Method for calculating the deflection of the vertical using a curved surface function

Abstract

This invention discloses a method for calculating vertical deviation using surface functions. The method comprises the following steps: S1, data preprocessing: preprocessing the measured GNSS / leveling data to provide data for constructing the geoid difference surface function; S2, geoid difference surface function construction: based on all calculated point pairs, fitting the geoid difference surface of the entire engineering area using radial basis functions; S3, vertical deviation calculation: solving for the vertical deviation and its components based on the calculated geoid difference surface function. This invention utilizes GNSS / leveling data and uses radial basis functions to fit the overall geoid difference surface of the survey area, ensuring a smooth and consistent fitted surface that passes strictly through all reference points. It solves the problem that traditional methods for calculating vertical deviation based on GNSS / leveling data are only suitable for flat terrain and short baseline scenarios, and lack accuracy in mountainous areas and long-distance tunnel projects. This method achieves high-precision interpolation of the vertical deviation and its components at any point within the engineering area.

Description

Technical Field

[0001] This invention relates to a method for accurately calculating the vertical deviation of terrain in engineering areas, and in particular to a method for calculating vertical deviation using surface functions. Background Technology

[0002] Currently, conventional methods for calculating vertical deviation based on GNSS / leveling data all assume that the vertical deviation at both ends of the baseline section varies linearly. They then use the difference in geoid distance between the two ends of the baseline as the observed value, selecting the components of the vertical deviation along the meridian and zonal axes as parameters to be determined, and establishing an observation error equation. Under multi-baseline conditions, this method can solve for the vertical deviation and its components by simultaneously solving multiple sets of error equations and using the least squares method. However, when engineering geological conditions are complex, especially in mountainous or other complex terrain areas, the spatial distribution of the vertical deviation exhibits significant nonlinear and non-uniform variations, failing to meet the fundamental assumption of linear variation in the vertical deviation at both ends of the baseline. This makes it difficult to guarantee the accuracy of existing methods, limiting their applicability to applications with flat terrain and short baseline lengths. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a method for calculating vertical deviation using surface functions. It innovatively uses radial basis functions to fit the geoid difference surface of the entire engineering area, constructs a surface function correlation model between the geoid difference and the plane coordinates, and realizes accurate calculation of vertical deviation in complex engineering areas.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: The method for calculating vertical deviation using surface functions described in this invention includes data preprocessing, construction of geoid difference surface functions, and calculation of vertical deviation. S1, Data Preprocessing: The GNSS / leveling data measured in the engineering field are preprocessed to provide a data foundation for the construction of the geoid difference surface function. The steps are as follows: S1.1, Obtain all GNSS / leveling data measured in the engineering field and form point pairs. ;in, , , and They represent the first The latitude, longitude, geodetic height, and orthographic height of each reference point; , and Obtained from GNSS observations, Obtained from leveling observations; , This represents the total number of reference points; S1.2, Calculate the central meridian of the project and mean elevation surface ,Right now (1) S1.3, through the aforementioned Using the central meridian, all reference points are projected onto the mean elevation surface using the Gaussian projection method. The projected Gaussian plane coordinates are then centroidalized and axially modified to ultimately form point pairs. ;in, and For the first The plane coordinates of the reference points The east direction is positive. North is the positive axis. and They represent the first The geodetic height and orthographic height of each benchmark point; S2, Construction of the geoid difference surface function: Based on all point-pair data calculated in step S1.3 The radial basis functions are used to fit the geoid difference surface across the entire engineering area. The steps are as follows: S2.1, a thin-plate spline function is selected as the kernel function to construct the radial basis function equation for the geoid difference, i.e. (2) in, ; Represents a thin-plate spline function. , , Indicates the parameter to be determined; and For the first The planar coordinates of one reference point; S2.2, Construct the radial basis function equation system, that is (3) in, ; ; ; S2.3, Solving for the parameter vector ,Right now (4) S2.4, Construct the geoid difference surface function for the engineering area. ,Right now (5) in, The geoid difference surface function representing the engineering area is about plane coordinates. The function; , ; Given the parameters, they can be obtained from equation (4); and For the first The planar coordinates of one reference point; S3, calculation of perpendicularity deviation: Based on the geoid difference surface function obtained in Section S2.4, the vertical deviation and its components are solved as follows: S3.1, Construction exist Direction (East) and The first partial derivative in the direction (north), i.e. (6) in, express exist The first partial derivative in the direction (eastward); express exist The first partial derivative of the direction (north); the meanings of the other parameters are consistent with those in equation (5); S3.2, Find any point in the project area. The perpendicular deviation at a point and its component, i.e. (7) in, and These represent the components of the perpendicular deviation on the east-west circle and the north-south circle, respectively. Indicates the deviation of the perpendicular line; , is the conversion factor for arcseconds.

[0005] Compared with the prior art, the advantages of the present invention are reflected in the following aspects: (1) It can effectively adapt to complex terrain and long baseline scenarios: This invention utilizes GNSS / leveling data and employs radial basis functions to fit the geoid difference surface of the entire survey area, ensuring a smooth and consistent fit that passes strictly through all reference points. By calculating the partial derivatives of the constructed surface function at the reference points with respect to the meridian and zonal directions, the precise vertical deviation and its components at the reference points can be obtained. This effectively adapts to complex terrain and long baseline scenarios, solving the problem that traditional methods for calculating vertical deviation based on GNSS / leveling data are only suitable for flat terrain and short baseline scenarios, and lack accuracy in mountainous areas and long-distance tunnel projects.

