A method, product, medium and device for measuring vertical deflection based on auxiliary points

Abstract

The present application discloses a plumb line deviation measurement method, product, medium and device based on auxiliary points, which relates to the field of plumb line deviation measurement. The method first evenly arranges n auxiliary points around the measuring station; uses a level to measure the height difference between the measuring station and each auxiliary point, and uses a GNSS receiver to observe the GNSS data of the measuring station and each auxiliary point; calculates the projection baseline vectors of each auxiliary point based on the height difference and GNSS data; obtains the plumb line vector at the measuring station by using the least squares method based on the projection baseline vectors of each auxiliary point; uses the GNSS data of the measuring station for single point positioning to obtain the geodetic coordinates of the measuring station, and further obtains the ellipsoidal normal vector at the measuring station; uses the ellipsoidal normal vector and the plumb line vector at the measuring station to calculate the plumb line deviation at the measuring station and the azimuth where the maximum plumb line deviation is located, and can realize low-cost, high-precision and real-time rapid measurement of the plumb line deviation at the measuring station.

Description

Technical Field

[0001] The present application relates to the technical field of vertical deflection measurement, and particularly to a vertical deflection measurement method, product, medium and device based on auxiliary points. Background Art

[0002] Vertical deflection refers to the angle between the vertical direction of a point on the ground and the ellipsoidal normal. Vertical deflection has very important applications in the fields of geodesy, geophysical inversion, resource exploration, earthquake and volcanic monitoring, satellite launch and precise orbit determination, and auxiliary navigation.

[0003] Existing vertical deflection measurement methods mainly include astronomical geodetic method, digital zenith camera method, GNSS leveling method, gravity measurement method, earth gravity field model method, GNSS network and conventional network combined adjustment method, etc. Among them, the astronomical geodetic method obtains the coordinates of the same point through astronomical measurement and geodetic measurement, and is calculated by the vertical deflection formula. It is a direct measurement method. This method has a large workload, complex operation, and many inconveniences in practical applications. The GNSS leveling method is affected by the density of leveling points and terrain undulation, and has low accuracy. The gravity measurement method is greatly affected by the accuracy and resolution of gravity anomaly data. The earth gravity field model method directly uses the gravity potential coefficient to determine the vertical deflection, and this method is greatly affected by the accuracy of the gravity field model and terrain undulation. The GNSS network and conventional network combined adjustment method has low accuracy. Summary of the Invention

[0004] The purpose of the present application is to provide a vertical deflection measurement method, product, medium and device based on auxiliary points to achieve low-cost, high-precision and real-time rapid measurement of vertical deflection at the measurement station.

[0005] To achieve the above purpose, the present application provides the following solutions.

[0006] On the one hand, the present application provides a vertical deflection measurement method based on auxiliary points, including:

[0007] Uniformly arrange n auxiliary points around the measurement station; where n≥3;

[0008] Use a level to measure the height difference from the measurement station to each auxiliary point, and use a GNSS receiver to observe the GNSS data of the measurement station and each auxiliary point;

[0009] Calculate the projection baseline vector of each auxiliary point based on the height difference and GNSS data;

[0010] Based on the projection baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the measurement station;

[0011] Single-point positioning is performed using the GNSS data of the survey station to obtain the geodetic coordinates of the survey station, and then the ellipsoidal normal vector at the survey station is obtained.

[0012] Using the ellipsoidal normal vector and the vertical vector at the survey station, the vertical deflection at the survey station and the azimuth of the maximum vertical deflection are calculated.

[0013] Optionally, the uniformly arranging n auxiliary points around the survey station specifically includes:

[0014] Uniformly arrange n auxiliary points around the survey station. The distances from each auxiliary point to the survey station are as equal as possible, and the angles formed by adjacent auxiliary points and the survey station are as equal as possible.

[0015] Optionally, the using a level to measure the height difference from the survey station to each auxiliary point and using a GNSS receiver to observe the GNSS data of the survey station and each auxiliary point specifically includes:

[0016] Using a precision level or a static level to measure the height difference h from the survey station O to each auxiliary point i Oi ; i = 1, 2,... n;

[0017] Install a GNSS receiver at the survey station O and each auxiliary point i. Each point is observed for at least two time periods, and each time period is observed for at least 1 h to obtain the GNSS data of each point.

