Intelligent real-time ar engineering surveying method and system

By generating a 3D space using the AR camera on the RTK handheld device and combining it with the adjustment algorithm to calculate the position coordinates of the point to be measured, the measurement accuracy problem caused by poor satellite signal or obstacles is solved, achieving centimeter-level measurement accuracy and efficient operation.

CN116518949BActive Publication Date: 2026-04-07GUANGZHOU HI TARGET SURVEYING INSTRUMENT CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-04-19
Publication Date
2026-04-07

AI Technical Summary

Technical Problem

Existing engineering surveying techniques suffer from decreased measurement accuracy when there are poor satellite signals, poor network signals, or obstacles between two points, making it difficult to meet centimeter-level measurement requirements.

Method used

A 3D space is generated using the AR camera on the RTK handheld device, the positions of control points are marked, and the position coordinates of the point to be measured are calculated by combining the distances of multiple control points using an adjustment algorithm. The observation equation is then constructed and solved using the least squares method.

Benefits of technology

It achieves centimeter-level measurement accuracy even in situations with poor satellite signal or the presence of obstacles, reducing operational errors and measurement inaccuracies, and improving the reliability and efficiency of measurements.

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Abstract

This invention discloses an intelligent real-time AR engineering measurement method and system. The method includes: spatial recognition of the current environment using an AR camera mounted on an RTK handheld device to generate a three-dimensional space of the current environment; setting up a base station and measuring the position coordinates of control points using an RTK rover station, then marking the positions of the control points in the three-dimensional space using the AR camera; moving the AR camera from the control points to the point to be measured, and measuring the distance between the control points and the point to be measured in the three-dimensional space; and solving for the position coordinates of the point to be measured using an adjustment algorithm and at least two sets of distance observation equations from the control points to the point to be measured. Although this invention also relies on control points for calculation, it utilizes an AR camera for scene recognition to construct a three-dimensional space, solving the problem that the distance between the control points and the point to be measured must be a straight line without obstructions, while simultaneously meeting the centimeter-level measurement accuracy requirements of engineering surveying.
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Description

Technical Field

[0001] This invention relates to the field of positioning and measurement technology, specifically to an intelligent real-time AR engineering measurement method and system. Background Technology

[0002] Engineering surveying plays a vital role in basic engineering projects such as railways, highways, bridges, buildings, and tunnels.

[0003] In engineering surveying, RTK (Real-Time Kinematic) real-time dynamic measurement technology is mainly used. RTK technology can obtain coordinates with centimeter-level positioning accuracy in real time. Its working principle involves placing one receiver at a reference point with known coordinates as a base station, and placing one or more receivers on a carrier as rover stations. The base station and rover stations simultaneously receive signals transmitted by the same satellite at the same time. The observation values ​​obtained by the base station are compared with known position information to obtain differential correction values. These correction values ​​are then transmitted in a timely manner to the rover station on the same satellite via data links such as radio or network, thus providing the rover station with high-precision real-time coordinate values ​​corrected by the differential correction values.

[0004] However, if the base station and the mobile terminal are located in areas with poor signal strength or are subject to interference or obstruction, the uploaded or received information will be out of sync, leading to a significant decrease in measurement accuracy. For example, when an RTK mobile station is set up near water, high-voltage lines, or transformers, satellite signals will be interfered with, and the coordinates cannot be fixed. When an RTK mobile station is set up under tall buildings, under large trees, under bridges, or in culverts, satellite signals will be blocked or refracted, and measurement accuracy will also decrease.

[0005] Currently, in scenarios with poor satellite or network signals, measurements can be taken by translating the point to be measured. This involves measuring the coordinates of the external point to be measured and the distance between the two points using a laser rangefinder, and then calculating the coordinates of the point to be measured.

[0006] Although total stations have very high distance measurement accuracy, they also have significant drawbacks. First, they require annual calibration to prevent errors from occurring. Second, they are expensive, with market prices ranging from 10,000 to 500,000 yuan, which significantly increases operating costs. Third, they are large and heavy, making them laborious to use in areas with complex terrain. Fourth, they cannot be used if there are obstacles between the station and the point to be measured.

