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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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

本发明公开了一种基于三维基线的控制点稳定性判定方法,其特征在于,包括以下步骤:(1)、对GNSS三维控制网中控制点进行两期观测,对全网每次原始观测数据进行最小二乘法平差处理,得到空间直角坐标等成果(2)、对单条基线进行判定;(3)、对全部基线进行判定:对所有基线进行步骤(2)的判定,若有2条以上的同端点基线不稳定,则判定其公共点不稳定。由于GNSS三维控制网的平差基准对水平距离差和竖直方向上的较差结果没有影响,故本方法判定不稳定点较为可靠,且适用于两次或多次观测的网形不一致的情形。

Figure 201811133110

The invention discloses a method for determining the stability of control points based on a three-dimensional baseline, which is characterized by comprising the following steps: (1) two-phase observation of control points in a GNSS three-dimensional control network, and each original observation of the entire network is performed. The data is adjusted by least square method, and the results such as spatial rectangular coordinates are obtained (2), a single baseline is judged; (3), all baselines are judged: all baselines are judged in step (2), if there are 2 The above baselines at the same endpoint are unstable, and the common point is determined to be unstable. Since the adjustment datum of the GNSS three-dimensional control network has no effect on the horizontal distance difference and the poor results in the vertical direction, this method is more reliable to determine the unstable point, and it is suitable for the situation where the network shape of two or more observations is inconsistent. .

Figure 201811133110

Description

一种基于三维基线的控制点稳定性判定方法A method for determining the stability of control points based on 3D baseline

技术领域technical field

本发明涉及工程测绘,具体地指一种基于三维基线的控制点稳定性判定的方法。The invention relates to engineering surveying and mapping, in particular to a method for determining the stability of control points based on a three-dimensional baseline.

背景技术Background technique

为适应水利工程(如长隧洞)以及其它交通工程的要求,一般采用二(三)等施工平面控制网、CPⅠ和CPⅡ平面控制网以满足工程测量精度要求(平面控制网一般为GNSS控制网),并定期或不定期对控制网进行复测,以发现可能发生的坐标变位。In order to meet the requirements of water conservancy projects (such as long tunnels) and other traffic projects, two (three) construction plane control networks, CP I and CP II plane control networks are generally used to meet the requirements of engineering measurement accuracy (the plane control network is generally GNSS control network) , and re-test the control network regularly or irregularly to find out the possible coordinate displacement.

现有技术中,一般采用两期观测的绝对坐标差、相邻点坐标差的相对误差(称方法1)进行不稳定点分析,或直接采用边长差、方位角差进行不稳定点分析(称方法2),但现有技术存在以下缺陷:方法1不能找到全部的不稳定点,方法2依据先验中误差给出限差,并不能准确地估计每个边长的误差,导致稳定性判定不可靠。方法1和方法2均要求两次或多次观测的网形、观测纲要一致,而这一条件难以满足。In the prior art, the absolute coordinate difference and the relative error of the coordinate difference between adjacent points of two-phase observations are generally used to analyze unstable points, or the difference in side length and azimuth angle are directly used to analyze unstable points ( It is called method 2), but the prior art has the following defects: method 1 cannot find all unstable points, method 2 gives a limit according to the error in the priori, and cannot accurately estimate the error of each side length, resulting in stability Judgment is unreliable. Both method 1 and method 2 require that the network shape and observation outline of two or more observations are consistent, and this condition is difficult to meet.

因此,需要开发出一种简单可靠的控制点稳定性判定方法。Therefore, it is necessary to develop a simple and reliable method for determining the stability of control points.

发明内容SUMMARY OF THE INVENTION

本发明的目的就是要解决上述背景技术的不足,提供一种基于三维基线的控制点稳定性判定的方法。The purpose of the present invention is to solve the above-mentioned deficiencies of the background technology, and to provide a method for determining the stability of a control point based on a three-dimensional baseline.

本发明的技术方案为:一种基于三维基线的控制点稳定性判定方法,其特征在于,包括以下步骤:The technical scheme of the present invention is: a method for determining the stability of a control point based on a three-dimensional baseline, which is characterized in that it includes the following steps:

(1)对GNSS三维控制网中控制点进行两期空间直角坐标观测,对全网每次原始观测数据进行最小二乘法平差处理;(1) Carry out two-phase space rectangular coordinate observation for the control points in the GNSS three-dimensional control network, and perform least squares adjustment for each original observation data of the entire network;

(2)对单条基线进行判定(2) Judging a single baseline

2.1)利用平差后的数据计算各基线两次观测在NEU站心空间直角坐标系中水平距离的较差ΔP、竖直距离的较差ΔU;2.1) Use the adjusted data to calculate the difference ΔP of the horizontal distance and the difference ΔU of the vertical distance between the two observations of each baseline in the Cartesian coordinate system of the NEU station center space;

2.2)利用平差后的数据计算得到各基线第一期、第二期在NEU站心空间直角坐标系中方差协方差矩阵

Figure BDA0001814054560000021
利用
Figure BDA0001814054560000022
计算得到各基线第一期、第二期在水平方向上距离的方差
Figure BDA0001814054560000023
竖直方向上距离的方差
Figure BDA0001814054560000024
根据两期观测相互独立有水平距离较差之方差
Figure BDA0001814054560000025
竖直距离较差之方差
Figure BDA0001814054560000026
计算得到两期观测水平距离较差之中误差σΔP、竖直距离较差之中误差σΔU;2.2) Calculate the variance covariance matrix of the first and second phases of each baseline in the NEU station center space rectangular coordinate system using the adjusted data
Figure BDA0001814054560000021
use
Figure BDA0001814054560000022
Calculate the variance of the distance between the first and second periods of each baseline in the horizontal direction
Figure BDA0001814054560000023
The variance of the distance in the vertical direction
Figure BDA0001814054560000024
According to the two periods of observation are independent of each other, there is a variance of the horizontal distance difference
Figure BDA0001814054560000025
The variance of the vertical distance difference
Figure BDA0001814054560000026
The error σ ΔP in the poor horizontal distance and the error σ ΔU in the poor vertical distance of the two observations are obtained by calculation;

2.3)若满足判定式|ΔP|≤2σΔP且|ΔU|≤2σΔU,则判定基线稳定,若不满足则判定基线不稳定;2.3) If the judgment formula |ΔP|≤2σ ΔP and |ΔU|≤2σ ΔU are satisfied, the baseline is determined to be stable; if not, the baseline is determined to be unstable;

(3)对全部基线进行判定:(3) Judging all baselines:

对所有基线进行步骤(2)的判定,若有2条以上的同端点基线不稳定,则判定其公共点不稳定。Perform the judgment of step (2) on all the baselines. If more than two baselines with the same endpoint are unstable, the common point is determined to be unstable.