[0018] Optionally, the calculating the projection baseline vector of each auxiliary point based on the height difference and GNSS data specifically includes:

[0019] Perform baseline solution and three-dimensional unconstrained adjustment of the baseline vector network on the GNSS data of each point to obtain the three-dimensional direct coordinates (X O , Y O , Z O ) of the survey station and the geodetic coordinates (L i , B i , H i ) of each auxiliary point i;

[0020] Calculate the geodetic coordinates of the projection points of each auxiliary point in the horizontal plane where the survey station is located where R is the average radius of the earth and S i is the horizontal distance from each auxiliary point i to the survey station O;

[0021] Convert the geodetic coordinates of the projection points of each auxiliary point i into three-dimensional rectangular coordinates

[0022] According to the formula Obtain the three-dimensional baseline vector after projection of each auxiliary point i, simply referred to as the projection baseline vector.

[0023] Optionally, the plumb line vector at the measuring station is obtained by using the least squares method based on the projection baseline vectors of each auxiliary point, which specifically includes:

[0024] Let the plumb line vector at the measuring station be Since the plumb line vector is theoretically orthogonal to each projection baseline vector on the horizontal plane where the measuring station is located, there is ΔX Oi′ ×a + ΔY Oi′ ×b - ΔZ Oi′ = 0; where a and b are the components of the plumb line vector in the X and Y directions respectively;

[0025] Transform ΔX Oi′ ×a + ΔY Oi′ ×b - ΔZ Oi′ = 0 into the equation ΔZ Oi′ = ΔX Oi′ ×a + ΔY Oi′ ×b;

[0026] Solve the n equations corresponding to the n projection baseline vectors by using the least squares method to calculate the plumb line vector at the measuring station

[0027] Optionally, the GNSS data of the measuring station is used for single-point positioning to obtain the geodetic coordinates of the measuring station, and then the ellipsoidal normal vector at the measuring station is obtained, which specifically includes:

[0028] Use the GNSS data of the measuring station for single-point positioning to obtain the geodetic coordinates (B O , L O , H O ) of the measuring station;

[0029] Establish an earth ellipsoid model, where the ellipsoid axis is represented as A1A2, the ellipsoidal normal at the measuring station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2⊥A1O1;

[0030] Let the three-dimensional rectangular coordinates of point O1 be The three-dimensional rectangular coordinates of point O3 are (0, 0, -O3A2), and the ellipsoidal normal vector at the measuring station is obtained

[0031] Optionally, the plumb line deviation at the measuring station and the azimuth where the maximum plumb line deviation is located are calculated by using the ellipsoidal normal vector and the plumb line vector at the measuring station, which specifically includes:

[0032] Use the ellipsoidal normal vector at the measuring station and the plumb line vector According to the formula Calculate the vertical deflection θ at the survey station;

[0033] Let CO be the vertical line at the survey station. Through the Gauss projection of the geodetic coordinates of points O and C, the plane rectangular coordinates obtained are (x O , y O ) and (x C , y C );

[0034] According to the formula Calculate the azimuth α where the maximum value of the vertical deflection is located.

[0035] On the other hand, the present application also provides a computer program product, including a computer program, which when executed by a processor implements a method for measuring vertical deflection based on auxiliary points. The method for measuring vertical deflection based on auxiliary points includes:

[0036] Obtain the height differences from the survey station to each auxiliary point measured by a level and the GNSS data of the survey station and each auxiliary point observed by a GNSS receiver; there are n auxiliary points arranged around the survey station; n≥3;

[0037] Calculate the projection baseline vectors of each auxiliary point based on the height differences and GNSS data;

[0038] Based on the projection baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the survey station;

[0039] Use the GNSS data of the survey station for single-point positioning to obtain the geodetic coordinates of the survey station, and then obtain the ellipsoidal normal vector at the survey station;

[0040] Use the ellipsoidal normal vector and the vertical vector at the survey station to calculate the vertical deflection at the survey station and the azimuth where the maximum value of the vertical deflection is located.

[0041] On the other hand, the present application also provides a computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements a method for measuring vertical deflection based on auxiliary points. The method for measuring vertical deflection based on auxiliary points includes:

[0042] Obtain the height differences from the survey station to each auxiliary point measured by a level and the GNSS data of the survey station and each auxiliary point observed by a GNSS receiver; there are n auxiliary points arranged around the survey station; n≥3;

[0043] Calculate the projection baseline vectors of each auxiliary point based on the height differences and GNSS data;

[0044] Based on the projection baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the survey station;

[0045] Single point positioning is performed using the GNSS data of the survey station to obtain the geodetic coordinates of the survey station, and then the ellipsoidal normal vector at the survey station is obtained.

[0046] Using the ellipsoidal normal vector and the vertical vector at the survey station, the vertical deflection at the survey station and the azimuth of the maximum vertical deflection are calculated.

