CN114001650A - Method for encrypting conversion parameters of earth coordinate system and arbitrary plane coordinate system - Google Patents
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Abstract
The invention discloses a method for encrypting conversion parameters of a terrestrial coordinate system and an arbitrary plane coordinate system. The method comprises the following steps: determining an intermediate projection coordinate system a 1; determining that the final conversion result meets the conversion precision requirement and an intermediate projection coordinate system A1; step two: converting the coordinates to an intermediate projected coordinate system a1 using four parameters between the local coordinate system a and the intermediate projected coordinate system a 1; step three: the coordinates are converted to the target coordinate system B using a projection relationship or a parameter conversion relationship between the intermediate projection coordinate system a1 and the target coordinate system B. The invention overcomes the defects that the existing conversion methods need to acquire local coordinate system parameters and easily cause parameter leakage; the method has the advantage of realizing the confidentiality of the local coordinate system parameters in the coordinate conversion process.
Description
Technical Field
The invention relates to a method for encrypting conversion parameters of a terrestrial coordinate system and an arbitrary plane coordinate system. More particularly, it is a method for realizing the conversion between the local coordinate system and the arbitrary plane coordinate system without using the local coordinate system parameters.
Background
In order to promote the use of the newly established local coordinate system, it is generally necessary to convert the historical data into the new local coordinate system, which requires the implementation of mutual conversion between the newly established local coordinate system and an arbitrary planar coordinate system. For example, the existing publication No. CN106202000A, entitled "method for converting seven parameters between a national three-dimensional coordinate system and an arbitrary local planar coordinate system", discloses a method for converting between a national three-dimensional coordinate system and a local planar coordinate system, which is characterized in that a planar coordinate is corrected by adding a constant, an elevation value is corrected by using three parameters, and the method has the function of obtaining a converted seven parameters with higher precision. The prior publication No. CN107479078B, entitled "method and system for converting geodetic coordinates into independent plane coordinates in railway survey", discloses a method for converting geodetic coordinates into independent plane coordinates applied in railway survey, which obtains plane coordinates by means of expansion ellipsoid gaussian projection transformation.
Some city local independent coordinate system parameters are classified data, and for popularization and use of the independent coordinate system, coordinate point pairs, drawings in various formats and the like in other coordinates have to be converted into the coordinate system, and the independent coordinate system parameters need to be acquired by conversion methods existing in the current market, so that parameter leakage is easily caused. The prior art has no report related to the conversion between a parameter-secret local coordinate system and an arbitrary plane coordinate system.
Therefore, it is necessary to develop a coordinate transformation method with secret parameters without using independent coordinate system parameters.
Disclosure of Invention
The invention aims to provide a method for encrypting conversion parameters of a local coordinate system and an arbitrary plane coordinate system, which realizes the coordinate conversion between the local coordinate system and the arbitrary plane coordinate system under the condition of not using parameters such as a central meridian, a north offset, an east offset and the like of the local coordinate system, thereby realizing the confidentiality of the parameters of the local coordinate system in the coordinate conversion process.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for encrypting conversion parameters of a terrestrial coordinate system and an arbitrary plane coordinate system is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: determining an intermediate projection coordinate system a 1;
determining an intermediate projection coordinate system a 1; because the direct use of parameters to convert the coordinates from the local coordinate system A to the target coordinate system B usually exceeds the precision limit difference, and the optional selection of the intermediate projection coordinate system A1 can not meet the precision requirement, the invention determines the intermediate projection coordinate system A1 through the precision index;
step two: converting the coordinates of the local coordinate system A into an intermediate projection coordinate system A1 by using the parameter conversion relation between the local coordinate system A and the intermediate projection coordinate system A1; the intermediate projection coordinate system A1 is used as a transition coordinate system in the conversion process of the invention;
step three: the coordinates are transformed to the target coordinate system B using a projective or parametric transformation relationship between the intermediate projective coordinate system a1 and the target coordinate system B. The invention converts the local coordinate system A to the target coordinate system B through the middle projection coordinate system A1, thereby realizing the secrecy of the local coordinate system parameters in the coordinate conversion process and ensuring that the conversion precision meets the tolerance requirement.