优选的,所述步骤2.1)中,令基线两端点为控制点A、B,记作基线AB,平差后的空间直角坐标分别为(XA,YA,ZA)和(XB,YB,ZB),将控制点A、B的空间直角坐标(XA,YA,ZA)和(XB,YB,ZB)转换算成经纬度坐标(BA,LA,HA)和(BB,LB,HB),以及NEU站心空间直角坐标(NA,EA,UA)和(NB,EB,UB),从而NEU站心空间直角坐标下:Preferably, in the step 2.1), let the two ends of the baseline be the control points A and B, denoted as the baseline AB, and the spatial Cartesian coordinates after adjustment are respectively (X A , Y A , Z A ) and (X B , Y B , Z B ), convert the spatial Cartesian coordinates (X A , Y A , Z A ) and (X B , Y B , Z B ) of control points A and B into latitude and longitude coordinates (B A , L A , H A ) and (B B , L B , H B ), as well as the NEU station center space Cartesian coordinates (NA , E A , U A ) and (N B , E B , U B ) , so that the NEU station center space is at a right angle Under the coordinates:

控制点A、B水平方向上的距离PAB满足:The distance P AB in the horizontal direction of the control points A and B satisfies:

Figure BDA0001814054560000027
Figure BDA0001814054560000027

其中:NAB=NB-NA,EAB=EB-EAWhere: N AB =N B -N A , E AB =E B -E A ,

控制点A、B竖直方向上的距离UAB满足:The distance U AB in the vertical direction of the control points A and B satisfies:

UAB=UB-UAU AB = U B - U A ,

经过第一期基线控制点A、B的坐标(XA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1))计算,得到PAB (1)、UAB (1)Coordinates (X A (1) , Y A (1) , Z A (1) ), (X B (1) , Y B (1) , Z B (1) after the first phase of baseline control points A and B ) is calculated to obtain P AB (1) , U AB (1) ;

经过第二期基线控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到PAB (2)、UAB (2),则有After the second phase of baseline control points A, B coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) to calculate to get P AB (2) and U AB (2) , then we have

基线AB水平距离较差ΔPAB=PAB (2)-PAB (1) Poor baseline AB level distance ΔP AB =P AB (2) -P AB (1)

基线AB竖直距离较差ΔUAB=UAB (2)-UAB (1)Baseline AB vertical distance difference ΔU AB =U AB (2) -U AB (1) .

进一步的,所述步骤2.2)中,空间直角坐标系下:Further, in the step 2.2), under the space Cartesian coordinate system:

控制点A、B的方差协方差矩阵为:The variance covariance matrix of control points A and B is:

Figure BDA0001814054560000031
Figure BDA0001814054560000031

空间直角坐标系中控制点A、B的坐标差如下:The coordinate difference between the control points A and B in the space rectangular coordinate system is as follows:

Figure BDA0001814054560000032
Figure BDA0001814054560000032

即有dL=K0L,其中:That is, dL=K 0 L, where:

dL=(ΔXAB ΔYAB ΔZAB)T dL=(ΔX AB ΔY AB ΔZ AB ) T

Figure BDA0001814054560000033
Figure BDA0001814054560000033

L=(XA YA ZA XB YB ZB)T L=(X A Y A Z A X B Y B Z B ) T

因此,ΔXAB、ΔYAB和ΔZAB之间的方差协方差矩阵如下:Therefore, the variance covariance matrix between ΔX AB , ΔY AB and ΔZ AB is as follows:

Figure BDA0001814054560000034
Figure BDA0001814054560000034

在NEU站心空间直角坐标系下,N、E、U之间的方差协方差矩阵:由

Figure BDA0001814054560000035
其中
Figure BDA0001814054560000036
可知:In the NEU station center space Cartesian coordinate system, the variance covariance matrix between N, E, and U: by
Figure BDA0001814054560000035
in
Figure BDA0001814054560000036
It is known that:

Figure BDA0001814054560000037
Figure BDA0001814054560000038
Figure BDA0001814054560000037
which is
Figure BDA0001814054560000038

因此,N、E、U之间的方差协方差矩阵如下:Therefore, the variance-covariance matrix between N, E, U is as follows:

Figure BDA0001814054560000039
Figure BDA0001814054560000039

变换矩阵R中的经纬度为两点的平均值,即The latitude and longitude in the transformation matrix R is the average of the two points, that is

B=(BA+BB)/2,L=(LA+LB)/2;B=(B A +B B )/2, L=(L A +L B )/2;

通过基线第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到基线AB第一期在NEU站心空间直角坐标系中方差协方差矩阵

Figure BDA0001814054560000041
Coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) of control points A and B through the baseline ) calculation to obtain the variance covariance matrix of the first phase of baseline AB in the NEU station center space rectangular coordinate system
Figure BDA0001814054560000041

通过基线第二期控制点A、B的坐标(XA (2),YA (2),ZA (2))和(XB (2,YB (2),ZB (2))计算,得到基线AB第二期在NEU站心空间直角坐标系中方差协方差矩阵

Figure BDA0001814054560000042
Coordinates (X A (2) , Y A (2) , Z A (2) ) and (X B (2 , Y B (2) , Z B (2) ) of control points A and B through the baseline second period Calculate to get the variance covariance matrix of the second phase of baseline AB in the NEU station center space rectangular coordinate system
Figure BDA0001814054560000042

更进一步的,所述步骤2.2)中,NEU站心空间直角坐标下控制点A、B水平方向上的距离PAB满足:Further, in the described step 2.2), the distance P AB on the horizontal direction of the control points A and B under the NEU station center space Cartesian coordinates satisfies:

Figure BDA0001814054560000043
Figure BDA0001814054560000043

其中:NAB=NB-NA,EAB=EB-EA Among them: N AB =N B -N A , E AB =E B -E A

对函数式求全微分得:

Figure BDA0001814054560000044
Totally differentiate the functional expression to get:
Figure BDA0001814054560000044

Figure BDA0001814054560000045
Figure BDA0001814054560000046
which is
Figure BDA0001814054560000045
which is
Figure BDA0001814054560000046

应用协方差传播律,得到:

Figure BDA0001814054560000047
Applying the covariance propagation law, we get:
Figure BDA0001814054560000047