[0047] On the other hand, the present application also provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the computer program to implement a method for measuring vertical deflection based on auxiliary points. The method for measuring vertical deflection based on auxiliary points includes:

[0048] Obtain the height differences from the survey station to each auxiliary point measured by a level and the GNSS data of the survey station and each auxiliary point observed by a GNSS receiver; where there are n auxiliary points arranged around the survey station; n≥3;

[0049] Calculate the projection baseline vectors of each auxiliary point based on the height differences and GNSS data.

[0050] Based on the projection baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the survey station.

[0051] Single point positioning is performed using the GNSS data of the survey station to obtain the geodetic coordinates of the survey station, and then the ellipsoidal normal vector at the survey station is obtained.

[0052] Using the ellipsoidal normal vector and the vertical vector at the survey station, the vertical deflection at the survey station and the azimuth of the maximum vertical deflection are calculated.

[0053] According to the specific embodiments provided by the present application, the following technical effects are disclosed:

[0054] The present application provides a method, product, medium, and device for measuring vertical deflection based on auxiliary points. By arranging 3 or more auxiliary points around the survey station, using a level to measure the height differences from the survey station to each auxiliary point, and using a GNSS receiver to observe the GNSS data of the survey station and each auxiliary point, accurate measurement of basic data is achieved using conventional surveying instruments, with simple operation and low cost; subsequently, the projection baseline vectors of each auxiliary point are calculated based on the height differences and GNSS data, and the vertical vector at the survey station is obtained using the least squares method. The ellipsoidal normal vector at the survey station is obtained using the geodetic coordinates of the survey station, and then the vertical deflection at the survey station and the azimuth of the maximum vertical deflection can be calculated in real-time, quickly, and accurately, achieving high-precision measurement of vertical deflection. Description of the Drawings

[0055] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the accompanying drawings required for use in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0056] Figure 1 Schematic flow chart of a plumb line deviation measurement method based on auxiliary points according to the present application;

[0057] Figure 2 Schematic diagram for plumb line deviation measurement;

[0058] Figure 3 Schematic diagram for solving the ellipsoidal normal vector. Detailed implementation manners

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0060] The purpose of the present application is to provide a plumb line deviation measurement method, product, medium and device based on auxiliary points, which combines auxiliary points to use GNSS and precise leveling to measure the plumb line deviation, so as to realize low-cost, high-precision and real-time rapid measurement of the plumb line deviation at the measurement station.

[0061] To make the above objects, features and advantages of the present application more obvious and understandable, the following will further describe the present application in detail with reference to the accompanying drawings and specific implementation manners.

[0062] Refer to Figure 1 , a plumb line deviation measurement method based on auxiliary points provided by the present application includes the following steps 1 to 6.

[0063] Step 1: Uniformly arrange n auxiliary points around the measurement station.

[0064] The inventive concept of the present application lies in combining auxiliary points and using GNSS and precise leveling to measure the plumb line deviation. Therefore, 3 or more auxiliary points need to be uniformly arranged around the measurement station. The auxiliary points should be as close as possible to the measurement station, and the angles formed by adjacent two auxiliary points and the measurement station should be as equal as possible.

[0065] Such as Figure 2As shown in the figure, O is the measuring station, FO is the ellipsoidal normal at the measuring station, and CO is the vertical line at the measuring station. Three or more auxiliary points are evenly arranged around the measuring station O. Let the auxiliary point be i, and i = 1, 2,... n. n is the number of auxiliary points, and n is a positive integer greater than or equal to 3. i′ is the projection point of the auxiliary point i in the horizontal plane where the measuring station is located. Figure 2 In the illustrated embodiment, n = 4, that is, four auxiliary points are evenly arranged around the measuring station O, which are respectively denoted as auxiliary points 1, 2, 3, and 4, and their projection points in the horizontal plane where the measuring station is located are respectively denoted as 1′, 2′, 3′, and 4′.

[0066] Step 2: Use a level to measure the height difference between the measuring station and each auxiliary point, and use a GNSS receiver to observe the GNSS data of the measuring station and each auxiliary point.

[0067] Use a conventional level such as a precise level or a static level to measure the height difference h between the measuring station O and each auxiliary point i. Oi When using a level to measure the height difference between two points, place the level in the middle of the measuring station O and the auxiliary point i to be measured.

[0068] Install GNSS receivers at the measuring station O and each auxiliary point i. Each point (including the measuring station and the auxiliary points) is observed for at least two time periods, and each time period is observed for at least 1 h to obtain the corresponding observation data, that is, the GNSS data of each point.

[0069] Step 3: Calculate the projection baseline vectors of each auxiliary point based on the height difference and GNSS data.

[0070] Perform data processing such as baseline solution and three-dimensional unconstrained adjustment of the baseline vector network on the GNSS data of each point, and the three-dimensional direct coordinates (X O , Y O , Z O ) of the measuring station and the geodetic coordinates (L i , B i , H i ) of each auxiliary point i can be obtained.

