CN109520522B - Control point stability determination method based on three-dimensional baseline - Google Patents

Control point stability determination method based on three-dimensional baseline Download PDF

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CN109520522B
CN109520522B CN201811133110.XA CN201811133110A CN109520522B CN 109520522 B CN109520522 B CN 109520522B CN 201811133110 A CN201811133110 A CN 201811133110A CN 109520522 B CN109520522 B CN 109520522B
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point
coordinates
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control point
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CN109520522A (en
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邸国辉
刘幼华
周国成
陈劲林
张小明
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Hubei Provincial Water Resources and Hydropower Planning Survey and Design Institute
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Abstract

The invention discloses a control point stability judgment method based on a three-dimensional baseline, which is characterized by comprising the following steps of: (1) performing two-stage observation on control points in the GNSS three-dimensional control network, performing least square adjustment processing on each original observation data of the whole network to obtain achievements (2) such as space rectangular coordinates, and judging a single base line; (3) and judging all base lines: and (3) judging all baselines in the step (2), and if more than 2 homonymous baselines are unstable, judging that the common point is unstable. As the adjustment reference of the GNSS three-dimensional control network has no influence on the horizontal distance difference and the poor result in the vertical direction, the method is more reliable in determining the unstable point and is suitable for the situation that the net shapes of two or more times of observation are inconsistent.

Description

Control point stability determination method based on three-dimensional baseline
Technical Field
The invention relates to engineering surveying and mapping, in particular to a method for judging stability of control points based on a three-dimensional baseline.
Background
In order to meet the requirements of hydraulic engineering (such as long tunnels) and other traffic engineering, a second (third) construction plane control network, a CP I (general navigation satellite system) and a CP II (general navigation satellite system) plane control network are generally adopted to meet the requirement of engineering measurement accuracy (the plane control network is generally a GNSS (global navigation satellite system) control network), and the control network is retested periodically or aperiodically to find out possible coordinate deflection.
In the prior art, the unstable point analysis is generally performed by using the absolute coordinate difference of two-stage observation and the relative error of the coordinate difference of adjacent points (called method 1), or the unstable point analysis is performed by directly using the side length difference and the azimuth angle difference (called method 2), but the prior art has the following defects: the method 1 cannot find all unstable points, and the method 2 gives a limit difference according to errors in the prior, so that the error of each side length cannot be accurately estimated, and the stability judgment is unreliable. Both method 1 and method 2 require the consistency of the net shape and observation outline of two or more observations, which is difficult to satisfy.
Therefore, it is necessary to develop a simple and reliable control point stability determination method.
Disclosure of Invention
The present invention is directed to solve the above-mentioned drawbacks of the background art, and provides a method for determining stability of a control point based on a three-dimensional baseline.
The technical scheme of the invention is as follows: a control point stability judgment method based on a three-dimensional baseline is characterized by comprising the following steps:
(1) performing two-stage space rectangular coordinate observation on control points in the GNSS three-dimensional control network, and performing least square adjustment processing on each time of original observation data of the whole network;
(2) making a determination of a single baseline
2.1) calculating the difference delta P of the horizontal distance and the difference delta U of the vertical distance of each base line observed twice in the rectangular coordinate system of the NEU station center space by using the data after adjustment;
2.2) calculating by using the data after the adjustment to obtain a variance covariance matrix of the first phase and the second phase of each base line in the rectangular coordinate system of the NEU station center space
Figure BDA0001814054560000021
By using
Figure BDA0001814054560000022
Calculating to obtain the variance of the distance between the first phase and the second phase of each base line in the horizontal direction
Figure BDA0001814054560000023
Variance of distance in vertical direction
Figure BDA0001814054560000024
According to two-stage observation, there is a variance with a poor horizontal distance
Figure BDA0001814054560000025
Variance of poor vertical distance
Figure BDA0001814054560000026
Calculating to obtain the mean error sigma of the two-stage observation horizontal distance differenceΔPMean error σ of poor vertical distanceΔU；
2.3) if the judgment formula | delta P | is less than or equal to 2 sigmaΔPAnd | delta U | is less than or equal to 2 sigmaΔUIf the baseline is not stable, the baseline is not stable;
(3) all baselines were judged:
and (3) judging all baselines in the step (2), and if more than 2 homonymous baselines are unstable, judging that the common point is unstable.