In the above technical solution, in the step one, the method for determining the intermediate projection coordinate system a1 includes the following steps,
step 11: the central meridian L of the local coordinate system A0Adding an offset to obtain a central meridian L of the intermediate projection coordinate system A11；
Step 12: based on the reference ellipsoid of the local coordinate system A, the major semiaxis a of the reference ellipsoid (i.e. the reference ellipsoid of the local coordinate system A) is taken0And flat ratio f0Adding a constant to the semiaxis of length (or oblateness or both) to obtain an expansion ellipsoid E1, and recording the semiaxis of length a of the expansion ellipsoid (i.e. expansion ellipsoid E1)1Flat rate of f1；
Step 13: a set of grid points P covering the area (i.e. the application area of the local coordinate system a) is taken0Projection transformation method using real parameters of local coordinate system (central meridian is L)1) Converting the coordinates of the grid points into an intermediate projection coordinate system A1, which is marked as P1(ii) a While using projective relations or parametric transformation relations to transform P0Conversion to the target coordinate system B, denoted PB0；
Step 14: by P0And P1Calculating the conversion parameter between the local coordinate system and the intermediate projection coordinate system A1 (seeThe number calculation basis can be three parameters, four parameters, affine transformation, etc.); in the example of four-parameter transformation, the transformation parameters between the local coordinate system a and the intermediate projection coordinate system a1 include two offsets (Δ x, Δ y), a rotation angle (α), and a scale factor (m);
step 15: p is converted by using the four parameters obtained in step 140Converting to the intermediate projection coordinate system A1, and converting the coordinates to the target coordinate system B by using the projection relation or parameter conversion relation between the intermediate projection coordinate system A1 and the target coordinate system B to obtain PB1；
Step 16: comparison PB0And PB1The error between the two-dimensional data of the two-dimensional data,
when P is presentB0And PB1The maximum error between the x coordinate and the y coordinate (i.e. the difference between the two sets of corresponding pairs of coordinates) meets the precision requirement (usually less than 1mm), the reference ellipsoid E1 obtained in step 12 is the expansion ellipsoid used in the next step, and the intermediate projection coordinate system obtained in step 13 is the intermediate projection coordinate system a 1;
when P is presentB0And PB1If the maximum error between the x coordinate and the y coordinate does not meet the precision requirement, repeating the steps 12 to 16 until PB0And PB1The maximum error between the x coordinate and the y coordinate meets the precision requirement.
In the above technical solution, in step 14, the conversion parameters between the local coordinate system a and the intermediate projection coordinate system a1 include three parameters, four parameters, affine transformation, and the like.
In the above technical solution, in the second step, the coordinates are converted to the intermediate projection coordinate system a1 by using the four parameters between the local coordinate system a and the intermediate projection coordinate system a1 acquired in the step 14, and the coordinates (x) in the intermediate projection coordinate system can be calculated by the following formula (1) by taking the four parameters as an example1,y1)，
In the above formula (1), x1,y1For the middle projectionCoordinates under the coordinate system a 1;
m, alpha, delta x and delta y are four conversion parameters; wherein Δ x is the x-axis offset; Δ y is the y-axis offset; alpha is a rotation angle; m is a scale factor;
and x and y are coordinates of a local coordinate system A.
In the above technical solution, in step three, the coordinates are converted to the target coordinate system B by using the projection relationship or the parameter conversion relationship between the intermediate projection coordinate system a1 and the target coordinate system B, which specifically includes the following steps:
step 31: since the expansion ellipsoid E1 is close to the reference ellipsoid of the local coordinate system A, when the target coordinate system B and the local coordinate system A adopt the same ellipsoid, the step 32 is performed; when the target coordinate system B and the local coordinate system A adopt different ellipsoids, the step 33 is executed;
step 32: and performing projection transformation by using the projection parameters of the intermediate projection coordinate system A1 and the projection parameters of the target coordinate system B to obtain the coordinates under the target coordinate system B, so that the whole conversion process is completed.
Step 33: firstly, the conversion relation between the plane coordinate systems established by taking the ellipsoids corresponding to the local coordinate system A and the target coordinate system B as reference ellipsoids is confirmed, and the plane coordinate system A of the local coordinate system A and the reference ellipsoid is recordedSAnd the plane coordinate system B of the reference ellipsoid and the target coordinate system BS(ii) a Converting the coordinates under the intermediate projection coordinate system A1 into A through projection transformationS；
Step 34: a is converted by the conversion relation mentioned in step 33SIs converted into a planar coordinate system BS；
Step 35: will be a plane coordinate system BSThe coordinates of the target coordinate system B are converted into a target coordinate system B by utilizing projection transformation;
so far, the whole conversion process is completed.