[0007] Therefore, existing methods for external measurement by translating the point to be measured must not only ensure that the temporary point to be measured can receive a good signal, but also ensure that there are no obstacles between the two points.

[0008] In view of this, it is necessary to improve the existing method of translating the point to be measured in order to achieve centimeter-level engineering measurements when there are differences in satellite signals, network signals, or obstacles between the two points. Summary of the Invention

[0009] To address the aforementioned deficiencies, the technical problem to be solved by this invention is to provide an intelligent real-time AR engineering measurement method and system, in order to solve the problem that existing technologies not only need to ensure that the location of the temporary measurement point can also receive a good signal, but also need to ensure that there are no obstacles between the two points.

[0010] Therefore, the intelligent real-time AR engineering measurement method provided by the present invention includes the following steps:

[0011] The AR camera mounted on the RTK handheld device is moved to perform spatial recognition of the current environment and generate a three-dimensional space of the current environment.

[0012] Set up a base station, use an RTK rover to measure the position coordinates of the control points, and then use an AR camera to mark the position of the control points in three-dimensional space;

[0013] Move the AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space;

[0014] According to the adjustment algorithm, the position coordinates of the point to be measured are calculated by using at least two sets of control point position coordinates and the distance from the control point to the point to be measured.

[0015] In the above method, preferably, the position coordinates of the point to be measured are calculated by using a weighted adjustment algorithm based on the distance measured at each control point.

[0016] In the above method, preferably, the adjustment algorithm is divided into two parts: horizontal plane and elevation. The specific steps for constructing the observation equation and solving it to obtain the position coordinates of the point to be measured are as follows:

[0017] Construct the distance observation equation s between the i-th control point and the point to be measured in the horizontal plane. i Distance observation corrections Error equation of distance observations v s ;

[0018] Construct the elevation observation equation s between the i-th control point and the point to be measured in the elevation direction. i Correction of elevation observation values Error equation of elevation observations v s ;

[0019] The coordinates E of the point to be measured are obtained by using the least squares method and adding appropriate distance weighting, E = (C TPC) - 1 C T PL+E 0 ;

[0020] Where C is the coefficient matrix, C T Let P be the transpose of the coefficient matrix C, P be the weight matrix, L be the observation matrix, and E be the value matrix. 0 These are the approximate coordinates of the point to be measured;

[0021] P i Let be the weight of the i-th control point;

[0022] x 0 ,y 0 ,z 0 The approximate coordinates of the point to be measured can be calculated from the planar distances between any two control points in the current three-dimensional space of the environment and the point to be measured.

[0023] In the above method, preferably, the distance observation equation s between the i-th control point and the point to be measured is... i Distance observation corrections Error equation of distance observations v s They are respectively:

[0024]

[0025]

[0026] v s =CX-L s ;

[0027] x i ,y i ,z i Let i be the coordinates of the i-th control point;

[0028] x, y, z are the coordinates of the point to be measured, calculated using the coordinates of the i-th control point;

[0029] The observed distance L from the i-th control point to the point to be measured i Expanding using Taylor's formula, we get:

[0030]

[0031]

[0032] Among them, l i It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment. It is the distance from the i-th control point to the measured point in the approximate coordinates of the current three-dimensional space. C x and C y Let be the direction cosines of the distance from the i-th control point to the point to be measured in the horizontal plane.

[0033]

[0034] and These are the coefficients of the Taylor expansion, and

[0035] The error equation v s Written in matrix form: v = CE - L;

[0036] in,

[0037] The elevation observation equation from the i-th control point to the point to be measured is h i Elevation observation correction v hi Error equation of elevation observations v h They are respectively:

[0038] h i =zz i ;

[0039]

[0040]

[0041] in, Let be the elevation from the i-th control point to the point to be measured in the current three-dimensional space of the environment;

[0042]

[0043] In the above method, preferably, the Gaussian iteration method is used to solve for the least squares solution in the horizontal plane; the elevation is directly solved using the least squares method.

[0044] In the above method, preferably, nominal precision and distance are used to weight p. i Conduct an assessment. l i It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment.