Preferably, in step 2.1), the two end points of the baseline are set as control points A, B and are recorded as baseline AB, and the squared spatial rectangular coordinates after adjustment are respectively (X)A,YA,ZA) And (X)B,YB,ZB) The spatial rectangular coordinate (X) of the control point A, BA,YA,ZA) And (X)B,YB,ZB) Converted into longitude and latitude coordinates (B)A,LA,HA) And (B)B,LB,HB) And NEU station center space rectangular coordinates (N)A,EA,UA) And (N)B,EB,UB) Thus, NEU station center space rectangular coordinates:
distance P in horizontal direction of control point A, BABSatisfies the following conditions:
Figure BDA0001814054560000027
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA，
Distance U in vertical direction of control point A, BABSatisfies the following conditions:
UAB＝UB-UA，
coordinates (X) passing through first phase baseline control point A, BA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1)) Calculating to obtain PAB (1)、UAB (1)；
Coordinate (X) passing through second phase baseline control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain PAB (2)、UAB (2)Then there is
Poor baseline AB horizontal distance Δ PAB＝PAB (2)-PAB (1)
Poor vertical distance delta U of base line ABAB＝UAB (2)-UAB (1)。
Further, in the step 2.2), under a spatial rectangular coordinate system:
the variance covariance matrix for control point A, B is:
Figure BDA0001814054560000031
the coordinate difference of the control point A, B in the rectangular spatial coordinate system is as follows:
Figure BDA0001814054560000032
i.e. with dL ═ K0L, wherein:
dL＝(ΔXAB ΔYAB ΔZAB)T
Figure BDA0001814054560000033
L＝(XA YA ZA XB YB ZB)T
thus, Δ XAB、ΔYABAnd Δ ZABThe variance covariance matrix between is as follows:
Figure BDA0001814054560000034
variance covariance matrix between N, E, U in NEU centroid space rectangular coordinates: by
Figure BDA0001814054560000035
Wherein
Figure BDA0001814054560000036
Therefore, the following steps are carried out:
Figure BDA0001814054560000037
namely, it is
Figure BDA0001814054560000038
Thus, the variance covariance matrix between N, E, U is as follows:
Figure BDA0001814054560000039
transforming the longitude and latitude in the matrix R to an average of two points, i.e.
B＝(BA+BB)/2,L＝(LA+LB)/2；
Coordinates (X) through baseline first phase control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain a variance covariance matrix of the base line AB first stage in the NEU station center space rectangular coordinate system
Figure BDA0001814054560000041
Coordinate (X) through baseline second phase control point A, BA (2),YA (2),ZA (2)) And (X)B (2,YB (2),ZB (2)) Calculating to obtain a variance covariance matrix of the second phase AB of the base line in the rectangular coordinate system of the NEU station center space
Figure BDA0001814054560000042
Further, in said step 2.2), the distance P in the horizontal direction of the control point A, B in the rectangular coordinates of the NEU station center spaceABSatisfies the following conditions:
Figure BDA0001814054560000043
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA
And (3) solving the function equation by total differentiation:
Figure BDA0001814054560000044
namely, it is
Figure BDA0001814054560000045
Namely, it is
Figure BDA0001814054560000046
Applying covariance propagation law to obtain:
Figure BDA0001814054560000047
wherein,
Figure BDA0001814054560000048
from DNEUObtaining the compound;
K3according to the coordinates of the control point A, B under the rectangular coordinates of the NEU station center spaceSo as to obtain the compound with the characteristics of,
for the vertical direction, there are
Figure BDA0001814054560000049
Cov (U) among themAB,UAB) From DNEUTo obtain
Coordinates (X) through baseline first phase control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain the variance of the distance of the first period of the base line AB in the horizontal direction
Figure BDA00018140545600000410
Variance of distance in vertical direction of baseline AB first phase
Figure BDA00018140545600000411
Coordinate (X) passing through second phase baseline control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain the variance of the distance of the second phase of the base line AB in the horizontal direction
Figure BDA00018140545600000412
Variance of distance in vertical direction of base line AB second phase
Figure BDA00018140545600000413
Because the first stage and the second stage are independent of each other, there are:
Figure BDA0001814054560000051
Figure BDA0001814054560000052
will find out
Figure BDA0001814054560000053
Is substituted into formula (7),
Figure BDA0001814054560000054
Substitution in equation (8) yields the variance of the baseline AB horizontal distance
Figure BDA0001814054560000055
Variance of poor base line AB vertical distance
