Parametric coordinate transformation method based on residual weighted compensation

Abstract

This invention relates to the field of spatial data processing technology, specifically to a parametric coordinate transformation method based on residual weighted compensation. S1: Determine common points in the source coordinate system; each point has coordinates in the target coordinate system. S2: Use the coordinates of the common points to determine the values ​​of the final transformation parameters in the transformation formula. S3: Calculate the difference between the transformed coordinates of the common points and the coordinates of the common points in the target coordinate system based on the calculated final transformation parameters. S4: Calculate the weighting coefficients between the points to be transformed and the common points in the source coordinate system. Obtain the compensation amount by weighted averaging based on the residuals and weighting coefficients. Use this compensation amount to compensate the points to be transformed in the source coordinate system, obtaining the compensated intermediate coordinates. S5: Substitute the compensated intermediate coordinates into the transformation formula to obtain the final transformed coordinates. This invention's compensation mechanism can adapt to different terrains and Earth curvature conditions, exhibiting good universality and effectively correcting coordinate errors.

Description

Technical Field

[0001] This invention relates to the field of spatial data processing technology, specifically to a parametric coordinate transformation method based on residual weighted compensation. Background Technology

[0002] With the widespread use of Geographic Information Systems (GIS) and Global Positioning Systems (GPS), the transformation between different coordinate systems has become particularly important. Traditional coordinate transformation methods, such as four-parameter and seven-parameter transformations, are mainly used to solve the problem of benchmark transformation between different coordinate systems. The four-parameter transformation is suitable for small-scale coordinate system transformations in local areas, while the seven-parameter transformation is suitable for a wider range of coordinate system transformations, including transformations in three-dimensional space. However, when dealing with large-scale or complex terrain areas, these traditional methods may be affected by errors introduced by factors such as the curvature of the Earth and topographic relief, thus affecting the transformation accuracy. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a parametric coordinate transformation method based on residual weighted compensation, which can reduce coordinate transformation error and improve transformation accuracy.

[0004] The technical solution adopted by this invention to solve its technical problem is a parametric coordinate transformation method based on residual weighted compensation, which includes the following steps:

[0005] S1: Determine at least two common points in the source coordinate system, each of which has coordinates in the target coordinate system.

[0006] S2: Using the coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; optimize using the least squares method to obtain the values ​​of the final transformation parameters;

[0007] S3: Calculate the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system based on the obtained final transformation parameters;

[0008] S4: Calculate the weight coefficients between the point to be transformed in the source coordinate system and the common points of each source coordinate system; calculate the compensation amount, and obtain the compensation amount by weighted averaging based on the residuals corresponding to the common points of each source coordinate system and the weight coefficients; use the compensation amount to compensate the coordinate points to be transformed in the source coordinate system to obtain the compensated intermediate coordinates.

[0009] S5: Substitute the compensated intermediate coordinates into the transformation formula to obtain the final transformed coordinates;

[0010] S6: Repeat steps S4 and S5 until all coordinate points to be transformed in the source coordinate system have been transformed.

[0011] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x...i y i The coordinates of the common point in the target coordinate system are (X... i Y i ), i = (1, 2, ..., n), where n is an integer ≥ 2;

[0012] The transformation formula mentioned in step S2 is a four-parameter transformation formula.

[0013]

[0014] The initial transformation parameter a is obtained through the four-parameter transformation formula. j ,b j ,c j ,d j The set; the final transformation parameters a, b, c, d are obtained by weighted averaging; where

[0015] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. i ,Δy i ;

[0016]

[0017] In step S4, the weighting coefficient w i The calculation formula is as follows:

[0018]

[0019] Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. i ,y i The coordinates of the common points of the source coordinate system;

[0020] Compensation amount v x v y The calculation formula is as follows:

[0021]

[0022] Where n is an integer ≥ 2;

[0023] Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0024]

[0025] Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation;

[0026] The transformation formula in step S5 is as follows:

[0027]

[0028] Among them, X t Y t These are the final coordinates.

