KR20140132639A - Method of coordinates transformation to world geodetic system using triangles mesh warping with minimal control point - Google Patents

Abstract

A method for converting coordinates of a world geodetic system through triangle warping is a method for converting coordinates of a geodetic reference system which converts a digital map and a land registration map, manufactured based on a local geodetic system, into a world geodetic system. The method comprises: a step of selecting common points; a step of forming triangle nets of a local geodetic system and a world geodetic system respectively using the common points; and a step of converting all coordinates of the local geodetic system triangle net into the corresponding coordinates of the world geodetic system triangle net through triangle warping in batches by forming the local geodetic system and the world geodetic system using the common points. Therefore, the method can conveniently secure accurate performance of the world geodetic system at low costs by performing coordinate conversion only by obtaining minimal common points regardless of the degree of scale.

Description

[0001] The present invention relates to a method and apparatus for transforming a world geodetic coordinate system using triangular warping,

In the present invention, a regional geodetic system including a target area and a world geodetic triangular network are constructed with minimum common points, and the phase relations of the respective triangular meshes are made the same, and then all the coordinates of each triangle of the regional geodetic system are corresponded The coordinate transformation by the transform coefficient and the statistical distortion amount modeling and correction by a large amount of common point results are performed by performing batch coordinate transformation with all the coordinates of the world geodetic triangle of the world geodetic system, And the method by the above.

In general, Korea's land boundaries are registered and managed in the cadastral map based on the local geodetic system. However, according to the global promotion of the cadastral re-surveying project and the global trend, the conversion to the world geodetic coordinate system based on the three- . The reason for the global trend to convert the geodetic reference system from the existing regional geodetic system to the world geodetic system is as follows.

First, the geodetic reference system of the country should be accurate and up-to-date because it is the infrastructure information that is the basis of all the location information of the country. For this purpose, new geodetic surveying technologies have been developed, such as using satellites. These technologies define the world geodetic system for use worldwide and provide the information. Therefore, the introduction of the world geodetic system is necessary for precise and accurate positioning using the most advanced positioning system.

As technology advances and information exchanges become more active, international cooperation organizations recommend that the world use one standard. Therefore, in Korea, it is necessary to change all the cadastral maps stored in the local geodetic system to the world geodetic system in a timely manner to introduce the world geodetic system in a timely manner.

Hereinafter, the conventional process of converting the regional geodetic system to the global geodetic system (digital geodetic coordinate system standard work guide / geographical information source) described above with reference to FIG. 1 will be described in detail.

All common point selection and actual survey phase ( S10 )

The process of establishing a plan for conversion and selecting the conversion method after considering the various statuses at the time of the production of the digital topographic map and ensuring the common point and converting it into the world geodetic system according to the guidelines, I have.

World geodetic system  Basic conversion steps ( S20 )

The basic transformation to the world geodetic system converts the planar rectangular coordinates of the local geodetic system into the latitude and longitude of the local geodetic system, converts the latitude and longitude of the local geodetic system to the three dimensional orthogonal center coordinates, After converting to Cartesian coordinates, the global latitude of the world geodetic system should be converted to the planar Cartesian coordinates of the world geodetic system.

Distortion amount calculation step ( S30 )

A total distortion amount calculation step ( S32 )

Referring to FIG. 2A, the planar rectangular coordinate system based on the global geodetic system is derived through the basic conversion step of the planar rectangular coordinate system based on the local geodetic system to the world geodetic system. (X-axis, Y-axis) between the planar rectangular coordinate system of the world geodetic system standard and the converted planar rectangular coordinate system.

Emergency Common Removal Steps ( S34 )

Referring to FIG. 2B, the non-phase-shifting means that the amount of distortion of each axis (X-axis, Y-axis) is significantly larger than the amount of distortion common to most of the common points. In order to secure the reliability of the distortion modeling result and to maintain consistency, it is necessary to judge and eliminate the commonality which is more than three times (± 3σ) more than the standard deviation (± σ) of the distortion amount of each axis of the plane rectangular coordinate system do.

