CN109520522A - A kind of control point determination of stability method based on threedimensional baseline - Google Patents
A kind of control point determination of stability method based on threedimensional baseline Download PDFInfo
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Abstract
The control point determination of stability method based on threedimensional baseline that the invention discloses a kind of, it is characterized in that, the following steps are included: (1), in GNSS three dimensional control network control point carry out the observation of two phases, least square adjustment processing is carried out to each original observed data of the whole network, the achievements such as rectangular space coordinate (2) is obtained, single baseline is determined；(3), whole baselines are determined: all baselines is carried out with the judgement of step (2), if there are 2 or more same endpoint unstabilities of base line fixed, determine that its common point is unstable.Since the adjustment Datum of GNSS three dimensional control network does not influence the poor outcome on horizontal distance difference and vertical direction, therefore this method determines that unstable fixed point is more reliable, and the situation that the net form for being suitable for observing twice or repeatedly is inconsistent.
Description
Technical field
The present invention relates to engineering mappings, in particular to a kind of method of control point determination of stability based on threedimensional baseline.
Background technique
It is generally flat using constructions such as two (three) for the requirement for adapting to hydraulic engineering (such as long tunnel) and other traffic engineering
Face controls net, CP I and II horizontal control network of CP, and to meet engineering survey required precision, (horizontal control network is generally GNSS control
Net), and periodically or non-periodically control is netted and carries out repetition measurement, to have found that it is likely that the coordinate displacement of generation.
In the prior art, generally using the absolute coordinate of two phases observation, poor, consecutive points coordinate difference relative error (claims method
1) unstable point analysis is carried out, or directlys adopt that side length is poor, the angle of cut carries out unstable point analysis (title method 2), but is existing
Technology has the following deficiencies: that method 1 cannot find whole unstable fixed points, and method 2 is poor to rising limit according to error in priori, not
The error that can accurately estimate each side length, causes determination of stability unreliable.Method 1 and method 2 are required to twice or repeatedly
Net form, the observational program of observation are consistent, and this condition is difficult to meet.
Therefore, it is necessary to develop a kind of simple and reliable control point determination of stability method.
Summary of the invention
The purpose of the present invention is to solve the deficiency of the above background technology, provides a kind of control point based on threedimensional baseline
The method of determination of stability.
The technical solution of the present invention is as follows: a kind of control point determination of stability method based on threedimensional baseline, which is characterized in that
The following steps are included:
(1) observation of two phase rectangular space coordinates is carried out to control point in GNSS three dimensional control network, to the whole network original sight every time
Measured data carries out least square adjustment processing；
(2) single baseline is determined
2.1) using the data after adjustment calculate each baseline observe in the heart rectangular coordinate system in space of the station NEU twice level away from
From poor Δ P, vertical distance poor Δ U；
2.2) each baseline first phase, the second phase is calculated in the station NEU heart rectangular space coordinate using the data after adjustment
Variance-covariance matrix in systemIt utilizesEach baseline first is calculated
The variance of phase, the second phase distance in the horizontal directionThe variance of distance on vertical directionThe variance for having horizontal distance poor independently of each other according to the observation of two phases
The poor variance of vertical distanceBe calculated two phases observation horizontal distance it is poor among error
σΔP, vertical distance it is poor among error σΔU；
If 2.3) meet determining type | Δ P |≤2 σΔPAnd | Δ U |≤2 σΔU, then determine baseline stability, determine if being unsatisfactory for
Unstability of base line is fixed；
(3) whole baselines are determined:
All baselines are carried out with the judgement of step (2), if there are 2 or more same endpoint unstabilities of base line fixed, determines its public affairs
Concurrent is unstable.
