A high-precision monitoring method for scene elevation difference based on riemannian manifold

Abstract

The application provides a scene elevation difference high-precision monitoring method based on a Riemann manifold, and specifically comprises the following steps: constructing a global navigation satellite system (GNSS) four-receiver vertical plane array, acquiring spatial data of a scene to be measured, extracting GNSS vertical plane four-baseline data according to the relative position relationship of the receivers, combining baseline length and angle constraints to construct an optimization objective function, constructing a Riemann manifold structure based on the objective function, converting the baseline optimization problem into a geometric pose adjustment problem of a rigid body formed by the four vertical plane baselines in Euclidean space, gradually adjusting the baseline position by calculating the gradient of the objective function, and finding an optimal solution, and further calculating the elevation difference in combination with the optimization solution result. The method realizes scene elevation difference monitoring through the GNSS vertical plane four-baseline structure, captures the nonlinear structure of the terrain data by using the Riemann manifold, maps the complex Riemann manifold calculation to the Euclidean space, simplifies the optimization process, and improves the scene elevation difference precision.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and positioning technology, and in particular relates to a high-precision monitoring method for field elevation difference based on Riemannian manifold. Background Technology

[0002] Elevation monitoring has wide applications in various fields such as Geographic Information Systems (GIS), building engineering, disaster early warning, and navigation. However, traditional elevation monitoring methods often fail to provide sufficient measurement accuracy when dealing with complex nonlinear terrain and are susceptible to various error factors, making it difficult to meet the demands for high precision and efficiency. Currently, most traditional methods rely on simple geometric models, which often exhibit low accuracy when handling complex nonlinear terrain and suffer from performance bottlenecks in multi-scale data processing, thus failing to effectively address the growing demand for high-precision and high-efficiency monitoring.

[0003] To address the aforementioned issues, research has shown that Riemannian manifolds can effectively capture the inherent nonlinear structure of terrain data, thus providing a more accurate solution for elevation difference monitoring. Therefore, the elevation difference monitoring method based on Riemannian manifolds can achieve higher accuracy in elevation measurements of nonlinear terrain, effectively improving the overall accuracy of elevation monitoring, meeting increasingly stringent high-precision requirements, and providing strong technical support for applications in related fields. Summary of the Invention

[0004] In view of this, the present invention aims to overcome the shortcomings of the above-mentioned problems in the prior art and proposes a high-precision monitoring method for field elevation difference based on Riemannian manifold, which can effectively overcome the accuracy bottleneck of the prior art under complex terrain conditions and improve monitoring efficiency.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] The first aspect of this invention provides a high-precision monitoring method for field elevation differences based on Riemannian manifolds, comprising:

[0007] Step 1: Construct a GNSS four-receiver vertical array, obtain the positioning coordinates of the four receivers A, B, C, and D to form a spatial dataset, and obtain the four baseline x, y, z, and s data between adjacent receivers based on the relative positional relationship between the receivers.

[0008] Step 2: The baselines x, y, z, and s all have a modulus of m, and adjacent baselines are pairwise orthogonal. Based on the baseline lengths and the included angle constraints, construct the objective function to be optimized:

[0009]

[0010] Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively.

[0011] The constraints are:

[0012] ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1

[0013] Where x, y, z, and s are all of length m, x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint is added between the new baseline and x and y. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1.

[0014] Step 3: Based on the objective function, construct a Riemannian manifold structure using the principles of Riemannian geometry, wherein the Riemannian manifold structure provides constraints and search space for the optimization process;

[0015] Step 4: Transform the baseline optimization process into a geometric pose adjustment problem of a rigid body composed of the four vertical plane baselines in Euclidean space, forming a new objective function to be optimized. By calculating the vector gradient of the new objective function, the baseline position is gradually adjusted to find the optimal solution and ensure that the geometric constraints of the baseline are satisfied.

[0016] Step 5: Obtain the baseline optimization results x1, y1, z1, s1, and further calculate the elevation difference of the field to be measured.

[0017] Furthermore, step 1 includes:

[0018] Receiver B is located horizontally to the right of receiver A, and processes the data between receiver A and receiver B to construct a baseline x;

[0019] The receiver C is located vertically above the receiver B, and processes the data between the receiver B and the receiver C to construct a baseline y;

[0020] The receiver D is located horizontally to the left of the receiver C, and processes the data between the receiver C and the receiver D to construct a baseline z;

[0021] Receiver A is located vertically below receiver D, and processes the data between receiver D and receiver A to construct a baseline s;

[0022] Furthermore, the modulus m of the four baselines in step 2 can be arbitrarily set according to the scenario.