[0029] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x... r y r The coordinates of the common point in the target coordinate system are (X... r Y r r = (1, 2, ..., n), where n is an integer ≥ 3;

[0030] The transformation formula described in step S2 is a six-parameter transformation formula:

[0031]

[0032] The initial transformation parameter e is obtained through the six-parameter transformation formula. q f q α q ,β q g q h q The set; the final transformation parameters e, f, α, β, g, h are obtained through least squares optimization; where

[0033] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. r ,Δy r

[0034]

[0035] Δx r =X r -X f

[0036] Δy r =Y r -Y f

[0037] In step S4, the weighting coefficient w rThe calculation formula is as follows:

[0038]

[0039] Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. r ,y r The coordinates of the common points of the source coordinate system;

[0040] Compensation amount v x v y The calculation formula is as follows:

[0041]

[0042] Where n is an integer ≥ 3;

[0043] Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0044] x t =x s +v x

[0045] y t =y s +v y

[0046] Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation;

[0047] The transformation formula in step S5 is as follows:

[0048]

[0049] Among them, X t Y t These are the final coordinates.

[0050] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x... k y k , z k The coordinates of the common point in the target coordinate system are (X... k Y k Z k k = (1, 2, ..., n), where n is an integer ≥ 3;

[0051] The transformation formula described in step S2 is a seven-parameter transformation formula:

[0052]

[0053] The initial transformation parameter l is obtained through the seven-parameter transformation formula. k o k p k , t k u k δ k γ k The set of values; the final transformation parameters l, o, p, t, u, δ, γ are obtained through least squares optimization; where

[0054] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. k ,Δy k ,Δz k

[0055]

[0056] Δx k =X k -X f

[0057] Δy k =Y k -Y f

[0058] Δz k =Z k -Z f

[0059] In step S4, the weighting coefficient w k The calculation formula is as follows:

[0060]

[0061] Where: x s ,y s , z s , where x is the coordinate point to be transformed in the source coordinate system. k ,y k , z k The coordinates of the common points of the source coordinate system;

[0062] Compensation amount v x v y v z The calculation formula is as follows:

[0063]

[0064] Where n is an integer ≥ 3;

[0065] Using compensation amount v x v y v z The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0066] x t =x s +v x

[0067] y t =y s +v y

[0068] z t =z s +z y

[0069] Where: x s ,y s , z s , where x is the coordinate point to be transformed in the source coordinate system. t ,y t , z t The intermediate coordinates after compensation;

[0070] The transformation formula in step S5 is as follows:

[0071]

[0072] Among them, X t Y t Z t These are the final coordinates.

[0073] The beneficial effects of this invention are: it improves the accuracy of coordinate transformation in large-scale or complex terrain areas. Through comparison with actual cases, the error can be controlled within a smaller range after adopting the method of this invention, significantly improving the accuracy of coordinates.

[0074] The compensation mechanism is adaptable to different terrains and Earth curvature conditions, exhibiting good universality. Whether in plains, mountains, or hilly areas, and at different geographical latitudes, this method can effectively correct coordinate errors through residual analysis and adjustment of compensation parameters.

[0075] By introducing residuals and compensation amounts, the flexibility and accuracy of the coordinate transformation method are enhanced. In different application scenarios, appropriate compensation amounts can be dynamically determined based on the actual terrain and data characteristics, making the coordinate transformation results more consistent with practical needs. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating the present invention; Detailed Implementation

[0077] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0078] like Figure 1 As shown, the parametric coordinate transformation method based on residual weighted compensation of the present invention includes the following steps:

[0079] S1: Determine at least two common points in the source coordinate system, each of which has coordinates in the target coordinate system;

[0080] Common points in the source coordinate system and common points in the target coordinate system can be obtained through field measurements, extraction from existing map data, etc. For example, in a city planning project, at least three locations with obvious landmarks (such as the corners of large buildings, city control points, etc.) within the city are selected as selection points to ensure that the coordinates of these points in both the source coordinate system (such as the local city-independent coordinate system) and the target coordinate system (such as the national geodetic coordinate system) can be accurately obtained.

[0081] S2: Using the coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; optimize using the least squares method to obtain the values ​​of the final transformation parameters;

[0082] S3: Calculate the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system based on the final transformation parameters.

