KR20060100157A - Distorting modeling method for transforming the presize position of partial/positional information - Google Patents

Abstract

The present invention is directed to a variation modeling method for precise position information transformation of spatial information / position information for accurately converting position coordinates of spatial information and geographic information within the accuracy required by a user by overcoming limitations of coordinate transformation parameters and coordinate transformation equations. As regards the present invention, (1) determining a conversion parameter for position coordinate conversion of spatial information and geographic information; (2) reading the planar rectangular coordinates of the digitized spatial information and the geographical information to be transformed into a data file format and calculating the geodesic coordinates (or geographic coordinates) by reverse projection; (3) The three-dimensional rectangular coordinates calculated in step (2) are three-dimensional rectangular coordinates based on the International Terrestrial Reference Frame (ITRF) coordinate system, which is a three-dimensional rectangular coordinate system based on the GRS80 ellipsoid which is a geodetic reference by using the conversion parameter. Calculating as; (4) inversely calculating the three-dimensional rectangular coordinates (X _new , Y _new , Z _new ) converted in step (3) to geodetic coordinates; (5) applying geodetic coordinates, the result of which is calculated in step (4), to the inverse calculation equation of the transverse Melcatol projection formula and calculating the planar rectangular coordinates; (6) dividing the difference between the calculated planar Cartesian coordinates and the planar Cartesian coordinates determined through GPS observation by dividing the x- and y-axis components; (7) modeling the x, y variation and elevation variation calculated in step (6); (8) calculating and displaying variation components in x, y and elevation directions at each grid point of the grid file of the variation model to be determined; And (9) adding the residual variation of the x-axis, y-axis, and the elevation axis estimated to the trend equations of the x-axis, the y-axis, and the elevation axis determined in step (7) to complete modeling of the variation, and finally, the contour diagram of the variation amount for each axis. Characterized in that the step consisting of constructing.

Spatial information, location information, coordinate transformation, parameter, coordinate transformation, variation, modeling

Description

Distorting Modeling method for Transforming the Presize Position of Partial / Positional information}

1 is a diagram showing the influence of coordinate transformation and coordinate variation,

2 is a diagram illustrating a spatial coordinate system mismatch problem according to a scale change;

FIG. 3 is a diagram illustrating the influence of an error occurring in the position coordinates of spatial information due to contour mismatches of adjacent portions during coordinate transformation between blocks;

4 is a conceptual diagram of a coordinate transformation process and variation modeling according to the present invention;

5 to 10 are diagrams illustrating a coordinate transformation process.

FIG. 11 is a diagram illustrating that the bias of data is removed to avoid incomplete variation modeling in the distribution of common points in which variation amounts exist after coordinate transformation based only on parameters.

FIG. 12 is a diagram illustrating optimization of an analytical covariance function determined by applying a least squares method to empirical covariance, and determining an initial covariance value C (o ) and a correlation distance A which are parameters.

The present invention relates to a variation modeling method for precise position information conversion of spatial information / position information.

In particular, the present invention relates to a modeling method for precise position information conversion of spatial information / position information for accurately converting position coordinates of spatial information and geographic information within the accuracy required by a user by overcoming limitations of coordinate transformation parameters and coordinate transformation equations. .

In general, coordinates for displaying the location information of the terrain and features in space can be displayed on the basis of various types of geospheroids (geodesic reference). The existence of various types of geospheroids means that the size of the ellipsoids is different and that the center and the axis of rotation of the ellipsoids are inconsistent, so that the geospatial system (geodetic coordinate system) set up based on this ellipsoid is also inconsistent. Such inconsistency between the ellipsoid and geodetic coordinate system has resulted in inconsistency of location information between regions and countries.In the recent era of positioning using satellites, geodetic systems and satellites, which are the standards of survey and map coordinates in the past, There is a big difference between the geocentric coordinate systems that are used as the basis for positioning. Such a difference causes a problem that a user who acquires location information using satellite cannot immediately use location information, and in order to enable users to use location information directly using satellites, it is necessary to correlate with the existing geodetic coordinate system. It was necessary to have. Therefore, in order to have such a relationship, a complicated mathematical theory and several steps must be performed to transform the coordinates of each other (coordinate transformation), and it is necessary to develop more accurate theories and steps for more accurate position coordinate transformation.

