CN104913780B - The high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes - Google Patents
The high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes Download PDFInfo
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Abstract
The invention discloses a kind of high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes, it passes through on survey station point, make the optical axis of zenith telescope point to zenith direction to shoot zenith region, obtain CCD star chart pictures, and the image coordinate of wherein fixed star is calculated, pass through the GNSS geodetic coordinates measured and GNSS time signal control exposure epoch, the survey station deviation of plumb line calculated with reference to EGM2008 gravity field models, zenith region fixed star information is obtained in star catalogue is applicable, realize the match cognization of the zenith section region fixed star and fixed star in CCD star chart pictures of celestial sphere in star catalogue, zenith astronomic coordinate is iterated to calculate using least square method, the deviation of plumb line of observation station can be calculated with reference to geodetic coordinates.The present invention is relative to prior art, the features such as with easy to operate, time saving and energy saving and high measurement accuracy, the quick measurement suitable for the high-precision deviation of plumb line.
Description
Technical field
The present invention relates to a kind of astronomical geodesy method of deviation of plumb line, more particularly to a kind of integrated GNSS and CCD days
Push up the high-precision deviation of plumb line method for fast measuring of cylinder.
Background technology
The angle between normal line vector n on ground on any gravity vector g and corresponding ellipsoid is defined as the point
The deviation of plumb line.The deviation of plumb line characterizes the direction of gravity, is geodesic survey reduction, earth gravitational field and geoid's model essence
Change, study the necessary earth physical quantity of the figure of the earth, have important use in terms of geodesic survey and space technology.
The deviation of plumb line is the performance of earth interior Mass Distribution, available for inverting air abnormal refraction research, monitors the earth
Internal soundness is migrated and energy accumulation, the natural calamity such as monitoring earthquake, volcano eruption, it can also be used to Underground abnormal quality,
Carry out resource exploration.In military field, basic data necessary to the deviation of plumb line is guided missile, rocket launching etc..
In the prior art, conventional deviation of plumb line observation procedure, the main traditional astronomical geodesy method, gravity of including is surveyed
Amount method, astrogravimetric method and GPS leveling measuring methods.But, these above-mentioned method generally existing basic datas
Gatherer process is complicated, or just can not effectively obtain at all, later data processing procedure very complicated, the shortcomings of waste time and energy or
It is not enough：
Traditional astronomical geodesy method, generally using astronomical theodolites such as T4, J05, is equipped with a set of punctual, time service system
System.Telgte methods are commonly used in the observation of its astronomical latitude, and the observation of astronomical longitude commonly uses double star equal altitude method and includes wireless simultaneously
Electric time signal.The deviation of plumb line precision that this method is obtained can reach 0.3 ".
But, for this traditional astronomical geodesy method, generally, it is used in order that accuracy of observation is sufficiently high
Astronomical theodolite volume it is all very big, very heavy；And the operation of instrument is too high to observer's skill requirement, observation time very
It is long, extremely inefficient.Moreover, its conventional punctual, time dissemination system, not only complex operation, precision is relatively low, and easily error.
Gravimetric Method, mainly by means of the gravity anomaly on geoid and earth ellipsoid face, utilizes Stokes
Or VeningMeinesz formula calculate the deviation of plumb line.
However, the premise of this method assumes that no disturbance material outside geoid, and it is with the proviso that, it is necessary to right
Global gravity anomaly data are, it is known that this is very difficult and not real.Therefore, this method does not obtain independent answer also
With, and the measurement accuracy of the deviation of plumb line of this method is also relatively low.
Astrogravimetric method, its essence is combine astronomical geodesy method and Gravimetric Method to determine vertical line
Deviation.Then this method is encrypted firstly the need of the deviation of plumb line value of a number of astrogeodetic point using Gravimetric Method
Gravity anomaly data, the deviation of plumb line value of other points is determined using least square collocation or Multi-surface fitting method.
The major defect of this method is that the deviation of plumb line precision obtained is relatively low.
GPS leveling measuring methods, it is necessary to carry out GPS measurements and the measurement of the level simultaneously, obtain base length, geodetic azimuth and
The difference of height anomaly, it is possible to obtain the deviation of plumb line.
The limitation however, use of this method is had ready conditions, such as, carried out for the larger region of some hypsographies
The difficulty of precise leveling is too big, and baseline can not be long, and due to the influence of base length and geodetic azimuth, causes it to ask
The deviation of plumb line precision gone out is relatively low.
The content of the invention
There is pervasive characteristic it is an object of the present invention to provide one kind, and the data acquisition of the high-precision deviation of plumb line is saved
Shi Shengli, a kind of relatively simple high-precision deviation of plumb line of integrated GNSS and CCD zenith telescopes of processing method of data are quickly surveyed
Amount method.
The present invention to achieve the above object the technical scheme adopted is that a kind of integrated GNSS and CCD zenith telescopes it is high-precision
Spend deviation of plumb line method for fast measuring, it is characterised in that comprise the following steps：
The first step, sets up CCD zenith telescopes on survey station point, its optical axis is pointed to zenith direction, and zenith region is continuously existed
0 ° and 180 ° of directions are shot, and obtain CCD star chart pictures, and obtain by high-precision electronic level meter the inclination number of zenith telescope
According to by GNSS acquisition observation time information and the geodetic coordinates of survey station point；
Second step, the CCD star chart pictures of the FITS forms shot to CCD zenith telescopes are read out, then carry out ambient noise
Eliminate；
3rd step, the CCD star charts picture after being eliminated to noise carries out the automatic search in fixed star astrology region；
4th step, with the two-dimentional Moment Methods of improved amendment, calculates the energy in the above-mentioned fixed star astrology region searched out automatically
The image coordinate at amount center；
5th step, is handled being applicable star catalogue, by the GNSS temporal informations obtained and the geodetic coordinates of survey station point,
The rough astronomic coordinate of survey station point is calculated with reference to EGM2008.According to result in star catalogue with CCD star charts as corresponding region is entered
Row interception, and the independent equatorial coordinate system and apparent magnitude information in time of exposure zenith region are calculated, and independent equatorial coordinate system is projected
Plane coordinates is converted on to section；
6th step, is identified to the fixed star that the astrology in CCD images and star catalogue are projected in plane, matches；
7th step, according to the star pair that the match is successful, using in least square method computational photogrammetry projective transformation formula
Coordinate Conversion coefficient, and the initial equatorial coordinates of survey station point is iterated to calculate, it is reconverted into the initial astronomic coordinate of survey station point；
8th step, the zenith telescope slope correction data that high-precision electronic level meter is obtained and Ghandler motion correction data conversion are extremely
On meridian direction and fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches direction, the accurate astronomic coordinate of survey station point is determined；
9th step, the survey station point geodetic coordinates calculated with reference to GNSS measurement data, utilizes Helmert formula, you can meter
Calculate the deviation of plumb line of survey station point.
