Parameter coordinate transformation method based on residual weighted compensation

Abstract

The invention relates to the technical field of spatial data processing, in particular to a parameter coordinate transformation method based on residual weighted compensation. The method comprises the following steps: S1, determining common points in a source coordinate system, wherein each point has coordinates in a target coordinate system; s2, determining the value of a final transformation parameter in a transformation formula by using the coordinates corresponding to the common points; s3, calculating a difference value between the transformed common point coordinate and the common point coordinate of the target coordinate system according to the obtained final transformation parameter; s4, calculating a weight coefficient between the point to be converted and the common point in the source coordinate system, obtaining a compensation amount through weighted average according to the residual error and the weight coefficient, and compensating the coordinate point to be converted in the source coordinate system by using the compensation amount to obtain a compensated intermediate coordinate; s5, substituting the compensated middle coordinate into a transformation formula to obtain a transformed final coordinate; according to the invention, the compensation mechanism can adapt to different terrain and earth curvature conditions, has good universality, and effectively corrects coordinate errors.

Description

Technical Field

[0001] The present invention relates to the technical field of spatial data processing, and in particular to a parameter coordinate transformation method based on residual weighted compensation. Background Art

[0002] With the widespread use of geographic information systems (GIS) and global positioning systems (GPS), conversion 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 datum conversion between different coordinate systems. The four-parameter transformation is suitable for small-scale coordinate system conversions in local areas, while the seven-parameter transformation is applicable to a wider range of coordinate system conversions, including conversions in three-dimensional space. However, when these traditional methods are used to process large areas or complex terrain, errors introduced by factors such as the curvature of the earth and terrain undulations may affect the conversion accuracy. Summary of the Invention

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

[0004] The technical solution adopted by the present invention to solve the technical problem is a parameter 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 corresponding coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; and obtain the final transformation parameter values through least squares optimization.

[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 according to the final transformation parameters obtained;

[0008] S4: Calculate the weight coefficient between the point to be converted in the source coordinate system and the common point of each source coordinate system; calculate the compensation amount, and obtain the compensation amount by weighted average according to the residual corresponding to the common point of each source coordinate system and the weight coefficient; compensate the coordinate point to be converted in the source coordinate system using the compensation amount to obtain the compensated intermediate coordinate;

[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 converted in the source coordinate system are converted.

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

[0012] In step S2, the transformation formula is a four-parameter transformation formula.

[0013]

[0014] The initial transformation parameter a is obtained by the four-parameter conversion formula j ,b j ,c j ,d j The final transformation parameters a, b, c, d are obtained by weighted average;

[0015] In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w i The calculation formula is as follows:

[0018]

[0019] Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x i ,y i is the common point coordinate of the source coordinate system;

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

[0021]

[0022] Wherein, n is an integer ≥ 2;

[0023] Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[0024]

[0025] Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation;

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

[0027]

[0028] Among them, X t , Y t is the final coordinate.

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

[0030] In step S2, the transformation formula is a six-parameter transformation formula:

[0031]

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

[0033] In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w rThe calculation formula is as follows:

[0038]

[0039] Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x r ,y r is the common point coordinate of the source coordinate system;

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

[0041]

[0042] Wherein, n is an integer ≥ 3;

[0043] Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[0044] x t =x s +v x

[0045] y t =y s +v y

[0046] Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation;

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

[0048]

[0049] Among them, X t , Y t is the final coordinate.

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

[0051] In step S2, the transformation formula is a seven-parameter transformation formula:

[0052]

[0053] The initial transformation parameter l is obtained by the seven-parameter conversion formula k , o k , p k , t k ,u k , δ k , γ k The final transformation parameters l, o, p, t, u, δ, γ are obtained by least squares optimization;

[0054] In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w k The calculation formula is as follows:

[0060]

[0061] Where: x s ,y s , z s , is the coordinate point to be converted in the source coordinate system, x k ,y k , z k is the common point coordinate of the source coordinate system;

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

[0063]

[0064] Wherein, n is an integer ≥ 3;

[0065] Using compensation v x , v y , v z Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[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 , is the coordinate point to be converted in the source coordinate system, x t ,y t , z t is the middle coordinate after compensation;

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

[0071]

[0072] Among them, X t , Y t , Z t is the final coordinate.

[0073] The beneficial effect of the present invention is to improve the accuracy of coordinate transformation in large areas or complex terrain areas. Through actual case comparison, after adopting the method of the present invention, the error can be controlled within a smaller range, significantly improving the accuracy of coordinates.

