Two-dimensional transformation method for multi-dimensional space relationship between GNSS ambiguity vectors

Abstract

The application discloses a two-dimensional conversion method for multi-dimensional space relation among GNSS ambiguity vectors, comprising the following steps: constructing a GNSS double difference mathematical model, and obtaining a multi-dimensional ambiguity vector floating point solution and a variance-covariance matrix thereof by using a least square method; obtaining an optimal integer solution and a suboptimal integer solution of the ambiguity vector by means of a least square ambiguity decorrelation adjustment method according to the ambiguity vector floating point solution and the variance-covariance matrix thereof; taking the ambiguity vector floating point solution, the optimal integer solution and the suboptimal integer solution as end points, calculating an elliptic norm side length of an edge formed by any two end points and an A-inner product included angle between any two edges; and constructing a two-dimensional Euclidean triangle based on the elliptic norm side length and the A-inner product included angle, so as to convert a complex and abstract multi-dimensional space relation among the ambiguity vector floating point solution, the optimal integer solution and the suboptimal integer solution into a simple and direct two-dimensional triangle relation; and the application provides important method support for analyzing a GNSS ambiguity confirmation reliability influence mechanism.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, specifically a two-dimensional conversion method for multidimensional spatial relationships between GNSS ambiguity vectors. Background Technology

[0002] The correct fixation of the ambiguity vector of the Global Navigation Satellite System (GNSS) is the key to using GNSS for precise positioning at the centimeter or millimeter level, and the reliability of GNSS ambiguity confirmation is a prerequisite for the correct fixation of ambiguity.

[0003] Existing ambiguity confirmation methods include the success rate / failure rate index method, the statistical difference test method, the dual judgment method of the success rate / failure rate index method and the statistical difference test method, and the ambiguity confirmation method based on the ambiguity integer aperture estimation theory. Among these, the most commonly used ambiguity confirmation method is the statistical difference test method based on the R-ratio test. It determines whether to accept the optimal integer solution of the ambiguity vector as the fixed solution by distinguishing whether there is a significant difference between the optimal integer solution and the second-best integer solution of the ambiguity vector, or whether the optimal integer solution of the ambiguity vector is sufficiently close to the floating-point solution of the ambiguity vector. However, at present, the reliability of the confirmation of one-dimensional and two-dimensional ambiguity vectors can only be studied based on the statistical difference test method based on the R-ratio test. It is still difficult to reveal the confirmation reliability mechanism of multi-dimensional ambiguity vectors with more than two dimensions. In addition, the floating-point solution, optimal integer solution, and second-best integer solution of multi-dimensional ambiguity vectors have complex and abstract multi-dimensional spatial relationships (such as angles and distances between vectors), and there is currently a lack of methods for analyzing the multi-dimensional spatial relationships between ambiguity vectors. Summary of the Invention

[0004] To address the aforementioned technical shortcomings, the purpose of this invention is to provide a two-dimensional transformation method for the multidimensional spatial relationship between GNSS ambiguity vectors. This method transforms the complex and abstract multidimensional spatial relationship between floating-point solutions, optimal integer solutions, and suboptimal integer solutions of ambiguity vectors into a simple and intuitive two-dimensional triangular relationship. This provides important methodological support for the analysis of the impact mechanism on the reliability of GNSS ambiguity confirmation.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] This invention provides a two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors, comprising the following steps:

[0007] Step S1: Construct a GNSS double-difference mathematical model using GNSS pseudorange observations and carrier phase observations. Obtain the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix based on the GNSS double-difference mathematical model and the least squares method.

[0008] Step S2: Based on the floating-point solution of the multidimensional fuzzy vector and its variance-covariance matrix, use the least squares fuzzy decorrelation adjustment method to obtain the optimal integer solution and the second-best integer solution of the multidimensional fuzzy vector.

[0009] Step S3: Using the elliptic norm theory, with the floating-point solution of the fuzzy vector, the optimal integer solution of the fuzzy vector, and the second-best integer solution of the fuzzy vector as endpoints, calculate the elliptic norm side length of the side formed by any two endpoints.

[0010] Step S4: Using the A-inner product theory, calculate the angle between the A-inner product of two vectors with the floating-point solution of the ambiguity vector, the optimal integer solution of the ambiguity vector, and the second-best integer solution of the ambiguity vector as vertices respectively, and check whether the angle between any two vectors is not greater than 180°.