Figure BDA0001814054560000056
Obtaining the error in the poor AB horizontal distance of the base line after the evolution
Figure BDA0001814054560000057
Error in the base line AB vertical distance
Figure BDA0001814054560000058
Further, the method for converting the space rectangular coordinate of the control point to the geodetic coordinate comprises the following steps:
Figure BDA0001814054560000059
Figure BDA00018140545600000510
Figure BDA00018140545600000511
wherein: n is the radius of the unitary-mortise ring; a is the long radius of the reference ellipsoid; b is the short radius of the reference ellipsoid; e is the first eccentricity of the reference ellipsoid; e' is the second eccentricity of the reference ellipsoid; and is
Figure BDA00018140545600000512
Figure BDA00018140545600000513
Figure BDA00018140545600000514
Figure BDA00018140545600000515
Further, the method for converting the spatial rectangular coordinate of the control point to the spatial rectangular coordinate of the station center comprises the following steps:
let j point be the coordinate under the station center rectangular coordinate system with o point as the center (N)oj,Eoj,Uoj) The o point is any control point of the control network, only 1 point is selected as the o point in one control network, and the coordinates of the j point and the o point under the space rectangular coordinate system are respectively (X)j,Yj,Zj)、(Xo,Yo,Zo) The coordinates of the j point and the o point in the geodetic coordinate system are respectively (B)j,Lj,Hj)、(Bo,Lo,Ho) Then, then
Figure BDA0001814054560000061
Preferably, in the step (1), a control point in the GNSS three-dimensional control network is selected as a fixed point to perform least square adjustment processing.
The invention has the beneficial effects that:
1. as the adjustment reference of the GNSS three-dimensional control network has no influence on the horizontal distance difference and the poor result in the vertical direction, the method is more reliable in determining the unstable point.
2. The variance with poor corresponding horizontal distance and the variance with poor corresponding vertical distance of two observations are obtained according to the variance covariance matrix between any two control points, and the theory of the method is strict.
3. The method is suitable for the conditions of net shape and observation outline consistency or inconsistency of two or more times of observation, such as the damage of individual control points of the construction control net, and the analysis of unstable points is not influenced.
Drawings
FIG. 1 is a schematic diagram showing the relationship between a rectangular coordinate and a rectangular coordinate of a station center space
FIG. 2 is a schematic diagram of common point judgment
FIG. 3 is a schematic diagram of the control point network in the embodiment
Detailed Description
The following specific examples further illustrate the invention in detail.
As shown in fig. 1-2, the method for determining stability of a control point based on a three-dimensional baseline provided by the invention comprises the following steps.
(1) Performing two-stage space rectangular coordinate observation on control points in the GNSS three-dimensional control network, performing least square adjustment processing on each original observation data of the whole network,
(2) making a determination of a single baseline
2.1) calculating the difference delta P of the horizontal distance and the difference delta U of the vertical distance of each base line observed twice in the rectangular coordinate system of the NEU station center space by using the data after adjustment;
take the baseline AB formed by the two control points A, B as an example:
the two end points of the base are control points A, B, and the spatial rectangular coordinates after the adjustment are respectively equal to (X)B,YB,ZB) The spatial rectangular coordinate (X) of the control point A, BA,YA,ZA) And (X)B,YB,ZB) Converted into longitude and latitude coordinates (B)A,LA,HA) And (B)B,LB,HB) And NEU station center space rectangular coordinates (N)A,EA,UA) And (N)B,EB,UB)，
The method for converting the space rectangular coordinate of the control point into the geodetic coordinate comprises the following steps:
Figure BDA0001814054560000071
Figure BDA0001814054560000072
Figure BDA0001814054560000073
wherein: n is the radius of the unitary-mortise ring; a is the long radius of the reference ellipsoid; b is the short radius of the reference ellipsoid; e is the first eccentricity of the reference ellipsoid; e' is the second eccentricity of the reference ellipsoid; and is
Figure BDA0001814054560000074
Figure BDA0001814054560000075
Figure BDA0001814054560000076
Figure BDA0001814054560000077
For WGS4 reference ellipsoids, a-6378137 m and b-6356752.314 m.