[0074] The compensation mechanism is adaptable to varying terrain and Earth curvature conditions, demonstrating good universality. Whether in plains, mountainous areas, or hilly regions, or at varying geographic latitudes, this method can effectively correct coordinate errors by analyzing residuals and adjusting compensation parameters.

[0075] The introduction of residuals and compensation enhances the flexibility and accuracy of the coordinate transformation method. In different application scenarios, the appropriate compensation can be dynamically determined based on the actual terrain and data characteristics, making the coordinate transformation results more in line with actual needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a schematic flow diagram of the present invention; DETAILED DESCRIPTION

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

[0078] like Figure 1 As shown, the parameter 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] The common points of the source coordinate system and the target coordinate system can be obtained through field measurements, extraction of existing map data, etc. For example, in a certain urban planning project, at least three locations with obvious geographical features (such as corners of large buildings, urban control points, etc.) in 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 corresponding coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; and obtain the final transformation parameter values through least squares optimization.

[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 according to the final transformation parameters obtained;

[0083] S4: Calculate the weight coefficient between the point to be converted in the source coordinate system and the common point of each source coordinate system; calculate the compensation amount, and obtain the compensation amount by weighted average according to the residual corresponding to the common point of each source coordinate system and the weight coefficient; compensate the coordinate point to be converted in the source coordinate system using the compensation amount to obtain the compensated intermediate coordinate;

[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 converted in the source coordinate system are converted.

[0086] In the process of converting the local city independent coordinate system to the national geodetic coordinate system, it is only necessary to measure several points corresponding to the initial points in the city independent coordinate system in the national geodetic coordinate system, and then use this transformation method to realize the conversion of the points in the entire city independent coordinate system to the national geodetic coordinate system, thereby improving the efficiency of the conversion.

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

[0088] In step S2, the transformation formula is a four-parameter transformation formula.

[0089]

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

[0091] Initial transformation parameter a j ,b j ,c j ,d j There are 4 unknowns in total. Using two sets of common points, we can find a set of initial transformation parameters. Therefore, if there are n sets of common points, the number of sets of initial transformation parameters m is For example, if there are 3 groups of common points, then 15 groups of initial transformation parameters will be solved; if there are 4 groups of common points, then 70 groups of initial transformation parameters will be solved; the more groups of common points there are, the more groups 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 point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w i The calculation formula is as follows:

[0095]

[0096] Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x i ,y i is the coordinate of the common point of the source coordinate system; the number of common points in the source coordinate system is the number of weight coefficients; the farther away from the common point of the source coordinate system, the smaller the weight coefficient, that is, the smaller the impact on the subsequent compensation calculation results.

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

[0098]

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

[0100] Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[0101] x t =x s +v x

[0102] y t =y s +v y

[0103] Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation;

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

[0105]

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

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

[0108] The common points of the source coordinate system and the target coordinate system can be obtained through field measurements, extraction of existing map data, etc. For example, in a certain urban planning project, at least three locations with obvious geographical features (such as corners of large buildings, urban control points, etc.) in 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] In step S2, the transformation formula is a six-parameter transformation formula:

[0110]

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

[0112] In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w r The calculation formula is as follows:

[0117]

[0118] Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x r ,y r is the common point coordinate 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 coefficient of the point to be converted and the initial point in the source coordinate system is multiplied by the sum of the residuals of each initial point, and then divided by the sum of the weight coefficients of the point to be converted and each initial point. After calculation, a compensation value is generated for each initial point, making the final compensation amount more accurate.

[0122] Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[0123] x t =x s +v x

[0124] y t =y s +v y

[0125] Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation;

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

[0127]

[0128] Among them, X t , Y t is the final coordinate.

[0129] In the process of converting the local city independent coordinate system to the national geodetic coordinate system, it is only necessary to measure several points corresponding to the initial points in the city independent coordinate system in the national geodetic coordinate system, and then use this transformation method to realize the conversion of the points in the entire city independent coordinate system to the national geodetic coordinate system, thereby improving the efficiency of the conversion.

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

[0131] In step S2, the transformation formula is a seven-parameter transformation formula:

[0132]

[0133] The initial transformation parameter l is obtained by the seven-parameter conversion formula k , o k , p k , t k ,u k , δ k , γ k The final transformation parameters l, o, p, t, u, δ, γ are obtained by least squares optimization;

[0134] In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w k The calculation formula is as follows:

[0140]

[0141] Where: x s ,ys , z s , is the coordinate point to be converted in the source coordinate system, x k ,y k , z k is the common point coordinate 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 coefficient of the point to be converted and the initial point in the source coordinate system is multiplied by the sum of the residuals of each initial point, and then divided by the sum of the weight coefficients of the point to be converted and each initial point. After calculation, a compensation value is generated for each initial point, making the final compensation amount more accurate.

