Scene elevation difference high-precision monitoring method based on Riemannian manifold

Abstract

The invention provides a scene elevation difference high-precision monitoring method based on Riemannian manifold, and the method specifically comprises the steps: constructing a global navigation satellite system (GNSS) four-receiver vertical plane array, obtaining to-be-measured field domain space data, and extracting GNSS vertical plane four-baseline data according to the relative position relation of receivers; combining the baseline length and the included angle constraint to construct an optimization objective function; constructing a Riemannian manifold structure based on the objective function; converting a baseline optimization problem into a geometric pose adjustment problem of a rigid body formed by four vertical plane baselines in Euclidean space, gradually adjusting the position of the baseline by calculating the gradient of an objective function, and searching for an optimal solution; and further calculating the elevation difference in combination with an optimized calculation result. According to the method, scene elevation difference monitoring is realized through a GNSS vertical plane four-baseline structure, a nonlinear structure of topographic data is captured by using a Riemannian manifold, complex Riemannian manifold calculation is mapped to an Euclidean space, the optimization process is simplified, and the scene elevation difference precision is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite navigation and positioning, and in particular relates to a high-precision monitoring method for scene elevation difference based on Riemann manifold. Background Art

[0002] Elevation monitoring has a wide range of applications in many fields, including geographic information systems (GIS), construction engineering, disaster warning, and navigation. However, traditional elevation monitoring methods often fail to provide sufficient measurement accuracy when faced with complex nonlinear terrains, and are easily affected by various error factors, making it difficult to meet the requirements of high precision and high efficiency. At present, most traditional methods rely on simple geometric models, which often show low accuracy when dealing with complex nonlinear terrains, and have performance bottlenecks in multi-scale data processing, and cannot effectively meet the growing demand for high-precision and high-efficiency monitoring.

[0003] To solve the above problems, research shows that Riemann 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 Riemann manifolds can achieve higher accuracy in elevation measurement of nonlinear terrain, effectively improve the overall accuracy of elevation monitoring, meet the increasingly stringent high-precision requirements, and provide 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 scene elevation difference based on Riemann manifold, which can effectively overcome the accuracy bottleneck of the prior art under complex terrain conditions and improve the monitoring efficiency.

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

[0006] The first aspect of the present invention provides a high-precision monitoring method for scene elevation difference based on Riemann manifold, comprising:

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

[0008] Step 2: The modulus lengths of the baselines x, y, z, and s are all m, and two adjacent baselines are orthogonal to each other. Based on the baseline lengths and the angle constraints, the objective function to be optimized is constructed:

[0009]

[0010] Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation;

[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] Among them, the modulus lengths of x, y, z, and s are all m, x and y are orthogonal to each other, and the cosine value is 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1;

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

[0015] Step 4: Convert the baseline optimization process into a geometric posture adjustment problem of a rigid body formed by the four vertical baselines in the Euclidean space, form a new objective function to be optimized, and gradually adjust the baseline position by calculating the vector gradient of the new objective function to find the optimal solution and ensure that the geometric constraints of the baseline are met;

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

[0017] Furthermore, the step 1 comprises:

[0018] The receiver B is located horizontally to the right of the receiver A, and processes the data between the receiver A and the 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] The receiver A is located vertically below the receiver D, and processes the data between the receiver D and the receiver A to construct a baseline s;

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

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

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

[0025] The second aspect of the present invention provides a high-precision monitoring device for scene elevation difference based on Riemann manifold, comprising:

[0026] Data collection and baseline construction are used to construct a GNSS four-receiver vertical plane array to obtain spatial data of the field to be measured; according to the relative position relationship of the receivers, the four baseline data of the GNSS vertical plane are extracted to provide preliminary spatial information for subsequent calculations;

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

[0028] The modulus lengths of the baselines x, y, z, and s are all m, and two adjacent baselines are orthogonal to each other. Based on the baseline lengths and the angle constraints, the objective function to be optimized is constructed:

[0029]

[0030] Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation;

[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] Among them, the modulus lengths of x, y, z, and s are all m, x and y are orthogonal to each other, and the cosine value is 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1;

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

[0035] An optimization solution module is used to convert the baseline optimization problem into a geometric posture adjustment problem of a rigid body formed by four vertical surface baselines in Euclidean space, form a new target optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new target function to find the optimal solution;

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

[0037] A third aspect of the present invention provides an electronic device, comprising a processor and a memory that is communicatively connected to the processor and is used to store executable instructions of the processor, wherein the processor is used to execute the above-mentioned high-precision monitoring method of scene elevation difference based on Riemann manifold.