Preferably, in the step 2.1), enabling baseline two-end-point is control point A, B, is denoted as baseline AB, the space after adjustment
Rectangular co-ordinate is respectively (XA,YA,ZA) and (XB,YB,ZB), by the rectangular space coordinate (X of control point A, BA,YA,ZA) and (XB,YB,
ZB) conversion be counted as latitude and longitude coordinates (BA,LA,HA) and (BB,LB,HB) and the station NEU heart rectangular space coordinate (NA,EA,UA) and
(NB,EB,UB), thus under the heart rectangular space coordinate of the station NEU:
Distance P in A, B horizontal direction of control pointABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA,
Distance U on A, B vertical direction of control pointABMeet:
UAB=UB-UA,
By the coordinate (X of first phase control line point A, BA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1)) calculate, it obtains
PAB (1)、UAB (1)；
By the coordinate (X of second phase control line point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, it obtains
To PAB (2)、UAB (2), then have
The poor Δ P of baseline AB horizontal distanceAB=PAB (2)-PAB (1)
The poor Δ U of baseline AB vertical distanceAB=UAB (2)-UAB (1)。
Further, in the step 2.2), under rectangular coordinate system in space:
The variance-covariance matrix of control point A, B are as follows:
The coordinate difference of control point A, B are as follows in rectangular coordinate system in space:
There is dL=K0L, in which:
DL=(Δ XAB ΔYAB ΔZAB)T
L=(XA YA ZA XB YB ZB)T
Therefore, Δ XAB、ΔYABWith Δ ZABBetween variance-covariance matrix it is as follows:
It stands under heart rectangular coordinate system in space in NEU, the variance-covariance matrix between N, E, U: byIts
InKnown to:
I.e.
Therefore, the variance-covariance matrix between N, E, U is as follows:
Longitude and latitude in transformation matrix R is the average value of two o'clock, i.e.,
B=(BA+BB)/2, L=(LA+LB)/2；
Pass through the coordinate (X of the baseline first phase control point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, it obtains
To the baseline AB first phase NEU station heart rectangular coordinate system in space in variance-covariance matrix
Pass through the coordinate (X of the baseline second phase control point A, BA (2),YA (2),ZA (2)) and (XB (2,YB (2),ZB (2)) calculate, it obtains
Baseline AB second phase variance-covariance matrix in the heart rectangular coordinate system in space of the station NEU
Further, in the step 2.2), under the heart rectangular space coordinate of the station NEU in A, B horizontal direction of control point
Distance PABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA
Functional expression differential of demanding perfection is obtained:
I.e.I.e.
It propagates and restrains using covariance, obtain:
Wherein,From DNEUIn obtain；
K3It is obtained according to the coordinate of control point A, B under the heart rectangular space coordinate of the station NEU,
For vertical direction, have
Wherein, cov (UAB,UAB) from DNEUIn obtain
Pass through the coordinate (X of the baseline first phase control point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, it obtains
To the variance of baseline AB first phase distance in the horizontal directionThe variance of baseline AB first phase distance in the vertical direction
By the coordinate (X of second phase control line point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, it obtains
To the variance of baseline AB second phase distance in the horizontal directionThe variance of baseline AB second phase distance in the vertical direction
Since the first phase and second phase observation are mutually indepedent, have:
By what is acquiredSubstitution formula (7),In substitution formula (8), baseline AB water is obtained
It puts down apart from poor varianceThe poor variance of baseline AB vertical distanceIt is taken after evolution and is just obtaining baseline AB level
The error among poorError among baseline AB vertical distance is poor
Further, the rectangular space coordinate at control point to geodetic coordinates conversion method are as follows:
Wherein: N is the radius of prime vertical；A is the major radius of reference ellipsoid；B is the short radius of reference ellipsoid；E is reference
First eccentricity of ellipsoid；E ' is the second eccentricity of reference ellipsoid；And
Further, by the rectangular space coordinate at control point to the conversion method to heart rectangular space coordinate of standing are as follows:
If j point is that the coordinate under the station heart rectangular coordinate system centered on o point is (Noj,Eoj,Uoj), o point takes control net
Any control point only selects 1 point as o point in one control net, and the coordinate of j point, o point under rectangular coordinate system in space is distinguished
For (Xj,Yj,Zj)、(Xo,Yo,Zo), the coordinate of j point, o point under earth coordinates is respectively (Bj,Lj,Hj)、(Bo,Lo,Ho), then
Preferably, it is that fixed point progress least square method is flat that a control point in GNSS three dimensional control network is chosen in step (1)
Difference processing.