Recently, as the construction of various geographic information using GIS (Geographic Information System) and the use of Global Positioning System (GPS) have become commonplace, the inconsistency between the location information of geographic data and the location information measured by GPS Due to the inconvenience and confusion of the user occurred. Therefore, in the country, the existing geodetic coordinate system that provided location information based on the geodetic coordinate system was converted to the geocentric coordinate system.

Currently, the geodetic criteria employed in Korea uses Bessel (1841) ellipsoid, and the geodetic coordinate system uses the local geodetic coordinate system (Korean geodetic coordinate system) set on this Bessel ellipsoid. However, in the country, GRS80 ellipsoid and ITRF2000 coordinate system are determined as a new geodetic reference and geodetic coordinate system, and 7 conversion parameters and conversion equations are announced to enable mutual conversion. However, the current seven coordinate transformation parameters and transformation equations are impossible to accurately coordinate the geospatial information required by the user due to limitations in the accuracy of the transformation parameters and the formal error of the coordinate transformation equation. It aims to coordinate coordinates of digital maps rather than coordinate transformations.

The existing coordinate transformation method is the most commonly used method as a similar transformation method using only three coordinate transformation parameters or seven coordinate transformation parameters. The above method is a coordinate transformation method in which the angle does not change while maintaining the phenomenon, and the length coordinates of the line and the position coordinates of the point do not change. This method is used when there are no systematic errors in the two geodetic networks. Same as (1).

: 지역적인 측지좌표계의 3차원 직각좌표

: 3D Cartesian Coordinates of Local Geodetic Coordinate System

: 상대되는 측지좌표계의 3차원 직각좌표

: Three-dimensional rectangular coordinates of the geodetic coordinate system

:

좌표계에서

좌표계간의 원점이동량

:

In the coordinate system

Homing amount between coordinate systems

             R: 3 ㅧ 3 right angle rotation matrix

             S: scale factor 1 + ?? S, ?? S: microscale

In the case of the similar transformation method used for the coordinate transformation of the position information, the number of parameters included is small, the model is simple, so it can be easily executed in software, and the two coordinate systems are homogeneous (when there is no local distortion in scale or direction). Although there is an advantage that it is suitable for connection, the existing position information coordinate conversion method includes a large error after the conversion, the following problems occur.

First, in the case of converting by the conventional similar transformation method for coordinate transformation of position information in geographic information, the conversion accuracy cannot be improved due to the presence of coordinate variation (or error) in the position information to be converted. The reason for the above is that, as shown in FIG. 1, the amount of variation present in the location information in the existing geodetic coordinate system remains unchanged even after conversion.

Second, as shown in FIG. 1, in the coordinate transformation by the method of similar transformation, the coordinate reference point or space converted because the amount of coordinate variation existing in the position coordinate of the reference point or spatial information remains unchanged even after being converted to the new coordinate. The location coordinates of the information are incorrect. Therefore, the relative accuracy can be increased by measuring the location in the field using the converted reference point or the location information of the spatial information. However, the absolute accuracy, that is, the position coordinate of the spatial information based on the newly adopted reference system contains a large error, which greatly increases the accuracy. Falls. In addition, if the spatial coordinates are measured in the field by connecting a reference point or an observation station other than the reference point used when calculating the conversion parameter, a large error is included.

Therefore, the digital map, various geographic information, and spatial information data produced according to the reference point and the grade of the reference point to be used are adjacent to each other when the coordinate transformation is performed by calculating coordinate transformation parameters for each block as shown in FIG. Inconsistency of the contours occurs in the portion, in particular, as shown in the accompanying drawings, it can be seen that a large error occurs due to the inconsistency of the contours of the adjacent portions that occur when the coordinate transformation between the different coordinate transformation parameters occurs. have.

Therefore, performing coordinate transformation of spatial information, geographic information, and digital map using only coordinate transformation parameters becomes inconsistent coordinates nationwide, and the survey is inconsistent with each other by connecting reference points or constant stations located in adjacent blocks. However, there is a problem that it is inevitable to include spatial coordinate system (longitude and latitude line) mismatch, contour mismatch and location error for the same area.

