Single-target vision-assisted Beidou observation station coordinate monitoring method

Abstract

The invention provides a single-target vision-assisted Beidou observation station coordinate monitoring method, which comprises the following steps of: firstly, acquiring initial coordinates of an observation station and a target, and performing coordinate conversion to obtain initial east-north-sky coordinates of the observation station; in real-time monitoring, the current pixel coordinates of the target and the current Beidou coordinates of the observation station are collected, the visual displacement is obtained by comparing the current pixel coordinates and the initial pixel coordinates of the target, northeast coordinate correction is carried out by combining a preset visual azimuth angle, and the visual northeast displacement of the target is obtained. And then performing visual estimation based on the displacement and the initial east-north-sky coordinates of the observation station to obtain the current visual east-north-sky coordinates of the observation station. And finally, fusing with the current Beidou coordinate of the observation station, and outputting the current northeast-east-sky coordinate of the observation station. According to the single-target vision-assisted Beidou observation station coordinate monitoring method provided by the invention, Beidou positioning is assisted based on single-target vision, the monitoring precision and continuity in an environment in which Beidou signals are shielded or interfered are improved, and stable and reliable displacement monitoring capability is maintained in a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of engineering measurement technology, specifically relating to a single-target visual-assisted BeiDou station coordinate monitoring method. Background Technology

[0002] Currently, the BeiDou Navigation Satellite System is widely used for displacement monitoring in infrastructure such as geological disaster prevention, water conservancy projects, and bridges and tunnels. However, in complex environments such as canyons, urban canyons, reservoir gates, and slope obstructions, satellite signals are easily interfered with by obstruction or multipath effects, leading to decreased positioning accuracy or even signal loss, making continuous and high-precision displacement monitoring difficult. To compensate for the shortcomings of satellite positioning in obstructed environments, existing technologies have adopted visual sensing systems for assisted positioning. However, most of these methods rely on deploying multiple reference targets and inferring station displacement through the spatial geometric relationships of these targets. Precise measurement of the world coordinates of multiple targets is required during on-site deployment, resulting in a complex and time-consuming installation process, high hardware costs, and difficult system maintenance. Furthermore, in multi-target systems, obstruction or damage to any target can lead to visual positioning failure, exhibiting poor adaptability and insufficient robustness in complex and dynamic outdoor environments, thus limiting its widespread application in emergency monitoring, temporary projects, and rapid deployment scenarios. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a single-target visual-assisted BeiDou station coordinate monitoring method to solve the aforementioned problems. This method is based on single-target visual-assisted BeiDou positioning, which improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, and maintains stable and reliable displacement monitoring capabilities in complex environments.

[0004] To address the aforementioned technical problems, this invention provides a single-target visual-assisted BeiDou station coordinate monitoring method, comprising the following steps: Obtain the initial BeiDou coordinates of the station and the initial pixel coordinates of the target; Based on the initial BeiDou coordinates of the station, coordinate transformation is performed to obtain the initial northeast celestial coordinates of the station; Real-time monitoring and acquisition of the target's current pixel coordinates and the station's current BeiDou coordinates; The visual displacement of the target is obtained based on the current pixel coordinates and the initial pixel coordinates of the target; Based on the target visual displacement and the preset visual azimuth angle, the northeast coordinate correction is performed to obtain the target visual northeast displacement. Visual estimation is performed based on the target's visual northeast displacement and the station's initial northeast celestial coordinates to obtain the station's current visual northeast celestial coordinates. The current visual northeast-sky coordinates of the station and the current BeiDou coordinates of the station are fused to obtain the current northeast-sky coordinates of the station.

[0005] In the above scheme, the current pixel coordinates of the target and the current BeiDou coordinates of the station are acquired in real time. Based on the target's visual displacement and a preset visual azimuth angle, northeast coordinate correction is performed to obtain the target's visual northeast displacement. Then, the current visual northeast celestial coordinates of the station are obtained through visual estimation and fused with the station's current BeiDou coordinates to finally output the station's current northeast celestial coordinates. This scheme improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional methods that rely solely on BeiDou positioning, such as insufficient accuracy and susceptibility to interruptions. Only a single reference target needs to be deployed, simplifying the implementation process and reducing deployment costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. Through the effective fusion of visual and BeiDou data, stable and reliable displacement monitoring capabilities are maintained in complex environments, enhancing overall robustness. The output data is compatible with common BeiDou data formats, facilitating direct integration into existing monitoring platforms. It can be widely used for displacement monitoring of various infrastructures and has significant engineering application value.