The method for converting the space rectangular coordinate of the control point into the geodetic coordinate comprises the following steps:
let j point be the coordinate under the station center rectangular coordinate system with o point as the center (N)oj,Eoj,Uoj) The o point is any control point of the control network, only 1 point is selected as the o point in one control network, and the coordinates of the j point and the o point under the space rectangular coordinate system are respectively (X)j,Yj,Zj)、(Xo,Yo,Zo) The coordinates of the j point and the o point in the geodetic coordinate system are respectively (B)j,Lj,Hj)、(Bo,Lo,Ho) Then, then
Figure BDA0001814054560000078
Converting the spatial rectangular coordinates of the control points into longitude and latitude coordinates and the spatial rectangular coordinates of the NEU station center belongs to the conventional prior art.
Under the NEU heart space rectangular coordinates:
distance P in horizontal direction of control point A, BABSatisfies the following conditions:
Figure BDA0001814054560000081
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA，
Distance U in vertical direction of control point A, BABSatisfies the following conditions:
UAB＝UB-UA，
coordinates (X) passing through first phase baseline control point A, BA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1)) Calculating to obtain PAB (1)、UAB (1)；
Coordinate (X) passing through second phase baseline control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain PAB (2)、UAB (2)Then there is
ΔPAB＝PAB (2)-PAB (1)
ΔUAB＝UAB (2)-UAB (1)。
2.2)
a. Calculating delta X under a first-phase space rectangular coordinate system and a second-phase space rectangular coordinate systemAB、ΔYABAnd Δ ZABVariance covariance matrix between
Figure BDA0001814054560000082
The control point A, B has a spatial rectangular coordinate of (X)A,YA,ZA) And (X)B,YB,ZB) The covariance matrix D between the two control pointsXYZComprises the following steps:
Figure BDA0001814054560000083
the difference in coordinates of these two control points is as follows:
Figure BDA0001814054560000084
i.e. with dL ═ K0L, wherein:
dL＝(ΔXAB ΔYAB ΔZAB)T
Figure BDA0001814054560000091
L＝(XA YA ZA XB YB ZB)T
thus, Δ XAB、ΔYABAnd Δ ZABThe variance covariance matrix between is as follows:
Figure BDA0001814054560000092
coordinate (X) of first phase control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Substituting into the above formulas (1) - (3) to obtain
Figure BDA0001814054560000093
b. Calculating variance covariance matrix under first-stage and second-stage NEU station center space rectangular coordinate system
Figure BDA0001814054560000094
Under the rectangular coordinate system of the NEU station center space
By
Figure BDA0001814054560000095
Wherein
Figure BDA0001814054560000096
Therefore, the following steps are carried out:
Figure BDA0001814054560000097
namely, it is
Figure BDA0001814054560000098
Thus, the variance covariance matrix between N, E, U is as follows:
Figure BDA0001814054560000099
transforming the longitude and latitude in the matrix R to an average of two points, i.e.