Third, in the case of performing coordinate transformation by calculating the coordinate transformation parameter for each block, as shown in FIG. That is, as shown in FIG. 3, it can be seen that a large error occurs due to the inconsistency of the contours of adjacent parts generated at the coordinate transformation between blocks having different coordinate transformation parameters.

Therefore, the coordinate transformation of spatial information, geographic information, and digital maps using only coordinate transformation parameters becomes inconsistent coordinates nationwide, and when surveying by connecting reference points or permanent observation stations located in adjacent blocks. There is a problem that a large error occurs.

In order to solve the problems caused by the conventional method of converting the positional coordinates of the spatial information, geographic information, and the numerical map as described above, the present invention adds the variation modeling to the coordinate transformation method using only the conventional transformation parameters. The present invention provides a variation modeling method for precise position information transformation of spatial information / position information to solve problems of errors occurring during transformation.

One embodiment of the present invention for achieving the above object, (1) determining a conversion parameter for transforming the coordinates of the spatial information and geographic information; (2) reading the planar rectangular coordinates of the digitized spatial information and the geographical information to be transformed into a data file format and calculating the geodesic coordinates (or geographic coordinates) by reverse projection; (3) The three-dimensional rectangular coordinates calculated in step (2) are three-dimensional rectangular coordinates based on the International Terrestrial Reference Frame (ITRF) coordinate system, which is a three-dimensional rectangular coordinate system based on the GRS80 ellipsoid which is a geodetic reference by using the conversion parameter. Calculating as; (4) inversely calculating the three-dimensional rectangular coordinates (X _new , Y _new , Z _new ) converted in step (3) to geodetic coordinates; (5) applying geodetic coordinates, the result of which is calculated in step (4), to the inverse calculation equation of the transverse Melcatol projection formula and calculating the planar rectangular coordinates; (6) dividing the difference between the calculated planar Cartesian coordinates and the planar Cartesian coordinates determined through GPS observation by dividing the x- and y-axis components; (7) modeling the x, y variation and elevation variation calculated in step (6); (8) calculating and displaying variation components in x, y and elevation directions at each grid point of the grid file of the variation model to be determined; And (9) adding the residual variation of the x-axis, y-axis, and the elevation axis estimated to the trend equations of the x-axis, the y-axis, and the elevation axis determined in step (7) to complete modeling of the variation, and finally, the contour diagram of the variation amount for each axis. Characterized in that the step consisting of constructing.

Hereinafter, the present invention will be described with reference to the accompanying drawings.

First, a first step of determining conversion parameters (parameters 3, 4, 5, 6, 7, and 10) for position coordinate conversion of spatial information and geographic information is performed.

That is, the mathematical model equations used to determine the coordinate transformation parameters based on similarity (isotropy) may use Bursa-Wolf model equation, Molodensky-Badekas model equation, and Veis model equation. The conversion parameters are determined by calculating the unknown parameters of the mathematical model equations according to the least squares condition.

In addition, as the mathematical model equations used to determine the coordinate transformation parameter based on non-similarity (nonlinearity), the Karakisky-Tompson model, the Vaniceik-Well model, and the Affine model can be used.

In the first step, a common point (reference point, survey point) having coordinates based on an old geodetic reference (local geodetic coordinate system) and a new geodetic reference (global center coordinate system) is used to determine coordinate transformation parameters based on similarity and non-similarity. Should be used.

Then, the planar rectangular coordinates of the digitized spatial information and geographic information to be transformed (lateral melcatol and pan-lateral melcatol coordinates) are read in various data file formats (* .DXF, * .SHP) and geodetic coordinates (or geographic coordinates). To perform the second step of calculating by the inverse projection equation.

That is, the digitized spatial information and geographic information are databased using various formats provided by CAD or GIS software. The positional coordinates of the information are indicated by plane rectangular coordinates. Read a database constructed in (* .DXF, * .SHP) format and inversely calculate the planar Cartesian coordinates into geodesic coordinates (geographic coordinates or longitude and latitude coordinates) by transverse Meltocol projection. Convert to 3D rectangular coordinates based on the dimensional rectangular coordinate system.

The equation for converting the geodetic coordinates into three-dimensional rectangular coordinates is as follows.

는 측지좌표(위도와 경도)이고, h는 타원체고, e는 편평룰, a는 Bessel타원체의 장반경(6377397.155 m)이다.here

Is the geodetic coordinates (latitude and longitude), h is the ellipsoid, e is the flat rule, and a is the long radius of the Bessel ellipsoid (6377397.155 m).