[0038] A 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-mentioned high-precision monitoring method for scene elevation differences based on Riemann manifolds.

[0039] Compared with the prior art, the high-precision monitoring method of scene elevation difference based on Riemann manifold described in the present invention has the following advantages:

[0040] First, Riemann manifold is a geometric object with unique curvature deformation characteristics, which can well describe nonlinear and complex terrain surfaces. Different from traditional plane geometry or simple surface models, it can more accurately capture the ups and downs, curvature and irregularity of the terrain, thereby more accurately calculating the elevation difference of the scene, especially in areas with drastic terrain changes, such as mountainous areas and canyons, and can better reflect the actual terrain conditions;

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

[0042] Third, the present invention maps the operations on the Riemann manifold to the Euclidean space, which has a small amount of calculation and low complexity, and is suitable for low-cost processors such as single-chip microcomputers. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

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

[0045] Figure 2 A flow chart of a method for high-precision monitoring of scene elevation differences based on Riemann manifold provided by the present invention. DETAILED DESCRIPTION

[0046] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0047] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0048] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

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

[0050] Embodiment 1:

[0051] like Figure 1-2 As shown, the present invention provides a high-precision monitoring method for scene elevation difference based on Riemann manifold, comprising the following steps:

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

[0053] Specifically, the receiver B is located horizontally to the right of the receiver A, and processes the data between the receiver A and the 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] The receiver A is located vertically below the receiver D, and processes the data between the receiver D and the receiver A to construct a baseline s;

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

[0058]

[0059] Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation;

[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] Among them, the modulus lengths of x, y, z, and s are all m, and m can be set arbitrarily according to the scene. x and y are mutually orthogonal, and the cosine value is 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1;

[0063] (3) Based on the objective function, the Riemannian manifold structure is constructed using the Riemannian geometry principle:

[0064]

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

[0066] (4) converting the baseline optimization process into a geometric posture adjustment problem of a rigid body formed by the four vertical baselines in Euclidean space, forming a new objective function to be optimized, and gradually adjusting the baseline position by calculating the vector gradient of the new objective function to find the optimal solution and ensure that the geometric constraints of the baseline are satisfied;

[0067] The geometric posture is adjusted by rotating the Euler angle, and the baseline optimization process is converted into the rotation of the Euler angle to achieve the mapping of the Riemann manifold to the 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 order of ZYX (aerospace order), that is, first rotate α° around the z-axis, then rotate β° around the y-axis, and then rotate γ° around the x-axis. At this time, the rotation matrix can be obtained:

[0069]

[0070] in,

[0071]

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

[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 position information of the current baseline, combined with the metric tensor of the manifold and its gradient information, a local optimization search is performed to determine the position of the next search baseline;

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

[0081]

[0082] Among them, αk ,β k ,γ k Represents the current Euler angle, α k+1 ,β k+1 ,γ k+1 represents the Euler angle for the next update, h represents the search step length, It indicates that partial derivatives of the new objective function to be optimized are calculated respectively;

[0083] (5) Obtain the baseline optimization results x1, y1, z1, s1, and further calculate the elevation difference of the field to be measured. Wherein, x1, y1, z1, s1 all include three components of east, north and celestial, and the elevation difference is the celestial component corresponding to the baseline optimization result x1.

[0084] Embodiment 2:

[0085] A high-precision monitoring device for scene elevation difference based on Riemann manifold, comprising:

[0086] Data collection and baseline construction are used to construct a GNSS four-receiver vertical plane array to obtain spatial data of the field to be measured; according to the relative position relationship of the receivers, the four baseline data of the GNSS vertical plane are extracted to provide preliminary spatial information for subsequent calculations;

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

[0088] The modulus lengths of the baselines x, y, z, and s are all m, and two adjacent baselines are orthogonal to each other. Based on the baseline lengths and the angle constraints, the objective function to be optimized is constructed:

[0089]

[0090] Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation;

[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] Among them, the modulus lengths of x, y, z, and s are all m, x and y are orthogonal to each other, and the cosine value is 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1;

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

[0095] An optimization solution module is used to convert the baseline optimization problem into a geometric posture adjustment problem of a rigid body formed by four vertical surface baselines in Euclidean space, form a new target optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new target function to find the optimal solution;

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

[0097] Embodiment three:

[0098] An electronic device includes a processor and a memory which is in communication with the processor and is used to store instructions executable by the processor. The processor is used to execute the above-mentioned high-precision monitoring method of scene elevation difference based on Riemann manifold.