B＝(BA+BB)/2,L＝(LA+LB)/2；
Geodetic coordinates of first phase control point A, B through baseline
Figure BDA00018140545600000910
To obtain
Figure BDA00018140545600000911
Geodetic coordinates of second phase control point A, B through baseline
Figure BDA00018140545600000912
To obtain
Figure BDA00018140545600000913
c. Calculating the mean error sigma of the two-phase observation horizontal distance differenceΔPMean error σ of poor vertical distanceΔU：
Distance P in the horizontal direction of control point A, B under rectangular coordinates of NEU center spaceABSatisfies the following conditions:
Figure BDA0001814054560000101
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA
And (3) solving the function equation by total differentiation:
Figure BDA0001814054560000102
namely, it is
Figure BDA0001814054560000103
Namely, it is
Figure BDA0001814054560000104
Applying covariance propagation law to obtain:
Figure BDA0001814054560000105
wherein,
Figure BDA0001814054560000106
from DNEUObtaining the compound;
K3according to the coordinates of the control point A, B under the rectangular coordinates of the NEU station center spaceSo as to obtain the compound with the characteristics of,
for the vertical direction, there are
Figure BDA0001814054560000107
Cov (U) among themAB,UAB) From DNEUTo obtain
NEU cardiac space rectangular coordinates and by baseline first phase control point A, B
Figure BDA0001814054560000108
To obtain
Figure BDA0001814054560000109
NEU cardiac space rectangular coordinates and by baseline first phase control point A, B
Figure BDA00018140545600001010
To obtain
Figure BDA00018140545600001011
Because the first stage and the second stage are independent of each other, there are:
Figure BDA00018140545600001012
Figure BDA00018140545600001013
will find out
Figure BDA00018140545600001014
Is substituted into formula (7),
Figure BDA00018140545600001015
Substituted into formula (8) to obtain
Figure BDA00018140545600001016
Is obtained by squaring and then taking
Figure BDA00018140545600001017
2.3) if there is a difference in horizontal distance between two observations
Figure BDA00018140545600001018
And has a poor vertical direction
Figure BDA00018140545600001019
Indicates Δ PABAnd Δ UABThe baseline AB is stable, i.e., control point A, B is stable, primarily due to observation errors; otherwise, if at least one of the two control points is deemed unstable, the baseline is unstable.
(3) And checking horizontal distance difference and poor vertical direction of two observations of all baselines, and if more than 2 baselines (AC and BC) with the same end point can not pass the check, judging that the common point (C) is unstable, and referring to fig. 2.
The following is an application example of the present scheme
The calculation of the example is a control network formed by four control points synchronously observed, the selected data are the four control points in a certain water diversion project, the control network formed by 6 GNSS baselines, and a control point network diagram is shown in FIG. 3.
TABLE 1 phase 1 GNSS survey to obtain WGS84 space rectangular coordinates (single point location)
Figure BDA0001814054560000111
TABLE 2 phase 2 GNSS measurements followed by WGS84 space rectangular coordinates (single point positioning)
Figure BDA0001814054560000112
The two-stage observation raw data are shown in the table 1-2 above, and baseline calculation is performed on the two-stage observation data to ensure that the baseline meets the precision requirement. According to the prior art 1 in the background art, a control point GPS2802 is used as a fixed point, and three-dimensional constraint adjustment (least square adjustment processing) is performed, and after adjustment, the coordinates of the control point are as follows:
TABLE 3 homonymous point WGS84 space rectangular coordinate after adjustment
Figure BDA0001814054560000121
The geodetic coordinates and the station center coordinates of the control points can be calculated from the spatial rectangular coordinates of table 3 and are shown in tables 4-5 below:
TABLE 4 control Point geodetic coordinates
Figure BDA0001814054560000122
TABLE 5 control Point centroid coordinates
Figure BDA0001814054560000123
To further explore other control point stabilities, the variance covariance matrix for the baseline between any two points in the entire control net is shown in table 6 below:
TABLE 6 covariance matrix D of variance for all baselines in the control netXYZ
Figure BDA0001814054560000131
And calculating the horizontal distance and the height difference in the vertical direction obtained by the two-stage observation, and the medium error of the poor horizontal distance and the medium error of the poor height difference in the vertical direction.
TABLE 7 determination of poor baseline horizontal distance
Figure BDA0001814054560000141
TABLE 8 poor determination of baseline head
Figure BDA0001814054560000142
As can be seen from tables 7 to 8, the change from the GPS2881 to the GPS2802, GPS2605, and GPS2629 baselines is not significant, and is a stable baseline, so the GPS2881 is determined to be a stable point, and similarly, the GPS2605 and GPS2629 are determined to be stable points, and finally the conclusion is reached: all control points in the control network are stable points.