The technical effect directly brought by the technical proposal is that, deviation of plumb line method for fast measuring is based on GNSS and CCD days
Cylinder is pushed up, on the basis of measurement accuracy and resolution ratio needs is met, using improved data acquisition and processing method, is reduced vertical
The time that line deviation acquisition process is consumed, measurement efficiency is improved, disclosure satisfy that high measurement accuracy and without territory restriction etc.
It is required that.
Preferably, it is 3 × 3 median filtering methods that above-mentioned ambient noise, which eliminates used method, is comprised the following steps that：
Step one, 3 × 3 neighborhoods put centered on some pixel are determined；
Step 2, by the gray value (x of each pixel in the neighborhood1,x2,x3,...,xn) by being ranked up from small to large：
x1≤x2≤x3...≤xn；
Step 3, the intermediate value Y of the gray value of each pixel is calculated by formula：
Step 4, the gray value of original central point is replaced with intermediate value Y, carries out medium filtering；
Step 5, is determined 3 × 3 neighborhoods put centered on one other pixel, repeats the above steps two to step 4,
Until whole pixel filters are completed.
What the optimal technical scheme was directly brought has the technical effect that, fixed star discrimination improves about 60%, increasing before and after denoising
Add observed quantity, largely reducing influence of the random noise for CCD fixed star image procossings.Deviation of plumb line meridional component and the fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches
The standard deviation of component compared to 0.016 " and 0.021 " is averagely reduced respectively before denoising, inner symbol precision increases.
3 × 3 medium filterings be it is a kind of based on sequencing statistical it is theoretical can remove the non-linear processing methods of noise, it is substantially former
Reason is that the gray value in digital picture is replaced with the Mesophyticum of each point gray value in 3 × 3 neighborhoods of the point.
Here neighborhood is commonly known as window, after window is moved up and down in the picture, is filtered using intermediate value
Ripple can carry out denoising to image well.
Further preferably, the automatic search in above-mentioned fixed star astrology region is carried out using algorithm of region growing.
What the optimal technical scheme was directly brought has the technical effect that, is carried out using algorithm of region growing in CCD star chart pictures
The astrology search for automatically, its method is simple, and the time of required cost is shorter.
Reason is that the general principle of algorithm of region growing is one minimal gray threshold value of setting, if certain in ccd image
Region is made up of the close some adjacent pixels of gray value, and each grey scale pixel value is all higher than minimal gray threshold value in the region,
Then judge the region as a fixed star astrology region.
Further preferably, the above-mentioned two-dimentional Moment Methods of improved amendment, are on the two-dimentional Moment Methods of conventional amendment, with repeatedly
Threshold value is improved for computational methods, its step is as follows：
1st step, extracts maximum gradation value g in CCD star chart picturesmaxWith minimum gradation value gmin, order
2nd step, according to threshold value TkCCD star chart pictures are divided into astrology region and background area, wherein, astrology region position
Put (xi,yj) gray value gk+1(xi,yj) ＞ 0, and the gray value of background area is 0, as shown by the equation：
Then, the average gray value in astrology region is tried to achieve by formula (4)：
OrderFormula (4) is substituted into, can be obtained：
3rd step, sets a positive number μ, if | Tk-Tk+1| ＜ μ, then iterative process is terminated, is tried to achieve by formula (6)
Optimal threshold：
T=Tk+B (6)
If | Tk-Tk+1| >=μ, then make Tk=Tk+1, proceed the iterative calculation of the 2nd step.
4th step, by formula (7) and formula (8), obtains astrology regional center coordinate in CCD star chart pictures：
What the optimal technical scheme was directly brought has the technical effect that, on the basis of conventional two dimension amendment square algorithm, with repeatedly
Threshold value T is improved for method so that astrology centralized positioning precision is greatly improved, positioning precision standard deviation is controlled in 0.1-0.15 pictures
Element, the influence to deviation of plumb line measurement accuracy is controlled 0.1 " in.Further preferably, the above-mentioned processing for being applicable star catalogue is by adjusting
With the NOVAS-F programs in AURIGA, and combine the temporal information that GNSS is obtained, the star place observed to epoch of observation with
It is applicable star catalogue epoch fixed star prosposition and puts each influent factor having differences and corrected, with obtaining fixed star in star catalogue apparent place put；
Then, region corresponding with CCD fixed star star images in star catalogue is intercepted, interception process is divided into two steps：
The first step, first can to this observation period in star catalogue before the digital zenith telescopes of integrated CCD and GPS are observed
It can be intercepted by the fixed star information in survey station point zenith region, star catalogue possibly be present at zenith area when intercepting scope with by observation
Fixed star in the visual field of domain is all covered as principle, its survey station point equatorial coordinates (α2,δ2) tried to achieve by equation below (9)：
δ2=Φ2
α2=Λ2+GAST (9)
In above formula (9), (Φ2,Λ2) be survey station point initial astronomic coordinate, the initial astronomic coordinate be using GNSS the earth
Measurement result and EGM2008 gravity field models calculate the deviation of plumb line of survey station point, then push away survey station point astronomic coordinate, take near
Seemingly it is worth to；
The star catalogue interception scope is more than digital zenith telescope visual field；
After interception scope is determined, with apparent position calculation of star model to being likely to occur within the range in observation period
Fixed star information intercepted, and these information are stored；
Second step, before fixed star matching work is carried out, need to further be intercepted to above star catalogue region, enable the region
Enough completely corresponding with CCD fixed star image-regions, it is as follows that it intercepts condition：
αmin＜ α1＜ αmax
δmin＜ δ1＜ δmax (10)
In above formula (10)：
(α1,δ1) for the equatorial coordinates of fixed star in the visual field of zenith region；
αmin、αmax、δmin、δmaxDepending on the equatorial coordinates (α of survey station point2,δ2) and digital zenith telescope visual field Fi, it is counted
Calculate formula as follows：
αmin=α2-Fi/2
αmax=α2+Fi/2 (11)
δmin=δ2-Fi/2
δmax=δ2+Fi/2
It is described independent equatorial coordinate system is projected in plane be converted to plane coordinates be by projective transformation formula (12) and
(13) calculate：
M=tan (q- δ2) (13)
In above formula (12) and (13)：
Cotq=cot δ1cos(α1-α2)；
(l, m) is fixed star plane coordinates；
(α1,δ1) for the equatorial coordinates of fixed star in the visual field of zenith region。
Explanation：It is above-mentioned that " star place that epoch of observation observes puts what is had differences with applicable star catalogue epoch fixed star prosposition
Each influent factor " refers in the processing procedure of star catalogue is applicable, and is seen based on the zenith telescope on earth surface survey station point
The fixed star in the zenith region measured, by stellar proper motion, the precession of the equinoxes, nutating, annual parallax, annual aberration, diurnal parallax, Sunday
The influence of the factors such as aberration, astronomical refraction, the star place that epoch of observation observes is put with applicable star catalogue epoch fixed star prosposition and deposited
In difference, the present invention calls the NOVAS-F programs in AURIGA, with reference to the GNSS temporal informations obtained and the earth of survey station point
Coordinate, is corrected above influent factor, obtains the independent equatorial coordinate system and apparent magnitude information in time of exposure zenith region.