[0023] Furthermore, step 4 includes: adjusting the geometric pose by Euler angle rotation, wherein the complex Riemannian manifold calculation is mapped to Euclidean space by transforming the baseline optimization process into the rotation of the Euler angles.

[0024] Furthermore, step 5 includes: for the baseline optimization results x1, y1, z1, s1, each includes three components: eastward, northward, and celestial, wherein the elevation difference is the celestial component corresponding to the baseline optimization result x1.

[0025] A second aspect of the present invention provides a high-precision monitoring device for field elevation differences based on Riemannian manifolds, comprising:

[0026] Data acquisition and baseline construction are used to construct a GNSS four-receiver vertical array to acquire spatial data of the field under test; based on the relative positions of the receivers, the GNSS vertical four-baseline data are extracted to provide preliminary spatial information for subsequent calculations;

[0027] The objective function building module is used to construct an optimization objective function based on baseline length and the geometric relationship between baselines.

[0028] The baselines x, y, z, and s all have a modulus of m, and adjacent baselines are pairwise orthogonal. Based on the baseline lengths and the included angle constraints, the objective function to be optimized is constructed as follows:

[0029]

[0030] Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively.

[0031] The constraints are:

[0032] ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1

[0033] Where x, y, z, and s are all of length m, x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint is added between the new baseline and x and y. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1.

[0034] A Riemannian manifold construction module is used to construct a Riemannian manifold structure based on the objective function, and to define a search space based on the Riemannian manifold;

[0035] The optimization solution module is used to transform the baseline optimization problem into a geometric pose adjustment problem of a rigid body composed of four vertical plane baselines in Euclidean space, form a new objective optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new objective function to find the optimal solution.

[0036] The elevation difference calculation module is used to combine the optimized solution results to further calculate the elevation difference of the field under test, providing a basis for accurate elevation monitoring.

[0037] A third aspect of the present invention provides an electronic device, including a processor and a memory communicatively connected to the processor and used to store executable instructions of the processor, the processor being used to execute the above-described method for high-precision monitoring of field elevation differences based on Riemannian manifolds.

[0038] The fourth aspect of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for high-precision monitoring of field elevation differences based on Riemannian manifolds.

[0039] Compared with existing technologies, the high-precision monitoring method for field elevation differences based on Riemannian manifolds described in this invention has the following advantages:

[0040] First, the Riemannian manifold is a geometric object with unique curvature deformation characteristics, which can well describe nonlinear and complex terrain surfaces. Unlike traditional planar geometry or simple curved surface models, it can more accurately capture the undulations, curvatures and irregularities of the terrain, thus more accurately calculating the elevation difference of the scene, especially in areas with drastic terrain changes, such as mountains and canyons, and can better reflect the actual terrain conditions.

[0041] Secondly, in the field of terrain analysis technology, Riemannian manifold breaks through traditional limitations, accurately analyzing both macroscopic terrain and microscopic local details, with a wide range of applications. At the same time, it can flexibly optimize the calculation model and parameters according to different scales and accuracy requirements, effectively meeting the needs of various application scenarios, and has extremely strong adaptability and versatility.

[0042] Third, this invention maps operations on Riemannian manifolds to Euclidean space, resulting in lower computational load and complexity, making it suitable for low-cost processors such as microcontrollers. Attached Figure Description

[0043] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0044] Figure 1 This is a schematic diagram of the vertical plane four-baseline structure of the present invention.

[0045] Figure 2 The flowchart of a high-precision monitoring method for field elevation difference based on Riemannian manifold provided by the present invention is shown. Detailed Implementation

[0046] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0047] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0048] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] Example 1:

[0051] like Figure 1-2 As shown, this invention provides a high-precision monitoring method for field elevation differences based on Riemannian manifolds, comprising the following steps:

[0052] (1) Construct a GNSS four-receiver vertical array, obtain the positioning coordinates of the four receivers A, B, C, and D, form a spatial dataset, and obtain the four baseline x, y, z, and s data between adjacent receivers based on the relative positional relationship between the receivers.

[0053] Specifically, receiver B is located horizontally to the right of receiver A, and processes the data between receiver A and receiver B to construct a baseline x;

[0054] The receiver C is located vertically above the receiver B, and processes the data between the receiver B and the receiver C to construct a baseline y;

[0055] The receiver D is located horizontally to the left of the receiver C, and processes the data between the receiver C and the receiver D to construct a baseline z;

[0056] Receiver A is located vertically below receiver D, and processes the data between receiver D and receiver A to construct a baseline s;

[0057] (2) The baselines x, y, z, and s all have a modulus of m, and adjacent baselines are pairwise orthogonal. Based on the baseline lengths and the included angle constraints, the objective function to be optimized is constructed as follows:

[0058]

[0059] Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively.

