) Then, there are:
(αi-α0)2+(δi-δ0)2＝R2 (7)
can obtain the product
Figure BDA0002053244940000033
And 5: acquiring astronomical coordinates of survey station
Objective function fitting according to least squares
Figure BDA0002053244940000034
The equation obtained from equation (8) is:
Figure BDA0002053244940000041
Figure BDA0002053244940000042
the astronomical coordinate (alpha) with high precision of the station can be obtained by the least square fitting circle algorithm0,δ0)：
Figure BDA0002053244940000043
Compared with the prior art, the method can be free from the influence of a coarse value when positioning is carried out by adopting the mode, eliminates the factors directly influencing the positioning precision, and realizes the high-precision positioning of the station to be measured.
Drawings
FIG. 1: positioning flow chart block diagram
FIG. 2: installation schematic diagram of double-shaft inclinometer in digital zenith instrument
FIG. 3: schematic diagram of change of fixed star image point image coordinate system
FIG. 4: fixed star projection principle diagram
FIG. 5: biaxial inclinometer shafting error schematic diagram
FIG. 6: astronomical coordinate pointed by optical axis of biaxial inclinometer
FIG. 7: resolving result of astronomical coordinates of station survey
FIG. 8: comparison of astronomical longitudes
FIG. 9: comparison of astronomical latitudes
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
Referring to fig. 1: the invention relates to a digital zenith instrument positioning method based on spherical triangles, which comprises five steps of extracting inclination angle data of a double-shaft inclinometer installed on a zenith instrument, constructing an inclination correction model, resolving astronomical coordinates and compensating shafting.
Referring to fig. 2: the method specifically comprises the following steps:
step 1: erecting a digital zenith instrument on a measuring station, leveling the instrument, shooting a star map by rotating, and shooting 16 star maps by the digital zenith instrument in a positioning cycle; processing the star map by using methods such as gray scale weighting and the like, extracting inclination angle data recorded in the star map, and identifying fixed star points in the star map;
step 2: constructing a tilt correction model by using the model,
step 2.1: the installation angle of the double-shaft inclination angle sensor is beta, the angle measured by the double-shaft inclination angle meter is generally about 2', and the angle still belongs to a small angle. The included angle between two directions of the CCD image sensor and the horizontal plane is theta1And theta2. Then there are:
Figure BDA0002053244940000051
referring to fig. 3: the method specifically comprises the following steps:
step 2.2: on a CCD image sensor, coordinates o-x are established0y0z0When the digital zenith instrument is in a horizontal state, a coordinate system o-xyz is established, and since the angle measured by the biaxial inclination angle sensor is a small angle, ox during inclination can be considered0The angle between the coordinate axis and the coordinate axis ox in the horizontal state is theta1，oy0The included angle between the axis and the oy axis is theta2Then there is sin θ1＝θ1， cosθ1＝1，sinθ2＝θ2，cosθ21, imaging a star light on a CCD (charge coupled device) image sensor through an instrument focus (0,0, f), and imaging a star point on a coordinate system o-x0y0z0The image coordinate value in (b) is (x)0,y00), when the star point image coordinate is corrected to be in a horizontal state, the star point image coordinate is (x, y,0), thenIs provided with
Figure BDA0002053244940000052
Step 2.3: the fixed star light can be equivalent to parallel light at an infinite position, the direction vectors of the fixed star light are parallel, and the coordinates of the corrected star point image are as follows:
Figure BDA0002053244940000053
referring to fig. 4: the method specifically comprises the following steps:
and step 3: solution of astronomical coordinates