What the optimal technical scheme was directly brought has the technical effect that, 1, new star catalogue intercept method be divided into two steps, exist respectively
Star catalogue is intercepted twice before observation and in observation, what the optimal technical scheme was directly brought has the technical effect that, before observation
The fixed star that possibly be present at zenith region is realized and intercepted, then need to only be intercepted out when to observation generating date in the first step
Intercepted in star catalogue so that the match is successful that rate is significantly improved for fixed star identification, the whole identification matching process used time is less than 0.3 second；
2nd, star catalogue interception scope have to be larger than digital zenith telescope visual field, it can be ensured that the fixed star in digital zenith telescope visual field is not
As for any omission of appearance；Generally, above-mentioned star catalogue can be intercepted to scope to select as 2 times of digital zenith telescope visual field, so,
It is easy to practical operation, operating efficiency can be improved.
Further preferably, identification, the matching of above-mentioned fixed star are carried out using quadrangle algorithm, and its matching principle is CCD
The four edges ratio of the quadrangle of four bright star compositions is identical in the quadrangle and star catalogue of four bright star compositions in star chart picture, i.e.,
Formula (14)：
Order(i=1,2,3,4), then side ratio SCiStandard deviation calculated by formula (15)：
In above formula (15),
Then think that four bright stars minimum σ in CCD star chart pictures are matched with four bright stars in star catalogue；
According to four bright stars that the match is successful, initial coordinate transformation model is calculated by formula (16), (17)：
In above formula (16), (17)：
(X, Y) is the plane coordinates after bright star projection in star catalogue；
(x, y) is the image coordinate of the astrology in CCD star chart pictures；
Then, using least square method, initial coordinate transformation model is calculated by formula (18)：
Other astrology in initial coordinate transformation model, CCD star chart pictures according to obtained by calculating in addition to four bright stars are sat
Mark, and the plane coordinates of the star of other in star catalogue complete the matchings of institute any stars；
Coordinate Transformation Models are recalculated further according to the matching result of all stars, are rejected after the poor fixed star of matching result,
Calculate final Coordinate Transformation Models.
What the optimal technical scheme was directly brought has the technical effect that, Quadrilateral Method implement comparison it is easy and identification matching
Precision is higher.
Further preferably, the calculating of above-mentioned astronomic coordinate refers to, obtains the image coordinate and star of the astrology in CCD star chart pictures
After the Coordinate Transformation Models of plane coordinates in table after fixed star projection, CCD star chart pictures are photographed using 0 ° and 180 ° of directions, are pressed
Following steps carry out what survey station point astronomic coordinate was calculated：
(1) step, it is assumed that survey station point is located at the center of ccd image, i.e., (x, y)z=(0,0)；
(2) step, according to the Coordinate Transformation Models calculated, obtains the initial plane coordinate (X, Y) of survey station pointz, then root
The initial equatorial coordinates of survey station point is calculated according to the inverse operation formula of photogrammetric projective transformation formula；
(3) step, the initial equator of survey station point that the CCD star charts picture shot respectively according to 0 ° and 180 ° of directions is obtained is sat
Mark, (19), (20) calculate the initial astronomic coordinate (Φ of survey station point as follows1,Λ1)、(Φ2,Λ2)：
Φ=δ (19)
Λ=α-GAST (20)
In above-mentioned formula (19), (20)：
(Φ, Λ) is survey station point astronomic coordinate；
(δ, α) is survey station point equatorial coordinates；
GAST is the Greenwich hour angles calculated according to GNSS time information；
Then, (Φ is calculated by formula (21), (22)1,Λ1)、(Φ2,Λ2) average value：
(4) step, by (Φ, Λ) inverse to equatorial coordinates, survey station is recalculated according to photogrammetric projective transformation formula
Point plane coordinates (X, Y)z1、(X,Y)z2；
The CCD image coordinates (x, y) of survey station point are calculated further according to Formula of Coordinate System Transformationz1、(x,y)z2；
(5) step, repeats above iterative process, until the difference of the astronomic coordinate of twice adjacent calculation is less than a certain give
Fixed number value, then calculating process terminate, take the average of the last result of calculation of astronomic coordinate twice to be sat as the astronomy of observation station
Mark；
(6) step, the instrument horizontal data obtained according to high-precision electronic level meter, is calculated by formula (23), (24)
The horizontal corrected value of instrument：
δΦl=cos (θ+β) n1-sin(θ+β)n2 (23)
δΛl=sin (θ+β) n1+cos(θ+β)n2/cosΦ (24)
In above-mentioned formula (23), (24)：
θ is the reference axis of CCD coordinate systems in image and the angle of east-west direction；
β is the reference axis of CCD coordinate systems in image and the angle of high-precision electronic level meter axle；
n1、n2The instrument tilting value recorded for high-precision electronic level meter；
Ghandler motion corrected value is calculated by formula (25), (26) again, with the CCD image datas that are obtained to instrument by Ghandler motion shadow
Ring and carry out Ghandler motion correction：
δΦp=-(xpcosΛ-ypsinΛ) (25)
δΛp=-(xpsinΛ+ypcosΛ)tanΦ (26)；
In above-mentioned formula (25), (26)：
(xp,yp) be instantaneous pole coordinate；
(Φ, Λ) is the astronomic coordinate of survey station point.
