CN114925333A - Method and system for coordinate transformation - Google Patents
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Abstract
The application relates to the technical field of positioning and discloses a coordinate conversion method and a system thereof. The method comprises the following steps: constructing a balancing transformation model for coordinate transformation, wherein the balancing transformation model comprises a residual error of an observation equation; performing system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error; determining that the system error check fails, and introducing a nonparametric component into the adjustment conversion model to construct a semi-parametric adjustment conversion model; solving a conversion parameter of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method; and carrying out coordinate conversion according to the conversion parameters. The method and the device can improve the coordinate conversion precision.
Description
Technical Field
The present invention relates to the field of navigation positioning technologies, and in particular, to a method and a system for coordinate transformation.
Background
Coordinate transformation plays an important role in the mapping field, and coordinate transformation is inevitably needed in geometric correction in Remote Sensing (RS) image processing, transformation of grid coordinates and Geographic coordinates of a Geographic Information System (GIS), transformation of Scanning coordinates and engineering measurement coordinates in three-dimensional Laser Scanning (TDLS), and transformation of measurement results between different coordinate systems. However, the accuracy of coordinate transformation is low due to the accumulation of errors, local deformation, transformation model errors and other influences (herein, they are collectively summarized as system errors) in the transformation, and this phenomenon is more remarkable especially in the high-accuracy application field.
Coordinate transformation usually adopts a three-parameter model method and a seven-parameter model method, and meanwhile, the research of transformation between any frames and epochs based on a coordinate system mainly adopts the seven-parameter model method under the information constraint of a speed field and the like. However, these parametric model transformations are not effective in improving the effect of systematic errors in the transformation. At present, in coordinate transformation and frame transformation, a parameter model transformation method is optimized by a plurality of scholars by inhibiting the influence of system errors, for example, liu yuhang (2008), ginger wave (2012), liu yi (2012), zhou yong tie (2014), liu si (2014) and zhao fu yan (2015) and the like introduce a half-parameter adjustment model into the coordinate transformation, and a better resolving result is obtained by using a compensation least square method; the system error is classified into a design matrix of a conversion model by the aid of the pandun cloud (2018), and the partial EIV model is used for processing, so that the precision of coordinate conversion is improved. Although the improvement improves the influence of system errors to a certain extent, the calculation effect depends on the selection of the regularization parameters and the smoothing factors.
Disclosure of Invention
The application aims to provide a coordinate conversion method, and the coordinate conversion precision is improved.
One embodiment of the present application discloses a method for coordinate transformation, comprising:
constructing a balancing transformation model for coordinate transformation, wherein the balancing transformation model comprises a residual error of an observation equation;
performing system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error;
determining that the system error check fails, and introducing a nonparametric component into the adjustment conversion model to construct a semi-parametric adjustment conversion model;
solving a conversion parameter of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method; and
and carrying out coordinate conversion according to the conversion parameters.
In a preferred embodiment, before the step of performing systematic error checking on the input coordinate data based on the residual normal distribution hypothesis test, the method further includes: the step of preprocessing the input coordinate data to remove outliers, the step of preprocessing the input coordinate data to remove outliers further comprising: performing χ on the inputted coordinate data 2 And (4) distribution inspection, namely judging whether abnormal data exist, and if so, detecting the abnormal value by using a COOK distance method, a quasi-calibration method, a median detection method, a clustering method, a 3 delta method based on residual distribution or a Baarda detection method.
In a preferred embodiment, the adjustment conversion model adopts a seven-parameter model, and the seven-parameter model comprises 3 translation parameters (Δ X, Δ Y, Δ Z) and 3 rotation parameters (epsilon) X ，ε Y ，ε z ) And 1 conversion parameter of scale change parameter m, wherein the adjustment conversion model is as follows:
wherein (X) 1 ，Y 1 ，Z 1 ) And (X) 2 ，Y 2 ，Z 2 ) Is a set of common point coordinates under different coordinate systems, i represents the ith pair of common points under different coordinate systems and i is 1,2 i Is a residual, V x ，V y ，V z Respectively, the residuals over the coordinate components.