Biased common point removal step ( S36 )

Referring to FIG. 2C, the biasedness is such that the common points are not uniformly distributed but rather concentrated and concentrated. In order to prevent the incomplete distortion modeling due to irregular data distribution by causing a problem that the predicted value of the specific point is waved out among the unevenly distributed common points, biased data is analyzed to obtain a certain spatial distribution and the biased data is removed.

Distortion amount tendency analysis and distortion amount calculation step ( S38 )

Referring to FIG. 2D, trends of the X-axis and Y-axis distortion amounts of the common points in which the unsteadiness and the bias are eliminated are analyzed, and the trends of the X-axis and Y-axis tendency equations by the least squares method using the linear regression equations Or determine the unknown using an inverse square transform (affine transformation) equation. After calculating the tendency value at the common point position by using the determined tendency equation or anisotropic convolution transformation, the residual distortion amount of the X axis and the Y axis is calculated by adding or subtracting the tendency value from the amount of distortion of the common point.

The coordinate transformation step to which the distortion amount is applied ( S40 )

Distortion amount modelling  step ( S42 )

의 가우시안 공분산 함수를 사용하도록 한다. 공분산 함수식에서 S는 거리, A는 상관거리,

:

일 때에

로써 취한 값인 초기 분산값이다. Referring to FIG. 2E, the empirical covariance function for the amount of residual distortion in the X axis and the Y axis is calculated, but Least Square Curve Fitting is used for the empirical covariance function. We choose the appropriate analytical model for the empirical covariance functions and calculate the initial covariance (variance) values and the correlation distance, which are two transform coefficients. The analytic covariance function

Gaussian covariance function. In the covariance function, S is the distance, A is the correlation distance,

:

When

Is the initial variance value that is taken as.

Estimation of Distortion in Grid Spacing ( S44 )

로 나타내는 식을 사용하도록 한다. 위 식에서

는 추정된 왜곡량이고, 벡터

의 요소들은 데이터 점들과 보간점간의 거리를 사용하여 해석적 공분산 함수로부터 구한 값이다. 또한, 매트릭스

의 요소들은 공통점들의 모든 조합에 의하여 거리를 사용하여 해석적 공분산 함수로부터 계산된다. 벡터

은 각 공통점들에서 왜곡을 포함하고 있는 관측치이다.The X-axis and Y-axis distortion amounts are calculated from the lattice points of the lattice file of the distortion amount model to be generated and determined from the X-axis and Y-axis distortion amounts at the common points, Lt; / RTI > In case of applying the distortion modeling by the least square collocation method

Is used. In the above equation

Is an estimated distortion amount, and vector

Are the values obtained from the analytical covariance function using the distance between the data points and the interpolation point. Also,

Are calculated from the analytical covariance function using the distance by all combinations of common points. vector

Are observations that contain distortions at each common point.

Distortion amount grid file generation step ( S46 )

Referring to FIG. 2F, a range of distortion amount (latitude and longitude range) is determined so as to cover the range of the digital topographic map producing region, and a distortion amount grid file is created. The distortion amounts of the X-axis and the Y-axis calculated through the tendency equations of the X and Y axes are added to the estimated values of the residual distortion amounts of the X and Y axes. A grid file is created at intervals of 0.005 ° (1 / 1,000 digit map size) distortion amount of the finally calculated X axis and Y axis. The names of the grid files for each axis are specified by dx.txt and dy.txt.

The final transformed performance derivation step ( S48 )

If we calculate the correlation between the amount of distortion and distance described above, calculate the amount of distortion for the four corners of the 1 / 1,000 digital topographic map, interpolate the interior point using the amount of distortion of the four corners of the 1 / 1,000 digital topographic map, The transformed performance can be derived.

However, the above conventional coordinate transformation method has the following problems.

The coordinate transformation method according to the related art performs coordinate transformation (basic transformation step) by considering the geometric elements between the ellipsoid of the local geodetic reference system and the ellipsoid of the world geodetic reference system (origin movement, movement direction of the axis, The local distortion amount is estimated to model the most reasonable amount of distortion, and this is applied to the amount of distortion of each corner point of the 1/1000 digital topographic map, and the internal points of the 1/1000 digital topographic map are subjected to interpolation by interpolation. The procedure is very complicated.

In particular, since the conventional coordinate transformation method (basic transformation step) is performed using the geometric transformation coefficient (7 parameters) of the local geodetic system, there are too many variables to be considered.