[0011] Step S5: Construct a two-dimensional Euclidean triangle with the floating-point solution, the optimal integer solution, and the suboptimal integer solution of the ambiguity vector as the three vertices, the three elliptic norm side lengths as the three sides, and the three A-inner product angles as the three interior angles. Transform the complex and abstract multidimensional spatial relationship between the floating-point solution, the optimal integer solution, and the suboptimal integer solution of the GNSS multidimensional ambiguity vector into a simple and intuitive two-dimensional Euclidean triangle relationship.

[0012] Preferably, in step S1, it is assumed that two GNSS receivers observe multi-frequency, multi-system GNSS at the same time. t Frequency One satellite, For the first i The number of frequency observation satellites i =1, 2, …, t Furthermore, each system selects a reference satellite within each system and each frequency to form a double-difference mathematical model, thus forming... n = m - t One double-difference pseudorange observation equation and n The GNSS double-difference mathematical model is composed of two double-difference carrier phase observation equations, combined with a double-difference stochastic model of pseudorange and carrier phase observations:

[0013] ;

[0014] ;

[0015] In the formula, and These are the expectation and variance of the double-difference pseudorange observations, respectively. and These are the expectation and variance of the double-difference carrier phase observations, respectively. and These are the double-difference pseudorange observation vector and the double-difference carrier phase observation vector, respectively. and These are the baseline vector and the multidimensional double-difference ambiguity vector, respectively. for The rank of the double difference coefficient matrix is ​​given by the following formula. , , and These are the first in multi-frequency multi-system GNSS. i The wavelength of each frequency and the dimension of the double-difference ambiguity vector, where i =1, 2,…, t ;

[0016] It is the cofactor matrix of the double-difference observation vectors; and These are the standard deviations of the non-differential pseudorange observations and the non-differential carrier phase observations, respectively.

[0017] Preferably, in step S1, the specific steps for obtaining the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix using the least squares method are as follows:

[0018] The baseline vector is obtained using the least squares method. b floating-point solution and multidimensional ambiguity vector a floating-point solution and its variance-covariance matrix and :

[0019] ;

[0020] ;

[0021] In the formula, It is a symmetric positive definite matrix. for n A column vector of real numbers.

[0022] Preferably, in step S2, according to and The ambiguity vector is obtained using the least squares ambiguity decorrelation adjustment method. a optimal integer solution and suboptimal integer solutions , and All n A 3D real-valued column vector; the key to high-precision GNSS positioning lies in the correct fixing of the GNSS ambiguity vector and whether the optimal integer solution of the ambiguity vector is accepted. A fixed solution for the ambiguity vector High-precision and reliable GNSS positioning is crucial. The step of deciding whether to accept the optimal integer solution of the ambiguity vector as a fixed solution is called the ambiguity acceptability test, which falls under the category of ambiguity confirmation. Currently, ambiguity confirmation methods mainly include the success rate / failure rate index method, the statistical difference test method, the dual-judgment method based on the success rate index method and the statistical difference test method, and the ambiguity confirmation method based on the ambiguity integer aperture estimation theory. Among these methods, the statistical difference test method based on the R-ratio test is the most commonly used, and its definition is as follows:

[0023] ;

[0024] In the formula, μ This is the threshold for the R-ratio test, and its value is generally set to 1.5, 2.0, 2.5, 3.0, etc. and These are the optimal integer solutions for the ambiguity vector. and suboptimal integer solutions The residual quadratic form, referred to as the optimal quadratic form and the suboptimal quadratic form, if and only if When established, the optimal integer solution of the ambiguity vector is considered to be... and suboptimal integer solutions There is a clear distinction or the optimal integer solution for the ambiguity vector. Sufficiently close to the floating-point solution of the ambiguity vector Then accept the optimal integer solution of the ambiguity vector. Fixed solution for ambiguity vector ;

[0025] Using the least squares algorithm, the ambiguity vector was successfully fixed. For baseline vector b The solution with the baseline vector fixed is obtained by solving it again. and its variance-covariance matrix :

[0026] ;

[0027] In the formula, For the baseline vector floating-point solution Floating-point solution of ambiguity vector The mutual covariance matrix between them;

[0028] While the statistical difference test based on the R-ratio test improves the reliability of ambiguity confirmation or fixed ambiguity solutions to some extent, it is difficult to apply the formula... The mechanism of ambiguity confirmation reliability is revealed, and the formula is... Multidimensional fuzzy vector floating-point solution Optimal integer solution and suboptimal integer solutions The relationships between GNSS ambiguity vectors are complex and abstract, and currently there is a lack of methods for analyzing the hyperdimensional spatial relationships between them and the reliability mechanism of ambiguity confirmation. Therefore, this invention proposes a two-dimensional transformation method for the hyperdimensional spatial relationships between GNSS ambiguity vectors, utilizing elliptic norm theory and A-inner product theory.