[0099] Embodiment 4:

[0100] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned high-precision monitoring method for scene elevation difference based on Riemann manifold.

[0101] Matters not covered by the present invention are known technologies.

[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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-precision monitoring method for scene elevation difference based on Riemann manifold, characterized by: include: Step 1: Build a GNSS four-receiver vertical array, obtain the positioning coordinates of the four receivers A, B, C, and D, form a spatial data set, and obtain the four baseline x, y, z, and s data between adjacent receivers based on the relative position relationship between the receivers; Step 2: Assume that the modulus lengths of baselines x, y, z, and s are all m, and that two adjacent baselines are orthogonal to each other. Based on the baseline length and angle constraints, construct the objective function to be optimized: Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation; The constraints are: ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1 Among them, the modulus lengths of x, y, z, and s are all m, x and y are orthogonal to each other, and the cosine value is 0. Each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1; Step 3: Based on the objective function, using the principle of Riemannian geometry, construct a Riemannian manifold structure, wherein the Riemannian manifold structure provides constraint conditions and search space for the optimization process; Step 4: Convert the baseline optimization process into a geometric posture adjustment problem of a rigid body composed of four vertical baselines in Euclidean space, form a new objective function to be optimized, and gradually adjust the baseline position by calculating the vector gradient of the new objective function to find the optimal solution and ensure that the geometric constraints of the baseline are met; Step 5: Obtain the baseline optimization results x1, y1, z1, s1, and further calculate the surface elevation difference of the field to be measured.

2. The method for high-precision monitoring of scene elevation difference based on Riemann manifold according to claim 1 is characterized in that: The step 1 comprises: The receiver B is located horizontally to the right of the receiver A, and processes the data between the receiver A and the 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; The receiver A is located vertically below the receiver D, and processes the data between the receiver D and the receiver A to construct a baseline s.

3. The method for high-precision monitoring of scene elevation difference based on Riemann manifold according to claim 1 is characterized in that: The modulus length m of the four baselines in step 2 is set according to the scenario.

4. The method for high-precision monitoring of scene elevation difference based on Riemann manifold according to claim 1 is characterized in that: The step 4 comprises: The geometric pose adjustment is performed by Euler angle rotation, wherein the complex Riemannian manifold calculation is mapped to the Euclidean space by converting the baseline optimization process into the rotation of the Euler angle.

5. The method for high-precision monitoring of scene elevation difference based on Riemann manifold according to claim 1 is characterized in that: The step 5 includes: for the baseline optimization result bases x1, y1, z1, s1, they all include three components: east, north and celestial, wherein the scene elevation difference is the celestial component corresponding to the baseline optimization result x1.

6. A high-precision monitoring device for scene elevation difference based on Riemann manifold, characterized in that: include: Data collection and baseline construction are used to build a GNSS four-receiver vertical array to obtain spatial data of the field to be measured; According to the relative position relationship of the receiver, the four baseline data of the GNSS vertical plane are extracted to provide preliminary spatial information for subsequent calculations; The optimization objective function building module is used to build the optimization objective function based on the baseline length and the geometric relationship between baselines: Assume that the modulus lengths of baselines x, y, z, and s are all m, and that two adjacent baselines are orthogonal to each other. Based on the baseline length and angle constraints, the objective function to be optimized is constructed: Among them, a, b, c, d are double difference observations, and A, B, C, D are the 3×3 coefficient matrices obtained after the baselines x, y, z, s are processed by mathematical equivalent transformation; The constraints are: ||x||=||y||=||z||=||s||=m,<x,y> =0,<x,z> =-1,<y,z> =0<x,s> =0,<y,s> =-1 Among them, the modulus lengths of x, y, z, and s are all m, x and y are orthogonal to each other, the cosine value is 0, and each time a baseline is added, an angle constraint between the new baseline and x and y is added. The adjacent baselines of x, y, z, and s are orthogonal, the cosine values ​​of x and z are -1, the cosine values ​​of y and z are 0, the cosine values ​​of x and s are 0, and the cosine values ​​of y and s are -1; A Riemann manifold construction module, used to construct a Riemann manifold structure according to the objective function, and define a search space based on the Riemann manifold; An optimization solution module is used to convert the baseline optimization problem into a geometric posture adjustment problem of a rigid body formed by four vertical surface baselines in Euclidean space, form a new target optimization function, and gradually adjust the position of the baseline by calculating the vector gradient of the new target function to find the optimal solution; The elevation difference calculation module is used to combine the optimization solution results to further calculate the elevation difference of the field to be measured, providing a basis for accurate field elevation monitoring.

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

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