[0045] This invention also provides an intelligent real-time AR engineering measurement system, including a base station and an RTK rover station, as well as an AR camera and an RTK handheld device, wherein the RTK handheld device is equipped with:

[0046] The 3D space generation module is used to identify the current environment based on the movement of the AR camera and generate a 3D space.

[0047] The marking module is used to measure the position coordinates of the control points by the RTK rover station and mark the positions of the control points in the three-dimensional space using an AR camera.

[0048] The measurement module is used to move the AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space;

[0049] The calculation module is used to calculate the position coordinates of the point to be measured based on the adjustment algorithm, using at least two sets of control point position coordinates and the distance from the control point to the point to be measured.

[0050] In the above system, preferably, the calculation module uses a weighted adjustment algorithm based on the distances from each control point to the point to be measured to calculate the position coordinates of the point to be measured.

[0051] In the above system, preferably, the adjustment algorithm is divided into two parts: horizontal plane and elevation. The specific steps for constructing the observation equation and solving it to obtain the position coordinates of the point to be measured are as follows:

[0052] Construct the distance observation equation s between the i-th control point and the point to be measured in the horizontal plane. i Distance observation corrections Error equation of distance observations v s ;

[0053] Construct the elevation observation equation s between the i-th control point and the point to be measured in the elevation direction. i Correction of elevation observation values Error equation of elevation observations v s ;

[0054] The coordinates E of the point to be measured are obtained by using the least squares method and adding appropriate distance weighting, E = (C T PC) - 1 C T PL+E 0 ;

[0055] Where C is the coefficient matrix, C T Let P be the transpose of the coefficient matrix C, P be the weight matrix, L be the observation matrix, and E be the value matrix. 0 These are the approximate coordinates of the point to be measured;

[0056] P i Let be the weight of the i-th control point;

[0057] x0 ,y 0 ,z 0 The approximate coordinates of the point to be measured can be calculated from the planar distances between any two control points in the current three-dimensional space of the environment and the point to be measured.

[0058] In the above system, preferably, nominal accuracy and distance are used to weight p. i Conduct an assessment. l i It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment.

[0059] As can be seen from the above technical solution, the intelligent real-time AR engineering measurement method and system provided by the present invention solves the problem of low engineering measurement accuracy in existing technologies when there are poor satellite signals, poor network signals, or obstacles between two points. Compared with the prior art, the present invention has the following beneficial effects:

[0060] The coordinates of the control points are measured using RTK. Then, the AR camera of the RTK handheld device is used to perform spatial recognition of the current environment to generate a three-dimensional space of the current environment. Then, the distances from at least two control points to the test point in the three-dimensional space are used to construct the observation equation and solve it to obtain the position coordinates of the test point. Although the calculation is still performed using control points, the AR camera is used to recognize the scene and construct a three-dimensional space, which solves the problem that the control points and the test point must be in a straight line and without obstructions.

[0061] In addition, by combining measurement adjustment, the coordinates of the points to be measured are calculated to meet the centimeter-level measurement accuracy required for engineering surveying. Attached Figure Description

[0062] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the embodiments of the present invention or the prior art will be briefly introduced and explained 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.

[0063] Figure 1 The flowchart of the intelligent real-time AR engineering measurement method provided by the present invention;

[0064] Figure 2 This is a schematic diagram illustrating how the AR camera mounted on the RTK handheld device performs spatial recognition of the current environment and generates a three-dimensional space of the current environment in this invention.

[0065] Figure 3This is a schematic diagram illustrating the measurement of the distance from the control point to the point to be measured in three-dimensional space according to the present invention. Detailed Implementation

[0066] 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 embodiments described below 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.

[0067] To provide a clearer explanation and description of the technical solution and implementation of the present invention, several preferred specific embodiments for implementing the technical solution of the present invention are described below.

[0068] It should be noted that the directional terms such as "inner" and "outer", "front" and "back" and "left" and "right" in this article are based on the product's usage status. Obviously, the use of these directional terms does not limit the scope of protection of this solution.