The three-dimensional rectangular coordinate calculated in the second step is a three-dimensional rectangular coordinate system based on the new geodetic reference GRS80 ellipsoid using (3,4,5,6,7,9,10) parameters. The third step of calculating the three-dimensional rectangular coordinates based on the coordinate system of the International Terrestrial Reference Frame) is performed. The calculation formula in the third step uses a similar transformation, a Molodensky transformation or an Affine transformation using seven parameters.

Transformation formula

X _new , Y _new , Z _new : Three-dimensional rectangular coordinates on the New Geodetic Standard (GRS80)

: 구 측지기준(Bessel)상의 3차원 직각좌표

: 3D Cartesian Coordinates on Old Geodesic Bessel

: 3차원 직각좌표계(X,Y,Z방향)의 원점 이동량

: Origin movement amount in 3D rectangular coordinate system (X, Y, Z direction)

: 3차원 직각좌표계(X,Y,Z축)의 좌표계 회전량

: Rotational amount of coordinate system in 3D Cartesian coordinate system (X, Y, Z axis)

S : Scale change

Molodenski Conversion

는 측지기준 원점의 좌표이고, 기타 요소들은 식(3)에서 정의한 것과 동일하다.here

Is the coordinate of the geodetic reference origin, and the other factors are the same as defined in equation (3).

A fourth step of inversely calculating the three-dimensional rectangular coordinates X _{?? w} , Y _{?? w} , and Z _{?? w} transformed in the third step into geodetic coordinates is performed. The inverse calculation is calculated until it converges to the precision required by extrapolation using the following equation.

In addition, the geodetic coordinates, which are the results calculated in the fourth stage, are carried out in the fifth step of calculating the planar rectangular coordinates using an inverse calculation equation of the transverse melcatel projection formula developed on the basis of the new geodetic standard GRS80 ellipsoid.

here,

And a sixth step of dividing the difference between the planar rectangular coordinates calculated through the coordinate transformation process of the first to fifth steps with respect to the common points and the planar rectangular coordinates determined through GPS observation by dividing the x-axis and y-axis components. Perform the steps. The difference between the planar Cartesian coordinates is called "the x-axis and the y-axis variation", and the variation with respect to the z-axis is called "the elevation variation". At this time, the "elevation variation" means the difference between the value of the ellipsoidal height after subtracting the precision geoid height and the existing normal elevation.

In addition, by analyzing the trends of the x-axis, y-axis fluctuations and elevation variations determined in the sixth step, the regression equations by the least square method are determined using linear and nonlinear regression equations, and the determined regression equations (herein referred to as trend equations) Subtract the trend value to calculate the remaining variation of the x-axis, y-axis variation and the elevation variation.

In the eighth step, the variation modeling is performed using the residual variation of the x-axis, y-axis, and elevation variation calculated in the seventh step, as shown in FIG. , Modeling using interpolation method and Total Least Square (TLS) method, and can improve the accuracy of spatial information and geographic information by more than 80% by modeling the variation of each axis with the grid file of the standard to obtain.

The variation modeling process will now be described with reference to FIGS. 5 to 10.

First, x, y variance and elevation variance are calculated and analyzed at each common point, and the non-similar points are classified and removed to secure data quality and maintain consistency. In other words, the excessively large variance points cause large errors in the modeling and should be removed. The size of the limit is about 2 m but can be more than that.

As shown in FIG. 11, the biased data is analyzed to obtain a constant spatial distribution, and the biased data is removed. The reason for removing the bias of the data as described above is that the prediction value may be biased at a specific point in the data that is not evenly distributed, so that incomplete variation modeling due to irregular data distribution may be performed.

In addition, by analyzing the trends of x, y fluctuations and elevation fluctuations of the data with unbiased data, linear and nonlinear regression equations are used to determine the least squares regression equation, and the determined regression equations are used. Subtract the value to calculate the remaining variation of the x- and y-axis variations and the elevation variation.

The empirical covariance function for the residual variances of the x, y and elevation axes is then calculated. The empirical covariance function uses a developed computer program. The empirical covariance function is used to select an analytical model for the empirical covariance functions using the Least Square Curve Fitting. Calculate the value and correlation length.