[0029] Preferably, step S4 specifically includes:

[0030] set up G for n If a Helmet positive definite matrix is ​​given, then the vector... elliptic norm or G -norm for:

[0031] ;

[0032] In the formula, for n dimensional vector in the real number field ;

[0033] Floating-point solution with ambiguity vector Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector The endpoints form three edges, which are obtained from the floating-point solution of the ambiguity vector. and optimal integer solution The edge formed by the endpoints , from the ambiguity vector floating-point solution and suboptimal integer solutions The edge formed by the endpoints And the optimal integer solution from the ambiguity vector and suboptimal integer solutions The edge formed by the endpoints Using the theory of elliptic norm Calculate vectors elliptic norm or The formula for the L1 norm is:

[0034] ;

[0035] In the formula, and L1 is a real vector, and L2 is also a vector. sum vector The two-dimensional distance between them; and so on, to obtain the vector. The elliptic norm L2 and vector The formula for the elliptic norm L3 is as follows:

[0036] ;

[0037] ;

[0038] In the formula, , ,and and All are real number vectors, L2 and L3 are vectors respectively. sum vector Two-dimensional distance and vector between sum vector The two-dimensional distance between them;

[0039] A-internal product theory: Let A be... n If a real symmetric positive definite matrix of order 1 is given, then the vector... sum vector The A-inner product is defined as follows:

[0040] ;

[0041] In the formula, and , and Vectors based on A-inner product sum vector Angle between The calculation formula is:

[0042] ;

[0043] In the formula, for The inverse cosine function, and They are vectors sum vector The elliptic norm or A-norm, obtained using the formula of A-inner product theory. And the formula for the angle between vectors based on the A-inner product , using fuzzy vector floating-point solution A vector with vertices based on the A-inner product. sum vector included angle for:

[0044] ;

[0045] And so on, using the optimal integer solution of the ambiguity vector. A vector with vertices based on the A-inner product. sum vector included angle for:

[0046] ;

[0047] suboptimal integer solution of ambiguity vector A vector with vertices based on the A-inner product. sum vector included angle for:

[0048] ;

[0049] Test the angle of the A-inner product between any two sides Is it no greater than 180°, otherwise .

[0050] The beneficial effects of this invention are as follows: By constructing a GNSS double-difference mathematical model, this invention obtains the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix, the optimal integer solution of the ambiguity vector, and the second-best integer solution of the ambiguity vector using the least squares method and the least squares ambiguity reduction adjustment method; by using elliptic norm theory, it constructs the two-dimensional side length based on the elliptic norm between any two multidimensional vectors; and by using A-inner product theory, it establishes the two-dimensional included angle based on the A-inner product between any two multidimensional vectors, forming a two-dimensional Euclidean triangle with vertices representing the floating-point solution, optimal integer solution, and second-best integer solution of the ambiguity vector, side lengths based on the elliptic norm, and interior angles based on the two-dimensional included angle of the A-inner product. This transforms the complex and abstract multidimensional spatial relationship between the floating-point solution, optimal integer solution, and second-best integer solution of the ambiguity vector into a simple and intuitive two-dimensional triangular relationship, providing important methodological support for the analysis of the impact mechanism of GNSS ambiguity confirmation reliability. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart illustrating a two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors provided in an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of the transformation of a two-dimensional Euclidean triangle into a multidimensional spatial relationship between ambiguity vectors based on the side length of the elliptic norm and the angle between the A-inner product, provided as an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Examples, such as Figure 1 As shown, a two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors includes the following steps:

[0056] Step S1: Construct a GNSS double-difference mathematical model using GNSS pseudorange and carrier phase observations. Based on the GNSS double-difference mathematical model and the least squares method, obtain the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix, i.e.:

[0057] Assume two GNSS receivers observe multi-frequency, multi-system GNSS at the same time. t Frequency satellites ( For the first i The number of frequency observation satellites i =1, 2, …, t Furthermore, each system selects a reference satellite within each system and frequency to form a double-difference mathematical model, thus enabling the formation of... n = m - t One double-difference pseudorange observation equation and n The GNSS double-difference mathematical model is composed of two double-difference carrier phase observation equations, combined with a double-difference stochastic model of pseudorange and carrier phase observations:

[0058] ;

[0059] ;

[0060] In the formula, and These are the expectation and variance of the double-difference pseudorange observations, respectively. and These are the expectation and variance of the double-difference carrier phase observations, respectively. and These are the double-difference pseudorange observation vector and the double-difference carrier phase observation vector, respectively. and These are the baseline vector and the multidimensional double-difference ambiguity vector, respectively. for The rank of the double difference coefficient matrix is ​​given by the following formula. , and These are the first in multi-frequency multi-system GNSS. i The wavelength of each frequency and the dimension of the double-difference ambiguity vector, where i =1, 2,…, t ; It is the cofactor matrix of the double-difference observation vectors; and These are the standard deviations of the non-differential pseudorange observations and the non-differential carrier phase observations, respectively.

[0061] According to the formula and formula The baseline vector can be obtained using the least squares method. b floating-point solution and multidimensional ambiguity vector a floating-point solution and its variance-covariance matrix and :

[0062] ;

[0063] ;

[0064] In the formula, It is a symmetric positive definite matrix. for n A 3D real column vector;

[0065] Step S2: Based on the floating-point solution of the multidimensional ambiguity vector and its variance-covariance matrix, the optimal integer solution and the second-best integer solution of the multidimensional ambiguity vector are obtained using the least squares ambiguity decorrelation adjustment method, i.e.:

[0066] according to and The ambiguity vector can be obtained using the least squares ambiguity decorrelation adjustment method. a optimal integer solution and suboptimal integer solutions ,and and All n A 3D real column vector;

[0067] Step S3: Using elliptic norm theory, with the floating-point solution, the optimal integer solution, and the second-best integer solution of the ambiguity vector as endpoints, calculate the elliptic norm side length of the edge formed by any two endpoints, i.e.:

[0068] Elliptic norm theory: Let G for n If a Helmet positive definite matrix is ​​given, then the vector... elliptic norm or G -norm for:

[0069] ;

[0070] In the formula, for n dimensional vector in the real number field ;

[0071] If the ambiguity vector is used as a floating-point solution Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector If the endpoints are , then three edges can be formed, which are obtained from the floating-point solution of the ambiguity vector. and optimal integer solution The edge formed by the endpoints , from the ambiguity vector floating-point solution and suboptimal integer solutions The edge formed by the endpoints And the optimal integer solution from the ambiguity vector and suboptimal integer solutions The edge formed by the endpoints Using the formulas of elliptic norm theory Calculate vectors elliptic norm or The formula for the L1 norm can be written as:

[0072] ;

[0073] In the formula, and L1 is a real vector, and L2 is also a vector. sum vector The two-dimensional distance between them. And so on, vectors... The elliptic norm L2 and vector The formulas for the elliptic norm L3 can be written as follows:

[0074] ;

[0075] ;

[0076] In the formula, , ,and and All are real vectors. L2 and L3 are also vectors. sum vector Two-dimensional distance and vector between sum vector The two-dimensional distance between them;

[0077] Step S4: Using the A-Dot Product theory, calculate the angle between the A-Dot Product of two vectors with vertices representing the floating-point solution, the optimal integer solution, and the second-best integer solution of the ambiguity vector, respectively. Verify that the angle between any two sides of the A-Dot Product is no greater than 180°.