[0069] Please see Figure 1 , Figure 1 The present invention provides a flowchart of an intelligent real-time AR engineering measurement method.

[0070] like Figure 1 As shown, the present invention provides an intelligent real-time AR engineering measurement method, which includes the following steps:

[0071] Step 110: Use the AR camera mounted on the RTK handheld device to perform spatial recognition of the current environment and generate a three-dimensional space of the current environment, such as... Figure 2 As shown.

[0072] Step 120: Set up the base station and use the RTK rover to measure the position coordinates of the control points. Then, use an AR camera to mark the position of the control points in three-dimensional space.

[0073] The three-dimensional space referred to below is the three-dimensional space of the current environment generated in step 110.

[0074] Step 130: Move the RTK handheld device and AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space.

[0075] Step 140: Based on the adjustment algorithm, use at least two sets of distance observation equations from control points to the point to be measured to solve for the position coordinates of the point to be measured.

[0076] Specifically, the RTK rover is placed within 20 meters of the target point in a location with good signal. Once the RTK rover successfully receives and stabilizes the satellite signal, the AR camera on the RTK handheld device marks the current location of the RTK rover as a control point. The RTK handheld device and AR camera are then slowly moved to the target point, the location of the target point is marked, and the distance from the control point to the target point is measured in three-dimensional space to obtain a set of data.

[0077] Repeat the above steps, marking other control points and measuring the distances from each control point to the target point, to complete multiple sets of data. For example, the distance from the first control point A1 to the target point is L1, the distance from the second control point A2 to the target point is L2, the distance from the third control point A3 to the target point is L3, and the distance from the nth control point An to the target point is Ln. Figure 3 As shown.

[0078] The position coordinates of the target point are obtained by solving the observation equations from each control point to the target point. The observation equations include the distance observation equations, corrections, and error equations in the horizontal plane (xy plane) and the elevation observation equations, corrections, and error equations in the vertical plane (z plane).

[0079] As is well known, in any measurement work, measurement errors caused by operator mistakes are unavoidable in practical applications. Therefore, the method of this invention uses a distance-weighted adjustment algorithm from multiple control points to the point to be measured to reduce the impact of operator errors and measurement errors, thereby improving measurement accuracy.

[0080] The following section uses a 3D application as an example to explain in detail the specific algorithm for obtaining the position coordinates of the point to be measured by solving the observation equations from each control point to the point to be measured.

[0081] This application divides the adjustment algorithm into two parts: a horizontal plane and an elevation plane. The horizontal plane is divided into the xy-coordinate plane, and the elevation plane is the vertical plane of the z-coordinate plane. Let the coordinates of the i-th control point be (x... i ,y i ,z i The coordinates of the point to be measured are (x, y, z) obtained by calculating the coordinates of the i-th control point.

[0082] In the planar part, the distance observation equation s from the i-th control point to the point to be measured is constructed. i Distance observation correction v i Error equation of distance observations v s They are respectively:

[0083]

[0084]

[0085] vs =CX-L s ;

[0086] The observed distance L from the i-th control point to the point to be measured i Expanding using Taylor's formula, we get:

[0087]

[0088] in:

[0089] It is the distance from the i-th control point to the measured point in the approximate coordinates of the current three-dimensional space.

[0090] l i It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment.

[0091] C x and C y Let be the direction cosines from the i-th control point to the point to be measured in the xy-plane.

[0092]

[0093] and These are the coefficients of the Taylor expansion, and

[0094] The error equation v s In matrix form, v = CE - L.

[0095] in,

[0096] In the elevation section, the elevation observation equation h from the i-th control point to the point to be measured is constructed. i Elevation observation correction v hi Error equation of elevation observations v h They are respectively:

[0097] h i =zz i ;

[0098]

[0099]

[0100] in, Let be the elevation from the i-th control point to the point to be measured in the current three-dimensional space of the environment.

[0101]

[0102] Based on the principle of least squares and with the addition of a corresponding distance weighting P, the solution for the coordinates E of the point to be measured is:

[0103] E = (C T PC) -1 C T PL+E 0 .