Above-mentioned Helmert formula are formula (27) and formula (28)：
ξ=Φ-φ (27)
η=(Λ-λ) cos φ (28)；
In above-mentioned formula (27), (28)：
ξ is the meridional component of the deviation of plumb line；
η is the fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches component of the deviation of plumb line；
(Φ, Λ) is survey station point astronomic coordinate；
(φ, λ) is survey station point geodetic coordinates.
What the optimal technical scheme was directly brought has the technical effect that, the CCD star chart pictures shot with 0 ° and 180 ° of directions
Result iterates to calculate the deviation of plumb line of survey station point, it is possible to increase the computational accuracy of survey station point coordinates, eliminates digital zenith telescope
The influence that optical axis is not exclusively overlapped with mechanical axis.
In summary, the present invention has the advantages that relative to prior art：
1st, the essence that method of the invention is easy to operate, takes a short time, consume the deviation of plumb line that financial resource and material resource are few, obtained
Degree is high；And with pervasive characteristic, the quick measurement suitable for the high-precision deviation of plumb line.
2nd, star catalogue interception of the present invention, is intercepted to star catalogue twice before observation and in observation respectively so that
The match is successful that rate is significantly improved for fixed star image recognition, and the whole identification matching process used time is less than 0.3 second.
3rd, the processing method of method data of the invention is relatively easy：Single observation data handling procedure control 30s with
Interior, single observes computational accuracy ± 0.3 " within.
Brief description of the drawings
Fig. 1 is FB(flow block) of the invention；
Fig. 2 be 1 continuous 75 group of observed result of embodiment astronomical longitude and astronomical latitude direction on most or value with every group
The difference v of observationiCurve map；
Fig. 3 is the poor distribution situation block diagram of group internal standard of observation in the astronomical latitude group of the embodiment of the present invention 1；
Fig. 4 is the poor distribution situation block diagram of group internal standard of observation in the astronomical longitude group of the embodiment of the present invention 1.
Embodiment
With reference to the accompanying drawings and examples, the present invention is described in detail.
As shown in figure 1, the high-precision deviation of plumb line method for fast measuring of the integrated GNSS and CCD zenith telescopes of the present invention, its
It is characterised by, comprises the following steps：
The first step, sets up CCD zenith telescopes on survey station point, its optical axis is pointed to zenith direction, and zenith region is continuously existed
0 ° and 180 ° of directions are shot, and obtain CCD star chart pictures, and obtain by high-precision electronic level meter the inclination number of zenith telescope
According to by GNSS acquisition observation time information and the geodetic coordinates of survey station point；
Second step, the CCD star chart pictures of the FITS forms shot to CCD zenith telescopes are read out, then carry out ambient noise
Eliminate；
3rd step, the CCD star charts picture after being eliminated to noise carries out the automatic search in fixed star astrology region；
4th step, with the two-dimentional Moment Methods of improved amendment, calculates the energy in the above-mentioned fixed star astrology region searched out automatically
The image coordinate at amount center；
5th step, is handled being applicable star catalogue, by the GNSS temporal informations obtained and the geodetic coordinates of survey station point,
The rough astronomic coordinate of survey station point is calculated with reference to EGM2008.Star catalogue is intercepted according to survey station astronomic coordinate result of calculation, calculated
The independent equatorial coordinate system in time of exposure zenith region and apparent magnitude information, and independent equatorial coordinate system is projected in plane be converted to
Plane coordinates；
6th step, is identified to the fixed star that the astrology in CCD images and star catalogue are projected in plane, matches；
7th step, according to the star pair that the match is successful, using least square method, iterates to calculate photogrammetric projective transformation formula
In Coordinate Conversion coefficient and survey station point initial equatorial coordinates, be reconverted into the initial astronomic coordinate of survey station point；
8th step, the zenith telescope slope correction data that high-precision electronic level meter is obtained and Ghandler motion correction data conversion are extremely
On meridian direction and fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches direction, the accurate astronomic coordinate of survey station point is determined；
9th step, the survey station point geodetic coordinates calculated with reference to GNSS measurement data, according to Helmert formula, you can meter
Calculate the deviation of plumb line of survey station point.
It is 3 × 3 median filtering methods that above-mentioned ambient noise, which eliminates used method, is comprised the following steps that：
Step one, 3 × 3 neighborhoods put centered on some pixel are determined；
Step 2, by the gray value (x of each pixel in the neighborhood1,x2,x3,...,xn) by being ranked up from small to large：
x1≤x2≤x3...≤xn；
Step 3, the intermediate value Y of the gray value of each pixel is calculated by formula：
Step 4, the gray value of original central point is replaced with intermediate value Y, carries out medium filtering；
Step 5, is determined 3 × 3 neighborhoods put centered on one other pixel, repeats the above steps two to step 4,
Until whole pixel filters are completed.
The automatic search in above-mentioned fixed star astrology region is carried out using algorithm of region growing.
The above-mentioned two-dimentional Moment Methods of improved amendment, are on the two-dimentional Moment Methods of conventional amendment, with iterative calculation method
Threshold value is improved, its step is as follows：
1st step, extracts maximum gradation value g in CCD star chart picturesmaxWith minimum gradation value gmin, order
2nd step, according to threshold value TkCCD star chart pictures are divided into astrology region and background area, wherein, astrology region position
Put (xi,yj) gray value gk+1(xi,yj) ＞ 0, and the gray value of background area is 0, as shown by the equation：
Then, the average gray value in astrology region is tried to achieve by formula (4)：
OrderFormula (4) is substituted into, can be obtained：
3rd step, sets a positive number μ, if | Tk-Tk+1| ＜ μ, then iterative process is terminated, is tried to achieve by formula (6)
Optimal threshold：
T=Tk+B (6)
If | Tk-Tk+1| >=μ, then make Tk=Tk+1, proceed the iterative calculation of second step.