In a preferred example, the adjustment conversion model adopts a four-parameter model, the four-parameter model includes 2 translation parameters (Δ X, Δ Y), 1 rotation angle θ, and 1 conversion parameter of scale change parameter m, and the adjustment conversion model is:
wherein (X) 1 ，Y 1 ) And (X) 2 ，Y 2 ) I represents the i-th pair of common points in different coordinate systems, and i is 1,2, i, m (m ≧ 2), k is mcos θ, μ is msin θ, v i Is a residual, V x ，V y Respectively, the residuals over the coordinate components.
In a preferred embodiment, the step of solving the conversion parameter for the half-parameter adjustment conversion model by using a half-parameter kernel estimation method further includes:
step1, determining a given kernel function K (-) and an initial window width
Step2, defining a kernel weight function W i (t k ) And calculating an initial M k Wherein, in the step (A),
step3, passing through a formula
Determining an estimated value of a transformation parameter X
And corresponding non-parametric component estimation
Wherein, P is a weight matrix, Z is a full rank matrix, I is a unit matrix, and Y is a common coordinate difference matrix, where Y is ZX + Δ, and Δ represents a true error term;
step4, iteratively executing the step2 and the step3 by a generalized cross-validation method until iteration is terminated after a condition is met so as to determine an optimal window width and a corresponding optimal estimated value of the conversion parameter X
Wherein the optimum window width
Is to make
The window width h when the minimum value is reached, wherein J (h) is a hat matrix corresponding to the window width,
is y i A corresponding estimate value.
In a preferred embodiment, the kernel function selects one or more of the following group:
(1)
(2)K 2 (x)＝[π(1+x 2 )] -1 ；
(3)
(4)
(5)
(6)
(7)
(8)
(9)
in a preferred embodiment, the window width is adopted
As an initial value.
In a preferred embodiment, the method further comprises the following steps: according to the solved estimated value of the optimal conversion parameter X
And (5) carrying out coordinate conversion.
In a preferred embodiment, when the system error check is determined to pass, the least square-based adjustment transformation model is used for solving transformation parameters
Then use
And (5) carrying out coordinate conversion.
One embodiment of the present application discloses a system for coordinate transformation, comprising:
the adjustment conversion model building module is used for building an adjustment conversion model for coordinate conversion, and the adjustment conversion model comprises a residual error of an observation equation;
the preprocessing module is used for carrying out system error verification on the input coordinate data based on the normal distribution hypothesis test of the residual error;
a half-parameter adjustment conversion model building module, which is used for determining that the system error check is not passed and introducing a nonparametric component into the adjustment conversion model;
the calculation module is used for solving the conversion parameters of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method; and
and the conversion module is used for carrying out coordinate conversion according to the conversion parameters.
In a preferred embodiment, the system for coordinate transformation is a receiver, a server or an embedded device.
In the embodiment of the application, the nonparametric part in the conversion is described by introducing the nonparametric part, and the corrected conversion model contains both the parametric component and the nonparametric component, so that the mathematical model is more in line with the actual measurement. In addition, the method selects the optimal window width by selecting the appropriate kernel density function and a generalized cross-validation method, so that a coordinate conversion parameter solution considering the system error is obtained, and the final conversion precision is improved.
The present specification describes a number of technical features distributed throughout the various technical aspects, and if all possible combinations of technical features (i.e. technical aspects) of the present specification are listed, the description is made excessively long. In order to avoid this problem, the respective technical features disclosed in the above summary of the invention of the present application, the respective technical features disclosed in the following embodiments and examples, and the respective technical features disclosed in the drawings may be freely combined with each other to constitute various new technical solutions (which should be regarded as having been described in the present specification) unless such a combination of the technical features is technically infeasible. For example, in one example, feature a + B + C is disclosed, in another example, feature a + B + D + E is disclosed, and features C and D are equivalent technical means that serve the same purpose, technically only one feature is used, but not both, and feature E may be technically combined with feature C, then the solution of a + B + C + D should not be considered as already described because the technology is not feasible, and the solution of a + B + C + E should be considered as already described.
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FIG. 1 is a schematic flow chart of a coordinate transformation method according to a first embodiment of the present application
FIG. 2 is a schematic diagram of a coordinate transformation system according to a second embodiment of the present application
Detailed Description
In the following description, numerous technical details are set forth in order to provide a better understanding of the present application. However, it will be understood by those skilled in the art that the technical solutions claimed in the present application may be implemented without these technical details and with various changes and modifications based on the following embodiments.