[0104] Where C is the coefficient matrix, C T Let P be the transpose of the coefficient matrix C, P be the weight matrix, L be the observation matrix, and E be the value matrix. 0 These are the approximate coordinates of the point to be measured.

[0105] In the plane adjustment section, L represents...

[0106] In the elevation adjustment section, L represents...

[0107] P i Let be the weight of the i-th control point.

[0108]

[0109] Since the above equation uses the first-order term of Taylor's formula, in practical algorithm implementation, the Gaussian iteration method can be used to solve it, and the equation is:

[0110] E i =E 0 ;

[0111] E i+1 =(C T PC) -1 C T PL+E i ;

[0112]

[0113]

[0114] Because the accuracy of distance observations from each control point to the measured point varies during actual measurements, it is necessary to statistically analyze the accuracy indicators for different distances. Experiments show that the longer the distance, the lower the relative accuracy. Therefore, the nominal accuracy plus distance is used for weighted evaluation, and its weighting... l i It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment.

[0115] Based on the above method, the present invention also provides an intelligent real-time AR engineering measurement system, including a base station and an RTK rover station, as well as an AR camera and an RTK handheld device. The AR camera is used to identify the current environment by moving the AR camera and generate a three-dimensional space. The RTK handheld device is equipped with:

[0116] The 3D space generation module is used to identify the current environment based on the movement of the AR camera and generate a 3D space.

[0117] The marking module is used to measure the position coordinates of the control points by the RTK rover station and mark the positions of the control points in the three-dimensional space using an AR camera.

[0118] The measurement module is used to move the AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space;

[0119] The calculation module is used to calculate the position coordinates of the point to be measured based on the adjustment algorithm, using at least two sets of control point position coordinates and the distance from the control point to the point to be measured.

[0120] The distance-weighted adjustment algorithm for multiple control points in the calculation module described above obtains the position coordinates of the point to be measured, reducing the impact of operator errors and measurement errors, and improving measurement accuracy. The specific algorithm has been explained in detail in the above method and will not be repeated here.

[0121] Based on the above description of specific embodiments, the intelligent real-time AR engineering measurement method provided by the present invention has the following advantages compared with the prior art:

[0122] First, the coordinates of the control points are measured using RTK. Then, the AR camera of the RTK handheld device is used to perform spatial recognition of the current environment, generating a three-dimensional space of the current environment. The coordinates of the test point are then calculated using the distance between the control point and the test point in the three-dimensional space. Although the calculation is still performed using control points, the AR camera is used to recognize the scene and construct a three-dimensional space, which solves the problem that the control point and the test point must be in a straight line and without obstructions. At the same time, combined with measurement adjustment, the coordinates of the test point are calculated to meet the centimeter-level measurement accuracy of engineering surveying.

[0123] Second, the measurement accuracy was improved by using a distance-weighted adjustment algorithm for multiple control points.

[0124] Third, in actual measurement processes, the greater the distance from the control point to the measured point, the lower the accuracy. Therefore, using nominal accuracy plus distance for weighted evaluation results in a weighted value. This is to improve measurement accuracy.

[0125] Fourth, it is low-cost, simple, and convenient to use, and the measurement results are accurate and reliable. Specifically, the solution of this invention does not require the purchase of additional equipment or the carrying of additional equipment to the field. Only the system software needs to be installed on the handheld device (Android device) of the RTK instrument to construct a three-dimensional space and mark the points to be measured using an AR camera, and then obtain the calculated data. After marking multiple sets of calculated data through the AR measurement camera, the coordinates of the points to be measured are calculated using a control point measurement adjustment algorithm, instead of simply using a single set of data for calculation, reducing the risk of operational errors and improving accuracy.

[0126] Fifth, the operation process is simple, reducing the operating costs for operators and making the measurement of coordinate points more efficient.

[0127] Finally, it should be noted that the terms "comprising," "including," or any other variations thereof as used herein are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a…" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0128] This invention is not limited to the above-described preferred embodiments. Anyone should know that any structural changes made under the guidance of this invention, and any technical solutions that are the same as or similar to this invention, fall within the protection scope of this invention.