[0078] A-internal product theory: Let A be... n If a real symmetric positive definite matrix of order 1 is given, then the vector... sum vector The A-inner product is defined as follows:

[0079] ;

[0080] In the formula, and , and Vectors based on A-inner product sum vector Angle between The calculation formula is:

[0081] ;

[0082] In the formula, for The inverse cosine function, and They are vectors sum vector The elliptic norm or A-norm, obtained using the formula of A-inner product theory. And the formula for the angle between vectors based on the A-inner product , using fuzzy vector floating-point solution A vector with vertices based on the A-inner product. sum vector included angle It can be written as:

[0083] ;

[0084] And so on, using the optimal integer solution of the ambiguity vector. A vector with vertices based on the A-inner product. sum vector included angle It can be written as:

[0085] ;

[0086] suboptimal integer solution of ambiguity vector A vector with vertices based on the A-inner product. sum vector included angle It can be written as:

[0087] ;

[0088] Step S5: Construct a two-dimensional Euclidean triangle with the floating-point solution, the optimal integer solution, and the second-best integer solution of the ambiguity vector as its three vertices, the three elliptic norm side lengths as its three sides, and the angle between the three A-inner products as its three interior angles. Transform the complex and abstract multidimensional spatial relationship between the floating-point solution, the optimal integer solution, and the second-best integer solution of the GNSS multidimensional ambiguity vector into a simple and intuitive two-dimensional Euclidean triangle relationship, namely:

[0089] Construction of 2D side lengths and sides: using fuzzy vector floating-point solutions Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector As endpoints, utilize and Vectors can be sum vector Between, vector sum vector Between and vectors sum vector The complex and abstract multidimensional spatial distance between vectors is transformed into a simple two-dimensional linear distance, namely the elliptic norms L1, L2, and L3; correspondingly, the vector... sum vector The multidimensional space edge between them is transformed into a two-dimensional edge d1 of length L1, and the vector... sum vector The multidimensional space edge between them is transformed into a two-dimensional edge d2 of length L2, and the vector... sum vector The multidimensional space edge between them is transformed into a two-dimensional edge d3 with a side length of L3;

[0090] Construction of two-dimensional angles: using floating-point solutions of ambiguity vectors respectively Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector As vertices, utilize , and It can be used Vectors of vertices sum vector Between, with Vectors of vertices sum vector Between and Vectors of vertices sum vector The complex and abstract multidimensional spatial angles are transformed into simple two-dimensional angles, namely the included angles based on the A-inner product. , and ;

[0091] Construction of a two-dimensional Euclidean triangle: using vectors respectively , and Let d1, d2, and d3 be the vertices, and let L1, L2, and L3 be the side lengths, with the included angle based on the A-inner product. , and For the angle, form a two-dimensional Euclidean triangle based on the side length of the ellipse norm and the angle between the A-inner product (e.g.) Figure 2 (as shown), in addition, The following conditions must be met:

[0092] ;

[0093] like ,but .

[0094] This invention utilizes a two-dimensional Euclidean transformation triangle to resolve the ambiguity vector using floating-point methods. Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector The complex and abstract multidimensional spatial relationships (side, distance or side length, angle) are transformed into intuitive and simple two-dimensional triangular relationships. This transformation provides important theoretical and methodological support for studying the impact mechanism of GNSS ambiguity confirmation reliability.

[0095] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors, characterized in that, Includes the following steps: Step S1: Construct a GNSS double-difference mathematical model using GNSS pseudorange observations and carrier phase observations. Based on the GNSS double-difference mathematical model, obtain the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix using the least squares method. Step S2: Based on the floating-point solution of the multidimensional fuzzy vector and its variance-covariance matrix, use the least squares fuzzy decorrelation adjustment method to obtain the optimal integer solution and the second-best integer solution of the multidimensional fuzzy vector. Step S3: Using the elliptic norm theory, with the floating-point solution of the fuzzy vector, the optimal integer solution of the fuzzy vector, and the second-best integer solution of the fuzzy vector as endpoints, calculate the elliptic norm side length of the side formed by any two endpoints. Step S4: Using the A-inner product theory, calculate the angle between the A-inner product of two vectors with the floating-point solution of the ambiguity vector, the optimal integer solution of the ambiguity vector, and the second-best integer solution of the ambiguity vector as vertices, and check whether the angle between any two sides is not greater than 180°. Step S5: Construct a two-dimensional Euclidean triangle with the floating-point solution, the optimal integer solution, and the suboptimal integer solution of the ambiguity vector as the three vertices, the three elliptic norm side lengths as the three sides, and the three A-inner product angles as the three interior angles. Transform the complex and abstract multidimensional spatial relationship between the floating-point solution, the optimal integer solution, and the suboptimal integer solution of the GNSS multidimensional ambiguity vector into a simple and intuitive two-dimensional Euclidean triangle relationship.