[0060] The constraints are:

[0061] ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1

[0062] Where x, y, z, and s are all of length m, and m can be set arbitrarily according to the scene. x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1.

[0063] (3) Based on the objective function, construct the Riemannian manifold structure using the principles of Riemannian geometry:

[0064]

[0065] Specifically, it forms a closed and bounded manifold embedded in Euclidean space. The Riemannian manifold structure provides constraints and search space for the optimization process;

[0066] (4) The baseline optimization process is transformed into a geometric pose adjustment problem of a rigid body composed of the four vertical plane baselines in Euclidean space, forming a new objective function to be optimized. By calculating the vector gradient of the new objective function, the baseline position is gradually adjusted to find the optimal solution and ensure that the geometric constraints of the baseline are satisfied.

[0067] Among them, geometric pose adjustment is performed by Euler angle rotation, which transforms the baseline optimization process into the rotation of the Euler angle, thereby realizing the mapping from Riemannian manifold to Euclidean space;

[0068] Specifically, α, β, γ represent Euler angles, and α, β, γ ∈ [-π, π]. The Euler angles α, β, γ are rotated in the ZYX order (spacecraft order), that is, first rotated α° around the z-axis, then rotated β° around the y-axis, and then rotated γ° around the x-axis. At this time, the rotation matrix can be obtained:

[0069]

[0070] in,

[0071]

[0072] Given an initial baseline x0, y0, z0, s0 on the Riemannian manifold, the next search baseline on the manifold can be determined as follows:

[0073] x=R(α,β,γ)x0

[0074] y=R(α,β,γ)y0

[0075] z=R(α,β,γ)z0

[0076] s=R(α,β,γ)s0

[0077] At this point, the new objective function to be optimized can be transformed into:

[0078] f(x,y,z,s)=f(R(α,β,γ)x0,R(α,β,γ)y0,R(α,β,γ)z0,R(α,β,γ)s0)=g(α,β,γ)

[0079] Based on the current baseline location information, combined with the manifold's metric tensor and its gradient information, a local optimization search is performed to determine the location of the next search baseline.

[0080] Specifically, the descent direction is determined by calculating the partial derivatives of the new objective function to be optimized, and the iteration of the Euler angles is as follows:

[0081]

[0082] Where, αk ,β k ,γ k Represents the current Euler angle, α k+1 ,β k+1 ,γ k+1 The Euler angles represent the next update, and h represents the search step size. This indicates that partial derivatives are calculated for each of the new objective functions to be optimized.

[0083] (5) Obtain the baseline optimization results x1, y1, z1, s1, and further calculate the elevation difference of the field to be measured. Among them, x1, y1, z1, s1 each include three components: eastward, northward, and celestial. The elevation difference is the celestial component corresponding to the baseline optimization result x1.

[0084] Example 2:

[0085] A high-precision monitoring device for field elevation difference based on Riemannian manifolds, comprising:

[0086] Data acquisition and baseline construction are used to construct a GNSS four-receiver vertical array to acquire spatial data of the field under test; based on the relative positions of the receivers, the GNSS vertical four-baseline data are extracted to provide preliminary spatial information for subsequent calculations;

[0087] The objective function building module is used to construct an optimization objective function based on baseline length and the geometric relationship between baselines.

[0088] The baselines x, y, z, and s all have a modulus of m, and adjacent baselines are pairwise orthogonal. Based on the baseline lengths and the included angle constraints, the objective function to be optimized is constructed as follows:

[0089]

[0090] Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively.

[0091] The constraints are:

[0092] ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1

[0093] Where x, y, z, and s are all of length m, x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint is added between the new baseline and x and y. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1.

[0094] A Riemannian manifold construction module is used to construct a Riemannian manifold structure based on the objective function, and to define a search space based on the Riemannian manifold;

[0095] The optimization solution module is used to transform the baseline optimization problem into a geometric pose adjustment problem of a rigid body composed of four vertical plane baselines in Euclidean space, form a new objective optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new objective function to find the optimal solution.

[0096] The elevation difference calculation module is used to combine the optimized solution results to further calculate the elevation difference of the field under test, providing a basis for accurate field elevation monitoring.

[0097] Example 3:

[0098] An electronic device includes a processor and a memory communicatively connected to the processor and used to store processor-executable instructions, the processor being used to execute the aforementioned method for high-precision monitoring of field elevation differences based on Riemannian manifolds.

[0099] Example 4:

[0100] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned method for high-precision monitoring of field elevation differences based on Riemannian manifolds.