Claims

1. An intelligent real-time AR engineering measurement method, characterized in that, Includes the following steps: The AR camera set on the RTK handheld device performs spatial recognition of the current environment and generates a three-dimensional space of the current environment. Set up a base station, use an RTK rover to measure the position coordinates of the control points, and then use an AR camera to mark the position of the control points in three-dimensional space; Move the AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space; The adjustment algorithm is divided into two parts: horizontal plane and elevation. Using at least two sets of distances from control points to the point to be measured, an observation equation is constructed, and the position coordinates of the point to be measured are obtained by solving it, including: Construct the distance observation equation between the i-th control point and the point to be measured in the horizontal plane. Distance observation corrections Error equation of distance observations ; Construct the elevation observation equation between the i-th control point and the point to be measured in the elevation direction. Correction of elevation observation values Error equation of elevation observations ; The coordinates of the point to be measured are obtained by using the least squares method and incorporating appropriate distance weighting. , ; in, The coefficient matrix, Coefficient matrix The transpose of the matrix, Let L be the weight matrix and L be the observation matrix. These are the approximate coordinates of the point to be measured; , Let be the weight of the i-th control point; where the nominal precision and distance are used to adjust the weight. Conduct an assessment. , It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment; , The approximate coordinates of the point to be measured are calculated from the planar distances between any two control points in the current three-dimensional space of the environment and the point to be measured.

2. The method according to claim 1, characterized in that, Distance observation equation between the i-th control point and the point to be measured Distance observation corrections Error equation of distance observations They are respectively: ; ; ; Let i be the coordinates of the i-th control point; The coordinates of the point to be measured are obtained by calculating the coordinates of the i-th control point; Observed distance from the i-th control point to the point to be measured Expanding using Taylor's formula, we get: , , in, It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment. It is the distance from the i-th control point to the measured point in the approximate coordinates of the current three-dimensional space. , and Let be the direction cosines of the approximate coordinates of the i-th control point to the point to be measured in the horizontal plane. , ; , ; and These are the coefficients of the Taylor expansion, and , ; Error equation Written in matrix form: ; in, , , ; Elevation observation equation from the i-th control point to the point to be measured Correction of elevation observation values Error equation of elevation observations They are respectively: in The elevation difference between the i-th control point and the approximate coordinates of the point to be measured in the current three-dimensional space of the environment; 3. The method according to claim 1, characterized in that, The least squares solution is obtained using the Gaussian iteration method within the horizontal plane. Elevation can be solved directly using the least squares method.

4. An intelligent real-time AR engineering surveying system, comprising a base station and an RTK rover station, characterized in that, It also includes an AR camera and an RTK handheld device, the RTK handheld device being equipped with: The 3D space generation module is used to identify the current environment based on the movement of the AR camera and generate the 3D space of the current environment. The marking module is used to measure the position coordinates of the control points by the RTK rover station and mark the positions of the control points in the three-dimensional space using an AR camera. The measurement module is used to move the AR camera from the control point to the point to be measured, and measure the distance from the control point to the point to be measured in three-dimensional space; The calculation module is used to divide the adjustment algorithm into two parts: horizontal plane and elevation. Using at least two sets of distances from control points to the point to be measured, it constructs observation equations and solves for the position coordinates of the point to be measured, including: Construct the distance observation equation between the i-th control point and the point to be measured in the horizontal plane. Distance observation corrections Error equation of distance observations ; Construct the elevation observation equation between the i-th control point and the point to be measured in the elevation direction. Correction of elevation observation values Error equation of elevation observations ; The coordinates of the point to be measured are obtained by using the least squares method and incorporating appropriate distance weighting. , ; in, The coefficient matrix, Coefficient matrix The transpose of the matrix, Let L be the weight matrix and L be the observation matrix. These are the approximate coordinates of the point to be measured; , Let be the weight of the i-th control point; where the nominal precision and distance are used to adjust the weight. Conduct an assessment. It is the distance in the horizontal plane from the i-th control point to the point to be measured in the current three-dimensional space of the environment; , The approximate coordinates of the point to be measured are calculated from the planar distances between any two control points in the current three-dimensional space of the environment and the point to be measured.

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