[0071] Then the geodetic coordinates of the projection points of each auxiliary point in the horizontal plane where the measuring station is located are (L i , B i , H i - where R is the average radius of the earth, and S i is the horizontal distance from each auxiliary point i to the measuring station O. That is the geodetic coordinate of i′.

[0072] Convert the geodetic coordinates of the projection points of each auxiliary point i into three-dimensional rectangular coordinates according to formula (1):

[0073]

[0074] In the formula, N i is the prime vertical radius of curvature at the auxiliary point i, and its calculation formula is where l is the semi-major axis of the reference ellipsoid and e is the first eccentricity of the ellipsoid.

[0075] From formula (2), the three-dimensional baseline vectors (hereinafter referred to as projection baseline vectors) after projection of each auxiliary point i can be obtained:

[0076]

[0077] where i′ = 1′, 2′,... n′.

[0078] Step 4: Based on the projection baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the measuring station.

[0079] Let the vertical vector at the measuring station be:

[0080]

[0081] where a and b are the components of the vertical vector in the X and Y directions respectively; the component in the Z direction is -1.

[0082] Since the vertical direction is theoretically orthogonal to each projection baseline vector on the horizontal plane where the measuring station is located, there is:

[0083] ΔX Ol ′×a + ΔY Oi ′×b - ΔZ Oi ′ = 0 (4)

[0084] By transforming formula (4), equation (5) can be obtained:

[0085] ΔZ Oi ′ = ΔX Oi ′×a + ΔY Oi ′×b (5)

[0086] There are n projection baseline vectors, and n equations (5) can be written; by solving these n equations (5) using the least squares method, the vertical vector at the measuring station can be calculated

[0087] Step 5: Use the GNSS data of the measuring station for single-point positioning to obtain the geodetic coordinates of the measuring station, and then obtain the ellipsoidal normal vector at the measuring station.

[0088] By using the GNSS data observed by the GNSS receiver installed on the measuring station for single-point positioning, the geodetic coordinates (BO , L O , H O ).

[0089] Establish Figure 3 the geoid model shown in the figure, where the ellipsoid axis is denoted as A1A2, the ellipsoid normal at the measuring station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2⊥A1O1. The point O2 is the intersection point of the ellipsoid normal OO3 passing through the point O and the equatorial plane of the earth. The coordinates of the measuring station O in the geocentric three-dimensional rectangular coordinate system are (X O , Y O , Z O ), and the geodetic coordinates are (B O , L O , H O ). Then the geodetic coordinates of the projection point O1 of the point O on the ellipsoid surface are (B O , L O , 0), and let its three-dimensional rectangular coordinates be Let the radius of curvature of the prime vertical of the ellipsoid at the measuring station be N, then there is:

[0090] A1O3 = Nsln(B O ) (6)

[0091] Also known:

[0092]

[0093] Then:

[0094] O3A2 = A1O3 - A1A2 (8)

[0095] Therefore, the three-dimensional rectangular coordinates of the point O3 can be obtained as (0, 0, -O3A2), and the ellipsoid normal vector at the measuring station can be obtained as:

[0096]

[0097] Step 6: Use the ellipsoid normal vector and the vertical vector at the measuring station to calculate the vertical deflection and the azimuth of the maximum vertical deflection at the measuring station.

[0098] Given the vertical vector and the ellipsoid normal vector the following formula holds:

[0099]

[0100] The calculation formula for the vertical deflection θ can be obtained as:

[0101]

[0102] As Figure 2As shown, CO is the vertical line at the measuring station. Given that the three-dimensional rectangular coordinates of the measuring station are (X O , Y O , Z O ), then the three-dimensional rectangular coordinates of point C are:

[0103]

[0104] Convert the three-dimensional rectangular coordinates of point C to geodetic coordinates Then, through Gauss projection of the geodetic coordinates of points O and C, their plane rectangular coordinates are obtained as (x O , y O ) and (x C , y C ) respectively. Then, the geodetic azimuth from point O to point C can be obtained:

[0105]

[0106] α is the azimuth where the maximum value of the vertical deflection is located, that is, at the azimuth of α at the measuring station, the maximum value of the vertical deflection is θ.