Step 3.1: a set of astronomical coordinates (alpha) pointed by the optical axis of the instrument is obtained by constructing a spherical triangle to solve the position information pointed by the optical axis of the instrumenti,δi) The north pole P of the celestial sphere, the approximate position (alpha ', delta') pointed by the optical axis and any star (alpha, delta) form a spherical triangle, and the theoretical coordinate values (x ', y') of the star (alpha, delta) in the image coordinate system can be solved as follows:
Figure BDA0002053244940000061
the offset derivative calculation is carried out on the formula (4), and the error equation of the image coordinate of any star can be obtained as
V＝BΔX+f (5)
Then there are:
ΔX＝-(BTB)-1BTf (6)
in the formula:
Figure BDA0002053244940000062
step 3.2: the deviation value DeltaX is added to the initial value to carry out 3 to 5 times of iterative calculation, and the astronomical coordinate (alpha) pointed by the optical axis can be solvedi,δi). Resolving each shot star map to obtain an optical axis pointing astronomical coordinate value;
referring to fig. 5: the method specifically comprises the following steps:
and 4, step 4: compensation of shafting
Step 4.1: compensating shafting errors between the optical axis and the rotating shaft by adopting a least square fitting circle algorithm to obtain an astronomical coordinate (alpha) of the station0,δ0) When the instrument rotates to shoot a star map, an optical axis forms a conical surface around a rotating shaft, a circle is drawn on a celestial sphere, and a circle fitting method is provided for eliminating shafting errors and overcoming the influence of a coarse value on a positioning result; according to the rotation characteristic of the optical axis, the coordinates of the rotating shaft are determined in a circle fitting mode, and the circle center coordinates, namely the astronomical coordinates of the measuring station represented by the direction of the rotating shaft, are (alpha)0,δ0) Then, there are:
(αi-α0)2+(δi-δ0)2＝R2 (7)
the optical axis is directed to an astronomical coordinate of (alpha)i,δi) (iii) converting (7) to the form of:
Figure BDA0002053244940000063
referring to fig. 6: it can be known from fig. 6 that the CCD image sensor has a tilt error of installation, that is, the optical axis does not coincide with the rotation axis, and specifically includes:
the objective function can be obtained by least square fitting
Figure BDA0002053244940000064
From formula (8):
Figure BDA0002053244940000071
astronomical coordinates (alpha) of the measuring station can be obtained by resolving through the formula (9)0,δ0)
Figure BDA0002053244940000072
See fig. 6, 7, 8, 9, table 1, table 2: analysis of test data
In the experiment process, the field angle of the adopted digital zenith instrument is 3 degrees multiplied by 3 degrees, the focal length value is 600mm, the resolution of the CCD image sensor is 4096 multiplied by 4096, the pixel size is 9um, the positioning experiment is carried out on the known measuring station, the astronomical coordinates of the measuring station are (109.12122 degrees and 34.31601 degrees), the shot fixed star-star image is identified, and the identified star point data are shown in table 1.
TABLE 1 Star data identified
CCD x coordinate/pixel CCD y-coordinate/pixel Star astronomical longitude/deg Star astronomical latitude/° Star number of stars
3855.801 3079.531 108.380 36.016 53726
656.146 2625.929 108.217 33.240 53673
732.742 3420.629 107.427 33.430 53426
1379.950 3921.460 107.036 34.055 53305
553.485 1213.632 109.619 32.918 54134
2725.060 3459.897 107.763 35.122 53525
3499.175 436.301 111.044 35.257 54581
1303.321 3712.895 107.235 33.958 53377
3473.853 3507.852 107.858 35.762 53563
1758.855 433.048 110.661 33.794 54471
2261.066 479.984 110.723 34.225 54491
3129.918 1422.246 109.948 35.125 54239
2713.148 668.033 110.631 34.639 54460
1929.762 1611.214 109.501 34.146 54086
2095.317 1554.488 109.594 34.276 54119
2800.351 962.432 110.349 34.766 54369
2989.667 440.333 110.926 34.830 54548
416.500 1054.500 109.750 32.775 54183
2038.889 2505.444 108.610 34.388 53801
The measurement data of the two-axis inclinometer are shown in table 2.