In addition, since many common points are selected and measured for distortion amount modeling, the cost is increased.

SUMMARY OF THE INVENTION Accordingly, the present invention has been made keeping in mind the above problems occurring in the prior art, and it is an object of the present invention to provide a digital terrain transformer (Local geodetic triangulation network, world geodetic triangulation network) including the target area with minimum commonality, without constructing a large amount of common points for mass compensation and modeling distortion, And a method of performing batch coordinate conversion by triangular warping with the world geodetic triangle corresponding to the coordinate points.

According to an aspect of the present invention, there is provided a coordinate transformation method of a geodetic reference system for transforming a digital geographic map and a cadastral map produced on the basis of a local geodetic system into a world geodetic system, , A step of selecting common points, a step of constructing a corresponding triangular network using the common points (a triangular network based on the regional geodetic coordinates of the common points and a triangular network based on the global geodetic coordinates of the common points) (Parcel boundary points, survey points, etc.) of all points within the triangle (local geodetic triangle and the world geodetic triangle).

As described above, according to the configuration of the present invention, the following effects can be expected.

First, the coordinate transformation process from the local geodetic system to the world geodetic system is simplified.

Second, despite the simple procedure, it is effective by providing almost the same accuracy as the coordinate transformation result by the procedure by the existing global geodetic coordinate transformation instruction.

Third, there is an economical effect of reducing the measurement cost by minimizing the common point selection.

Fourth, the 1 / 1,000 digital topographic map generated by the existing conversion method has an effect of preventing the possibility of error in the crossing due to the distortion amount between the lattice diagrams.

Fifth, since the degree of nonconformity of the region is reflected in the mutual amount of triangulated manganese (local geodetic coordinate value - world geodetic coordinate value) corresponding to the global geodetic system conversion in the cadastral map, There is a mitigating effect.

Brief Description of the Drawings Fig. 1 is a flowchart showing a conventional coordinate transformation method of a local geodetic system to a world geodetic system.
FIGS. 2A to 2F are tables and graphs illustrating characteristics of each step according to the flowchart of FIG. 1. FIG.
3 is a flowchart showing a method of collectively converting a global coordinate system of geodetic coordinates by triangular warping according to the present invention.
4 is a plan view showing an embodiment of an irregular triangular mesh lattice according to the present invention.
5 is a plan view showing the wafting transformation of the world geodetic system of the regional geodetic system according to the present invention;
6 is a table for an experiment utilizing common features according to the present invention.
7 is a table for an experiment using eight common points among 86 common points according to the present invention.
FIG. 8 is a table for an experiment example in which 78 out of 86 common points according to the present invention are verified.

Brief Description of the Drawings The advantages and features of the present invention, and how to achieve them, will become apparent with reference to the embodiments described in detail below with reference to the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Is provided to fully convey the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. The dimensions and relative sizes of layers and regions in the figures may be exaggerated for clarity of illustration. Like reference numerals refer to like elements throughout the specification.

Hereinafter, preferred embodiments of a method for collectively converting coordinates of the world geodetic system by irregular triangular warping according to the present invention will be described in detail with reference to the accompanying drawings.

GPS has been shifting to the world geodetic system worldwide due to the advancement and practical use of satellite geodetic technology such as GPS, and the coordinates of the cadastral map created by the existing regional geodetic system related to the cadastral re- It is an area of interest that the present invention aims to solve so that a reasonable and efficient coordinate transformation can be achieved in converting the geodetic reference system from the existing geodetic system to the world geodetic system in accordance with the trend.

Here, the world geodetic system is a reference system that allows the shape and size of the earth to be closest to the shape and size of the actual earth globally. It is a reference system that uses the earth's center of mass as the origin, , Earth Centered Earth Fixed). GPS (Global Positioning System) is the most representative example of using the earth-centered stationary coordinate system, and GPS is implementing its position in the earth-centered coordinate system because of its global utilization range.

Generally, for coordinate transformation to the world geodetic system, the coordinate transformation coefficient is first obtained. For example, the transform coefficient is determined using a seven-parameter transformation coefficient model called Molodensky-badekas. A large amount of common points can be ensured even after the conversion by the coordinate conversion coefficient for the conversion to the position accuracy, and the coordinate conversion can be finally completed through the distortion correction. Finally, it is possible to map the results when the results are compared with the results of coordinate conversion and the results of surveying through accuracy evaluation.