In the above technical solution, when the projection parameters of the target coordinate system B are the same as the secret, a middle projection coordinate system B1 may be established as a transition coordinate system in the same processing manner as the local coordinate system a, so that no secret parameters are involved in the conversion process.
The invention determines an intermediate projection coordinate system A1 which can lead the final conversion result to accord with the precision requirement by determining the reference ellipsoid of the changed intermediate projection coordinate system, namely, the transition coordinate system A1 can obtain the target result by utilizing the projection relation or the parameter conversion relation.
The invention has the following advantages:
the invention is applied to the conversion between a local coordinate system with confidential projection parameters and an arbitrary plane coordinate system, and the core of the invention lies in that a transition coordinate system (namely a middle projection coordinate system) is determined by changing a reference ellipsoid, thereby avoiding using the real projection parameters of the local coordinate system when the local independent coordinate system with confidential projection parameters is converted with any plane coordinate system, and simultaneously ensuring that the conversion precision meets the tolerance requirement, thereby realizing the confidentiality of the parameters of the local coordinate system in the coordinate conversion process.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail with reference to the accompanying drawings, which are not intended to limit the present invention, but are merely exemplary. While the advantages of the invention will be clear and readily understood by the description.
In order to promote the use of a newly established local coordinate system, data under the existing coordinate system and the newly established coordinate system need to be converted, but the parameter confidentiality problem of the local coordinate system needs to be considered, so that the invention establishes an intermediate transition coordinate system by using an expansion ellipsoid as transition, and provides a method for encrypting the conversion parameters of the local coordinate system and an arbitrary plane coordinate system.
The invention uses the expansion ellipsoid as the reference ellipsoid of the intermediate transition coordinate system, establishes an intermediate projection coordinate system A1 of which the central meridian is in a transition through deviation, converts the coordinate of the local coordinate system to the coordinate system A1 by a parameter method, and then converts the parameter of the transition coordinate system A1 to the target coordinate system B, thereby realizing the confidentiality of the local coordinate system parameter in the coordinate conversion process and simultaneously ensuring that the conversion precision meets the tolerance requirement.
Examples
The present invention will be described in detail with reference to an embodiment of the present invention, which is intended to be used for the conversion between an independent coordinate system a and a coordinate system B, and the present invention is also used for the conversion between an independent coordinate system and an arbitrary plane coordinate system in other parameter privacy areas.
In this embodiment, the CGCS2000 performs transformation between a coordinate system B (i.e., a target coordinate system) and a local coordinate system a (a central meridian is 117.55 °, a north offset is 0, and an east offset is 500km) of the gaussian krugger projection in a 117-degree band (hereinafter, x is a meridian direction).
As shown in fig. 1, the conversion method of the present embodiment specifically includes the following steps:
the method comprises the following steps: firstly, a batch of grid points including the whole Beijing city are taken and projected to a local coordinate system A and a coordinate system B respectively for precision inspection.
Secondly, determining an intermediate projection coordinate system A1;
the determination method of the intermediate projection coordinate system A1 comprises the following steps:
step 11: the central meridian L of the local coordinate system A0The offset of 0.3' results in the central meridian L of the intermediate projection coordinate system A11；
Step 12: selecting a reference ellipsoid of a local coordinate system A as a basis, and taking a major semi-axis a of the reference ellipsoid of the local coordinate system A0And flat ratio f0In this embodiment, the expansion ellipsoid E1 is obtained by adding an additional constant to the semimajor axis, and the semimajor axis of the expansion ellipsoid E1 is a1Flat rate of f1(the ellipsoid parameters are listed in table 1);
step 13: taking a set of grid points P covering the application area of the local coordinate system A0A method of projection transformation using the real parameters of the local coordinate system A (the central meridian is L)1) Converting the coordinates of the grid points into an intermediate projection coordinate system A1, which is marked as P1(ii) a Meanwhile, P is converted by using a projection conversion band (the projection conversion band is a specific use mode of projection relation)0Conversion to the target coordinate system B, denoted PB0；
Step 14: by P0And P1Calculating conversion parameters between a local coordinate system A and an intermediate projection coordinate system A1; in the embodiment, planar four-parameter conversion is adopted, and conversion parameters between the local coordinate system A and the intermediate projection coordinate system A1 comprise two offsets (Δ x, Δ y), a rotation angle (α) and a scale factor (m);