4th step, by formula (7) and formula (8), obtains astrology regional center coordinate in CCD star chart pictures：
The above-mentioned processing for being applicable star catalogue is NOVAS-F programs by calling in AURIGA, the time obtained with reference to GNSS
The geodetic coordinates of information and survey station point, the star place observed to epoch of observation is put with applicable star catalogue epoch fixed star prosposition
Each influent factor having differences is corrected, to obtain the independent equatorial coordinate system and TV star's information in time of exposure zenith region；
Above-mentioned equatorial coordinates is the star place coordinate obtained after star catalogue is handled；
Above-mentioned image plane coordinate is the astrology position coordinates that CCD fixed stars image procossing is obtained；
It is above-mentioned that independent equatorial coordinate system projects in plane to be converted to plane coordinates be by projective transformation formula (9) and (10)
Calculate：
M=tan (q- δ0) (10)
In above formula (9) and (10)：
Cotq=cot δ cos (α-α0)；
(l, m) is fixed star plane coordinates；
(δ0,α0) it is initial astronomic coordinate；
(δ, α) is independent equatorial coordinate system.
Identification, the matching of above-mentioned fixed star are carried out using quadrangle algorithm, and its matching principle is four in CCD star chart pictures
The four edges ratio of the quadrangle of four bright stars compositions is identical in the quadrangle and star catalogue of bright star composition, i.e. formula (11)：
Order(i=1,2,3,4), then side ratio SCiStandard deviation calculated by formula (12)：
In above formula (12), ν=Σ (SCi)/4；
Then think that four bright stars minimum σ in CCD star chart pictures are matched with four bright stars in star catalogue；
According to four bright stars that the match is successful, initial coordinate transformation model is calculated by formula (13), (14)：
In above formula (13), (14)：
(X, Y) is the plane coordinates after bright star projection in star catalogue；
(x, y) is the image coordinate of the astrology in CCD star chart pictures；
Then, using least square method, initial coordinate transformation model is calculated by formula (15)：
Other astrology in initial coordinate transformation model, CCD star chart pictures according to obtained by calculating in addition to four bright stars are sat
Mark, and the plane coordinates of the star of other in star catalogue complete the matchings of institute any stars；
Coordinate Transformation Models are recalculated further according to the matching result of all stars, are rejected after the poor fixed star of matching result,
Calculate final Coordinate Transformation Models.
The calculating of above-mentioned astronomic coordinate refers to, obtains fixed star throwing in the image coordinate and star catalogue of the astrology in CCD star chart pictures
After the Coordinate Transformation Models of the plane coordinates of movie queen, CCD star chart pictures are photographed using 0 ° and 180 ° of directions, are entered as follows
What row survey station point astronomic coordinate was calculated：
(1) step, it is assumed that survey station point is located at the center of CCD star chart pictures, i.e., (x, y)z=(0,0)；
(2) step, according to the Coordinate Transformation Models calculated, obtains the initial plane coordinate (X, Y) of survey station pointz, then root
The initial equatorial coordinates of survey station point is calculated according to the inverse operation formula of photogrammetric projective transformation formula；
(3) step, the initial equator of survey station point that the CCD star charts picture shot respectively according to 0 ° and 180 ° of directions is obtained is sat
Mark, calculates the initial astronomic coordinate (Φ of survey station point1,Λ1)、(Φ2,Λ2), such as shown in formula (16), (17)：
Φ=δ (16)
Λ=α-GAST (17)
In above-mentioned formula (16), (17)：
(Φ, Λ) is survey station point astronomic coordinate；
(δ, α) is survey station point equatorial coordinates；
GAST is the Greenwich hour angles calculated according to GNSS time information；
Then, (Φ is calculated by formula (18), (19)1,Λ1)、(Φ2,Λ2) average value：
(4) step, by (Φ, Λ) inverse to equatorial coordinates, survey station is recalculated according to photogrammetric projective transformation formula
Point plane coordinates (X, Y)z1、(X,Y)z2；
The CCD image coordinates (x, y) of survey station point are calculated further according to Formula of Coordinate System Transformationz1、(x,y)z2；
(5) step, repeats above iterative process, until the difference of the astronomic coordinate of twice adjacent calculation is less than a certain give
Fixed number value, then calculating process terminate, take the average of the last result of calculation of astronomic coordinate twice to be sat as the astronomy of observation station
Mark；
(6) step, the instrument horizontal data obtained according to high-precision electronic level meter, is calculated by formula (20), (21)
The horizontal corrected value of instrument：
δΦl=cos (θ+β) n1-sin(θ+β)n2 (20)
δΛl=sin (θ+β) n1+cos(θ+β)n2/cosΦ (21)
In above-mentioned formula (20), (21)：
θ is the reference axis of CCD coordinate systems in image and the angle of east-west direction；
β is the reference axis of CCD coordinate systems in image and the angle of high-precision electronic level meter axle；
n1、n2The instrument tilting value recorded for high-precision electronic level meter；
Ghandler motion corrected value is calculated by formula (22), (23) again, with the CCD image datas that are obtained to instrument by Ghandler motion shadow
Ring and carry out Ghandler motion correction：
δΦp=-(xpcosΛ-ypsinΛ) (22)
δΛp=-(xpsinΛ+ypcosΛ)tanΦ (23)；
In above-mentioned formula (22), (23)：
(xp,yp) be instantaneous pole coordinate；
(Φ, Λ) is the astronomic coordinate of survey station point.
Above-mentioned Helmert formula are formula (24) and formula (25)：
ξ=Φ-φ (24)
η=(Λ-λ) cos φ (25)；
In above-mentioned formula (24), (25)：
ξ is the meridional component of the deviation of plumb line；
η is the fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches component of the deviation of plumb line；
(Φ, Λ) is survey station point astronomic coordinate；
(φ, λ) is survey station point geodetic coordinates.
Embodiment 1
By taking certain university campus as an example, quickly surveyed using the high-precision deviation of plumb line of above-mentioned integrated GNSS and CCD zenith telescopes
Amount method, carries out the deviation of plumb line to the university campus and quickly measures.
Specific measurement process is as follows：
From on December 19,6 days to 2013 June in 2013, in experimentation, selection weather conditions therebetween are preferable, observation ring
34 day convenient night of border, the data acquisition and procession of integrated GNSS and CCD zenith telescopes is carried out, total observation group number is 275
A length of 15min, every group of average observed number of times are that 26 times, the every group star numbers used that are averaged are 724, group when group, every group of average observed
Interior average observed precision is 0.246 " (astronomical latitude), 0.269 " (astronomical longitude), and average observed group number is 11 groups the whole night, the whole night
Average observed precision is 0.10 " (astronomical latitude), 0.12 " (astronomical longitude).