[0107] The method for measuring the vertical deflection based on auxiliary points proposed in this application arranges 3 or more auxiliary points around the measuring station, measures the height differences between each auxiliary point and the measuring station using a level, and measures the baseline vectors from the measuring station to each auxiliary point using a GNSS receiver, and then projects them onto the same horizontal plane. Since each projected baseline vector is orthogonal to the direction of the vertical line at the measuring station, the vertical line vector at the measuring station can be obtained using the least squares principle. Further, single-point positioning is performed using the GNSS data of the measuring station to obtain the geodetic coordinates of the measuring station, and then the ellipsoidal normal vector at the measuring station is obtained. Finally, using the ellipsoidal normal vector and the vertical line vector at the measuring station, the vertical deflection at the measuring station and the azimuth where the maximum value of the vertical deflection is located can be obtained. The method of this application can be realized using conventional measuring instruments, namely GNSS receivers and levels. The measuring instruments also use conventional measuring methods. The auxiliary points can be dozens of meters away from the measuring station, and there are no special requirements for the terrain. Therefore, the workload is small, the operation is simple, it is very easy to implement, and the cost is low. The solution of the vertical line vector at the measuring station, the solution of the ellipsoidal normal at the measuring station, and the calculation of the vertical deflection can be realized using conventional computing devices, ensuring real-time, fast, and high-precision measurement of the vertical deflection.

[0108] The vertical deflection at the measuring station and the azimuth where the maximum value of the vertical deflection is located calculated by using the vertical deflection measurement method of this application can be widely applied in fields such as geodetic surveying, geophysical inversion, resource exploration, earthquake and volcanic monitoring, satellite launch and precise orbit determination, and auxiliary navigation. The following are several application examples to illustrate the vertical deflection measurement method of this application.

[0109] Application Example 1: In current engineering construction, the commonly used elevation system is the normal height system (with the quasi-geoid as the reference). The transfer of normal height mainly uses a level to measure step by step forward at each survey station currently, with very low efficiency. If the plumb line deviation between two points and the azimuth where the maximum plumb line deviation is located can be accurately obtained (the component of the plumb line deviation between the two points in the direction of the line connecting the two points needs to be obtained based on this), and the geodetic height difference between the two points has been accurately measured using GNSS (with the ellipsoid as the reference), the normal height difference between the two points can be accurately obtained, thus realizing the long-distance, cross-line-of-sight, and high-precision transfer of elevation using GNSS technology. For example, in the construction of a tunnel, elevation reference points must be arranged near the excavation surfaces on both sides of the tunnel, and the height difference between the reference points must be obtained through leveling. In the construction of a long tunnel, this work is very time-consuming and laborious. If the plumb line deviation at the excavation surface can be directly measured using the method of this application, the geodetic height difference obtained by GNSS measurement can be converted into the normal height difference, which will greatly improve work efficiency and reduce the workload of field survey personnel.

[0110] Application Example 2: As pointed out in this application, the height difference between the survey station and the auxiliary points is observed using a level. However, if it is necessary to observe the change of the plumb line deviation at the survey station for a long time and dynamically, a static level can be used to automatically observe the height difference between the survey station and the auxiliary points. Since the change of the plumb line deviation is often highly related to earthquakes, the method of this application can be used to realize the low-cost, high-precision, and automated continuous observation of the change of the plumb line deviation at the station, so as to be applied to earthquake research. Among the existing plumb line deviation measurement methods currently, there is no method that can dynamically and continuously observe the plumb line deviation.

[0111] In some embodiments, this application also provides a computer program product, including a computer program, which when executed by a processor implements a method for measuring the plumb line deviation based on auxiliary points, including: obtaining the height differences from the survey station to each auxiliary point measured by a level and the GNSS data of the survey station and each auxiliary point observed by a GNSS receiver; where n auxiliary points are arranged around the survey station; n≥3; calculating the projection baseline vectors of each auxiliary point based on the height differences and GNSS data; obtaining the plumb line vector at the survey station using the least squares method based on the projection baseline vectors of each auxiliary point; performing single-point positioning using the GNSS data of the survey station to obtain the geodetic coordinates of the survey station, and then obtaining the ellipsoidal normal vector at the survey station; using the ellipsoidal normal vector and the plumb line vector at the survey station to calculate the plumb line deviation at the survey station and the azimuth where the maximum plumb line deviation is located. The difference between the above method steps and Figure 1 the process steps is that the height differences from the survey station to each auxiliary point and the GNSS data of the survey station and each auxiliary point are directly obtained by the processor, and the other calculation processes are the same.

[0112] In some embodiments, the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for measuring the vertical deviation based on auxiliary points is implemented. The steps of the method are the same as those of Figure 1 the process steps, except that the height differences from the measuring station to each auxiliary point and the GNSS data of the measuring station and each auxiliary point are directly obtained by the processor, and the other calculation processes are the same.

[0113] In some embodiments, the present application further provides a computer device, which includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store transactions to be processed. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the method for measuring the vertical deviation based on auxiliary points can be implemented. The steps of the method are the same as those of Figure 1 the process steps, except that the height differences from the measuring station to each auxiliary point and the GNSS data of the measuring station and each auxiliary point are directly obtained by the processor, and the other calculation processes are the same.