[0083] S4: Calculate the weight coefficients between the point to be transformed in the source coordinate system and the common points of each source coordinate system; calculate the compensation amount, and obtain the compensation amount by weighted averaging based on the residuals corresponding to the common points of each source coordinate system and the weight coefficients; use the compensation amount to compensate the coordinate points to be transformed in the source coordinate system to obtain the compensated intermediate coordinates.

[0084] S5: Substitute the compensated intermediate coordinates into the transformation formula to obtain the final transformed coordinates;

[0085] S6: Repeat steps S4 and S5 until all coordinate points to be transformed in the source coordinate system have been transformed.

[0086] In the process of converting from the local city-independent coordinate system to the national geodetic coordinate system, it is only necessary to measure a number of points in the national geodetic coordinate system that correspond to the initial points in the city-independent coordinate system. Then, the conversion of all points in the city-independent coordinate system to the national geodetic coordinate system can be achieved through this transformation method, thus improving the efficiency of the conversion.

[0087] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x... i y i The coordinates of the common point in the target coordinate system are (X... i Y i ), i = (1, 2, ..., n), where n is an integer ≥ 2; it should be noted that when using the four-parameter conversion formula, in actual use, at least 3 pairs of common points need to be found, that is, n is a positive integer greater than 2.

[0088] The transformation formula mentioned in step S2 is a four-parameter transformation formula.

[0089]

[0090] The initial transformation parameter a is obtained through the four-parameter transformation formula. j ,b j ,c j ,d j The set; the final transformation parameters a, b, c, d are obtained through least squares optimization; where

[0091] Initial transformation parameter a j ,b j ,c j ,d j There are a total of 4 unknowns. Using the set of two sets of common points, one set of initial transformation parameters can be obtained. Therefore, if there are n sets of common points, then the number of sets of initial transformation parameters, m, is... For example, if there are 3 sets of common points, then 15 sets of initial transformation parameters will be solved; if there are 4 sets of common points, then 70 sets of initial transformation parameters will be solved. The more sets of common points there are, the more sets of initial transformation parameters will be obtained, and the more accurate the final transformation parameters will be.

[0092] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. i ,Δy i ;

[0093]

[0094] In step S4, the weighting coefficient w i The calculation formula is as follows:

[0095]

[0096] Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. i ,y i The coordinates of the common points of the source coordinate system; the number of common points in the source coordinate system corresponds to the number of weight coefficients; the farther away from the common points of the source coordinate system, the smaller the weight coefficient, which means it has less impact on the subsequent compensation calculation results.

[0097] Compensation amount v x v y The calculation formula is as follows:

[0098]

[0099] Where n is an integer ≥ 2; the value of n is the same as the number of common points.

[0100] Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0101] x t =x s +v x

[0102] y t =y s +v y

[0103] Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation;

[0104] The transformation formula in step S5 is as follows:

[0105]

[0106] Among them, X t Y t The final coordinates are obtained. In the process of converting from the local city-independent coordinate system to the national geodetic coordinate system, it is only necessary to measure a number of points in the national geodetic coordinate system that correspond to the initial points in the city-independent coordinate system. Then, this transformation method can be used to convert all points in the city-independent coordinate system to the national geodetic coordinate system, thus improving the efficiency of the conversion.

[0107] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x... r y r The coordinates of the common point in the target coordinate system are (X... r Y r ), r = (1, 2, ..., n), where n is an integer ≥ 3; using the six-parameter conversion formula, in practical use, at least 4 pairs of common points are required, that is, n is an integer greater than 3.

[0108] Common points in the source coordinate system and common points in the target coordinate system can be obtained through field measurements, extraction from existing map data, etc. For example, in a city planning project, at least three locations with obvious landmarks (such as the corners of large buildings, city control points, etc.) within the city are selected as selection points to ensure that the coordinates of these points in both the source coordinate system (such as the local city-independent coordinate system) and the target coordinate system (such as the national geodetic coordinate system) can be accurately obtained.