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
A first embodiment of the present application relates to a method of coordinate transformation, the flow of which is shown in fig. 1, the method comprising the steps of:
In one embodiment, the adjustment conversion model may employ a seven parameter model. The seven-parameter model comprises 3 translation parameters (Δ X, Δ Y, Δ Z), 3 rotation parameters (ε) X ，ε Y ，ε z ) And 1 scale change parameter m, wherein the adjustment conversion model is as follows:
wherein (X) 1 ，Y 1 ，Z 1 ) And (X) 2 ，Y 2 ，Z 2 ) Are respectively a group of common point coordinates under different coordinate systems, i represents the i-th pair of common points under different coordinate systems, and i is 1,2 i Is a residual, V x ，V y ，V z Respectively, the residuals over the coordinate components.
In another embodiment, the adjustment conversion model may employ a four-parameter model. The four-parameter model comprises 2 translation parameters (Δ X, Δ Y), 1 rotation angle θ, and 1 scale change parameter m, and the adjustment conversion model is:
wherein (X) 1 ，T 1 ) And (X) 2 ，Y 2 ) I represents the i-th pair of common points in different coordinate systems, and i is 1,2, i, m (m ≧ 2), k is mcos θ, μ is msin θ, v i Is a residual, V x ，V y Respectively, the residuals over the coordinate components.
Then, the adjustment conversion model is converted into a matrix form as: y ═ ZX + Δ. Wherein, Y is a public coordinate difference matrix, and delta is a true error term.
And 102, carrying out system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error.
In one embodiment, before performing the systematic error check, the method further comprises: preprocessing the input coordinate data to eliminate abnormal values. Specifically, χ is performed on the input coordinate data 2 Checking distribution, judging whether there is abnormal data, if there is abnormal data, using COOK distance method, quasi-standard detection method, median detection method, clustering method, 3 delta method based on residual distribution or Baarda detection methodThe value is detected. It should be understood that preprocessing the coordinate data to remove outliers is not a necessary step, and the application can be practiced without this step.
And 103, determining that the system error check fails, and introducing a nonparametric component into the adjustment conversion model to construct a semi-parametric adjustment conversion model. In the application, a nonparametric part in the conversion is described by introducing the nonparametric part, and the corrected conversion model contains both the parametric component and the nonparametric component, so that the mathematical model is more in line with the actual measurement.
In another embodiment, determining that the systematic error check passes, solving the transformation parameters based on a least squares based adjustment transformation model
Then use
And (5) carrying out coordinate conversion.
And 104, solving the conversion parameters of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method. In one embodiment, the step of solving the half-parameter adjustment transformation model by using a half-parameter kernel estimation method includes the following steps:
step1, determining a given kernel function K (-) and an initial window width
Step2, defining a kernel weight function W i (t k ) And calculating an initial M k Wherein, in the process,
step3, passing through a formula
Determining an estimated value of a transformation parameter X
And corresponding non-parametric component estimation
Wherein, P is a weight matrix, Z is a full rank matrix, I is a unit matrix, and Y is a public coordinate difference matrix;
step4, iteratively executing the step2 and the step3 by a generalized cross-validation method until iteration is terminated after a condition is met so as to determine an optimal window width and a corresponding optimal estimated value of the conversion parameter X
Optimum window width
Is to make
The window width h when the minimum value is reached, wherein J (h) is a hat matrix corresponding to the window width,
is y i A corresponding estimate.
According to the method, the semi-parameter kernel estimation method is introduced into the parameter solution of the coordinates for the first time, and the system error in the original conversion method is corrected, so that the higher conversion precision of the coordinates is obtained. In addition, the estimated system error can be further inverted and evaluated as required for reference and use in actual production.
In one embodiment, the kernel function selects one or more of the group:
(1)
(2)K 2 (x)＝[π(1+x 2 )] -1 ；
(3)
(4)
(5)
(6)
(7)
(8)
(9)
in one embodiment, the window width is adopted
As an initial value.
And 105, performing coordinate conversion according to the conversion parameters. In one embodiment, the method further comprises: according to the solved estimated value of the optimal conversion parameter X
And (5) carrying out coordinate conversion.