The invention has the benefit that
1. the adjustment Datum due to GNSS three dimensional control network does not have the poor outcome on horizontal distance difference and vertical direction
It influences, therefore this method determines that unstable fixed point is more reliable.
2. according to the variance-covariance matrix between any two control points obtained the correspondence horizontal distance observed twice compared with
The variance of the difference variance poor with corresponding vertical distance, the theory of this method are tight.
3. the consistent or inconsistent situation of the net form, the observational program that are suitable for observing twice or repeatedly, such as construction control network
Single control point damage, nor affect on the analysis of unstable fixed point.
Detailed description of the invention
Fig. 1 is rectangular space coordinate and station heart rectangular space coordinate relation schematic diagram
Fig. 2 is to judge common point schematic diagram
Fig. 3 is net of control points schematic diagram in embodiment
Specific embodiment
The present invention is described in further detail for specific embodiment below.
As shown in Figs. 1-2, the control point determination of stability method provided by the invention based on threedimensional baseline, including following step
Suddenly.
(1) observation of two phase rectangular space coordinates is carried out to control point in GNSS three dimensional control network, to the whole network original sight every time
Measured data carries out least square adjustment processing,
(2) single baseline is determined
2.1) using the data after adjustment calculate each baseline observe in the heart rectangular coordinate system in space of the station NEU twice level away from
From poor Δ P, vertical distance poor Δ U；
By taking the baseline AB that two control points A, B are formed as an example:
Base two-end-point is control point A, B, and the rectangular space coordinate after adjustment is respectively and (XB,YB,ZB), by control point A, B
Rectangular space coordinate (XA,YA,ZA) and (XB,YB,ZB) conversion be counted as latitude and longitude coordinates (BA,LA,HA) and (BB,LB,HB), and
The station NEU heart rectangular space coordinate (NA,EA,UA) and (NB,EB,UB),
The rectangular space coordinate at control point to geodetic coordinates conversion method are as follows:
Wherein: N is the radius of prime vertical；A is the major radius of reference ellipsoid；B is the short radius of reference ellipsoid；E is reference
First eccentricity of ellipsoid；E ' is the second eccentricity of reference ellipsoid；And
For WGS4 reference ellipsoid, a=6378137m, b=6356752.314m.
By the conversion method of the rectangular space coordinate at control point to geodetic coordinates are as follows:
If j point is that the coordinate under the station heart rectangular coordinate system centered on o point is (Noj,Eoj,Uoj), o point takes control net
Any control point only selects 1 point as o point in one control net, and the coordinate of j point, o point under rectangular coordinate system in space is distinguished
For (Xj,Yj,Zj)、(Xo,Yo,Zo), the coordinate of j point, o point under earth coordinates is respectively (Bj,Lj,Hj)、(Bo,Lo,Ho), then
The rectangular space coordinate conversion at control point is counted as latitude and longitude coordinates and the station NEU heart rectangular space coordinate belongs to often
The prior art of rule.