[0109] The transformation formula described in step S2 is a six-parameter transformation formula:

[0110]

[0111] The initial transformation parameter e is obtained through the six-parameter transformation formula. q f q α q ,β q g q h q The set of values; the final transformation parameters e, f, α, β, g, h are obtained by weighted averaging; where

[0112] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. r ,Δy r

[0113]

[0114] Δx r =X r -X f

[0115] Δy r =Y r -Y f

[0116] In step S4, the weighting coefficient w r The calculation formula is as follows:

[0117]

[0118] Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. r ,y r The coordinates of the common points of the source coordinate system;

[0119] Compensation amount v x v y The calculation formula is as follows:

[0120]

[0121] Where n is an integer ≥3; here, the weight coefficients of the points to be transformed and the initial points in the source coordinate system are multiplied by the sum of the residuals of each initial point, and then divided by the sum of the weight coefficients of the points to be transformed and the initial points; after calculation, each initial point generates a compensation value, making the final compensation amount more accurate.

[0122] Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0123] x t =x s +v x

[0124] y t =y s +v y

[0125] Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation;

[0126] The transformation formula in step S5 is as follows:

[0127]

[0128] Among them, X t Y t These are the final coordinates.

[0129] In the process of converting from the local city-independent coordinate system to the national geodetic coordinate system, it is only necessary to measure a number of points in the national geodetic coordinate system that correspond to the initial points in the city-independent coordinate system. Then, the conversion of all points in the city-independent coordinate system to the national geodetic coordinate system can be achieved through this transformation method, thus improving the efficiency of the conversion.

[0130] Furthermore, in step S1, the coordinates of the common point of the source coordinate system are (x... k y k , z k The coordinates of the common point in the target coordinate system are (X... k Y k Z k k = (1, 2, ..., n), where n is an integer ≥ 3;

[0131] The transformation formula described in step S2 is a seven-parameter transformation formula:

[0132]

[0133] The initial transformation parameter l is obtained through the seven-parameter transformation formula. k o k p k , t k u k δ k γ k The set of values; the final transformation parameters l, o, p, t, u, δ, γ are obtained through least squares optimization; where

[0134] In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. k ,Δy k ,Δz k

[0135]

[0136] Δx k =X k -X f

[0137] Δy k =Y k -Y f

[0138] Δz k =Z k -Z f

[0139] In step S4, the weighting coefficient w k The calculation formula is as follows:

[0140]

[0141] Where: x s ,ys , z s , where x is the coordinate point to be transformed in the source coordinate system. k ,y k , z k The coordinates of the common points of the source coordinate system;

[0142] Compensation amount v x v y v z The calculation formula is as follows:

[0143]

[0144] Where n is an integer ≥3; here, the weight coefficients of the points to be transformed and the initial points in the source coordinate system are multiplied by the sum of the residuals of each initial point, and then divided by the sum of the weight coefficients of the points to be transformed and the initial points; after calculation, each initial point generates a compensation value, making the final compensation amount more accurate.

[0145] Using compensation amount v x v y v z The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates:

[0146] x t =x s +v x

[0147] y t =y s +v y

[0148] z t =z s +z y

[0149] Where: x s ,y s , z s , where x is the coordinate point to be transformed in the source coordinate system. t ,y t , z t The intermediate coordinates after compensation;

[0150] The transformation formula in step S5 is as follows:

[0151]

[0152] Among them, X t Y t Z t These are the final coordinates.

[0153] The embodiments described herein are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape, and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A parametric coordinate transformation method based on residual weighted compensation, characterized in that, Includes the following steps: S1: Determine at least two common points in the source coordinate system, each of which has coordinates in the target coordinate system. S2: Using the coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; optimize using the least squares method to obtain the values ​​of the final transformation parameters; S3: Calculate the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system based on the final transformation parameters. S4: Calculate the weighting coefficients between the points to be transformed in the source coordinate system and the common points of each source coordinate system; The compensation amount is calculated by weighting the residuals corresponding to the common points of each source coordinate system and the weighting coefficients to obtain the compensation amount. The compensation amount is then used to compensate the coordinate points to be transformed in the source coordinate system to obtain the compensated intermediate coordinates. S5: Substitute the compensated intermediate coordinates into the transformation formula to obtain the final transformed coordinates; S6: Repeat steps S4 and S5 until all coordinate points to be transformed in the source coordinate system have been transformed.