The present invention intends to improve the complicated processes such as the coordinate transformation by the transformation coefficient and the distortion amount modeling and correction to perform coordinate transformation with the same positional accuracy.

The conversion of the regional geodetic system to the world geodetic system pathway means to convert the planar rectangular coordinate system of the regional geodetic system to the planar rectangular coordinate system of the world geodetic system. The conversion procedure according to the present invention is as shown in FIG. 3 and FIG. 4 as follows.

Common point selection step ( S110 )

Irregularity in common Triangular mesh  Configuration step ( S120 )

A common reference point of the target area is selected and a triangular network is constructed by the triangulation network based on the local reference system coordinates and the corresponding world geodetic system coordinates. In other words, two triangles (regional geodetic triangles and world geodetic triangles) having the same phase structure are constructed using common point coordinates.

Within a triangle  All coordinates Warping  Conversion step ( S130 )

Each corresponding triangle is formed in two triangular mangles constituted by common points to collectively convert the coordinates of all the points in the local geodetic triangle to the corresponding coordinates of the corresponding world geodetic triangle.

Hereinafter, the coordinate conversion procedure will be described in detail for each step.

Common point selection step ( S110 )

In order to convert the digital topographic maps and cadastral maps produced based on the existing regional geodetic system to the digital topographic map based on the world geodetic system, it is necessary to secure common points. These common points can be selected from the numerical cadastral map of the target area (securing the coordinate boundary register). In addition, if the global geodetic system has not been achieved, the world geodetic system will be achieved through separate surveys.

The present invention is characterized in that the number of common points is reduced by omitting separate distortion amount modeling as compared with the conventional coordinate transformation method. For example, the same coordinate conversion accuracy can be ensured even if the common points are minimized within 5 ~ 10% of the conventional common points. In addition, it is possible to utilize the GPS data in the case where the GPS data is not surveyed, and there is performance data of the common points currently held by the local governments.

Irregularity in common Triangular mesh  Configuration step ( S120 )

We use a delaunay triangle for an irregular triangle grid implementation. Here, the Neuron triangulation defines an optimized triangular network configuration algorithm that connects all established points.

Based on the common point, we can construct the optimized triangular network by performing the Threonine triangulation. A delaunay triangle is a triangle that does not contain any other points in the circumscribed circle for the three points making up the triangle. The conditions of these delaunay triangles are as follows. According to the Trion triangulum, the outer diameter of a triangle is at the same distance from the vertex of a triangle, so in the case of an acute angle triangle, the outer diameter is inside the triangle, but in the case of an obtuse triangle, the outer diameter is outside the triangle. If the circumcircle of a triangle contains a point that does not belong to the triangle, it is not a delaunay triangle.

Of all coordinates within the triangle Warping  Conversion step ( S130 )

Triangle warping is a two-dimensional extension of linear transformations on one dimension. The triangles P ₀ , P ₁ and P ₂ and the triangles Q ₀ , Q ₂ and Q ₃ are triangles of the TIN data generated by the end points of the corresponding objects and the control points, (Q ₀ , Q ₂ , Q ₃ ) when the point P constituting the object in the map is included in the triangle (P ₀ , P ₁ , P ₂ ). In this case, the point to be corrected is influenced more by the closer to the three vertexes of the triangle, and the farther away, the less affected. Also, the closer the delaunay triangle is to the equilateral triangle, the less the error in correcting the object where the mismatch occurs.

Referring to FIG. 5, a process for obtaining a point Q (XQ, YQ) generated as a result of performing warping from a point P (XP, YP) constituting an object in a map to be corrected is as follows.

In equation ⑴, having a value between P0 (XP0, YP0), P1 (XP1, YP1), P2 (XP2, YP2) is λ _0, λ _1, λ ₂ are 0 and 1 with the triangle vertex, that Is a linear function indicating the distance between the corresponding sides.

If λ ₀ , λ ₁ , λ ₂ are found in the above equations, they are expressed by the following equations (2) to (4).