It stands under heart rectangular space coordinate in NEU:
Distance P in A, B horizontal direction of control pointABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA,
Distance U on A, B vertical direction of control pointABMeet:
UAB=UB-UA,
By the coordinate (X of first phase control line point A, BA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1)) calculate, it obtains
PAB (1)、UAB (1)；
By the coordinate (X of second phase control line point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, it obtains
To PAB (2)、UAB (2), then have
ΔPAB=PAB (2)-PAB (1)
ΔUAB=UAB (2)-UAB (1)。
2.2)
A. Δ X under the first phase, second phase rectangular coordinate system in space is calculatedAB、ΔYABWith Δ ZABBetween variance and covariance square
Battle array
Its rectangular space coordinate of control point A, B is respectively (XA,YA,ZA) and (XB,YB,ZB), between the two control points
Variance-covariance matrix DXYZAre as follows:
The coordinate difference at the two control points is as follows:
There is dL=K0L, in which:
DL=(Δ XAB ΔYAB ΔZAB)T
L=(XA YA ZA XB YB ZB)T
Therefore, Δ XAB、ΔYABWith Δ ZABBetween variance-covariance matrix it is as follows:
By the coordinate (X of the first phase control point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) substitute into above formula (1)-
(3), it obtains
B. the variance-covariance matrix under the heart rectangular coordinate system in space of the station the first phase, the second phase NEU is calculated
It stands under heart rectangular coordinate system in space in NEU
ByWhereinKnown to:
I.e.
Therefore, the variance-covariance matrix between N, E, U is as follows:
Longitude and latitude in transformation matrix R is the average value of two o'clock, i.e.,
B=(BA+BB)/2, L=(LA+LB)/2；
By baseline first phase control point A, B geodetic coordinates andIt obtains
By baseline second phase control point A, B geodetic coordinates andIt obtains
C. calculate two phases observation horizontal distance it is poor among error σΔP, vertical distance it is poor among error σΔU:
Distance P under the heart rectangular space coordinate of the station NEU in A, B horizontal direction of control pointABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA
Functional expression differential of demanding perfection is obtained:
I.e.I.e.
It propagates and restrains using covariance, obtain:
Wherein,From DNEUIn obtain；
K3It is obtained according to the coordinate of control point A, B under the heart rectangular space coordinate of the station NEU,
For vertical direction, have
Wherein, cov (UAB,UAB) from DNEUIn obtain
By the NEU of the baseline first phase control point A, B stand heart rectangular space coordinate andIt obtains
By the NEU of the baseline first phase control point A, B stand heart rectangular space coordinate andIt obtains
Since the first phase and second phase observation are mutually indepedent, have:
By what is acquiredSubstitution formula (7),In substitution formula (8), obtainIt takes after evolution and just obtains
2.3) if observing resulting horizontal distance difference twice hasAnd poor on vertical direction hasThen illustrate Δ PABWith Δ UABIt is mainly caused by observation error, baseline AB stablizes, i.e. control point A, B stablizes；
Otherwise it is assumed that more unstable in the two control points, then the unstability of base line is fixed.
(3), poor in the horizontal distance difference and vertical direction observed twice to whole baselines checks, if having
2 or more same endpoint baselines (AC and BC) cannot then determine that its common point (C) is unstable, referring to fig. 2 by checking.
The following are the application examples of this programme
What this example calculated is the control net being made of the control point of four simultaneous observations, and the data selected are drawn for certain
Four control points in Hydraulic Projects, the control net being made of 6 GNSS baselines, net of control points figure are as shown in Figure 3.
WGS84 rectangular space coordinate (One-Point Location) is obtained after the measurement of the 1st phase GNSS of table 1
WGS84 rectangular space coordinate (One-Point Location) is obtained after the measurement of the 2nd phase GNSS of table 2
Two phases were observed shown in initial data table 1-2 as above, carried out Baselines to two phases observation data, it is ensured that baseline meets
Required precision.According to the existing method 1 in background technique using control point GPS2802 as fixed point, three-dimensional constraining adjustment is carried out
(least square adjustment processing), control point coordinates are as follows after adjustment:
3 adjustment secondary homonym point WGS84 rectangular space coordinate of table
As the rectangular space coordinate of table 3 can calculate control point geodetic coordinates, topocentric coordinates as shown in following table 4-5:
4 control point geodetic coordinates of table
5 control point topocentric coordinates of table
In order to further probe into other control point stability, for entirely controlling the baseline in net between any two points,
Covariance is as shown in table 6 below:
The variance-covariance matrix D of all baselines in the control net of table 6XYZ
Calculate two phases observe resulting horizontal distance, the height difference on vertical direction and the poor middle error of horizontal distance,
Vertical direction height difference it is poor among error.