The astronomical poor distribution situation of group internal standard of the above-mentioned group observations of whole process 275 is as follows：
In 275 group observationses, observation standard deviation is 0~0.05 in the group of astronomical latitude direction " between have 16 groups,
0.05~0.1 " having 9 groups between, 0.1~0.15 has 51 groups between " between have 42 groups, 0.15~0.2 ", 0.2
~0.25 " having 74 groups between, 0.25~0.3 has 15 groups between " between have 53 groups, 0.3~0.35 ", 0.35
~0.4 " having 6 groups between, 0.4~0.45 has 2 groups between " between have 4 groups, 0.45~0.5 ", 0.5~
0.55 " have 2 groups between, 0.55~0.6 " between have 1 group, it can thus be appreciated that in 275 groups of astronomical latitude observation standard deviations
Have 245 groups 0.3 " within, account for the 89% of sum；Have 30 groups 0.3 " more than, account for the 11% of sum.
Between observation standard deviation is 0~0.05 in the group of astronomical longitude direction " between have 12 groups, 0.05~0.1 "
Having 5 groups, 0.1~0.15 has 46 groups between " between have 19 groups, 0.15~0.2 ", 0.2~0.25 " between have
Have 18 groups between " between have 50 groups, 0.3~0.35 " 82 groups, 0.25~0.3,0.35~0.4 " between have 16
Having 15 groups between group, 0.4~0.45 ", 0.45~0.5 has 5 groups between " between have 2 groups, 0.5~0.55 ",
There is 1 group between " between there are 4 groups, 0.6~0.65 " 0.55~0.6, it can thus be appreciated that 275 groups of astronomical longitude observation marks
Have 214 groups 0.3 in quasi- difference " within, account for the 77.8% of sum；Have 61 groups 0.3 " more than, account for the 22.2% of sum.
By the observation and analysis to raw observation and observation condition, find to exceed for observation standard deviation in group
0.3 " observation group, is not adjusted to optimal mainly due to time keeping instrument horizontality is seen, or observing environment is not good, and wind-force is larger
Or zenith region cloud layer is thicker.These data are screened, chosen on same survey station point, the integrated GNSS of 10 days and CCD days
Cylinder deviation of plumb line measurement result is pushed up, and is divided into 75 groups of carry out data processings to acquired CCD star chart pictures, every group includes observation
The CCD star chart pictures that 15min is obtained.
By the result of the difference of above-mentioned 75 groups every group observationses and average value, observation in astronomical latitude group is drawn out respectively
The group internal standard difference Butut (Fig. 4) of observation in group internal standard difference Butut (Fig. 3) and astronomical longitude group.
In the measurements, it is general using bessel formula (i.e. equation below (26)) if the true value of observation is unknown
The middle error m of observation is asked for, the standard for weighing accuracy of observation is used as：
In above formula (27), n is observation frequency, and [vv] is the quadratic sum of each observation correction, in identical observation condition
Under some amount is repeatedly observed, take its arithmetic mean of instantaneous valueAs most or value, observation frequency is moreCloser to true
Value, can calculate each observation liCorrected value
Above-mentioned continuous 75 groups of observed results are chosen, Fig. 2 is drawn out：In astronomical longitude and astronomical latitude direction most or value
And the difference v of every group observationsiCurve map.
As shown in Fig. 2 in continuous 75 group observations, the difference per group observations with each observation arithmetic mean of instantaneous value is in day
Literary latitude direction has 74 groups ± 0.3 " within, only 1 group ± 0.3~0.4 " in；
Have 73 groups in astronomical longitude direction ± 0.3 " within, only 2 groups ± 0.3~0.4 " in.
It can be calculated according to bessel formula：In 75 group observationses in Fig. 2, the middle error of astronomical longitude observation for ±
0.112 ", the middle error of astronomical latitude observation be ± 0.124 ", comply fully with ± 0.3 in first-class astronomical observation specification " will
Ask.
Claims (7)
1. a kind of high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes, it is characterised in that including following
Step：
The first step, sets up CCD zenith telescopes on survey station point, its optical axis is pointed to zenith direction, it is continuous to zenith region at 0 ° and
180 ° of directions are shot, and obtain CCD star chart pictures, and obtain the tilt data of zenith telescope by high-precision electronic level meter, by
GNSS obtains the geodetic coordinates of observation time information and survey station point；
Second step, the CCD star chart pictures of the FITS forms shot to CCD zenith telescopes are read out, then carry out ambient noise elimination；
3rd step, the CCD star charts picture after being eliminated to noise carries out the automatic search in fixed star astrology region；
4th step, with the two-dimentional Moment Methods of improved amendment, in the energy for calculating the above-mentioned fixed star astrology region searched out automatically
The image coordinate of the heart；
5th step, is handled being applicable star catalogue, by the GNSS temporal informations obtained and the geodetic coordinates of survey station point, with reference to
EGM2008 calculates the rough astronomic coordinate of survey station point；
According to the rough astronomic coordinate of the survey station of calculating point in star catalogue with CCD star charts as corresponding region is intercepted, and
The independent equatorial coordinate system and apparent magnitude information in time of exposure zenith region are calculated, and independent equatorial coordinate system is projected on section
Be converted to plane coordinates；
6th step, is identified to the fixed star that the astrology in CCD images and star catalogue are projected in plane, matches；
7th step, according to the star pair that the match is successful, utilizes the coordinate in least square method computational photogrammetry projective transformation formula
Conversion coefficient, and the initial equatorial coordinates of survey station point is iterated to calculate, it is reconverted into the initial astronomic coordinate of survey station point；
8th step, the zenith telescope slope correction data that high-precision electronic level meter is obtained and Ghandler motion correct data conversion to meridian
On direction and fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches direction, the accurate astronomic coordinate of survey station point is determined；
9th step, the survey station point geodetic coordinates calculated with reference to GNSS measurement data, and according to Helmert formula, you can calculate
Go out the deviation of plumb line of survey station point；
It is 3 × 3 median filtering methods that the ambient noise, which eliminates used method, is comprised the following steps that：
Step one, 3 × 3 neighborhoods put centered on some pixel are determined；
Step 2, by the gray value (x of each pixel in the neighborhood1,x2,x3,...,xn) by being ranked up from small to large：x1≤x2
≤x3...≤xn；
Step 3, the intermediate value Y of the gray value of each pixel is calculated by formula：
Step 4, the gray value of original central point is replaced with intermediate value Y, carries out medium filtering；
Step 5, is determined 3 × 3 neighborhoods put centered on one other pixel, repeats the above steps two to step 4, until
Whole pixel filters are completed.
2. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, the automatic search in the fixed star astrology region is carried out using algorithm of region growing.
3. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, the improved two-dimentional Moment Methods of amendment, are on the two-dimentional Moment Methods of conventional amendment, with iterative calculation method pair
Threshold value is improved, and its step is as follows：
1st step, extracts maximum gradation value g in CCD star chart picturesmaxWith minimum gradation value gmin, order
<mrow>
<msup>
<mi>T</mi>
<mn>0</mn>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>g</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
1
2nd step, according to threshold value TkCCD star chart pictures are divided into astrology region and background area, wherein, astrology regional location
(xi,yj) gray value gk+1(xi,yj) ＞ 0, and the gray value of background area is 0, as shown by the equation：
Then, the average gray value in astrology region is tried to achieve by formula (4)：
<mrow>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
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<mi>&Sigma;</mi>
<mrow>
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<mi>g</mi>
<mi>k</mi>
</msub>
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<mi>x</mi>
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<mi>k</mi>
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<mi>k</mi>
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<mi>k</mi>
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<mi>&Sigma;</mi>
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<mi>g</mi>
<mi>k</mi>
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<mi>x</mi>
<mi>i</mi>
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<mi>k</mi>
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<mn>1</mn>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
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</mrow>
</mrow>
OrderFormula (4) is substituted into, can be obtained：
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<mo>+</mo>
<mn>1</mn>
</mrow>
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<mi>x</mi>
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<mi>T</mi>
<mi>k</mi>
</msup>
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<mi>g</mi>
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<mi>T</mi>
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<mi>k</mi>
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</mrow>
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<mo>-</mo>
<mo>-</mo>
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<mo>(</mo>
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</mrow>
</mrow>
3rd step, sets a positive number μ, if | Tk-Tk+1| ＜ μ, then iterative process is terminated, optimal threshold is tried to achieve by formula (6)
Value：
T=Tk+B (6)
If | Tk-Tk+1| >=μ, then make Tk=Tk+1, proceed the iterative calculation of second step；
4th step, by formula (7) and formula (8), obtains astrology regional center coordinate in CCD star chart pictures：
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<mi>x</mi>
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</mrow>
4. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, the processing for being applicable star catalogue is NOVAS-F programs by calling in AURIGA, and combines the time that GNSS is obtained
Information, the star place observed to epoch of observation is put each influent factor having differences with being applicable star catalogue epoch fixed star prosposition and entered
Row correction, with obtaining fixed star in star catalogue apparent place put；
Then, region corresponding with CCD fixed star star images in star catalogue is intercepted, interception process is divided into two steps：
The first step, before the digital zenith telescopes of integrated CCD and GNSS are observed, may lead to this observation period in star catalogue first
The fixed star information for crossing survey station point zenith region is intercepted, and star catalogue possibly be present at zenith region when intercepting scope with by observation and regard
Fixed star in is all covered as principle, its survey station point equatorial coordinates (α2,δ2) tried to achieve by equation below (9)：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&delta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&Phi;</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&Lambda;</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mi>G</mi>
<mi>A</mi>
<mi>S</mi>
<mi>T</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
In above formula (9), (Φ2,Λ2) be survey station point initial astronomic coordinate, the initial astronomic coordinate be use GNSS geodesic surveys
As a result the deviation of plumb line of survey station point is calculated with EGM2008 gravity field models, then push away survey station point astronomic coordinate, take approximation
Obtain；
The star catalogue interception scope is more than digital zenith telescope visual field；
After interception scope is determined, with apparent position calculation of star model to being likely to occur perseverance within the range in observation period
Star information is intercepted, and these information are stored；
Second step, before fixed star matching work is carried out, need to further be intercepted to above star catalogue region, enable the region complete
Entirely corresponding with CCD fixed star image-regions, it is as follows that it intercepts condition：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mi>min</mi>
</msub>
<mo><</mo>
<msub>
<mi>&alpha;</mi>
<mn>1</mn>
</msub>
<mo><</mo>
<msub>
<mi>&alpha;</mi>
<mi>max</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&delta;</mi>
<mi>min</mi>
</msub>
<mo><</mo>
<msub>
<mi>&delta;</mi>
<mn>1</mn>
</msub>
<mo><</mo>
<msub>
<mi>&delta;</mi>
<mi>max</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
In above formula (10)：
(α1,δ1) for the equatorial coordinates of fixed star in the visual field of zenith region；
αmin、αmax、δmin、δmaxDepending on the equatorial coordinates (α of survey station point2,δ2) and digital zenith telescope visual field Fi, it calculates public
Formula is as follows：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mi>min</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&alpha;</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mi>F</mi>
<mi>i</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mi>max</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&alpha;</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mi>F</mi>
<mi>i</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&delta;</mi>
<mi>min</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&delta;</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mi>F</mi>
<mi>i</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&delta;</mi>
<mi>max</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&delta;</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mi>F</mi>
<mi>i</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
It is described that independent equatorial coordinate system projects in plane to be converted to plane coordinates be based on projective transformation formula (12) and (13)
Draw：
<mrow>
<mi>l</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mi>a</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>-</mo>
<msub>
<mi>&delta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
M=tan (q- δ2) (13)
In above formula (12) and (13)：
Cotq=cot δ1cos(α1-α2)；
(l, m) is fixed star plane coordinates；
(α1,δ1) for the equatorial coordinates of fixed star in the visual field of zenith region.
5. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, identification, the matching of the fixed star are carried out using quadrangle algorithm, and its matching principle is four in CCD star chart pictures
The four edges ratio of the quadrangle of four bright stars compositions is identical in the quadrangle and star catalogue of bright star composition, i.e. formula (14)：
<mrow>
<mfrac>
<msub>
<mi>S</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>r</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>S</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
<mi>t</mi>
<mn>1</mn>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<msub>
<mi>S</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>r</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>S</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
<mi>t</mi>
<mn>2</mn>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<msub>
<mi>S</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>r</mi>
<mn>3</mn>
</mrow>
</msub>
<msub>
<mi>S</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
<mi>t</mi>
<mn>3</mn>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<msub>
<mi>S</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>r</mi>
<mn>4</mn>
</mrow>
</msub>
<msub>
<mi>S</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
<mi>t</mi>
<mn>4</mn>
</mrow>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
OrderThen side ratio SCiStandard deviation calculated by formula (15)：
<mrow>
<mi>&sigma;</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>&Sigma;</mi>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>SC</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>&nu;</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mn>3</mn>
</mfrac>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
In above formula (15), ν=∑ (SCi)/4；
Then think that four bright stars minimum σ in CCD star chart pictures are matched with four bright stars in star catalogue；
According to four bright stars that the match is successful, initial coordinate transformation model is calculated by formula (16), (17)：
<mrow>
<mi>X</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mn>11</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>12</mn>
</msub>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>13</mn>
</msub>
<mi>y</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>31</mn>
</msub>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>32</mn>
</msub>
<mi>y</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
3
<mrow>
<mi>Y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>23</mn>
</msub>
<mi>y</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>31</mn>
</msub>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>32</mn>
</msub>
<mi>y</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
In above formula (16), (17)：
(X, Y) is the plane coordinates after bright star projection in star catalogue；
(x, y) is the image coordinate of the astrology in CCD star chart pictures；
Then, using least square method, initial coordinate transformation model is calculated by formula (18)：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>11</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>12</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>13</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>23</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>31</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>32</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<msup>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>n</mi>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>n</mi>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
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Other astrology coordinates in initial coordinate transformation model, CCD star chart pictures according to obtained by calculating in addition to four bright stars, with
And the plane coordinates of the star of other in star catalogue completes the matching of institute's any stars；
Coordinate Transformation Models are recalculated further according to the matching result of all stars, rejects after the poor fixed star of matching result, calculates
Final Coordinate Transformation Models.
6. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, the calculating of the astronomic coordinate refers to, obtain fixed star projection in the image coordinate and star catalogue of the astrology in CCD star chart pictures
After the Coordinate Transformation Models of plane coordinates afterwards, CCD star chart pictures are photographed using 0 ° and 180 ° of directions, are carried out as follows
What survey station point astronomic coordinate was calculated：
(1) step, it is assumed that survey station point is located at the center of CCD star chart pictures, i.e., (x, y)z=(0,0)；
(2) step, according to the Coordinate Transformation Models calculated, obtains the initial plane coordinate (X, Y) of survey station pointz, further according to photography
The inverse operation formula of measurement projective transformation formula calculates the initial equatorial coordinates of survey station point；
(3) step, the initial equatorial coordinates of survey station point that the CCD star charts picture shot respectively according to 0 ° and 180 ° of directions is obtained, meter
Calculate the initial astronomic coordinate (Φ of survey station point1,Λ1)、(Φ2,Λ2), such as shown in formula (19), (20)：
Φ=δ (19)
Λ=α-GAST (20)
In above-mentioned formula (19), (20)：
(Φ, Λ) is survey station point astronomic coordinate；
(δ, α) is survey station point equatorial coordinates；
GAST is the Greenwich hour angles calculated according to GNSS time information；
Then, (Φ is calculated by formula (21), (22)1,Λ1)、(Φ2,Λ2) average value：
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4
(4) step, by (Φ, Λ) inverse to equatorial coordinates, recalculates survey station point according to photogrammetric projective transformation formula and puts down
Areal coordinate (X, Y)z1、(X,Y)z2；
The CCD image coordinates (x, y) of survey station point are calculated further according to Formula of Coordinate System Transformationz1、(x,y)z2；
(5) step, repeats above iterative process, until the difference of the astronomic coordinate of twice adjacent calculation gives fixed number less than a certain
Value, then calculating process terminates, and takes the average of the last result of calculation of astronomic coordinate twice as the astronomic coordinate of observation station；
(6) step, the instrument horizontal data obtained according to high-precision electronic level meter, instrument is calculated by formula (23), (24)
Horizontal corrected value：
δΦl=cos (θ+β) n1-sin(θ+β)n2 (23)
δΛl=sin (θ+β) n1+cos(θ+β)n2/cosΦ (24)
In above-mentioned formula (23), (24)：
θ is the reference axis of CCD coordinate systems in image and the angle of east-west direction；
β is the reference axis of CCD coordinate systems in image and the angle of high-precision electronic level meter axle；
n1、n2The instrument tilting value recorded for high-precision electronic level meter；
Calculate Ghandler motion corrected value by formula (25), (26) again, with the CCD image datas that are obtained on instrument by Ghandler motion influenceed into
Row Ghandler motion is corrected：
δΦp=-(xpcosΛ-ypsinΛ) (25)
δΛp=-(xpsinΛ+ypcosΛ)tanΦ (26)；
In above-mentioned formula (25), (26)：
(xp,yp) be instantaneous pole coordinate；
(Φ, Λ) is the astronomic coordinate of survey station point.
7. the high-precision deviation of plumb line method for fast measuring of integrated GNSS and CCD zenith telescopes according to claim 1, it is special
Levy and be, the Helmert formula are formula (27) and formula (28)：
ξ=Φ-φ (27)
η=(Λ-λ) cos φ (28)；
In above-mentioned formula (27), (28)：
ξ is the meridional component of the deviation of plumb line；
η is the fourth of the twelve Earthly Branches tenth of the twelve Earthly Branches component of the deviation of plumb line；
(Φ, Λ) is survey station point astronomic coordinate；
(φ, λ) is survey station point geodetic coordinates.
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| CN106949905B (en) * | 2016-01-06 | 2021-05-07 | 中国航空工业第六一八研究所 | Gravity plumb line deviation measuring device |
| CN106017444A (en) * | 2016-05-26 | 2016-10-12 | 广东工业大学 | Independent monitoring method for construction verticality of super-high building |
| CN105973213B (en) * | 2016-07-21 | 2018-06-29 | 武汉大学 | A kind of laser plumbing method and system for taking correction for deflection of vertical into account |
| CN108317993B (en) * | 2018-01-10 | 2020-03-06 | 山东科技大学 | Plumb line deviation measuring device and method integrating GNSS and laser tracker |
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| CN113819882B (en) * | 2021-09-09 | 2023-06-16 | 江苏海洋大学 | Method for calculating gravity potential difference between cross-sea elevation points |
| CN115437030B (en) * | 2022-08-23 | 2024-01-30 | 中国科学院云南天文台 | Star-guiding closed-loop tracking method and system for high-dispersion optical fiber spectrometer |
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