TABLE 2 measurement data of a two-axis inclinometer
Star map serial number X-axis reading /) " Y-axis reading /) " Star map serial number X-axis reading /) " Y-axis reading /) "
1 73.64 -74.67 9 -49.01 64.05
2 -6.81 -111.38 10 -108.15 13.86
3 -84.77 -81.06 11 54.97 11.47
4 -122.32 -8.87 12 100.45 5.56
5 100.24 5.36 13 -21.91 49.08
6 64.97 81.68 14 -13.74 10.86
7 -18.15 114.27 15 25.36 -10.15
8 -99.21 74.05 16 34.87 -32.81
The measurement data of the biaxial inclinometer is combined to perform inclination correction on the star point image coordinates, and the astronomical coordinates pointed by the optical axis of the instrument are calculated, and the result is shown in fig. 6. As can be seen from fig. 6, the CCD image sensor has a tilt error in mounting, that is, the optical axis does not coincide with the rotation axis. And fitting the astronomical coordinates pointed by the optical axis by adopting a least square fitting circle algorithm, and as can be seen from fig. 7, the influence of a coarse value on a positioning result can be overcome after the least square fitting is adopted. A large number of experiments are carried out by adopting the method, and the positions of the solved measuring station positions are compared, as shown in figure 8. The data analysis shows that the longitude and latitude difference between the position of the finally solved measuring station and the actual position is within 0.3 ″, the accuracy of the positioning result is high, and the influence of partial coarse values on the positioning result can be effectively overcome.

Claims (1)

1. A digital zenith instrument positioning method based on spherical triangles is carried out on a general digital zenith instrument, is provided with a star map and an identification program, and is characterized in that: the method comprises the following steps:
step 1: extracting inclination angle data of a double-shaft inclinometer installed on the zenith instrument;
step 2: constructing an inclination correction model of the biaxial inclinometer; the method specifically comprises the following steps:
step 2.1: the installation angle of the double-shaft tilt angle sensor is beta, the angle measured by the double-shaft tilt angle sensor is small, and two directions of the CCD image sensor can be obtainedAngle theta with horizontal plane1And theta2Comprises the following steps:
Figure FDA0002855608960000011
step 2.2: the focal coordinates of the biaxial inclinometer are (0,0, f), and the image coordinates of the star point in the inclined state are (x)0,y00), the image coordinate value when the star point image coordinate is corrected to the horizontal state is (x, y,0):
Figure FDA0002855608960000012
step 2.3: the fixed star light is parallel light at infinity, the directions of star light vectors are parallel, and the coordinates of the corrected star point image are as follows:
Figure FDA0002855608960000013
step 3; resolving astronomical coordinates; the method specifically comprises the following steps:
step 3.1: a spherical triangle is formed by a north pole P of a celestial sphere, an approximate position (alpha ', delta') pointed by an optical axis of a biaxial inclinometer and any star (alpha, delta), and theoretical coordinates of the star (alpha, delta) in an image coordinate system are (x ', y'):
Figure FDA0002855608960000014
the error equation of the image coordinate of any star is as follows:
V＝BΔX+f (5)
the following can be obtained:
ΔX＝-(BTB)-1BTf (6)
in the formula
Figure FDA0002855608960000021
Step 3.2: the deviation value DeltaX is added to the initial value to carry out 3 to 5 times of iterative calculation, and the astronomical coordinate (alpha) pointed by the optical axis can be solvedi,δi) Resolving astronomical coordinates of the shot plurality of star maps to obtain a group of data;
and 4, step 4: compensation of a biaxial inclinometer shafting; the method specifically comprises the following steps:
when the biaxial inclinometer rotates to shoot a star chart, an optical axis forms a conical surface around a rotating shaft, a circle is drawn on a celestial sphere, and in order to eliminate shafting errors and overcome the influence of a coarse value on a positioning result, a least square fitting circle algorithm is adopted to point to a coordinate (alpha) of the optical axisi,δi) Performing circle fitting to compensate shafting error between the optical axis and the rotating shaft, wherein the circle center coordinate, namely the astronomical coordinate of the measuring station represented by the rotating shaft direction is (alpha)0,δ0) Then, there are:
(αi-α0)2+(δi-δ0)2＝R2(7) can obtain the product
Figure FDA0002855608960000022
And 5: acquiring astronomical coordinates of a station; the method specifically comprises the following steps:
objective function fitting according to least squares
Figure FDA0002855608960000023
The equation obtained from equation (8) is:
Figure FDA0002855608960000024
Figure FDA0002855608960000025
obtaining high-precision astronomical coordinates (alpha) of station by least square fitting circle method0,δ0)：
Figure FDA0002855608960000026
Figure FDA0002855608960000027
。
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