step 15: p is converted by using the four parameters obtained in step 140Converting to the intermediate projection coordinate system A1, and then converting the coordinates to the target coordinate system B by using the projection relation between the intermediate projection coordinate system A1 and the target coordinate system B to obtain PB1；
Step 16: comparison PB0And PB1The error between the two-dimensional data of the two-dimensional data,
in this example, PB0And PB1The maximum error between the x coordinate and the y coordinate (the difference between the x coordinate and the y coordinate between the two sets of coordinate corresponding points) satisfies the accuracy requirement (the error is less than 1mm), so the reference ellipsoid E1 obtained in step 12 of this embodiment is the expansion ellipsoid used in the following step, and the intermediate projection coordinate system obtained in step 13 is the intermediate projection coordinate system a 1;
the intermediate projection coordinate system a1 determined in this example is shown in table 1 below:
table 1 determined intermediate projection coordinate system a1
Step two: converting the coordinates to an intermediate projected coordinate system a1 using four parameters between the local coordinate system a and the intermediate projected coordinate system a 1; the four parameters of the conversion between the local coordinate system and the intermediate projection coordinate system a1 calculated in step 14 of this embodiment are shown in table 2 below:
TABLE 2 conversion of four parameters
Converting the coordinates to an intermediate projection coordinate system A1 by using the four parameters between the local coordinate system A and the intermediate projection coordinate system A1 acquired in the step 14; the coordinates (x) in the intermediate projection coordinate system are calculated by the following formula (1)1,y1)，
In the above formula (1), x1,y1Coordinates under the intermediate projection coordinate system a 1;
m, alpha, delta x and delta y are four conversion parameters; wherein Δ x is the x-axis offset; Δ y is the y-axis offset; alpha is a rotation angle; m is a scale factor;
and x and y are coordinates of a local coordinate system A.
Step three: converting the coordinates to a target coordinate system B by using a projection relation or a parameter conversion relation between the intermediate projection coordinate system A1 and the target coordinate system B, which specifically comprises the following steps:
step 31: since the local coordinate system a in this embodiment is consistent with the reference ellipsoid of the target coordinate system B, step 32 is entered;
step 32: the projection parameters of the intermediate projection coordinate system a1 and the conversion parameters of the target coordinate system B are used for transformation to obtain the coordinates of the target coordinate system B of the present embodiment, so as to complete the conversion of the parameters of the non-local coordinate system of the independent local coordinate system a and the coordinate system B of the present embodiment.
The invention obtains an intermediate transition coordinate system (i.e. an intermediate projection coordinate system) by performing gaussian projection transformation under an expansion ellipsoid, and aims to make the conversion result passing through the intermediate coordinate system meet the precision requirement (as shown in fig. 1).
And (4) conclusion: the parameters of the local coordinate system are only used for determining the intermediate projection coordinate system A1 as the transition coordinate system, and the embodiment does not need to use the real parameters of the local coordinate system in the conversion process, thereby realizing the secrecy of the parameters of the local coordinate system in the coordinate conversion process.
And (3) verification: now, the precision verification is performed on the conversion method of the embodiment, which specifically includes the following steps:
the above conversion process is performed and the precision is verified, the coordinates obtained by the coordinate of the local coordinate system through direct projection conversion of real parameters are compared with the coordinate result obtained through the process conversion of the embodiment, the difference value is used as the precision judgment index, and the result is shown in the following table:
TABLE 3 conversion accuracy
And (4) conclusion: it can be seen from the above table that the present invention satisfies the precision requirement while ensuring the security of the parameters (the precision requirement of the coordinate system conversion is determined according to the practical application, in this embodiment, the error of the conversion precision requirement of X, Y directions of the independent local coordinate system a and the target coordinate system B is less than 1 mm).
Other parts not described belong to the prior art.
Claims (5)
1. A method for encrypting conversion parameters of a terrestrial coordinate system and an arbitrary plane coordinate system is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: determining an intermediate projection coordinate system a 1;
determining an intermediate projection coordinate system a 1;
step two: converting the coordinates to an intermediate projection coordinate system A1 by using conversion parameters between the local coordinate system A and the intermediate projection coordinate system A1;
step three: the coordinates are converted to the target coordinate system B using a projection relationship or a parameter conversion relationship between the intermediate projection coordinate system a1 and the target coordinate system B.