[0114] The present application can realize low-cost, high-precision, and real-time and rapid measurement of the vertical deviation at the measuring station by using a conventional measuring instrument, a GNSS receiver, and a level, and adopting a conventional measuring method, and has a wide application prospect.

[0115] Specific examples are used in this article to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for measuring the vertical deviation based on auxiliary points, characterized in that, Including: Uniformly arrange n auxiliary points around the measuring station; where n≥3; Use a level to measure the height difference from the measuring station to each auxiliary point, and use a GNSS receiver to observe the GNSS data of the measuring station and each auxiliary point; Calculate the projected baseline vector of each auxiliary point based on the height difference and GNSS data; Based on the projected baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the measuring station; Use the GNSS data of the measuring station for single-point positioning to obtain the geodetic coordinates of the measuring station, and then obtain the ellipsoidal normal vector at the measuring station; Single point positioning is performed using GNSS data observed by a GNSS receiver installed at the survey station to obtain the geodetic coordinates (B O , L O , H O ) of the survey station; Establish an earth ellipsoid model, where the ellipsoid axis is represented as A1A2, the ellipsoid normal at the measuring station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2⊥A1O1; The point O2 is the intersection point of the ellipsoid normal OO3 passing through the point O and the earth's equatorial plane; The coordinates of the measuring station O in the geocentric three-dimensional rectangular coordinate system are (X O , Y O , Z O ), and the geodetic coordinates are (B O , L O , H O ); Then the geodetic coordinates of the projection point O1 of the point O on the ellipsoid surface are (B O , L O , 0), and let the three-dimensional rectangular coordinates of the projection point O1 be Let the radius of curvature of the prime vertical of the ellipsoid at the measuring station be N, then there are: A1O3 = Nsin(B O ); It is also known that: Then: O3A2 = A1O3 - A1A2; Therefore, the three-dimensional rectangular coordinates of point O3 are (0, 0, -O3A2), and the ellipsoidal normal vector at the measuring station is: Use the ellipsoidal normal vector and the vertical vector at the measuring station to calculate the vertical deviation at the measuring station and the azimuth where the maximum vertical deviation is located; The vertical vector at the known measuring station and the ellipsoidal normal vector The following formula holds: The calculation formula for the vertical deviation θ is obtained as: CO is the vertical line at the measuring station, and the three-dimensional rectangular coordinates of the measuring station are known as (X O , Y O , Z O ). Then the three-dimensional rectangular coordinates of point C are: Convert the three-dimensional rectangular coordinates of point C to geodetic coordinates Then, through Gauss projection of the geodetic coordinates of points O and C, their plane rectangular coordinates are obtained as (x O , y O ), (x C , y C ), respectively. Then, the geodetic azimuth from point O to point C is obtained: α is the azimuth where the maximum vertical deviation is located, that is, at the azimuth α of the measuring station, the maximum vertical deviation is θ.

2. The perpendicular deviation measurement method based on auxiliary points according to claim 1, wherein The uniformly arranging n auxiliary points around the measuring station specifically includes: Uniformly arrange n auxiliary points around the measuring station. The distances from each auxiliary point to the measuring station are as equal as possible, and the angles formed by adjacent auxiliary points and the measuring station are as equal as possible.

3. The perpendicular deviation measurement method based on auxiliary points according to claim 2, wherein The using a level to measure the height difference from the measuring station to each auxiliary point and using a GNSS receiver to observe the GNSS data of the measuring station and each auxiliary point specifically includes: Using a precise level or a static level, measure the elevation difference h from the measuring station O to each auxiliary point i Oi ; i = 1, 2, … n; Install GNSS receivers at the measuring station O and each auxiliary point i. Each point is observed for at least two periods, and each period is observed for at least 1 h to obtain the GNSS data of each point.

4. The perpendicular deviation measurement method based on auxiliary points according to claim 3, wherein The calculating the projected baseline vector of each auxiliary point based on the height difference and GNSS data specifically includes: Perform baseline solution and three-dimensional unconstrained adjustment of the baseline vector network on the GNSS data of each point to obtain the three-dimensional direct coordinates (X O , Y O , Z O ) of the survey station and the geodetic coordinates (L i , B i , H i ) of each auxiliary point i; Calculate the geodetic coordinates of the projection points of each auxiliary point in the horizontal plane where the measuring station is located where R is the average radius of the earth, and S i is the horizontal distance from each auxiliary point i to the measuring station O; Convert the geodetic coordinates of the projection points of each auxiliary point i into three-dimensional rectangular coordinates According to the formula the three-dimensional baseline vectors after the projection of each auxiliary point i are obtained, which are simply referred to as the projected baseline vectors.