In order to better understand the technical solution of the present application, the following describes the coordinate transformation process in detail, and the listed details in this example are mainly for understanding and are not intended to limit the scope of the present application.
A, step a: data pre-processing
In order to inhibit the influence of abnormal points (such as gross error and strong influence points) in the data on the adjustment calculation result, firstly, performing data preprocessing on the input data: first, X is conducted 2 B, distribution inspection, wherein whether abnormal data exist is inspected, and if the abnormal data do not exist, the step b is directly carried out; if yes, detecting a multivariate abnormal value by using a COOK distance, and entering the step b after processing.
Step b: systematic error checking
Carrying out hypothesis testing by using the normal distribution of the residual errors, and directly obtaining a conversion result if the hypothesis passes; if not, go to step c.
Step c: and establishing a block error conversion model.
1) Establishing a block error model aiming at the seven-parameter model:
at present, a seven-parameter model is mostly adopted for coordinate transformation, and a burst model adopted for geodetic coordinate transformation is taken as an example for explanation. The Bursa model includes seven parameters, 3 translation parameters (Δ X, Δ Y, Δ Z), 3 rotation parameters (ε) X ，ε Y ，ε z ) 1 scale variation parameter m, the conversion model of which is shown in the following formula (1):
in the formula (1) (X) 1 ，Y 1 ，Z 1 ) And (X) 2 ，Y 2 ，Z 2 ) Respectively a set of common point coordinates under different coordinate systems. Writing equation (1) as an error equation:
v in formula (2) x ，V y ，V z Respectively, the residuals over the coordinate components.
Further sorting the formula (2) to obtain the corresponding error variance:
residual error in the above equation
Where i denotes the i-th pair of common points and i ═ 3, 4.
2) Establishing a block error model aiming at the four-parameter model:
the planar coordinate transformation usually adopts a four-parameter model, which includes four parameters to be estimated, namely 2 translation parameters (Δ X, Δ Y), 1 rotation angle θ and 1 scale change parameter m, and the transformation model is as follows:
in the formula (4) (X) 1 ，Y 1 ) And (X) 2 ，Y 2 ) Respectively a set of common point coordinates under different coordinate systems. Let κ be mcos θ, μ be msin θ then the above formula can be written:
the formula (5) can be further arranged into a uniform form of the formula (3).
If the multiple groups of common points exist and the adjustment resolving condition is met, writing the formula (3) into a matrix form:
Y＝ZX+Δ (6)
in the formula (6), Δ is a true error term.
Step d: in order to take model errors existing in modeling into consideration, a nonparametric component S is introduced, a half-parameter adjustment model is built, and accordingly, the formula (6) in the step a is rewritten into Y ═ ZX + S + delta.
Step e: adopting a semi-parameter kernel estimation method to solve the conversion model parameters, wherein the calculation process comprises the following steps:
step 1: selecting a probability density kernel K (-) over R and a window width h m And h is m > 0, defining a kernel weight function W i (t k )：
Where K (-) is a selected kernel function h m Is a corresponding window width and h m Is greater than 0. After a lot of data tests, the kernel function in the following form is selected in this embodiment:
window width determined by thumb rule for initial window width parameter
As an initial value, the value of the first value,
step 2: to solve for the parameters, assume X is known, based on
The kernel estimate that can be made for the non-parametric component S is of the form:
by
Can calculate the observed value y i The residual error of (c) is:
let M k ＝(W i (t j )) m×n Then observe the value y i The matrix form of the residuals of (a) is: (ZX-Y) (I-M) K ) And (P). Where I is the identity matrix and P is the weight matrix, which is set according to the accuracy of the solution, and if there is no such information, it can be set as the identity matrix.
Step 3: according to the least squares criterion, there are: (ZX-Y) T (I-M K ) T P(I-M K ) (ZX-Y) ═ min, then can be transformed into equation (7) as follows:
(Z T (I-M K ) T P(I-M K )Z) -1 Z T (I-M K ) T P(I-M K )Y (7)
if rank (Z) is t, t is the number of unknown parameters in the corresponding correction model, i.e. Z is a full rank matrix with Z T (I-M k ) T P(I-M k ) Z is nonsingular, makes
For the estimation of the parameter X, the estimation of X is:
will be provided with
Bringing in
In (b) to obtain
The estimated value of (c):
step 4: iteratively executing Step2-Step3 by a generalized cross-validation method (GCV method) until the iteration is terminated after a condition is met, thereby determining the optimal window width, and obtaining the corresponding optimal parameter component estimation value
And non-parametric component solution
Step 5: by obtaining estimates of the parameter components
Substituting into formula (1) can accomplish the corresponding coordinate transformation.