[0006] Further, obtaining the target visual displacement based on the target's current pixel coordinates and initial pixel coordinates includes: Obtain the intrinsic parameter matrix of the visual sensor and the object distance; wherein, the object distance is the straight-line spatial distance between the visual sensor and the target; The target pixel offset is obtained based on the target's current pixel coordinates and initial pixel coordinates; The visual displacement of the target is obtained by performing physical displacement conversion based on the intrinsic parameter matrix of the visual sensor, the object distance, and the target pixel offset.

[0007] In the above scheme, by introducing the intrinsic parameter matrix of the visual sensor and the preset object distance, the target pixel offset is accurately converted into the target visual displacement in physical space, achieving efficient and accurate mapping from image pixel coordinates to the northeast-northeast coordinate system. Then, based on this visual displacement and the initial northeast-northeast coordinates of the station, visual estimation is performed, and the result is fused with the station's current BeiDou coordinates to finally output the station's current northeast-northeast coordinates. This scheme effectively improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional single-reliance on BeiDou positioning which is prone to interruption. Only a single reference target needs to be deployed, simplifying the process and reducing costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. The output data is compatible with the common BeiDou data format, facilitating direct integration into existing monitoring platforms and enabling widespread application in displacement monitoring of various infrastructures.

[0008] Further, the step of performing northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement includes: Obtain the visual orientation rotation matrix based on the preset visual orientation angle; Based on the visual orientation rotation matrix and the target visual displacement, a visual coordinate rotation is performed to obtain the target visual northeast displacement.

[0009] In the above scheme, a visual azimuth rotation matrix is ​​obtained through the preset visual azimuth angle, and the visual displacement of the target is rotated based on this matrix to obtain a precise visual northeast displacement of the target. This scheme achieves a high-precision, direct mapping from two-dimensional image displacement to the northeast-sky coordinate system, improving the geographic reference consistency of visual monitoring results. This coordinate correction lays a solid foundation for subsequent visual estimation of the target's visual northeast displacement with the station's initial northeast-sky coordinates, and further coordinate fusion with the station's current BeiDou coordinates, enhancing the reliability and continuity of monitoring in environments where BeiDou signals are blocked or interfered with. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with common BeiDou data formats, facilitating integration into existing monitoring platforms. It can be widely applied to displacement monitoring of various infrastructures.

[0010] Further, the northeast coordinate correction is performed based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement; the process of setting the visual azimuth angle is as follows: Select a fixed reference point within the preset range of the measuring station; Based on this fixed reference point, obtain the reference point pixel coordinates and the reference point northeast-sky coordinates; The theoretical direction vector is obtained based on the reference point's northeast celestial coordinates and the station's initial northeast celestial coordinates. The observation direction vector is obtained based on the reference point pixel coordinates and preset visual sensor intrinsic parameters. The visual azimuth angle is obtained by on-site calibration based on the theoretical direction vector and the observed direction vector.

[0011] In the above scheme, a fixed reference point is selected on-site. The theoretical direction vector is obtained based on the reference point's northeast-sky coordinates and the station's initial northeast-sky coordinates. This vector is then combined with the observation direction vector obtained from the reference point's pixel coordinates and the intrinsic parameters of the visual sensor for on-site calibration, accurately obtaining the visual azimuth angle. This scheme improves the accuracy and reliability of obtaining the visual azimuth angle, overcoming the reliance on manual measurement or preset angles. A rotation matrix is ​​constructed based on this azimuth angle, accurately converting the target's visual displacement into its northeast-sky visual displacement, ensuring high-precision mapping of visual data to the northeast-sky coordinate system. This provides a precise foundation for subsequent visual estimation and coordinate fusion, enhancing the reliability, accuracy, and continuity of monitoring in environments where BeiDou signals are blocked or interfered with.