[0101] Matters not covered in this invention are common knowledge.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A high-precision monitoring method for field elevation difference based on Riemannian manifolds, characterized in that: include: Step 1: Construct a GNSS four-receiver vertical array, obtain the positioning coordinates of the four receivers A, B, C, and D to form a spatial dataset, and obtain the four baseline x, y, z, and s data between adjacent receivers based on the relative positional relationship between the receivers. Step 2: Assume that the modulus of baselines x, y, z, and s are all m, and that adjacent baselines are pairwise orthogonal. Based on the baseline length and included angle constraints, construct the objective function to be optimized: Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively. The constraints are: ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1 Where x, y, z, and s are all m in length, x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint is added between the new baseline and x and y. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1. Step 3: Based on the objective function, construct a Riemannian manifold structure using the principles of Riemannian geometry, wherein the Riemannian manifold structure provides constraints and search space for the optimization process; Step 4: Transform the baseline optimization process into a geometric pose adjustment problem of a rigid body composed of four vertical plane baselines in Euclidean space, forming a new objective function to be optimized. By calculating the vector gradient of the new objective function, the baseline position is gradually adjusted to find the optimal solution and ensure that the geometric constraints of the baseline are satisfied. Step 5: Obtain the baseline optimization results x1, y1, z1, s1, and further calculate the field elevation difference of the test area.

2. The high-precision monitoring method for field elevation difference based on Riemannian manifold according to claim 1, characterized in that: Step 1 includes: Receiver B is located horizontally to the right of receiver A, and processes the data between receiver A and receiver B to construct a baseline x; The receiver C is located vertically above the receiver B, and processes the data between the receiver B and the receiver C to construct a baseline y; The receiver D is located horizontally to the left of the receiver C, and processes the data between the receiver C and the receiver D to construct a baseline z; Receiver A is located vertically below receiver D, and processes the data between receiver D and receiver A to construct a baseline s.

3. The high-precision monitoring method for field elevation difference based on Riemannian manifold as described in claim 1, characterized in that: In step 2, the modulus m of the four baselines is set according to the scenario.

4. The high-precision monitoring method for field elevation difference based on Riemannian manifold according to claim 1, characterized in that: Step 4 includes: Geometric pose adjustment is achieved through Euler angle rotation, where the complex Riemannian manifold calculations are mapped to Euclidean space by transforming the baseline optimization process into the rotation of the Euler angles.

5. The high-precision monitoring method for field elevation difference based on Riemannian manifold according to claim 1, characterized in that: Step 5 includes: for the baseline optimization results x1, y1, z1, s1, each includes three components: eastward, northward, and celestial. Among them, the field elevation difference is the celestial component corresponding to the baseline optimization result x1.

6. A high-precision monitoring device for field elevation difference based on Riemannian manifolds, characterized in that, include: Data acquisition and baseline construction are used to build a GNSS four-receiver vertical array to acquire spatial data of the field under test. Based on the relative positions of the receivers, extract the four baseline data of the GNSS vertical plane to provide preliminary spatial information for subsequent calculations; The objective function building module is used to construct an optimization objective function based on baseline length and the geometric relationship between baselines. Assuming the baselines x, y, z, and s all have a modulus of m, and that adjacent baselines are pairwise orthogonal, the objective function to be optimized is constructed based on the baseline length and included angle constraints: Where a, b, c, and d are double-difference observations, and A, B, C, and D are 3×3 coefficient matrices obtained after mathematical equivalent transformation of baselines x, y, z, and s, respectively. The constraints are: ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1 Where x, y, z, and s are all m in length, x and y are orthogonal to each other and have a cosine value of 0. Each time a baseline is added, an angle constraint is added between the new baseline and x and y. Two adjacent baselines of x, y, z, and s are orthogonal. The cosine values ​​of x and z are -1, y and z are 0, x and s are 0, and y and s are -1. A Riemannian manifold construction module is used to construct a Riemannian manifold structure based on the objective function, and to define a search space based on the Riemannian manifold; The optimization solution module is used to transform the baseline optimization problem into a geometric pose adjustment problem of a rigid body composed of four vertical plane baselines in Euclidean space, form a new objective optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new objective function to find the optimal solution. The elevation difference calculation module is used to combine the optimized solution results to further calculate the elevation difference of the field under test, providing a basis for accurate field elevation monitoring.

7. An electronic device comprising a processor and a memory communicatively connected to the processor and used for storing processor-executable instructions, characterized in that: The processor is used to execute the high-precision monitoring method for field elevation difference based on Riemannian manifold as described in any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the high-precision monitoring method for field elevation difference based on Riemannian manifold as described in any one of claims 1-5.

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