2. The method for encrypting the conversion parameters between the earth coordinate system and the arbitrary plane coordinate system according to claim 1, wherein: in step one, the method for determining the intermediate projection coordinate system a1 includes the following steps:
step 11: the central meridian L of the local coordinate system A0Adding an offset to obtain the central meridian L of the intermediate projection coordinate system A11；
Step 12: based on the reference ellipsoid of the local coordinate system A, the major semi-axis a is taken0And flat ratio f0The minor semiaxis of which is a and/or the minor oblateness of which is trimmed to obtain an expansion ellipsoid E11Flat rate of f1；
Step 13: taking a set of grid points P covering the application area of the local coordinate system A0Converting the grid point coordinates into a middle projection coordinate system A1, which is marked as P, by using the real projection parameters of the local coordinate system A and using a projection transformation method1(ii) a While using projective relations or parametric transformation relations to transform P0Conversion to the target coordinate system B, denoted PB0；
Step 14: by P0And P1Calculating conversion parameters between a local coordinate system A and an intermediate projection coordinate system A1;
step 15: p is converted by using the conversion parameters obtained in step 140Converting to the intermediate projection coordinate system A1, and converting the coordinates to the target coordinate system B by using the projection relation or parameter conversion relation between the intermediate projection coordinate system A1 and the target coordinate system B to obtain PB1；
Step 16: comparison PB0And PB1The error between the two-dimensional data of the two-dimensional data,
when P is presentB0And PB1The maximum error between the x coordinate and the y coordinate meets the accuracy requirement of the related transformation, the reference ellipsoid E1 obtained in the step 12 is an expansion ellipsoid adopted in the following step, and the intermediate projection coordinate system obtained in the step 13 is an intermediate projection coordinate system A1;
when P is presentB0And PB1If the maximum error between the x coordinate and the y coordinate does not meet the precision requirement, repeating the steps 12 to 16 until PB0And PB1The maximum error between the x coordinate and the y coordinate meets the precision requirement.
3. The method for encrypting the conversion parameters between the earth coordinate system and the arbitrary plane coordinate system according to claim 2, wherein: in the second step, the coordinates are converted into an intermediate projection coordinate system A1 by using the parameter conversion relation between the local coordinate system A and the intermediate projection coordinate system A1 acquired in the step 14;
in step 14, the transformation parameters between the local coordinate system a and the intermediate projection coordinate system a1 include three-parameter, four-parameter, affine transformations.
4. The method for encrypting the conversion parameters between the earth coordinate system and the arbitrary plane coordinate system according to claim 3, wherein: in step three, the coordinates are converted to the target coordinate system B by using the projection relationship or the parameter conversion relationship between the intermediate projection coordinate system a1 and the target coordinate system B, which specifically includes the following steps:
step 31: since the expansion ellipsoid E1 is close to the reference ellipsoid of the local coordinate system A, when the target coordinate system B and the local coordinate system A adopt the same ellipsoid, the step 32 is performed; when the target coordinate system B and the local coordinate system A adopt different ellipsoids, the step 33 is executed;
step 32: carrying out projection transformation by using the projection parameters of the middle projection coordinate system A1 and the projection parameters of the target coordinate system B to obtain the coordinates under the target coordinate system B, and thus, completing the whole conversion process;
step 33: firstly, the conversion relation between the plane coordinate systems established by taking the ellipsoids corresponding to the local coordinate system A and the target coordinate system B as reference ellipsoids is confirmed, and the plane coordinate system A of the local coordinate system A and the reference ellipsoid is recordedSAnd the plane coordinate system B of the reference ellipsoid and the target coordinate system BS(ii) a Converting the coordinates under the intermediate projection coordinate system A1 into A through projection transformationS；
Step 34: a is converted by the conversion relation mentioned in step 33SIs converted into a planar coordinate system BS；
Step 35: will be a plane coordinate system BSThe coordinates of the target coordinate system B are converted into a target coordinate system B by utilizing projection transformation;
so far, the whole conversion process is completed.
5. The method for encrypting the conversion parameters between the earth coordinate system and the arbitrary plane coordinate system according to claim 4, wherein: when the system establishing parameters of the target coordinate system B are also secret-related, an intermediate projection coordinate system B1 is established as an intermediate transition coordinate system in the same processing mode as the local coordinate system A, so that secret-related parameters are not involved in the conversion process.
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