[0012] Further, based on the target's visual northeast displacement and the station's initial northeast celestial coordinates, visual estimation is performed to obtain the station's current visual northeast celestial coordinates; including: The current visual eastward coordinates of the station are obtained based on the eastward displacement in the target's visual northeastward displacement and the initial eastward coordinates in the station's initial northeastern celestial coordinates. The current visual north coordinates of the station are obtained based on the north displacement in the target's visual northeast displacement and the initial north coordinates in the station's initial northeast celestial coordinates. The initial celestial coordinates in the initial northeast celestial coordinates of the station are used as the current visual celestial coordinates of the station. The current visual coordinates of the station are obtained from the station's current visual coordinates in the east, north, and celestial directions.

[0013] In the above scheme, the current visual eastward displacement of the target is obtained by superimposing the initial eastward coordinates in the initial northeast celestial coordinates of the station; similarly, the current visual northward coordinates of the station are obtained, while keeping the initial celestial coordinates unchanged, thus obtaining the current visual northeast celestial coordinates of the station. By simplifying the calculation process, the inherent limitation of insufficient celestial observation capability of single-target visual monitoring is effectively solved, improving the efficiency and reliability of displacement estimation. While maintaining high-precision monitoring in the horizontal direction, the above scheme ensures stability in the elevation direction, thereby reducing computational complexity and implementation costs. A complete horizontal displacement monitoring system can be established with only a single target, providing a precise basis for coordinate fusion of visual estimation results and the station's current BeiDou coordinates, enhancing the continuity and robustness of monitoring in complex environments, and can be widely applied to displacement monitoring of various infrastructures.

[0014] Further, the current visual northeast-sky coordinates and the current BeiDou coordinates of the station are fused to obtain the current northeast-sky coordinates of the station; including: Preset fusion weight coefficients; The current eastward coordinates of the station are obtained by weighted fusion based on the eastward visual coordinates in the current visual northeast-sky coordinates of the station, the eastward BeiDou coordinates in the current BeiDou coordinates of the station, and the fusion weight coefficient. The current north direction coordinates of the station are obtained by weighted fusion based on the north direction visual coordinates in the current visual northeast celestial coordinates of the station, the north direction BeiDou coordinates in the current BeiDou coordinates of the station, and the fusion weight coefficient. The initial coordinates of the celestial direction in the current visual northeast celestial coordinates of the station are taken as the current celestial direction coordinates of the station. The current northeast-sky coordinates of the station are obtained based on the station's current east direction coordinates, current north direction coordinates, and current celestial direction coordinates.

[0015] In the above scheme, by pre-setting a fusion weighting coefficient, the eastward visual coordinates in the current visual northeast-sky coordinates of the station and the eastward BeiDou coordinates in the current BeiDou coordinates of the station are weighted and fused to obtain the station's current eastward coordinates. The northward coordinates are processed in the same way, and the initial sky direction coordinates are used as the station's current sky direction coordinates to finally obtain the station's current northeast-sky coordinates. This scheme effectively combines the advantages of visual monitoring and BeiDou positioning, improving the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, and overcoming the shortcomings of traditional methods that rely solely on BeiDou positioning. While maintaining high-precision monitoring in the horizontal direction, the stability of the sky direction coordinates is ensured by simplifying elevation processing.

[0016] This invention also provides a single-target vision-assisted BeiDou station coordinate monitoring system, comprising: The initial calibration module is used to obtain the initial BeiDou coordinates of the station, the northeast celestial coordinates of the target, and the initial pixel coordinates of the target; based on the initial BeiDou coordinates of the station, coordinate transformation is performed to obtain the initial northeast celestial coordinates of the station; The real-time monitoring module is used to monitor and obtain the current pixel coordinates of the target and the current BeiDou coordinates of the station in real time. The visual displacement calculation module is used to obtain the visual displacement of the target based on the current pixel coordinates and the initial pixel coordinates of the target. The northeast coordinate correction module is used to perform northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement. The visual coordinate estimation module is used to perform visual estimation based on the target's visual northeast displacement and the station's initial northeast celestial coordinates to obtain the station's current visual northeast celestial coordinates. The coordinate fusion module is used to fuse the current visual northeast-sky coordinates of the station and the current BeiDou coordinates of the station to obtain the current northeast-sky coordinates of the station.