其中,

Figure BDA0001814054560000048
从DNEU中得到;in,
Figure BDA0001814054560000048
from D NEU ;

K3根据控制点A、B在NEU站心空间直角坐标下的坐标得到,K 3 is obtained according to the coordinates of the control points A and B under the Cartesian coordinates of the NEU station center space,

对于竖直方向,有

Figure BDA0001814054560000049
For the vertical direction, we have
Figure BDA0001814054560000049

其中,cov(UAB,UAB)从DNEU中得到where cov(U AB ,U AB ) is obtained from D NEU

通过基线第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到基线AB第一期在水平方向上距离的方差

Figure BDA00018140545600000410
基线AB第一期在竖直方向上距离的方差
Figure BDA00018140545600000411
Coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) of control points A and B through the baseline ) calculation to get the variance of the distance in the horizontal direction of the first period of baseline AB
Figure BDA00018140545600000410
The variance of the distance in the vertical direction in the first period of baseline AB
Figure BDA00018140545600000411

经过第二期基线控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到基线AB第二期在水平方向上距离的方差

Figure BDA00018140545600000412
基线AB第二期在竖直方向上距离的方差
Figure BDA00018140545600000413
After the second phase of baseline control points A, B coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) calculation to obtain the variance of the distance in the horizontal direction of the second period of baseline AB
Figure BDA00018140545600000412
The variance of the distance in the vertical direction of the second period of baseline AB
Figure BDA00018140545600000413

由于第一期和第二期观测相互独立,有:Since the first and second period observations are independent of each other, there are:

Figure BDA0001814054560000051
Figure BDA0001814054560000051

Figure BDA0001814054560000052
Figure BDA0001814054560000052

将求得的

Figure BDA0001814054560000053
代入式(7)、
Figure BDA0001814054560000054
代入式(8)中,得到基线AB水平距离较差之方差
Figure BDA0001814054560000055
基线AB竖直距离较差之方差
Figure BDA0001814054560000056
开方后取正得到基线AB水平距离较差之中误差
Figure BDA0001814054560000057
基线AB竖直距离较差之中误差
Figure BDA0001814054560000058
will be obtained
Figure BDA0001814054560000053
Substitute into formula (7),
Figure BDA0001814054560000054
Substitute into formula (8) to get the variance of the baseline AB horizontal distance difference
Figure BDA0001814054560000055
The variance of the vertical distance difference of the baseline AB
Figure BDA0001814054560000056
After square root, take the positive value to get the error in the difference between the baseline AB horizontal distance and the difference
Figure BDA0001814054560000057
Baseline AB vertical distance is poor middle error
Figure BDA0001814054560000058

进一步的,控制点的空间直角坐标至大地坐标的转换方法为:Further, the conversion method from the spatial Cartesian coordinates of the control points to the geodetic coordinates is:

Figure BDA0001814054560000059
Figure BDA0001814054560000059

Figure BDA00018140545600000510
Figure BDA00018140545600000510

Figure BDA00018140545600000511
Figure BDA00018140545600000511

其中:N为卯酉圈的半径;a为参考椭球的长半径;b为参考椭球的短半径;e为参考椭球的第一偏心率;e′为参考椭球的第二偏心率;并且Wherein: N is the radius of the unitary circle; 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

Figure BDA00018140545600000512
Figure BDA00018140545600000512

Figure BDA00018140545600000513
Figure BDA00018140545600000513

Figure BDA00018140545600000514
Figure BDA00018140545600000514

Figure BDA00018140545600000515
Figure BDA00018140545600000515

进一步的,将控制点的空间直角坐标至至站心空间直角坐标的转换方法为:Further, the conversion method from the spatial rectangular coordinates of the control point to the spatial rectangular coordinates of the station center is:

设j点为在以o点为中心的站心直角坐标系下的坐标为(Noj,Eoj,Uoj),o点取控制网任一控制点,一个控制网中只选用1个点作为o点,j点、o点在空间直角坐标系下的坐标分别为(Xj,Yj,Zj)、(Xo,Yo,Zo),j点、o点在大地坐标系下的坐标分别为(Bj,Lj,Hj)、(Bo,Lo,Ho),则Let point j be the coordinates in the Cartesian coordinate system of the station center with point o as the center as (N oj , E oj , U oj ), point o takes any control point of the control network, and only one point is selected in one control network As point o, the coordinates of point j and point o in the space rectangular coordinate system are (X j , Y j , Z j ), (X o , Y o , Z o ), respectively, and point j and point o are in the geodetic coordinate system The coordinates below are (B j , L j , H j ), (B o , L o , H o ), then

Figure BDA0001814054560000061
Figure BDA0001814054560000061

优选的,步骤(1)中选取GNSS三维控制网中一控制点为固定点进行最小二乘法平差处理。Preferably, in step (1), a control point in the GNSS three-dimensional control network is selected as a fixed point for least squares adjustment processing.

本发明的有益效果为:The beneficial effects of the present invention are:

1.由于GNSS三维控制网的平差基准对水平距离差和竖直方向上的较差结果没有影响,故本方法判定不稳定点较为可靠。1. Since the adjustment datum of the GNSS three-dimensional control network has no effect on the horizontal distance difference and the poor results in the vertical direction, this method is more reliable for determining unstable points.

2.根据任两个控制点之间的方差协方差矩阵得到了两次观测的对应水平距离较差之方差和对应竖直距离较差之方差,本方法的理论严密。2. According to the variance covariance matrix between any two control points, the variance of the corresponding horizontal distance difference and the variance of the corresponding vertical distance difference of the two observations are obtained. The theory of this method is strict.

3.适用于两次或多次观测的网形、观测纲要一致或不一致的情形,如施工控制网的个别控制点毁坏,也不影响不稳定点的分析。3. It is suitable for the situation that the network shape and observation outline of two or more observations are consistent or inconsistent, such as the destruction of individual control points of the construction control network, and the analysis of unstable points is not affected.

附图说明Description of drawings

图1为空间直角坐标与站心空间直角坐标关系示意图Figure 1 is a schematic diagram of the relationship between the space rectangular coordinates and the space rectangular coordinates of the station center

图2为判断公共点示意图Figure 2 is a schematic diagram of judging common points

图3为实施例中控制点网示意图3 is a schematic diagram of a control point network in an embodiment

具体实施方式Detailed ways

下面具体实施例对本发明作进一步的详细说明。The following specific examples will further illustrate the present invention in detail.