5. The perpendicular deviation measurement method based on auxiliary points according to claim 4, characterized in that, The obtaining the vertical vector at the measuring station using the least squares method based on the projected baseline vectors of each auxiliary point specifically includes: Let the vertical vector at the measuring station be Since the vertical vector is theoretically orthogonal to each projection baseline vector on the horizontal plane where the measuring station is located, then there is ΔX Oi' ×a + ΔY Oi' ×b - ΔZ Oi' = 0; where a and b are the components of the vertical vector in the X and Y directions respectively; Transform ΔX Oi' ×a + ΔY Oi' ×b - ΔZ Oi' = 0 into the equation ΔZ Oi' = ΔX Oi' ×a + ΔY Oi' ×b; Solve the \(n\) equations corresponding to the \(n\) projection baseline vectors by the least squares method to calculate the vertical vector at the measuring station 6. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements a method for measuring vertical deviation based on auxiliary points. The method for measuring vertical deviation based on auxiliary points includes: Obtain the height difference from the measuring station to each auxiliary point measured by a level and the GNSS data of the measuring station and each auxiliary point observed by a GNSS receiver; where n auxiliary points are arranged around the measuring station; n≥3; Calculate the projected baseline vector of each auxiliary point based on the height difference and GNSS data; Based on the projected baseline vectors of each auxiliary point, use the least squares method to obtain the vertical vector at the measuring station; Use the GNSS data of the measuring station for single-point positioning to obtain the geodetic coordinates of the measuring station, and then obtain the ellipsoidal normal vector at the measuring station; Single point positioning is performed using GNSS data observed by a GNSS receiver installed at the survey station to obtain the geodetic coordinates (B O , L O , H O ) of the survey station; An Earth ellipsoid model is established, where the ellipsoid axis is represented as A1A2, the ellipsoid normal at the measuring station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2 ⊥ A1O1; point O2 is the intersection point of the ellipsoid normal OO3 passing through point O and the Earth's equatorial plane; the coordinates of the measuring station O in the geocentric three-dimensional rectangular coordinate system are (X O , Y O , Z O ), and the geodetic coordinates are (B O , L O , H O ); then the geodetic coordinates of the projection point O1 of point O on the ellipsoid surface are (B O , l O , 0). Let the three-dimensional rectangular coordinates of the projection point O1 be Let the radius of curvature of the prime vertical at the measuring station be N, then there is: A1O3 = N sin(B O ); It is also known that: A1A2 = Z O1 ; Then: O3A2 = A1O3 - A1A2; Therefore, the three-dimensional rectangular coordinates of point O3 are (0, 0, -O3A2), and the ellipsoidal normal vector at the measuring station is: Use the ellipsoidal normal vector and the vertical vector at the measuring station to calculate the vertical deviation at the measuring station and the azimuth where the maximum vertical deviation is located; The vertical vector at the known measuring station and the ellipsoidal normal vector The following formula holds: The calculation formula for the vertical deviation θ is obtained as: CO is the vertical line at the measuring station. Given that the three-dimensional rectangular coordinates of the measuring station are (X O , Y O , Z O ), then the three-dimensional rectangular coordinates of point C are: Convert the three-dimensional rectangular coordinates of point C to geodetic coordinates Then, through Gauss projection of the geodetic coordinates of points O and C, their plane rectangular coordinates are obtained as (x O , y O ), (x C , y C ), respectively. Then, the geodetic azimuth from point O to point C is obtained: α is the azimuth where the maximum vertical deviation is located, that is, at the azimuth α of the measuring station, the maximum vertical deviation is θ.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements a method for measuring the perpendicular deviation based on auxiliary points. The method for measuring the perpendicular deviation based on auxiliary points includes: Obtaining the height differences from the measuring station measured by a level to each auxiliary point and the GNSS data of the measuring station and each auxiliary point observed by a GNSS receiver; where n auxiliary points are arranged around the measuring station; n ≥ 3; Calculating the projection baseline vectors of each auxiliary point based on the height differences and the GNSS data; Obtaining the perpendicular vector at the measuring station by using the least squares method based on the projection baseline vectors of each auxiliary point; Performing single-point positioning by using the GNSS data of the measuring station to obtain the geodetic coordinates of the measuring station, and further obtaining the ellipsoidal normal vector at the measuring station; Single point positioning is performed using GNSS data observed by a GNSS receiver installed at the survey station to obtain the geodetic coordinates (B O , L O , H O ) of the survey station; Establish an Earth ellipsoid model, where the ellipsoid axis is represented as A1A2, the ellipsoid normal at the measurement station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2 ⊥ A1O1; point O2 is the intersection point of the ellipsoid normal OO3 passing through point O and the Earth's equatorial plane; the coordinates of the measurement station O in the geocentric three-dimensional rectangular coordinate system are (X O , Y O , Z O ), and the geodetic coordinates are (B O , L O , H O ); then the geodetic coordinates of the projection point O1 of point O on the ellipsoid surface are (B O , L O , 0), let the three-dimensional rectangular coordinates of the projection point O1 be (X O1 , Y O1 , Z O1 ); let the radius of curvature of the prime vertical at the measurement station be N, then there are: A1O3 = N sin(B O ); It is also known that: A1A2 = Z O1 ; Then: O3A2 = A1O3 - A1A2; Therefore, the three-dimensional rectangular coordinates of point O3 are (0, 0, -O3A2), and the ellipsoidal normal vector at the measuring station is: Calculating the perpendicular deviation at the measuring station and the azimuth where the maximum perpendicular deviation is located by using the ellipsoidal normal vector and the perpendicular vector at the measuring station; The vertical vector at the known measuring station and the ellipsoidal normal vector The following formula holds: The calculation formula for the perpendicular deviation θ is obtained as: CO is the vertical line at the measuring station, and the three-dimensional rectangular coordinates of the measuring station are known as (X O , Y O , Z O ). Then the three-dimensional rectangular coordinates of point C are: Convert the three-dimensional rectangular coordinates of point C to geodetic coordinates Then, through Gauss projection of the geodetic coordinates of points O and C, their plane rectangular coordinates are obtained as (x O , y O ), (x C , y C ), respectively. Then, the geodetic azimuth from point O to point C is obtained: α is the azimuth where the maximum perpendicular deviation is located, that is, at the azimuth α of the measuring station, the maximum perpendicular deviation is θ.

8. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement a method for measuring the perpendicular deviation based on auxiliary points. The method for measuring the perpendicular deviation based on auxiliary points includes: Obtaining the height differences from the measuring station measured by a level to each auxiliary point and the GNSS data of the measuring station and each auxiliary point observed by a GNSS receiver; where n auxiliary points are arranged around the measuring station; n ≥ 3; Calculating the projection baseline vectors of each auxiliary point based on the height differences and the GNSS data; Obtaining the perpendicular vector at the measuring station by using the least squares method based on the projection baseline vectors of each auxiliary point; Performing single-point positioning by using the GNSS data of the measuring station to obtain the geodetic coordinates of the measuring station, and further obtaining the ellipsoidal normal vector at the measuring station; Single point positioning is performed using GNSS data observed by a GNSS receiver installed at the survey station to obtain the geodetic coordinates (B O , L O , H O ) of the survey station; Establish an earth ellipsoid model, where the ellipsoid axis is represented as A1A2, the ellipsoid normal at the measuring station O is OO3, the intersection point of OO3 and the ellipsoid surface is O1, and A1A2⊥A1O1; point O2 is the intersection point of the ellipsoid normal OO3 passing through point O and the earth's equatorial plane; the coordinates of the measuring station O in the geocentric three-dimensional rectangular coordinate system are (X O , Y O , Z O ), and the geodetic coordinates are (B O , L O , H O ); then the geodetic coordinates of the projection point O1 of point O on the ellipsoid surface are (B O , l O , 0). Let the three-dimensional rectangular coordinates of the projection point O1 be Let the radius of curvature of the prime vertical of the ellipsoid at the measuring station be N, then there is: A1O3 = N sin(B O ); It is also known that: A1A2 = Z O1 ; Then: O3A2 = A1O3 - A1A2; Therefore, the three-dimensional rectangular coordinates of point O3 are (0, 0, -O3A2), and the ellipsoidal normal vector at the measuring station is: Calculating the perpendicular deviation at the measuring station and the azimuth where the maximum perpendicular deviation is located by using the ellipsoidal normal vector and the perpendicular vector at the measuring station; Known plumb line vector at the survey station and ellipsoidal normal vector The following formula holds: The calculation formula for the perpendicular deviation θ is obtained as: CO is the vertical line at the measuring station, and the three-dimensional rectangular coordinates of the measuring station are known as (X O , Y O , Z O ). Then the three-dimensional rectangular coordinates of point C are: Convert the three-dimensional rectangular coordinates of point C to geodetic coordinates Then, through Gauss projection of the geodetic coordinates of points O and C, their plane rectangular coordinates are obtained as (x O , y O ), (x C , y C ), respectively. Then, the geodetic azimuth from point O to point C is obtained: α is the azimuth where the maximum perpendicular deviation is located, that is, at the azimuth α of the measuring station, the maximum perpendicular deviation is θ.

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