The analytical covariance function uses the following types.

Gaussian Covariance Function

(5)

(5)

Reilly covariance function

(6)

(6)

Exponential covariance function

(7)

(7)

Natural Covariance Function

(8)

(8)

Makovov I Covariance Function

(9)

(9)

Makovov II covariance function

(10)

10

Wirth (1 / S) Covariance Function

(11)

(11)

: 거리,

: 상관거리,

:

일 때에

로써 취한값인 초기분산값이다. In each covariance function

: Street,

: Correlation distance,

:

When

It is the initial variance value that is taken as.

12 is a diagram illustrating optimization of an analytical covariance function determined by applying a least squares method to empirical covariance, and determining an initial covariance value C (o) and a correlation distance A which are parameters.

Then, an eighth step of calculating variation components in the x, y and elevation directions at each grid point of the grid file of the variation model to be determined using the least-squares colocation method and interpolation methods is performed. Here, the variation modeling by the least-squares colocation method is performed using the following equation.

는 추정된 변동량이고, 벡터

의 요소들은 데이터 점들과 보간점간의 거리를 상기 나열한 복수의 해석적 공분산 중 선택한 해석적 공분산 함수에 적용시켜 산출한다. 또한, 매트릭스

의 요소들은 데이터 점들의 모든 조합에 의한 거리를 해석적 공분산 함수에 적용시켜 산출한다. 그리고, 벡터 l은 각 데이터점들에서 왜곡을 포함하고 있는 관측치이다. 여기서 해석적 공분산함수에 의하여 결정되는 C(S)벡터와

메트릭스는 다음과 같이 개발하였다.In the above formula

Is the estimated variation, and the vector

The elements of are computed by applying the distance between the data points and the interpolation points to an analytic covariance function selected from the plurality of analytical covariances listed above. Also, the matrix

The elements of are calculated by applying the distances of all combinations of data points to the analytical covariance function. Vector l is an observation that includes distortion at each data point. Where the C (S) vector determined by the analytical covariance function

The matrix was developed as follows.

Then, using the equation (18) of the eighth step to determine the estimated value of the remaining variation of the x-axis, y-axis and elevation axis coordinates at a constant grid interval, the x-axis, y-axis and the elevation axis determined in the seventh step Finally, the variance modeling is completed by adding the residual variances of the estimated x-axis, y-axis, and elevation axis to the trend equation, and the ninth step of constructing the contour diagram of the variance for each axis is performed.

In addition, a tenth step of developing and providing appropriate coordinate transformation software is performed to perform coordinate transformation of spatial information and geographic information within the accuracy required by the user. That is, the coordinate conversion software includes a calculation process of the fifth step in the second step, and reads the variation amount value corresponding to the position coordinate required by the user from the variation model developed in the ninth step and calculates it in the fifth step. Calculate the final coordinate transformation value in addition to x (or E), y (or N) and elevation (normal elevation). The interpolation method should be used to calculate the variation value of the position coordinate (an estimated value of the residual variation of the x-axis, y-axis, and elevation axis coordinates) in the variance model, and the interpolation method uses linear and nonlinear interpolation. Coordinate transformation software makes it possible to read (* .DXF, * .SHP and other) formats.

In addition, the coordinate conversion software is a conversion software that can convert the spatial information and geographic information constructed based on the old geodetic criteria into information based on the new geodetic criteria, so that the coordinate transformation for the purpose of enhancing the accuracy and reliability of the coordinate transformation. The software meets the following conditions.

That is, the coordinate conversion software is easy and convenient for users, and provides time and conversion conditions so that the coordinate transformation of spatial information and geographic information is highly efficient, and only one transformation result is presented as the coordinate transformation result. For example, the coordinate conversion result provides an optimal coordinate conversion result. The quality of the data is maintained and the data structure is not changed.

Lastly, in order to evaluate the conversion accuracy of the converted spatial information and geographic information, the eleventh step of selecting a position clearly identified in the converted information, conducting GPS survey in the field, comparing and analyzing Perform

The present invention is not limited to the above embodiments, and various modifications and changes can be made by those skilled in the art, which are included in the spirit and scope of the present invention included in the appended claims.