如图1-2所示,本发明提供的基于三维基线的控制点稳定性判定方法,包括以下步骤。As shown in Figures 1-2, the method for determining the stability of a control point based on a three-dimensional baseline provided by the present invention includes the following steps.

(1)对GNSS三维控制网中控制点进行两期空间直角坐标观测,对全网每次原始观测数据进行最小二乘法平差处理,(1) Carry out two-phase space rectangular coordinate observation of the control points in the GNSS three-dimensional control network, and perform least squares adjustment for each original observation data of the entire network,

(2)对单条基线进行判定(2) Judging a single baseline

2.1)利用平差后的数据计算各基线两次观测在NEU站心空间直角坐标系中水平距离的较差ΔP、竖直距离的较差ΔU;2.1) Use the adjusted data to calculate the difference ΔP of the horizontal distance and the difference ΔU of the vertical distance between the two observations of each baseline in the Cartesian coordinate system of the NEU station center space;

以两个控制点A、B形成的基线AB为例:Take the baseline AB formed by two control points A and B as an example:

基两端点为控制点A、B,平差后的空间直角坐标分别为和(XB,YB,ZB),将控制点A、B的空间直角坐标(XA,YA,ZA)和(XB,YB,ZB)转换算成经纬度坐标(BA,LA,HA)和(BB,LB,HB),以及NEU站心空间直角坐标(NA,EA,UA)和(NB,EB,UB),The two ends of the base are the control points A and B, the spatial Cartesian coordinates after adjustment are sum (X B , Y B , Z B ), respectively, and the spatial Cartesian coordinates of the control points A and B (X A , Y A , Z A ) ) and (X B , Y B , Z B ) are converted into longitude and latitude coordinates (B A , L A , H A ) and (B B , L B , H B ), and the NEU station center space Cartesian coordinates (N A , E A ,U A ) and (N B ,E B ,U B ),

控制点的空间直角坐标至大地坐标的转换方法为:The conversion method from the spatial Cartesian coordinates of the control points to the geodetic coordinates is as follows:

Figure BDA0001814054560000071
Figure BDA0001814054560000071

Figure BDA0001814054560000072
Figure BDA0001814054560000072

Figure BDA0001814054560000073
Figure BDA0001814054560000073

其中:N为卯酉圈的半径;a为参考椭球的长半径;b为参考椭球的短半径;e为参考椭球的第一偏心率;e′为参考椭球的第二偏心率;并且Wherein: N is the radius of the unitary circle; 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

Figure BDA0001814054560000074
Figure BDA0001814054560000074

Figure BDA0001814054560000075
Figure BDA0001814054560000075

Figure BDA0001814054560000076
Figure BDA0001814054560000076

Figure BDA0001814054560000077
Figure BDA0001814054560000077

对于WGS4参考椭球,a=6378137m,b=6356752.314m。For the WGS4 reference ellipsoid, a=6378137m, b=6356752.314m.

将控制点的空间直角坐标至大地坐标的转换方法为:The conversion method from the spatial Cartesian coordinates of the control points to the geodetic coordinates is:

设j点为在以o点为中心的站心直角坐标系下的坐标为(Noj,Eoj,Uoj),o点取控制网任一控制点,一个控制网中只选用1个点作为o点,j点、o点在空间直角坐标系下的坐标分别为(Xj,Yj,Zj)、(Xo,Yo,Zo),j点、o点在大地坐标系下的坐标分别为(Bj,Lj,Hj)、(Bo,Lo,Ho),则Let point j be the coordinates in the Cartesian coordinate system of the station center with point o as the center as (N oj , E oj , U oj ), point o takes any control point of the control network, and only one point is selected in one control network As point o, the coordinates of point j and point o in the space rectangular coordinate system are (X j , Y j , Z j ), (X o , Y o , Z o ), respectively, and point j and point o are in the geodetic coordinate system The coordinates below are (B j , L j , H j ), (B o , L o , H o ), then

Figure BDA0001814054560000078
Figure BDA0001814054560000078

将控制点的空间直角坐标转换算成经纬度坐标以及NEU站心空间直角坐标属于常规的现有技术。Converting the spatial rectangular coordinates of the control point into longitude and latitude coordinates and the spatial rectangular coordinates of the NEU station center belongs to the conventional prior art.

在NEU站心空间直角坐标下:Under the Cartesian coordinates of the NEU station center space:

控制点A、B水平方向上的距离PAB满足:The distance P AB in the horizontal direction of the control points A and B satisfies:

Figure BDA0001814054560000081
Figure BDA0001814054560000081

其中:NAB=NB-NA,EAB=EB-EAWhere: N AB =N B -N A , E AB =E B -E A ,

控制点A、B竖直方向上的距离UAB满足:The distance U AB in the vertical direction of the control points A and B satisfies:

UAB=UB-UAU AB = U B - U A ,

经过第一期基线控制点A、B的坐标(XA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1))计算,得到PAB (1)、UAB (1)Coordinates (X A (1) , Y A (1) , Z A (1) ), (X B (1) , Y B (1) , Z B (1) after the first phase of baseline control points A and B ) is calculated to obtain P AB (1) , U AB (1) ;

经过第二期基线控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到PAB (2)、UAB (2),则有After the second phase of baseline control points A, B coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) to calculate to get P AB (2) and U AB (2) , then we have

ΔPAB=PAB (2)-PAB (1) ΔP AB =P AB (2) -P AB (1)

ΔUAB=UAB (2)-UAB (1)ΔU AB =U AB (2) −U AB (1) .

2.2)2.2)

a.计算第一期、第二期空间直角坐标系下ΔXAB、ΔYAB和ΔZAB之间的方差协方差矩阵

Figure BDA0001814054560000082
a. Calculate the variance covariance matrix between ΔX AB , ΔY AB and ΔZ AB in the first and second period spatial Cartesian coordinates
Figure BDA0001814054560000082

控制点A、B其空间直角坐标分别为(XA,YA,ZA)和(XB,YB,ZB),这两个控制点之间的方差协方差矩阵DXYZ为:The spatial Cartesian coordinates of control points A and B are (X A , Y A , Z A ) and (X B , Y B , Z B ), respectively, and the variance covariance matrix D XYZ between these two control points is:

Figure BDA0001814054560000083
Figure BDA0001814054560000083

这两个控制点的坐标差如下:The coordinate difference between these two control points is as follows:

Figure BDA0001814054560000084
Figure BDA0001814054560000084

即有dL=K0L,其中:That is, dL=K 0 L, where:

dL=(ΔXAB ΔYAB ΔZAB)T dL=(ΔX AB ΔY AB ΔZ AB ) T

Figure BDA0001814054560000091
Figure BDA0001814054560000091

L=(XA YA ZA XB YB ZB)T L=(X A Y A Z A X B Y B Z B ) T

因此,ΔXAB、ΔYAB和ΔZAB之间的方差协方差矩阵如下:Therefore, the variance covariance matrix between ΔX AB , ΔY AB and ΔZ AB is as follows:

Figure BDA0001814054560000092
Figure BDA0001814054560000092

将第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))代入上式(1)-(3),得到

Figure BDA0001814054560000093
Set the coordinates of the first phase control points A and B (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) Substituting into the above equations (1)-(3), we get
Figure BDA0001814054560000093

b.计算第一期、第二期NEU站心空间直角坐标系下的方差协方差矩阵

Figure BDA0001814054560000094
b. Calculate the variance covariance matrix in the first phase and the second phase NEU station center space rectangular coordinate system
Figure BDA0001814054560000094

在NEU站心空间直角坐标系下In the Cartesian coordinate system of the NEU station center space

Figure BDA0001814054560000095
其中
Figure BDA0001814054560000096
可知:Depend on
Figure BDA0001814054560000095
in
Figure BDA0001814054560000096
It is known that:

Figure BDA0001814054560000097
Figure BDA0001814054560000098
Figure BDA0001814054560000097
which is
Figure BDA0001814054560000098

因此,N、E、U之间的方差协方差矩阵如下:Therefore, the variance-covariance matrix between N, E, U is as follows:

Figure BDA0001814054560000099
Figure BDA0001814054560000099

变换矩阵R中的经纬度为两点的平均值,即The latitude and longitude in the transformation matrix R is the average of the two points, that is

B=(BA+BB)/2,L=(LA+LB)/2;B=(B A +B B )/2, L=(L A +L B )/2;

通过基线第一期控制点A、B大地坐标和

Figure BDA00018140545600000910
得到
Figure BDA00018140545600000911
Through the first phase of the baseline control points A, B geodetic coordinates and
Figure BDA00018140545600000910
get
Figure BDA00018140545600000911

通过基线第二期控制点A、B大地坐标和

Figure BDA00018140545600000912
得到
Figure BDA00018140545600000913
Through the second phase of the baseline control points A, B geodetic coordinates and
Figure BDA00018140545600000912
get
Figure BDA00018140545600000913

c.计算两期观测水平距离较差之中误差σΔP、竖直距离较差之中误差σΔUc. Calculate the error σ ΔP in the difference in the horizontal distance and the error σ ΔU in the difference in the vertical distance between the two observations:

NEU站心空间直角坐标下控制点A、B水平方向上的距离PAB满足:The distance P AB of the control points A and B in the horizontal direction in the Cartesian coordinates of the NEU station center satisfies:

Figure BDA0001814054560000101
Figure BDA0001814054560000101

其中:NAB=NB-NA,EAB=EB-EA Among them: N AB =N B -N A , E AB =E B -E A

对函数式求全微分得:

Figure BDA0001814054560000102
Totally differentiate the functional expression to get:
Figure BDA0001814054560000102

Figure BDA0001814054560000103
Figure BDA0001814054560000104
which is
Figure BDA0001814054560000103
which is
Figure BDA0001814054560000104

应用协方差传播律,得到:

Figure BDA0001814054560000105
Applying the covariance propagation law, we get:
Figure BDA0001814054560000105

其中,

Figure BDA0001814054560000106
从DNEU中得到;in,
Figure BDA0001814054560000106
from D NEU ;

K3根据控制点A、B在NEU站心空间直角坐标下的坐标得到,K 3 is obtained according to the coordinates of the control points A and B under the Cartesian coordinates of the NEU station center space,

对于竖直方向,有

Figure BDA0001814054560000107
For the vertical direction, we have
Figure BDA0001814054560000107

其中,cov(UAB,UAB)从DNEU中得到where cov(U AB ,U AB ) is obtained from D NEU

通过基线第一期控制点A、B的NEU站心空间直角坐标和

Figure BDA0001814054560000108
得到
Figure BDA0001814054560000109
The spatial Cartesian coordinates of the NEU station center through the control points A and B of the first phase of the baseline and
Figure BDA0001814054560000108
get
Figure BDA0001814054560000109

通过基线第一期控制点A、B的NEU站心空间直角坐标和

Figure BDA00018140545600001010
得到
Figure BDA00018140545600001011
The spatial Cartesian coordinates of the NEU station center through the control points A and B of the first phase of the baseline and
Figure BDA00018140545600001010
get
Figure BDA00018140545600001011

由于第一期和第二期观测相互独立,有:Since the first and second period observations are independent of each other, there are:

Figure BDA00018140545600001012
Figure BDA00018140545600001012

Figure BDA00018140545600001013
Figure BDA00018140545600001013

将求得的

Figure BDA00018140545600001014
代入式(7)、
Figure BDA00018140545600001015
代入式(8)中,得到
Figure BDA00018140545600001016
开方后取正得到
Figure BDA00018140545600001017
will be obtained
Figure BDA00018140545600001014
Substitute into formula (7),
Figure BDA00018140545600001015
Substitute into formula (8), we get
Figure BDA00018140545600001016
After opening the square, take it right and get it
Figure BDA00018140545600001017

2.3)若两次观测所得的水平距离差有

Figure BDA00018140545600001018
且竖直方向上的较差有
Figure BDA00018140545600001019
则说明ΔPAB和ΔUAB主要由观测误差造成,基线AB稳定,即控制点A、B稳定;否则,认为这两个控制点中至少有一点不稳定,则该基线不稳定。2.3) If the horizontal distance difference between the two observations is
Figure BDA00018140545600001018
And the difference in the vertical direction is
Figure BDA00018140545600001019
It means that ΔP AB and ΔU AB are mainly caused by observation errors, and the baseline AB is stable, that is, the control points A and B are stable; otherwise, it is considered that at least one of the two control points is unstable, and the baseline is unstable.

(3)、对全部基线进行两次观测的水平距离差和竖直方向上的较差进行检查,若有2条以上的同端点基线(AC和BC)不能通过检查,则判定其公共点(C)不稳定,参见图2。(3) Check the difference in the horizontal distance and the difference in the vertical direction of the two observations of all the baselines. If there are more than 2 baselines (AC and BC) with the same end point that fail to pass the inspection, determine their common point ( C) Instability, see Figure 2.