[0006] (2) Vertical deviation of the engineering area that can be interpolated with high precision: This invention is based on the constructed geoid difference surface function of the engineering area. and its First partial derivative in the direction (eastward) and First partial derivative in the direction (north) It can interpolate the vertical deviation and its components at any point within the engineering area with high precision. Attached Figure Description

[0007] Figure 1 This is a flowchart of the method described in Embodiment 1 of the present invention.

[0008] Figure 2 This is the distribution map of GNSS / leveling points described in Embodiment 2 of the present invention.

[0009] Figure 3 This is the geoid difference surface diagram of the engineering area described in Embodiment 2 of the present invention. Detailed Implementation

[0010] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are implemented based on the technical solution of the present invention, and detailed implementation methods and specific operation processes are given. However, the scope of protection of the present invention is not limited to the following embodiments.

[0011] Example 1: like Figure 1 As shown, the method for calculating perpendicularity deviation using surface functions according to the present invention includes the following steps: Step 501: Obtain all GNSS / leveling data measured in the engineering field to form raw data point pairs. ; Step 502: Perform preprocessing on the original data point pairs, including Gaussian projection, centroid modification, and axis modification, to form basic data point pairs. ; Step 503: Select the thin plate spline function as the kernel function to construct the radial basis function equation of the geoid difference; Step 504: Construct the radial basis function equation system; Step 505, Solve for the parameter vector ; Step 506: Construct the geoid difference surface function for the engineering area. ; Step 507: Construct the geoid difference surface function exist Direction (East) and The first-order partial derivative equation for the direction (north); Step 508: Input the planar coordinates of the point to be determined. ; Step 509, using the geoid difference surface function Find the point of the first-order partial derivative equation. The vertical deviation and its components at the point; Step 510: Determine whether to calculate the vertical deviation and its components of the next reference point; if the determination is "no", return to step 508; if the determination is "yes", terminate the calculation.

[0012] Implementation: 2: To verify the effectiveness and engineering applicability of the technical solution of this invention, 15 sets of GNSS / leveling data measured on-site at a large-scale engineering project were selected for testing and verification. Due to the confidentiality requirements of the engineering data, the specific data of all measured points cannot be disclosed. Therefore, only the distribution map of the measured points on-site at this project is shown. For details, please refer to [link to relevant documentation]. Figure 2 .

[0013] Based on the method of this invention, calculations were performed on the 15 sets of GNSS / leveling data (P101~P115) selected from the engineering site, and the results are as follows: like Figure 3 As shown, this is a geoid difference surface map of the engineering area fitted using the method of the present invention. The red dots represent 15 sets of GNSS / leveling data points selected from the actual measurements at the engineering site.

[0014] Table 1 shows the perpendicular deviations and their components at each point calculated using the method of the present invention, in arcseconds.

[0015] Table 1. Perpendicular deviations and their components at each point Finally, it should be emphasized that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still make modifications to the technical solutions described in the foregoing embodiments without creative effort, or make equivalent substitutions for some of the technical features. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating perpendicularity deviation using surface functions, characterized in that: This includes data preprocessing, construction of geoid difference surface function, and calculation of vertical deviation; S1, Data Preprocessing: Preprocessing of the measured GNSS / leveling data in the project provides a data foundation for the construction of the geoid difference surface function; S2, Construction of the geoid difference surface function: Based on all calculated point-pair data The radial basis function is used to fit the geoid difference surface of the entire engineering area; S3, calculation of perpendicularity deviation: Based on the obtained geoid difference surface function, the vertical deviation and its components are solved.

2. The method for calculating perpendicularity deviation using surface functions according to claim 1, characterized in that: Step S1 also includes: S1.1, Obtain all GNSS / leveling data measured during the engineering field, forming point-to-point data. ;in, , , and They represent the first The latitude, longitude, geodetic height, and orthographic height of each reference point; , and Obtained from GNSS observations, Obtained from leveling observations; , This represents the total number of reference points; S1.2, Calculate the central meridian of the project and mean elevation surface ,Right now: (1) S1.3, through the aforementioned Using the central meridian, all reference points are projected onto the mean elevation surface using the Gaussian projection method. The projected Gaussian plane coordinates are then centroidalized and axially modified to ultimately form point pairs. ;in, and For the first The plane coordinates of the reference points The east direction is positive. North is the positive axis. and They represent the first The geodetic height and orthographic height of each benchmark point.

3. The method for calculating perpendicularity deviation using surface functions according to claim 1, characterized in that: Step S2 also includes: Using a thin-plate spline function as the kernel function, the radial basis function equation for the geoid difference is constructed, namely: (2) in, ; Represents a thin-plate spline function. , ; Indicates the parameter to be determined; and For the first The planar coordinates of one reference point; Construct a system of radial basis function equations, namely: (3) in, ； ； ； Solve for the parameter vector ,Right now (4) Construct geoid difference surface function for the engineering area ,Right now: (5) in, The geoid difference surface function representing the engineering area is about plane coordinates. The function; , ; Given the parameters, they are obtained from equation (4); and For the first The planar coordinates of the reference points.

4. The method for calculating perpendicularity deviation using surface functions according to claim 1, characterized in that: Step S3 also includes: Build exist direction and The first-order partial derivative in the direction is: （6） in, express exist First-order partial derivative in the direction; express exist The first-order partial derivative of the direction; the meanings of the other parameters are consistent with those in equation (5); Find any point in the engineering area The perpendicular deviation at a point and its component, i.e. (7) in, and These represent the components of the perpendicular deviation on the east-west circle and the north-south circle, respectively. Indicates the deviation of the perpendicular line; , is the conversion factor for arcseconds.

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