2. The two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors as described in claim 1, characterized in that, In step S1, it is assumed that two GNSS receivers observe multi-frequency, multi-system GNSS at the same time. t Frequency One satellite, For the first i The number of frequency observation satellites i =1, 2, …, t Furthermore, each system selects a reference satellite within each system and each frequency to form a double-difference mathematical model, thus forming... n = m - t One double-difference pseudorange observation equation and n The GNSS double-difference mathematical model is composed of two double-difference carrier phase observation equations, combined with a double-difference stochastic model of pseudorange and carrier phase observations: ； ； In the formula, and These are the expectation and variance of the double-difference pseudorange observations, respectively. and These are the expectation and variance of the double-difference carrier phase observations, respectively. and These are the double-difference pseudorange observation vector and the double-difference carrier phase observation vector, respectively. and These are the baseline vector and the multidimensional double-difference ambiguity vector, respectively. for The rank of the double difference coefficient matrix is ​​given by the following formula. , , and These are the first in multi-frequency multi-system GNSS. i The wavelength of each frequency and the dimension of the double-difference ambiguity vector, where i =1, 2,…, t ; It is the cofactor matrix of the double-difference observation vectors; and These are the standard deviations of the non-differential pseudorange observations and the non-differential carrier phase observations, respectively.

3. The two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors as described in claim 2, characterized in that, In step S1, the specific steps for obtaining the floating-point solution of the GNSS multidimensional ambiguity vector and its variance-covariance matrix using the least squares method are as follows: The baseline vector is obtained using the least squares method. b floating-point solution and multidimensional ambiguity vector a floating-point solution Its variance-covariance matrix and : ； ； In the formula, It is a symmetric positive definite matrix. for n A column vector of real numbers.

4. The two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors as described in claim 3, characterized in that, In step S2, according to and The ambiguity vector is obtained using the least squares ambiguity decorrelation adjustment method. a optimal integer solution and suboptimal integer solutions , and All n A column vector of real numbers.

5. The two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors as described in claim 1, characterized in that, Step S3 specifically includes: set up G for n If a Helmet positive definite matrix is ​​given, then the vector... The elliptic norm based on G is: ； In the formula, for n dimensional vector real number field, ; Floating-point solution with ambiguity vector Optimal integer solution of ambiguity vector and the suboptimal integer solution of the ambiguity vector The endpoints form three edges, which are obtained from the floating-point solution of the ambiguity vector. and optimal integer solution The edge formed by the endpoints , from the ambiguity vector floating-point solution and suboptimal integer solutions The edge formed by the endpoints And the optimal integer solution from the ambiguity vector and suboptimal integer solutions The edge formed by the endpoints Using the G-based elliptic norm theory Calculate vectors Based on The formula for the elliptic norm L1 is: ； In the formula, and L1 is a real number vector, and L2 is a vector. sum vector The two-dimensional distance between them Solve the variance-covariance matrix of the ambiguity vector using floating-point methods. The inverse matrix; and so on, to obtain the vector. The elliptic norm L2 and vector The formula for the elliptic norm L3 is as follows: ； ； In the formula, , ,and and All are real number vectors, L2 and L3 are vectors respectively. sum vector Two-dimensional distance and vector between sum vector The two-dimensional distance between them.

6. The two-dimensional transformation method for multidimensional spatial relationships between GNSS ambiguity vectors as described in claim 5, characterized in that, Step S4 specifically includes: Let A be n If a real symmetric positive definite matrix of order 1 is given, then the vector... sum vector The A-inner product is defined as follows: ； In the formula, and , and Vectors based on A-inner product sum vector Angle between The calculation formula is: ； In the formula, for" The inverse cosine function, and They are vectors sum vector The elliptic norm based on A, using the formula of A-inner product theory. And the formula for the angle between vectors based on the A-inner product , using fuzzy vector floating-point solution A vector with vertices based on the A-inner product. sum vector Angle between for: ； And so on, using the optimal integer solution of the ambiguity vector. A vector with vertices based on the A-inner product. sum vector Angle between for: ； suboptimal integer solution of ambiguity vector A vector with vertices based on the A-inner product. sum vector Angle between for: ； Test the angle between any two sides using their A-inner product. Is it no more than 180°? If the angle is greater than 180°, then .

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