以下为本方案的应用实例The following is an application example of this scheme

本算例计算的是一个由四个同步观测的控制点构成的控制网,选择的数据为某引水工程中的四个控制点,由6条GNSS基线构成的控制网,控制点网图如图3所示。This example calculates a control network composed of four synchronously observed control points. The selected data are four control points in a water diversion project and a control network composed of 6 GNSS baselines. The control point network is shown in the figure. 3 shown.

表1第1期GNSS测量后得到WGS84空间直角坐标(单点定位)Table 1 WGS84 space Cartesian coordinates (single-point positioning) obtained after the first phase of GNSS survey

Figure BDA0001814054560000111
Figure BDA0001814054560000111

表2第2期GNSS测量后得到WGS84空间直角坐标(单点定位)Table 2 WGS84 space Cartesian coordinates (single-point positioning) obtained after the second phase of GNSS survey

Figure BDA0001814054560000112
Figure BDA0001814054560000112

两期观测原始数据如上表1-2所示,对两期观测数据进行基线解算,确保基线符合精度要求。根据背景技术中的现有方法1将控制点GPS2802作为固定点,进行三维约束平差(最小二乘法平差处理),平差后控制点坐标如下:The original data of the two-phase observation are shown in Table 1-2 above, and the baseline calculation is performed on the two-phase observation data to ensure that the baseline meets the accuracy requirements. According to the existing method 1 in the background technology, the control point GPS2802 is used as a fixed point, and three-dimensional constraint adjustment (least square method adjustment processing) is performed, and the coordinates of the control point after adjustment are as follows:

表3平差后同名点WGS84空间直角坐标Table 3 WGS84 space Cartesian coordinates of the point with the same name after adjustment

Figure BDA0001814054560000121
Figure BDA0001814054560000121

由表3的空间直角坐标可计算得控制点大地坐标、站心坐标如下表4-5所示:From the space rectangular coordinates in Table 3, the geodetic coordinates and station center coordinates of the control point can be calculated as shown in Table 4-5 below:

表4控制点大地坐标Table 4 Geodetic coordinates of control points

Figure BDA0001814054560000122
Figure BDA0001814054560000122

表5控制点站心坐标Table 5 Control point station center coordinates

Figure BDA0001814054560000123
Figure BDA0001814054560000123

为了进一步探究其他控制点稳定性,对于整个控制网中任意两点之间的基线,其方差协方差阵如下表6所示:In order to further explore the stability of other control points, for the baseline between any two points in the entire control network, the variance covariance matrix is shown in Table 6 below:

表6控制网中所有基线的方差协方差矩阵DXYZ Table 6 Variance covariance matrix D XYZ of all baselines in the control network

Figure BDA0001814054560000131
Figure BDA0001814054560000131

计算两期观测所得的水平距离、竖直方向上的高差,以及水平距离较差的中误差、竖直方向高差的较差之中误差。Calculate the horizontal distance and height difference in the vertical direction obtained from the two periods of observation, as well as the poor median error of the horizontal distance and the poor median error of the vertical height difference.

表7基线水平距离较差判定Table 7 Baseline horizontal distance poor judgment

Figure BDA0001814054560000141
Figure BDA0001814054560000141

表8基线高差的较差判定Table 8 Poor judgment of baseline height difference

Figure BDA0001814054560000142
Figure BDA0001814054560000142

由表7-8可知,点GPS2881至点GPS2802、GPS2605、GPS2629的基线的变化均不显著,为稳定基线,因而判定这点GPS2881为稳定点,同理,可判定点GPS2605、GPS2629为稳定点,最终得出结论:该控制网中所有控制点均为稳定点。It can be seen from Table 7-8 that the baseline changes from point GPS2881 to point GPS2802, GPS2605, and GPS2629 are not significant, which is a stable baseline. Therefore, this point GPS2881 is determined to be a stable point. Similarly, points GPS2605 and GPS2629 can be determined to be stable points. Finally, it is concluded that all control points in the control network are stable points.

Claims (7)

