CN109520522B - Control point stability determination method based on three-dimensional baseline - Google Patents
Control point stability determination method based on three-dimensional baseline Download PDFInfo
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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。
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. .
Description
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利用计算得到各基线第一期、第二期在水平方向上距离的方差竖直方向上距离的方差根据两期观测相互独立有水平距离较差之方差竖直距离较差之方差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 use Calculate the variance of the distance between the first and second periods of each baseline in the horizontal direction The variance of the distance in the vertical direction According to the two periods of observation are independent of each other, there is a variance of the horizontal distance difference The variance of the vertical distance difference 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:
其中:NAB=NB-NA,EAB=EB-EA,Where: 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-UA,U 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:
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:
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
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:
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:由其中可知:In the NEU station center space Cartesian coordinate system, the variance covariance matrix between N, E, and U: by in It is known that:
即 which is
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:
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 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
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 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
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:
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: Totally differentiate the functional expression to get:
即即 which is which is
应用协方差传播律,得到: Applying the covariance propagation law, we get:
其中,从DNEU中得到;in, 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 For the vertical direction, we have
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基线AB第一期在竖直方向上距离的方差 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 The variance of the distance in the vertical direction in the first period of baseline AB
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基线AB第二期在竖直方向上距离的方差 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 The variance of the distance in the vertical direction of the second period of baseline AB
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:
将求得的代入式(7)、代入式(8)中,得到基线AB水平距离较差之方差基线AB竖直距离较差之方差开方后取正得到基线AB水平距离较差之中误差基线AB竖直距离较差之中误差 will be obtained Substitute into formula (7), Substitute into formula (8) to get the variance of the baseline AB horizontal distance difference The variance of the vertical distance difference of the baseline AB After square root, take the positive value to get the error in the difference between the baseline AB horizontal distance and the difference Baseline AB vertical distance is poor middle error
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:
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
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
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:
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
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
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:
其中:NAB=NB-NA,EAB=EB-EA,Where: 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-UA,U 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 a. Calculate the variance covariance matrix between ΔX AB , ΔY AB and ΔZ AB in the first and second period spatial Cartesian coordinates
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:
这两个控制点的坐标差如下:The coordinate difference between these two control points is as follows:
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
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:
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 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
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 b. Calculate the variance covariance matrix in the first phase and the second phase NEU station center space rectangular coordinate system
在NEU站心空间直角坐标系下In the Cartesian coordinate system of the NEU station center space
由其中可知:Depend on in It is known that:
即 which is
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:
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大地坐标和得到 Through the first phase of the baseline control points A, B geodetic coordinates and get
通过基线第二期控制点A、B大地坐标和得到 Through the second phase of the baseline control points A, B geodetic coordinates and get
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σΔU:c. 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:
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: Totally differentiate the functional expression to get:
即即 which is which is
应用协方差传播律,得到: Applying the covariance propagation law, we get:
其中,从DNEU中得到;in, 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 For the vertical direction, we have
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得到 The spatial Cartesian coordinates of the NEU station center through the control points A and B of the first phase of the baseline and get
通过基线第一期控制点A、B的NEU站心空间直角坐标和得到 The spatial Cartesian coordinates of the NEU station center through the control points A and B of the first phase of the baseline and get
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:
将求得的代入式(7)、代入式(8)中,得到开方后取正得到 will be obtained Substitute into formula (7), Substitute into formula (8), we get After opening the square, take it right and get it
2.3)若两次观测所得的水平距离差有且竖直方向上的较差有则说明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 And the difference in the vertical direction is 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
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
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
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
表5控制点站心坐标Table 5 Control point station center coordinates
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
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
表8基线高差的较差判定Table 8 Poor judgment of baseline height difference
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.
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