The invention introduces a semi-parameter kernel estimation method into high-precision coordinate conversion, and provides a system error correction conversion method of a comprehensive semi-parameter kernel estimation method. Firstly, deducing from the angle of mathematical characteristics of a coordinate conversion model; and secondly, improving the existing coordinate conversion model while considering the system error, deriving a corresponding parameter solution of a system error correction conversion method and an estimated value of the model error by utilizing kernel estimation and integrating least squares, realizing the correction of the system error contained in the coordinate conversion, and researching and improving a kernel function and window width parameter selection method in the coordinate conversion method to obtain higher conversion precision.
The second embodiment of the present application relates to a coordinate transformation system, which is configured as shown in fig. 2 and includes a adjustment transformation model building module, a preprocessing module, a half-parameter adjustment transformation model building module, a calculation module, and a transformation module. The adjustment conversion model building module is used for building an adjustment conversion model for coordinate conversion, and the adjustment conversion model comprises a residual error of an observation equation. And the preprocessing module performs system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error. And the half-parameter adjustment conversion model building module is used for determining that the system error check is not passed and introducing a nonparametric component into the adjustment conversion model. And the calculation module is used for solving the conversion parameters of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method. And the conversion module is used for carrying out coordinate conversion according to the conversion parameters. In one embodiment, the system of coordinate transformation is a receiver, server, embedded device, or other such device.
The first embodiment is a method embodiment corresponding to the present embodiment, and the technical details in the first embodiment may be applied to the present embodiment, and the technical details in the present embodiment may also be applied to the first embodiment.
It will be appreciated by those skilled in the art that the functions of the implementation of the modules shown in the embodiments of the system for coordinate transformation described above can be understood with reference to the associated description of the method for coordinate transformation described above. The functions of the modules shown in the embodiment of the coordinate transformation system described above may be implemented by a program (executable instructions) running on a processor, or may be implemented by specific logic circuits. The coordinate transformation system according to the embodiment of the present invention may be stored in a computer-readable storage medium if it is implemented in the form of a software functional module and sold or used as a stand-alone product. Based on such understanding, the technical solutions of the embodiments of the present application may be essentially implemented or portions thereof contributing to the prior art may be embodied in the form of a software product stored in a storage medium, and including several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read Only Memory (ROM), a magnetic disk, or an optical disk. Thus, embodiments of the present application are not limited to any specific combination of hardware and software.
It is noted that, in the present patent application, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the use of the verb "comprise a" to define an element does not exclude the presence of another, same element in a process, method, article, or apparatus that comprises the element. In the present patent application, if it is mentioned that a certain action is executed according to a certain element, it means that the action is executed according to at least the element, and two cases are included: performing the action based only on the element, and performing the action based on the element and other elements. The expression of a plurality of, a plurality of and the like includes 2, 2 and more than 2, more than 2 and more than 2.
All documents mentioned in this specification are to be considered as being incorporated in their entirety into the disclosure of the present application so as to be subject to modification as necessary. It should be understood that the above description is only for the preferred embodiment of the present disclosure, and is not intended to limit the scope of the present disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of one or more embodiments of the present disclosure should be included in the scope of protection of one or more embodiments of the present disclosure.
In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
Claims (11)
1. A method of coordinate transformation, comprising:
constructing a balancing transformation model for coordinate transformation, wherein the balancing transformation model comprises a residual error of an observation equation;
performing system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error;
determining that the system error check fails, and introducing a nonparametric component into the adjustment conversion model to construct a semi-parametric adjustment conversion model;
solving a conversion parameter of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method; and
and carrying out coordinate conversion according to the conversion parameters.