1.一种基于三维基线的控制点稳定性判定方法,其特征在于,包括以下步骤:1. a control point stability determination method based on three-dimensional baseline, is characterized in that, comprises the following steps: (1)对GNSS三维控制网中控制点进行两期空间直角坐标观测,对全网每期原始观测数据进行最小二乘法平差处理;(1) Carry out two-phase space rectangular coordinate observation for the control points in the GNSS three-dimensional control network, and perform least squares adjustment for the original observation data of each phase of the entire network; (2)对单条基线进行判定(2) Judging a single baseline 2.1)利用平差后的数据计算各基线两次观测在NEU站心空间直角坐标系中水平距离的较差ΔP、竖直距离的较差ΔU;2.1) Use the adjusted data to calculate the difference ΔP of the horizontal distance and the difference ΔU of the vertical distance between the two observations of each baseline in the Cartesian coordinate system of the NEU station center space; 2.2)利用平差后的数据计算得到各基线第一期、第二期在NEU站心空间直角坐标系中方差协方差矩阵
Figure FDA0003002237620000011
利用
Figure FDA0003002237620000012
计算得到各基线第一期、第二期在水平方向上距离的方差
Figure FDA0003002237620000013
竖直方向上距离的方差
Figure FDA0003002237620000014
根据两期观测相互独立有水平距离较差之方差
Figure FDA0003002237620000015
竖直距离较差之方差
Figure FDA0003002237620000016
计算得到两期观测水平距离较差之中误差σΔP、竖直距离较差之中误差σΔU
2.2) Calculate the variance covariance matrix of the first and second phases of each baseline in the NEU station center space rectangular coordinate system using the adjusted data
Figure FDA0003002237620000011
use
Figure FDA0003002237620000012
Calculate the variance of the distance between the first and second periods of each baseline in the horizontal direction
Figure FDA0003002237620000013
The variance of the distance in the vertical direction
Figure FDA0003002237620000014
According to the two periods of observation are independent of each other, there is a variance of the horizontal distance difference
Figure FDA0003002237620000015
The variance of the vertical distance difference
Figure FDA0003002237620000016
The error σ ΔP in the poor horizontal distance and the error σ ΔU in the poor vertical distance of the two observations are obtained by calculation;
2.3)若满足判定式|ΔP|≤2σΔP且|ΔU|≤2σΔU,则判定基线稳定,若不满足则判定基线不稳定;2.3) If the judgment formula |ΔP|≤2σ ΔP and |ΔU|≤2σ ΔU are satisfied, the baseline is determined to be stable; if not, the baseline is determined to be unstable; (3)对全部基线进行判定(3) Judging all baselines 对所有基线进行步骤(2)的判定,若有2条以上的同端点基线不稳定,则判定其公共点不稳定。Perform the judgment of step (2) on all the baselines. If more than two baselines with the same endpoint are unstable, the common point is determined to be unstable.
2.如权利要求1所述基于三维基线的控制点稳定性判定方法,其特征在于,所述步骤2.1)中,令基线两端点为控制点A、B,记作基线AB,平差后的空间直角坐标分别为(XA,YA,ZA)和(XB,YB,ZB),将控制点A、B的空间直角坐标(XA,YA,ZA)和(XB,YB,ZB)转换成经纬度坐标(BA,LA,HA)和(BB,LB,HB),以及NEU站心空间直角坐标(NA,EA,UA)和(NB,EB,UB),从而NEU站心空间直角坐标系下:2. the control point stability determination method based on three-dimensional baseline as claimed in claim 1, is characterized in that, in described step 2.1), make baseline both ends be control points A, B, be denoted as baseline AB, after adjustment The spatial Cartesian coordinates of the control point A and B are (X A , Y A , Z A ) and (X B , Y B , Z B ), respectively, and the spatial Cartesian coordinates (X A , Y A , Z A ) and ( X B , Y B , Z B ) are converted into latitude and longitude coordinates (B A , L A , H A ) and (B B , L B , H B ), and the NEU station center space Cartesian coordinates (N A , E A , U A ) and (N B , E B , U B ), thus under the NEU station center space Cartesian coordinate system: 控制点A、B水平方向上的距离PAB满足:The distance P AB in the horizontal direction of the control points A and B satisfies:
Figure FDA0003002237620000017
Figure FDA0003002237620000017
其中:NAB=NB-NA,EAB=EB-EAWhere: N AB =N B -N A , E AB =E B -E A , 控制点A、B竖直方向上的距离UAB满足:The distance U AB in the vertical direction of the control points A and B satisfies: UAB=UB-UAU AB =U B -U A , 经过基线第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))、(XB (1),YB (1),ZB (1))计算,得到PAB (1)、UAB (1)Coordinates (X A (1) , Y A (1) , Z A (1) ), (X B (1) , Y B (1) , Z B (1) ) of control points A and B through the first phase of the baseline ) is calculated to obtain P AB (1) , U AB (1) ; 经过基线第二期控制点A、B的坐标(XA (2),YA (2),ZA (2))和(XB (2),YB (2),ZB (2))计算,得到PAB (2)、UAB (2),则有Coordinates (X A (2) , Y A (2) , Z A (2) ) and (X B (2) , Y B (2) , Z B (2) ) of control points A and B through the baseline second period ) to calculate to get P AB (2) and U AB (2) , then we have 基线AB水平距离较差ΔPAB=PAB (2)-PAB (1) Poor baseline AB level distance ΔP AB =P AB (2) -P AB (1) 基线AB竖直距离较差ΔUAB=UAB (2)-UAB (1)Baseline AB vertical distance difference ΔU AB =U AB (2) -U AB (1) .
3.如权利要求2所述基于三维基线的控制点稳定性判定方法,其特征在于,所述步骤2.2)中,空间直角坐标系下:3. the control point stability determination method based on three-dimensional baseline as claimed in claim 2, is characterized in that, in described step 2.2), under the space Cartesian coordinate system: 控制点A、B的方差协方差矩阵为:The variance covariance matrix of control points A and B is:
Figure FDA0003002237620000021
Figure FDA0003002237620000021
空间直角坐标系中控制点A、B的坐标差如下:The coordinate difference between the control points A and B in the space rectangular coordinate system is as follows:
Figure FDA0003002237620000022
Figure FDA0003002237620000022
即有dL′=K0L′,其中:That is, dL'=K 0 L', where: dL′=(ΔXAB ΔYAB ΔZAB)T dL'=(ΔX AB ΔY AB ΔZ AB ) T
Figure FDA0003002237620000023
Figure FDA0003002237620000023
L′=(XA YA ZA XB YB ZB)T L′=(X A Y A Z A X B Y B Z B ) T 因此,ΔXAB、ΔYAB和ΔZAB之间的方差协方差矩阵如下:Therefore, the variance covariance matrix between ΔX AB , ΔY AB and ΔZ AB is as follows:
Figure FDA0003002237620000024
Figure FDA0003002237620000024
在NEU站心空间直角坐标系下,N、E、U之间的方差协方差矩阵:由
Figure FDA0003002237620000031
其中
Figure FDA0003002237620000032
可知:
In the NEU station center space Cartesian coordinate system, the variance covariance matrix between N, E, and U: by
Figure FDA0003002237620000031
in
Figure FDA0003002237620000032
It is known that:
Figure FDA0003002237620000033
Figure FDA0003002237620000034
Figure FDA0003002237620000033
which is
Figure FDA0003002237620000034
因此,N、E、U之间的方差协方差矩阵如下:Therefore, the variance-covariance matrix between N, E, U is as follows:
Figure FDA0003002237620000035
Figure FDA0003002237620000035
变换矩阵R中的经纬度为两点的平均值,即The latitude and longitude in the transformation matrix R is the average of the two points, that is B=(BA+BB)/2,L=(LA+LB)/2;B=(B A +B B )/2, L=(L A +L B )/2; 通过基线第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到基线AB第一期在NEU站心空间直角坐标系中方差协方差矩阵
Figure FDA0003002237620000036
Coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) of control points A and B through the baseline ) calculation to obtain the variance covariance matrix of the first phase of baseline AB in the NEU station center space rectangular coordinate system
Figure FDA0003002237620000036
通过基线第二期控制点A、B的坐标(XA (2),YA (2),ZA (2))和(XB (2),YB (2),ZB (2))计算,得到基线AB第二期在NEU站心空间直角坐标系中方差协方差矩阵
Figure FDA0003002237620000037
Coordinates (X A (2) , Y A (2) , Z A (2) ) and (X B (2) , Y B (2) , Z B (2) ) of control points A and B through the baseline second period ) calculation to obtain the variance covariance matrix of the second phase of baseline AB in the NEU station center space rectangular coordinate system
Figure FDA0003002237620000037
4.如权利要求3所述基于三维基线的控制点稳定性判定方法,其特征在于,所述步骤2.2)中,NEU站心空间直角坐标系下控制点A、B水平方向上的距离PAB满足:4. the control point stability determination method based on three-dimensional baseline as claimed in claim 3, is characterized in that, in described step 2.2), the distance P on control point A, B horizontal direction under NEU station center space Cartesian coordinate system AB satisfies:
Figure FDA0003002237620000038
Figure FDA0003002237620000038
其中:NAB=NB-NA,EAB=EB-EA Among them: N AB =N B -N A , E AB =E B -E A 对函数式求全微分得:
Figure FDA0003002237620000039
Totally differentiate the functional expression to get:
Figure FDA0003002237620000039
Figure FDA00030022376200000310
Figure FDA00030022376200000311
which is
Figure FDA00030022376200000310
which is
Figure FDA00030022376200000311
应用协方差传播律,得到:
Figure FDA00030022376200000312
Applying the covariance propagation law, we get:
Figure FDA00030022376200000312
其中,
Figure FDA00030022376200000313
从DNEU中得到,
in,
Figure FDA00030022376200000313
from D NEU ,
K3根据控制点A、B在NEU站心空间直角坐标系下的坐标得到,K 3 is obtained according to the coordinates of the control points A and B in the Cartesian coordinate system of the NEU station center space, 对于竖直方向,有
Figure FDA0003002237620000041
For the vertical direction, we have
Figure FDA0003002237620000041
其中,cov(UAB,UAB)从DNEU中得到,where cov(U AB , U AB ) is obtained from D NEU , 通过基线第一期控制点A、B的坐标(XA (1),YA (1),ZA (1))和(XB (1),YB (1),ZB (1))计算,得到基线AB第一期在水平方向上距离的方差
Figure FDA0003002237620000042
基线AB第一期在竖直方向上距离的方差
Figure FDA0003002237620000043
Coordinates (X A (1) , Y A (1) , Z A (1) ) and (X B (1) , Y B (1) , Z B (1) ) of control points A and B through the baseline ) calculation to get the variance of the distance in the horizontal direction of the first period of baseline AB
Figure FDA0003002237620000042
The variance of the distance in the vertical direction in the first period of baseline AB
Figure FDA0003002237620000043
经过基线第二期控制点A、B的坐标(XA (2),YA (2),ZA (2))和(XB (2),YB (2),ZB (2))计算,得到基线AB第二期在水平方向上距离的方差
Figure FDA0003002237620000044
基线AB第二期在竖直方向上距离的方差
Figure FDA0003002237620000045
Coordinates (X A (2) , Y A (2) , Z A (2) ) and (X B (2) , Y B (2) , Z B (2) ) of control points A and B through the baseline second period ) calculation to obtain the variance of the distance in the horizontal direction of the second period of baseline AB
Figure FDA0003002237620000044
The variance of the distance in the vertical direction of the second period of baseline AB
Figure FDA0003002237620000045
由于第一期和第二期观测相互独立,有:Since the first and second period observations are independent of each other, there are:
Figure FDA0003002237620000046
Figure FDA0003002237620000046
Figure FDA0003002237620000047
Figure FDA0003002237620000047
将求得的
Figure FDA0003002237620000048
代入式(7)、
Figure FDA0003002237620000049
代入式(8)中,得到基线AB水平距离较差之方差
Figure FDA00030022376200000410
基线AB竖直距离较差之方差
Figure FDA00030022376200000411
开方后取正得到基线AB的水平距离较差之中误差
Figure FDA00030022376200000412
基线AB的竖直距离较差之中误差
Figure FDA00030022376200000413
will be obtained
Figure FDA0003002237620000048
Substitute into formula (7),
Figure FDA0003002237620000049
Substitute into formula (8) to get the variance of the baseline AB horizontal distance difference
Figure FDA00030022376200000410
The variance of the vertical distance difference of the baseline AB
Figure FDA00030022376200000411
After square root, take positive to get the error of the horizontal distance difference of baseline AB
Figure FDA00030022376200000412
The vertical distance of the baseline AB is poor and the error
Figure FDA00030022376200000413
5.如权利要求2所述基于三维基线的控制点稳定性判定方法,其特征在于,控制点的空间直角坐标至大地坐标的转换方法为:5. the control point stability determination method based on three-dimensional baseline as claimed in claim 2 is characterized in that, the conversion method of the space rectangular coordinate of control point to geodetic coordinate is:
Figure FDA00030022376200000414
Figure FDA00030022376200000414
Figure FDA00030022376200000415
Figure FDA00030022376200000415
Figure FDA00030022376200000416
Figure FDA00030022376200000416
其中:N’为卯酉圈的半径;a为参考椭球的长半径;b为参考椭球的短半径;e为参考椭球的第一偏心率;e′为参考椭球的第二偏心率;Wherein: N' is the radius of the unitary circle; 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 Rate; 并且and
Figure FDA0003002237620000051
Figure FDA0003002237620000051
Figure FDA0003002237620000052
Figure FDA0003002237620000052
Figure FDA0003002237620000053
Figure FDA0003002237620000053
Figure FDA0003002237620000054
Figure FDA0003002237620000054
6.如权利要求2所述基于三维基线的控制点稳定性判定方法,其特征在于,将控制点的空间直角坐标至站心空间直角坐标的转换方法为:6. the control point stability determination method based on three-dimensional baseline as claimed in claim 2, is characterized in that, the conversion method of the space rectangular coordinate of control point to station center space rectangular coordinate is: 设j点为在以o点为中心的站心直角坐标系下的坐标为(Noj,Eoj,Uoj),o点取控制网任一控制点,一个控制网中只选用1个点作为o点,j点、o点在空间直角坐标系下的坐标分别为(Xj,Yj,Zj)、(Xo,Yo,Zo),j点、o点在大地坐标系下的坐标分别为(Bj,Lj,Hj)、(Bo,Lo,Ho),则Let point j be the coordinates in the Cartesian coordinate system of the station center centered on point o as (N oj , E oj , U oj ), point o takes any control point of the control network, and only one point is selected in one control network As point o, the coordinates of point j and point o in the space rectangular coordinate system are (X j , Y j , Z j ), (X o , Y o , Z o ), respectively, and point j and point o are in the geodetic coordinate system The coordinates below are (B j , L j , H j ), (B o , L o , H o ), then
Figure FDA0003002237620000055
Figure FDA0003002237620000055
7.如权利要求1所述基于三维基线的控制点稳定性判定方法,其特征在于,步骤(1)中选取GNSS三维控制网中一控制点为固定点进行最小二乘法平差处理。7. The method for judging the stability of a control point based on a three-dimensional baseline as claimed in claim 1, wherein in step (1), a control point in the GNSS three-dimensional control network is selected as a fixed point for least squares adjustment.
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