[0145] Using compensation v x , v y , v z Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are:

[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 , is the coordinate point to be converted in the source coordinate system, x t ,y t , z t is the middle coordinate after compensation;

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

[0151]

[0152] Among them, X t , Y t , Z t is the final coordinate.

[0153] The embodiments of this specific implementation method are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, any equivalent changes made based on the structure, shape, and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A parameter coordinate transformation method based on residual weighted compensation, characterized in that: The steps include: 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 corresponding coordinates of the common points, determine the set of initial transformation parameters in the transformation formula; and obtain the final transformation parameter values through least squares optimization. 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 according to the final transformation parameters obtained; S4: Calculating the weight coefficient between the point to be transformed in the source coordinate system and the common point of each source coordinate system; Calculate the compensation amount, and obtain the compensation amount by weighted average based on the residual corresponding to the common point of each source coordinate system and the weight coefficient; use the compensation amount to compensate the coordinate point to be converted in the source coordinate system to obtain the compensated intermediate coordinate; 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 converted in the source coordinate system are converted.

2. The parameter coordinate transformation method based on residual weighted compensation according to claim 1, wherein: In step S1, the common point coordinates of the source coordinate system are (x i ,y i ), the common point coordinates of the target coordinate system are (X i , Y i ), i=(1, 2, ... n), n is an integer ≥ 2; In step S2, the transformation formula is a four-parameter transformation formula. The initial transformation parameter a is obtained by the four-parameter conversion formula j ,b j ,c j ,d j The final transformation parameters a, b, c, d are obtained by least squares optimization; where j = (1, 2, ... m), In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 weight coefficient w i The calculation formula is as follows: Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x i ,y i is the common point coordinate of the source coordinate system; Compensation amount v x , v y The calculation formula is as follows Wherein, n is an integer ≥ 2; Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are: x t =x s +v x and t =and s +v y Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation; The transformation formula in step S5 is as follows: Among them, X t , Y t is the final coordinate.

3. The parameter coordinate transformation method based on residual weighted compensation according to claim 1, wherein: In step S1, the common point coordinates of the source coordinate system are (x r ,y r ), the common point coordinates of the target coordinate system are (X r , Y r ), r=(1, 2, ... n), n is an integer ≥ 3; In step S2, the transformation formula is a six-parameter transformation formula: The initial transformation parameter e is obtained by the six-parameter conversion formula q , f q , α q , β q , g q , h q The final transformation parameters e, f, α, β, g, h are obtained by least squares optimization; where q = (1, 2, ... m), In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 Δy r =Y r -Y f In step S4, the weight coefficient w r The calculation formula is as follows: Where: x s ,y s is the coordinate point to be converted in the source coordinate system, x r ,y r is the common point coordinate of the source coordinate system; Compensation amount v x , v y The calculation formula is as follows Wherein, n is an integer ≥ 3; Using compensation v x , v y Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are: x t =x s +v x and t =and s +v y Among them, x s ,y s is the coordinate point to be converted in the source coordinate system, x t ,y t is the middle coordinate after compensation; The transformation formula in step S5 is as follows: Among them, X t , Y t is the final coordinate.

4. The parameter coordinate transformation method based on residual weighted compensation according to claim 1, wherein: In step S1, the common point coordinates of the source coordinate system are (x k ,y k , z k ), the common point coordinates of the target coordinate system are (X k , Y k , Z k ), k=(1, 2, ... n), n is an integer ≥ 3; In step S2, the transformation formula is a seven-parameter transformation formula: The initial transformation parameter l is obtained by the seven-parameter conversion formula k , o k , p k , t k ,u k , δ k , γ k The final transformation parameters l, o, p, t, u, δ, γ are obtained by least squares optimization; where k = (1, 2, ... m), In step S3, the difference between the coordinates of the common point after transformation and the coordinates of the common point in the target coordinate system is calculated based on the 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 Δy k =Y k -Y f Δz k =Z k -Z f In step S4, the weight coefficient w k The calculation formula is as follows: Where: x s ,y s , z s , is the coordinate point to be converted in the source coordinate system, x k ,y k , z k is the common point coordinate of the source coordinate system; Compensation amount v x , v y , v z The calculation formula is as follows Wherein, n is an integer ≥ 3; Using compensation v x , v y , v z Compensate the coordinate point to be converted in the source coordinate system, and the intermediate coordinates after compensation are: 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 , is the coordinate point to be converted in the source coordinate system, x t ,y t , z t is the middle coordinate after compensation; The transformation formula in step S5 is as follows: Among them, X t , Y t , Z t is the final coordinate.

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