7 baseline level of table is apart from poor judgement
The poor judgement of 8 baseline height difference of table
By table 7-8 it is found that the variation of the baseline of point GPS2881 to point GPS2802, GPS2605, GPS2629 is not significant,
For steady baseline, thus determine that this point GPS2881 is stable point, similarly, can determine that point GPS2605, GPS2629 are stable point,
Finally conclude that all control points are stable point in the control net.
Claims (7)
1. a kind of control point determination of stability method based on threedimensional baseline, which comprises the following steps:
(1) observation of two phase rectangular space coordinates is carried out to control point in GNSS three dimensional control network, to each issue of the whole network original observation number
According to progress least square adjustment processing；
(2) single baseline is determined
2.1) each baseline is calculated using the data after adjustment observe the horizontal distance in the heart rectangular coordinate system in space of the station NEU twice
The poor Δ U of poor Δ P, vertical distance；
2.2) each baseline first phase, the second phase is calculated in the heart rectangular coordinate system in space of the station NEU using the data after adjustment
Variance-covariance matrixIt utilizesBe calculated each baseline first phase,
The variance of second phase distance in the horizontal directionThe variance of distance on vertical directionThe variance for having horizontal distance poor independently of each other according to the observation of two phases
The poor variance of vertical distanceBe calculated two phases observation horizontal distance it is poor among error
σΔP, vertical distance it is poor among error σΔU；
If 2.3) meet determining type | Δ P |≤2 σΔPAnd | Δ U |≤2 σΔU, then determine baseline stability, baseline determined if being unsatisfactory for
It is unstable；
(3) whole baselines are determined
All baselines are carried out with the judgement of step (2), if there are 2 or more same endpoint unstabilities of base line fixed, determines its common point
It is unstable.
2. to go the control point determination of stability method in 1 based on threedimensional baseline such as right, which is characterized in that the step 2.1)
In, enabling baseline two-end-point is control point A, B, is denoted as baseline AB, and the rectangular space coordinate after adjustment is respectively (XA,YA,ZA) and
(XB,YB,ZB), by the rectangular space coordinate (X of control point A, BA,YA,ZA) and (XB,YB,ZB) conversion be counted as latitude and longitude coordinates (BA,
LA,HA) and (BB,LB,HB) and the station NEU heart rectangular space coordinate (NA,EA,UA) and (NB,EB,UB), the heart space so that NEU stands
Under rectangular co-ordinate:
Distance P in A, B horizontal direction of control pointABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA,
Distance U on A, B vertical direction of control pointABMeet:
UAB=UB-UA,
By the coordinate (X of first phase control line point A, BA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1)) calculate, obtain PAB (1)、UAB (1)；
By the coordinate (X of second phase control line point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, obtain PAB (2)、UAB (2), then have
The poor Δ P of baseline AB horizontal distanceAB=PAB (2)-PAB (1)
The poor Δ U of baseline AB vertical distanceAB=UAB (2)-UAB (1)。
3. to go the control point determination of stability method in 2 based on threedimensional baseline such as right, which is characterized in that the step 2.2)
In, under rectangular coordinate system in space:
The variance-covariance matrix of control point A, B are as follows:
The coordinate difference of control point A, B are as follows in rectangular coordinate system in space:
There is dL=K0L, in which:
DL=(Δ XAB ΔYAB ΔZAB)T
L=(XA YA ZA XB YB ZB)T
Therefore, Δ XAB、ΔYABWith Δ ZABBetween variance-covariance matrix it is as follows:
It stands under heart rectangular coordinate system in space in NEU, the variance-covariance matrix between N, E, U: byWhereinKnown to:
I.e.