2. The parametric coordinate transformation method based on residual weighted compensation as described in claim 1, characterized in that: In step S1, the coordinates of the common point of the source coordinate system are (x i y i The coordinates of the common point in the target coordinate system are (X... i Y i ), i = (1, 2, ..., n), where n is an integer ≥ 2; The transformation formula mentioned in step S2 is a four-parameter transformation formula. The initial transformation parameter a is obtained through the four-parameter transformation formula. j ,b j ,c j ,d j The set of values; the final transformation parameters a, b, c, d are obtained through least squares optimization; where j = (1, 2, ..., m). In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. i ,Δy i ; In step S4, the weighting coefficient w i The calculation formula is as follows: Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. i ,y i The coordinates of the common points of the source coordinate system; Compensation amount v x v y The calculation formula is as follows: Where n is an integer ≥ 2; Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates: x t =x s +v x and t / and s +v y Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation; The transformation formula in step S5 is as follows: Among them, X t Y t These are the final coordinates.

3. The parametric coordinate transformation method based on residual weighted compensation as described in claim 1, characterized in that: In step S1, the coordinates of the common point of the source coordinate system are (x r y r The coordinates of the common point in the target coordinate system are (X... r Y r r = (1, 2, ..., n), where n is an integer ≥ 3; The transformation formula described in step S2 is a six-parameter transformation formula: The initial transformation parameter e is obtained through the six-parameter transformation formula. q f q α q ,β q g q h q The set of values; the final transformation parameters e, f, α, β, g, h are obtained through least squares optimization; where q = (1, 2, ..., m). In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. r ,Δy r Δx r =X r -X f Dy r = Y r -Y f In step S4, the weighting coefficient w r The calculation formula is as follows: Where: x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. r ,y r The coordinates of the common points of the source coordinate system; Compensation amount v x v y The calculation formula is as follows: Where n is an integer ≥ 3; Using compensation amount v x v y The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates: x t =x s +v x and t / and s +v y Where, x s ,y s Let x be the coordinate point to be transformed in the source coordinate system. t ,y t The intermediate coordinates after compensation; The transformation formula in step S5 is as follows: Among them, X t Y t These are the final coordinates.

4. The parametric coordinate transformation method based on residual weighted compensation as described in claim 1, characterized in that: In step S1, the coordinates of the common point of the source coordinate system are (x k y k , z k The coordinates of the common point in the target coordinate system are (X... k , Y k Z k k = (1, 2, ..., n), where n is an integer ≥ 3; The transformation formula described in step S2 is a seven-parameter transformation formula: The initial transformation parameter l is obtained through the seven-parameter transformation formula. k o k p k , t k u k δ k γ k The set of values; the final transformation parameters l, o, p, t, u, δ, γ are obtained through least squares optimization; where k = (1, 2, ..., m). In step S3, the difference between the coordinates of the common points in the transformed coordinate system and the coordinates of the common points in the target coordinate system is calculated based on the obtained final transformation parameters. That is, the residual corresponding to the common point of each source coordinate system is Δx. k ,Δy k ,Δz k Δx k =X k -X f Dy k = Y k -Y f Δz k =Z k -Z f In step S4, the weighting coefficient w k The calculation formula is as follows: Where: x s ,y s , z s , where x is the coordinate point to be transformed in the source coordinate system. k ,y k , z k The coordinates of the common points of the source coordinate system; Compensation amount v x v y v z The calculation formula is as follows: Where n is an integer ≥ 3; Using compensation amount v x v y v z The coordinates of the points to be transformed in the source coordinate system are compensated to obtain the compensated intermediate coordinates: x t =x s +v x and t / and s +v y With t =z s +with y Where: x s ,y s , z s , where x is the coordinate point to be transformed in the source coordinate system. t ,y t , z t The intermediate coordinates after compensation; The transformation formula in step S5 is as follows: Among them, X t Y t Z t These are the final coordinates.

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