Claims (7)

1. A control point stability judgment method based on a three-dimensional baseline is characterized by comprising the following steps:
(1) performing two-stage space rectangular coordinate observation on control points in the GNSS three-dimensional control network, and performing least square adjustment processing on each stage of original observation data of the whole network;
(2) making a determination of a single baseline
2.1) calculating the difference delta P of the horizontal distance and the difference delta U of the vertical distance of each base line observed twice in the rectangular coordinate system of the NEU station center space by using the data after adjustment;
2.2) calculating by using the data after the adjustment to obtain a variance covariance matrix of the first phase and the second phase of each base line in the rectangular coordinate system of the NEU station center space
Figure FDA0003002237620000011
By using
Figure FDA0003002237620000012
Calculating to obtain the variance of the distance between the first phase and the second phase of each base line in the horizontal direction
Figure FDA0003002237620000013
Variance of distance in vertical direction
Figure FDA0003002237620000014
According to two-stage observation, there is a variance with a poor horizontal distance
Figure FDA0003002237620000015
Variance of poor vertical distance
Figure FDA0003002237620000016
Calculating to obtain the mean error sigma of the two-stage observation horizontal distance differenceΔPMean error σ of poor vertical distanceΔU；
2.3) if the judgment formula | delta P | is less than or equal to 2 sigmaΔPAnd | delta U | is less than or equal to 2 sigmaΔUIf the baseline is not stable, the baseline is not stable;
(3) making a determination of all baselines
And (3) judging all baselines in the step (2), and if more than 2 homonymous baselines are unstable, judging that the common point is unstable.
2. The method for determining the stability of the control points based on the three-dimensional baseline of claim 1, wherein in the step 2.1), the two end points of the baseline are taken as the control points A, B and are marked as the baseline AB, and the spatial rectangular coordinates after adjustment are respectively (X)A，YA，ZA) And (X)B，YB，ZB) The spatial rectangular coordinate (X) of the control point A, BA，YA，ZA) And (X)B，YB，ZB) Converted into latitude and longitude coordinates (B)A，LA，HA) And (B)B，LB，HB) And NEU station center space rectangular coordinates (N)A，EA，UA) And (N)B，EB，UB) And therefore, under the rectangular coordinate system of the NEU station center space:
distance P in horizontal direction of control point A, BABSatisfies the following conditions:
Figure FDA0003002237620000017
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA，
Distance U in vertical direction of control point A, BABSatisfies the following conditions:
UAB＝UB-UA，
coordinates (X) through baseline first phase control point A, BA (1)，YA (1)，ZA (1))、(XB (1)，YB (1)，ZB (1)) Calculating to obtain PAB (1)、UAB (1)；
Coordinates (X) through baseline second phase control point A, BA (2)，YA (2)，ZA (2)) And (X)B (2)，YB (2)，ZB (2)) Calculating to obtain PAB (2)、UAB (2)Then there is
Poor baseline AB horizontal distance Δ PAB＝PAB (2)-PAB (1)
Poor vertical distance delta U of base line ABAB＝UAB (2)-UAB (1)。
3. The method for determining stability of a control point based on a three-dimensional baseline according to claim 2, wherein in the step 2.2), under a spatial rectangular coordinate system:
the variance covariance matrix for control point A, B is:
Figure FDA0003002237620000021
the coordinate difference of the control point A, B in the rectangular spatial coordinate system is as follows:
Figure FDA0003002237620000022
i.e. with dL ═ K0L', wherein:
dL′＝(ΔXAB ΔYAB ΔZAB)T
Figure FDA0003002237620000023
L′＝(XA YA ZA XB YB ZB)T
thus, Δ XAB、ΔYABAnd Δ ZABThe variance covariance matrix between is as follows:
Figure FDA0003002237620000024
variance covariance matrix between N, E, U in NEU centroid space rectangular coordinates: by
Figure FDA0003002237620000031
Wherein
Figure FDA0003002237620000032
Therefore, the following steps are carried out:
Figure FDA0003002237620000033
namely, it is
Figure FDA0003002237620000034
Thus, the variance covariance matrix between N, E, U is as follows:
Figure FDA0003002237620000035
transforming the longitude and latitude in the matrix R to an average of two points, i.e.