Therefore, the variance-covariance matrix between N, E, U is as follows:
Longitude and latitude in transformation matrix R is the average value of two o'clock, i.e.,
B=(BA+BB)/2, L=(LA+LB)/2；
Pass through the coordinate (X of the baseline first phase control point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, obtain base
Line AB first phase variance-covariance matrix in the heart rectangular coordinate system in space of the station NEU
Pass through the coordinate (X of the baseline second phase control point A, BA (2),YA (2),ZA (2)) and (XB (2,YB (2),ZB (2)) calculate, obtain baseline
AB second phase variance-covariance matrix in the heart rectangular coordinate system in space of the station NEU
4. to go the control point determination of stability method in 3 based on threedimensional baseline such as right, which is characterized in that the step 2.2)
In, the distance P under the heart rectangular space coordinate of the station NEU in A, B horizontal direction of control pointABMeet:
Wherein: NAB=NB-NA, EAB=EB-EA
Functional expression differential of demanding perfection is obtained:
I.e.I.e.
It propagates and restrains using covariance, obtain:
Wherein,From DNEUIn obtain,
K3It is obtained according to the coordinate of control point A, B under the heart rectangular space coordinate of the station NEU,
For vertical direction, have
Wherein, cov (UAB,UAB) from DNEUIn obtain,
Pass through the coordinate (X of the baseline first phase control point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, obtain base
The variance of line AB first phase distance in the horizontal directionThe variance of baseline AB first phase distance in the vertical direction
By the coordinate (X of second phase control line point A, BA (1),YA (1),ZA (1)) and (XB (1),YB (1),ZB (1)) calculate, obtain base
The variance of line AB second phase distance in the horizontal directionThe variance of baseline AB second phase distance in the vertical direction
Since the first phase and second phase observation are mutually indepedent, have:
By what is acquiredSubstitution formula (7),In substitution formula (8), obtain baseline AB level away from
From poor varianceThe poor variance of baseline AB vertical distanceTaken after evolution just obtaining baseline AB it is horizontal away from
From error among poorError among the vertical distance of baseline AB is poor
5. such as the control point determination of stability method based on threedimensional baseline in claim 2, which is characterized in that the space at control point
Rectangular co-ordinate to geodetic coordinates conversion method are as follows:
Wherein: N is the radius of prime vertical；A is the major radius of reference ellipsoid；B is the short radius of reference ellipsoid；E is reference ellipsoid
The first eccentricity；E ' is the second eccentricity of reference ellipsoid；And
6. such as the control point determination of stability method based on threedimensional baseline in claim 2, which is characterized in that by the sky at control point
Between rectangular co-ordinate to stand heart rectangular space coordinate conversion method are as follows:
If j point is that the coordinate under the station heart rectangular coordinate system centered on o point is (Noj,Eoj,Uoj), o point takes control net any
Control point only selects 1 point as o point in one control net, and the coordinate of j point, o point under rectangular coordinate system in space is respectively
(Xj,Yj,Zj)、(Xo,Yo,Zo), the coordinate of j point, o point under earth coordinates is respectively (Bj,Lj,Hj)、(Bo,Lo,Ho), then
7. such as the control point determination of stability method based on threedimensional baseline in claim 1, which is characterized in that choosing in step (1)
Taking a control point in GNSS three dimensional control network is that fixed point carries out least square adjustment processing.
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| CN112379397A (en) * | 2020-11-24 | 2021-02-19 | 湖北省水利水电规划勘测设计院 | Measuring method for reducing errors in azimuth angle of tunnel ground control network |
| CN113779817A (en) * | 2021-11-11 | 2021-12-10 | 长江空间信息技术工程有限公司(武汉) | Method for analyzing reference stability of measurement control network |
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