Therefore, the point Q (XQ, YQ) generated as a result of performing the warping is expressed by Equation (5).

Since the precise position can be secured by only the basic transformation by the above procedure, it is not necessary to correct the determined amount of distortion by modeling residual amount of distortion to ensure accuracy after coordinate conversion.

<Experimental data>

In this experiment, as shown in Fig. 6, 86 common points of Uiwang City data, which is a pilot area of the National Standard Work Guideline (Ver 1.0), were used as basic data for analyzing the accuracy of the coordinate transformation result. Particularly, in this experiment, for the coordinate transformation using the triangular warping algorithm according to the present invention, a triangle network is constructed using only eight common points among the 86 common points as shown in FIG. 7, , And the remaining 78 common points were used as check points for accuracy verification.

(North) and Y-axis (East) on the planar Cartesian coordinate system that is basically transformed from the planar rectangular coordinate system based on the world geodetic system and the performance of the regional geodetic system. ΔX and ΔY are 0.665m and 0.518m, and standard deviations are 0.033 and 0.054, respectively, and it is necessary to compensate for the distortion amount separately. . On the other hand, the distortion amounts ΔX and ΔY of the coordinate transformation by the triangular warping according to the present invention are 0.00447m and 0.00514m, 0.00593 and 0.00309, respectively, and the standard deviation with respect to the plane position is 9.81mm, (0.5 mm x 500) of the accuracy of 25 cm.

In this experiment, we applied the method to derive a practical coordinate transformation method by verifying the accuracy of the distortions ΔX and ΔY of the coordinate transformation by the transformation of the national coordinate transformation coefficient and the coordinate transformation by using the common points constructed in the study site The results are as follows.

First, the mean values of the distortions ΔX and ΔY due to the transformations of the national coordinate transformations are 0.665m and 0.518m, and the standard deviations are 0.033 and 0.054, respectively. However, distortion of coordinate transformation due to triangular warping The average values of the amounts ΔX and ΔY are 0.00447m and 0.00514m, the standard deviation is 0.00593, 0.00309, and the standard deviation with respect to the plane position is 9.81mm. It can be understood that the distortion amount correction of the second embodiment is not necessary.

Second, by performing coordinate transformation by triangular warping consisting of 8 arbitrary common points, it is possible to obtain the optimum accuracy even if only a common point (about 5% ~ 10%) is applied, In the coordinate transformation method. Therefore, it can be confirmed that the method proposed by the present invention is a method for ensuring accuracy at low cost.

As described above, according to the present invention, since the amount of geometric distortion involved in coordinate transformation and the amount of distortion generated locally and irregularly are reflected in each vertex of all triangles including the target region, It can be seen that there is a technical idea that there is no need for separate geometric coordinate transformation and statistical distortion amount modeling. Within the scope of the basic technical idea of the present invention as such, many other changes will be possible to those of ordinary skill in the art.

Claims (5)

A coordinate conversion method of a geodetic reference system for converting a digital topographic map and a cadastral map produced on the basis of a regional geodetic system into a world geodetic system,
Selecting common points;
Constructing a triangle network of each of the regional geodetic system and the global geodetic system using the common point; And
Wherein the global geodetic triangulation network and the global geodetic triangulation network are constructed by using the coordinates of the common points so that all the coordinates of the local geodetic triangulation network are collectively triangulated by coordinates of the corresponding global geodetic triangulation network, Global Geodetic Coordinate Conversion Method by Triangle Warping. The method according to claim 1,
The above common points are the triangles characterizing the coordinate transformation by the transformation coefficient of the standard work instruction of the digital topographic coordinate system conversion standard and securing common within 5 ~ 10% of the method by statistical distortion amount modeling and correction by a large amount of common point performance World Geodetic Coordinate Batch Conversion Method by Warping. The method according to claim 1,
Wherein the triangulation network is an irregular triangulation network. The method of claim 3,
Wherein the triangulated network is a triangulated triangulation network (triangulated triangulation) that does not include any other points in a circumscribed circle about three points of common points constituting the triangles. The method according to claim 1,
Through the Wrapping transformation, the point P (XP, YP) is transformed into a point Q (XQ, YQ)
Wherein the point Q (XQ, YQ) is generated by equations (1) to (5) for the following linear function.

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