B＝(BA+BB)/2,L＝(LA+LB)/2；
Coordinates (X) through baseline first phase control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain a variance covariance matrix of the base line AB first stage in the NEU station center space rectangular coordinate system
Figure FDA0003002237620000036
Coordinate (X) through baseline second phase control point A, BA (2),YA (2),ZA (2)) And (X)B (2),YB (2),ZB (2)) Calculating to obtain a variance covariance matrix of the second phase AB of the base line in the rectangular coordinate system of the NEU station center space
Figure FDA0003002237620000037
4. The method for determining stability of control points based on three-dimensional baseline according to claim 3, wherein in step 2.2), distance P in the horizontal direction of control point A, B in the rectangular coordinate system of NEU center spaceABSatisfies the following conditions:
Figure FDA0003002237620000038
wherein: n is a radical ofAB＝NB-NA，EAB＝EB-EA
And (3) solving the function equation by total differentiation:
Figure FDA0003002237620000039
namely, it is
Figure FDA00030022376200000310
Namely, it is
Figure FDA00030022376200000311
Applying covariance propagation law to obtain:
Figure FDA00030022376200000312
wherein,
Figure FDA00030022376200000313
from DNEUThe obtained product is obtained by the method in the step (1),
K3obtained from the coordinates of control point A, B in the NEU station space rectangular coordinate system,
for the vertical direction, there are
Figure FDA0003002237620000041
Cov (U) among themAB，UAB) From DNEUThe obtained product is obtained by the method in the step (1),
coordinates (X) through baseline first phase control point A, BA (1),YA (1),ZA (1)) And (X)B (1),YB (1),ZB (1)) Calculating to obtain the variance of the distance of the first period of the base line AB in the horizontal direction
Figure FDA0003002237620000042
Variance of distance in vertical direction of baseline AB first phase
Figure FDA0003002237620000043
Coordinates (X) through baseline second phase control point A, BA (2),YA (2),ZA (2)) And (X)B (2),YB (2),ZB (2)) Calculating to obtain the variance of the distance of the second phase of the base line AB in the horizontal direction
Figure FDA0003002237620000044
Variance of distance in vertical direction of base line AB second phase
Figure FDA0003002237620000045
Because the first stage and the second stage are independent of each other, there are:
Figure FDA0003002237620000046
Figure FDA0003002237620000047
will find out
Figure FDA0003002237620000048
Is substituted into formula (7),
Figure FDA0003002237620000049
Substitution in equation (8) yields the variance of the baseline AB horizontal distance
Figure FDA00030022376200000410
Variance of poor base line AB vertical distance
Figure FDA00030022376200000411
Error in horizontal distance difference between base line AB obtained by taking positive after evolution
Figure FDA00030022376200000412
Error in vertical distance of base line AB
Figure FDA00030022376200000413
5. The method for determining the stability of the control points based on the three-dimensional baseline as claimed in claim 2, wherein the method for converting the spatial rectangular coordinates of the control points into the geodetic coordinates comprises the following steps:
Figure FDA00030022376200000414
Figure FDA00030022376200000415
Figure FDA00030022376200000416
wherein: n' is the radius of the unitary-mortise ring; a is the long radius of the reference ellipsoid; b is the short radius of the reference ellipsoid; e is the first eccentricity of the reference ellipsoid; e' is the second eccentricity of the reference ellipsoid;
and is
Figure FDA0003002237620000051
Figure FDA0003002237620000052
Figure FDA0003002237620000053
Figure FDA0003002237620000054
6. The method for determining the stability of the control points based on the three-dimensional baseline as claimed in claim 2, wherein the method for converting the spatial rectangular coordinates of the control points into the spatial rectangular coordinates of the station center comprises the following steps:
let j point be the coordinate under the station center rectangular coordinate system with o point as the center (N)oj,Eoj,Uoj) The o point is any control point of the control network, only 1 point is selected as the o point in one control network, and the coordinates of the j point and the o point under the space rectangular coordinate system are respectively (X)j,Yj,Zj)、(Xo,Yo,Zo) The coordinates of the j point and the o point in the geodetic coordinate system are respectively (B)j,Lj,Hj)、(Bo,Lo,Ho) Then, then
Figure FDA0003002237620000055
7. The method for determining stability of a control point based on a three-dimensional baseline of claim 1, wherein in the step (1), a control point in the GNSS three-dimensional control network is selected as a fixed point to perform least squares adjustment.
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