2. The method of coordinate transformation of claim 1,before the step of performing systematic error checking on the input coordinate data based on the residual normal distribution hypothesis test, the method further includes: preprocessing the input coordinate data to remove outliers, the preprocessing the input coordinate data to remove outliers further comprising: performing χ on the inputted coordinate data 2 And (4) distribution inspection, namely judging whether abnormal data exist, and if so, detecting abnormal values by using a COOK distance method, a quasi-standard detection method, a median detection method, a clustering method, a 3 delta method based on residual distribution or a Baarda detection method.
3. Method of coordinate transformation according to claim 1, characterized in that the adjustment transformation model employs a seven-parameter model comprising 3 translation parameters (Δ X, Δ Y, Δ Z), 3 rotation parameters (e ∈) X ,ε Y ,ε z ) And 1 conversion parameter of scale change parameter m, wherein the adjustment conversion model is as follows:
wherein (X) 1 ,Y 1 ,Z 1 ) And (X) 2 ,Y 2 ,Z 2 ) Are respectively a group of common point coordinates under different coordinate systems, i represents the i-th pair of common points under different coordinate systems and i is 1,2, …, m (m is more than or equal to 3), v is i Is a residual, V x ,V y ,V z Respectively, the residuals over the coordinate components.
4. The method of coordinate transformation according to claim 1, wherein the adjustment transformation model is a four-parameter model, the four-parameter model comprises 2 translation parameters (Δ X, Δ Y), 1 rotation angle θ, and 1 transformation parameter of scale variation parameter m, and the adjustment transformation model is:
wherein (X) 1 ,Y 1 ) And (X) 2 ,Y 2 ) Respectively represent a set of common point coordinates under different coordinate systems, i represents the i-th pair of common points under different coordinate systems, and i is 1,2, …, m (m is more than or equal to 2), k is mcos theta, mu is msin theta, v is i Is a residual, V x ,V y Respectively, the residuals over the coordinate components.
5. The method of coordinate transformation according to claim 3 or 4, wherein the step of solving the transformation parameters for the half-parameter adjustment transformation model by using a half-parameter kernel estimation method further comprises:
step1, determining a given kernel function K (-) and an initial window width
Step2, defining a kernel weight function W i (t k ) And calculating an initial M k Wherein, in the step (A),
M k ＝(W i (t j )) m×m ，i,j,k＝1,2,…,m；
step3, passing through a formula
Determining an estimated value of a transformation parameter X
And corresponding non-parametric component estimation
Wherein, P is a weight matrix, Z is a full rank matrix, I is a unit matrix, and Y is a common coordinate difference matrix, wherein, Y is ZX + Δ, and Δ represents a true error term;
step4, iteratively executing the step2 and the step3 by a generalized cross-validation method until iteration is terminated after a condition is met so as to determine an optimal window width and a corresponding optimal estimated value of the conversion parameter X
Wherein the optimum window width
Is to make
The window width h when the minimum value is reached, wherein J (h) is a hat matrix corresponding to the window width,
is y i A corresponding estimate.
6. The method of coordinate transformation according to claim 5, wherein the kernel function selects one or more of the group consisting of:
(1)
(2)K 2 (x)＝[π(1+x 2 )] -1 ；
(3)
(4)
(5)
(6)
(7)
(8)
(9)
7. method of coordinate transformation according to claim 5, characterized in that the window width is adapted
As an initial value.
8. The method of coordinate conversion of claim 5, further comprising: according to the solved estimated value of the optimal conversion parameter X
And (5) carrying out coordinate conversion.
9. The method of coordinate transformation of claim 1, wherein if the systematic error check is determined to pass, then the least-squares based adjustment transformation model is appliedDe-conversion parameter
Then use
And (5) carrying out coordinate conversion.
10. A system for coordinate transformation, comprising:
the adjustment conversion model building module is used for building an adjustment conversion model for coordinate conversion, and the adjustment conversion model comprises a residual error of an observation equation;
the preprocessing module is used for carrying out system error check on the input coordinate data based on the normal distribution hypothesis test of the residual error;
a half-parameter adjustment conversion model building module, which is used for determining that the system error check is not passed and introducing a nonparametric component into the adjustment conversion model;
the calculation module is used for solving the conversion parameters of the half-parameter adjustment conversion model by adopting a half-parameter kernel estimation method; and
and the conversion module is used for carrying out coordinate conversion according to the conversion parameters.
11. The system of coordinate transformation of claim 10, wherein the system of coordinate transformation is a receiver, a server, or an embedded device.
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