As described above, the present invention has an effect of providing a conversion tool capable of converting spatial information and geographic information constructed based on the old geodetic criteria into information based on the new geodetic criteria.

In addition, the present invention enables users to easily understand and use, provide time and calculation conditions for high efficiency, and only one conversion result is presented (the conversion result by direct calculation and inverse calculation is the same). ), It provides the optimal result of the self-conversion, and improves the accuracy and reliability of the coordinate transformation by maintaining the data quality and not changing the data structure.

Claims (8)

(1) determining transform parameters for transforming position coordinates of spatial information and geographic information; (2) reading the planar rectangular coordinates of the digitized spatial information and the geographical information to be transformed into a data file format and calculating the geodesic coordinates (or geographic coordinates) by reverse projection; (3) The three-dimensional rectangular coordinates calculated in step (2) are three-dimensional rectangular coordinates based on the International Terrestrial Reference Frame (ITRF) coordinate system, which is a three-dimensional rectangular coordinate system based on the GRS80 ellipsoid which is a geodetic reference by using the conversion parameter. Calculating as; (4) inversely calculating the three-dimensional rectangular coordinates (X _new , Y _new , Z _new ) converted in step (3) to geodetic coordinates; (5) applying geodetic coordinates, the result of which is calculated in step (4), to the inverse calculation equation of the transverse Melcatol projection formula and calculating the planar rectangular coordinates; (6) dividing the difference between the calculated planar Cartesian coordinates and the planar Cartesian coordinates determined through GPS observation by dividing the x- and y-axis components; (7) modeling the x, y variation and elevation variation calculated in step (6); (8) calculating and displaying variation components in x, y and elevation directions at each grid point of the grid file of the variation model to be determined; And (9) The remaining variation of the x-axis, y-axis and elevation axis is added to the trend equations of the x-axis, y-axis and elevation axis determined in the above step (7) to finally complete the modeling of the variance and calculate the contour plot of the variation of each axis. Drawing; Variable amount modeling method for precise position information conversion of spatial information / location information, characterized in that consisting of. According to claim 1, wherein step (1), Coordinate transformation parameter based on similarity or emergency letter is determined by using common point (reference point, survey point) with coordinates based on old geodetic standard (local geodetic coordinate system) and new geodetic standard (global center coordinate system). A variable amount modeling method for precise position information transformation of spatial information / position information. The method of claim 2, A variation amount modeling method for precise position information transformation of spatial information / position information, characterized in that for converting the geodetic coordinates into three-dimensional rectangular coordinates by the following equation. The method of claim 1, wherein the calculation formula in the step (3), A variation amount modeling method for precision position information transformation of spatial information / position information, characterized in that one of the similar transformation, Molodensky transformation or Affine transformation using the conversion parameter. The method of claim 1, wherein in step (5), the inverse calculation equation of the newly developed transverse melcatol projection equation is

A variation amount modeling method for precise position information conversion of spatial information / positional information, characterized in that the calculation is a planar rectangular coordinate from the latitude and longitude of the spatial information / positional information. here,

The method of claim 1, wherein the modeling of step (7), Calculating and analyzing the x, y variance and the elevation variance at each common point, and classifying and removing points of similarity to ensure data quality and maintain consistency; Analyzing the bias of the data to obtain a constant spatial distribution and removing the biased data; Calculating an empirical covariance function for the x, y variation and elevation variation of the debiased data; And Calculating an initial covariance (variance) value and a correlation length by selecting an analytical model for the empirical covariance functions using a least square curve fitting to the empirical covariance function; Variable amount modeling method for precise position information conversion of spatial information / location information, characterized in that consisting of. 2. The variation amount component of x, y and elevation directions at each lattice point of the lattice pile of the variation model to be determined in the step (8), Variance modeling method for precise position information conversion of spatial information / location information, characterized in that it is modeled using one of the least squares co-location method, interpolation method or Total Least Square (TLS) method. The method of claim 1, wherein in the eighth step, an estimated value of the remaining variation amount of the x-axis, y-axis, and elevation axis coordinates is: Calculated by interpolation method, the interpolation method is characterized in that the linear or nonlinear interpolation method, the coordinate conversion software is accurate to the spatial information / location information characterized in that the (* .DXF, * .SHP and other) format can be read A variation modeling method for location information conversion.

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