[0017] In the above scheme, an accurate benchmark is established between the initial northeast-sky coordinates of the station and the initial pixel coordinates of the target through an initial calibration module. The real-time monitoring module synchronously acquires the current pixel coordinates of the target and the current BeiDou coordinates of the station. The visual displacement calculation module obtains the visual displacement of the target based on this, and the northeast coordinate correction module converts it into the target's visual northeast displacement based on a preset visual azimuth angle. The visual coordinate estimation module uses this displacement and the station's initial northeast-sky coordinates to obtain the station's current visual northeast-sky coordinates. Finally, the coordinate fusion module fuses these coordinates with the station's current BeiDou coordinates to output the station's current northeast-sky coordinates. This scheme, through modular processing, achieves effective collaboration between visual and BeiDou data, improving monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, and overcoming the shortcomings of traditional single-reliance on BeiDou positioning. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with common BeiDou data formats, facilitating integration and enabling widespread application in displacement monitoring of various infrastructures.

[0018] Furthermore, the visual displacement calculation module is used to obtain the visual displacement of the target based on the current pixel coordinates and the initial pixel coordinates of the target; including: Obtain the intrinsic parameter matrix of the visual sensor and the object distance; wherein, the object distance is the straight-line spatial distance between the visual sensor and the target; The target pixel offset is obtained based on the target's current pixel coordinates and initial pixel coordinates; The visual displacement of the target is obtained by performing physical displacement conversion based on the intrinsic parameter matrix of the visual sensor, the object distance, and the target pixel offset.

[0019] In the above scheme, the visual displacement calculation module, by introducing the intrinsic parameter matrix of the visual sensor and a preset object distance, accurately converts the target pixel offset into the target visual displacement in physical space, achieving efficient and accurate mapping from image pixel coordinates to the northeast-northeast coordinate system. Then, based on this visual displacement and the initial northeast-northeast coordinates of the station, visual estimation is performed, and the result is fused with the station's current BeiDou coordinates to finally output the station's current northeast-northeast coordinates. This scheme effectively improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional single-reliance on BeiDou positioning which is prone to interruption. Only a single reference target needs to be deployed, simplifying the process and reducing costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. The output data is compatible with the common BeiDou data format, facilitating direct integration into existing monitoring platforms and enabling widespread application in displacement monitoring of various infrastructures.

[0020] Furthermore, the northeast coordinate correction module is used to perform northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement; including: Obtain the visual orientation rotation matrix based on the preset visual orientation angle; Based on the visual orientation rotation matrix and the target visual displacement, a visual coordinate rotation is performed to obtain the target visual northeast displacement.

[0021] In the above scheme, the northeast coordinate correction module obtains the visual azimuth rotation matrix through the preset visual azimuth angle, and performs visual coordinate rotation on the target's visual displacement based on this matrix, thereby obtaining the accurate visual northeast displacement of the target. This scheme achieves high-precision, direct mapping from two-dimensional image displacement to the northeast celestial coordinate system, improving the geographic reference consistency of visual monitoring results. This coordinate correction lays a solid foundation for subsequent visual estimation of the target's visual northeast displacement with the station's initial northeast celestial coordinates, and further coordinate fusion with the station's current BeiDou coordinates, enhancing the reliability and continuity of monitoring in environments where BeiDou signals are blocked or interfered with. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with the common BeiDou data format, facilitating integration into existing monitoring platforms. It can be widely applied to displacement monitoring of various infrastructures.

[0022] The present invention also provides a terminal device, comprising: a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, it implements the steps of a single-target visual-assisted BeiDou station coordinate monitoring method as described in the present invention. Attached Figure Description

[0023] Figure 1 This is a schematic flowchart of a single-target visual-assisted BeiDou station coordinate monitoring method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a single-target visual-assisted BeiDou station coordinate monitoring system architecture provided in an embodiment of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Please see Figure 1 This embodiment provides a single-target visual-assisted BeiDou station coordinate monitoring method, including the following steps: Step S1: Obtain the initial BeiDou coordinates of the station and the initial pixel coordinates of the target; Step S2: Perform coordinate transformation based on the initial BeiDou coordinates of the station to obtain the initial northeast celestial coordinates of the station; Step S3: Monitor and obtain the current pixel coordinates of the target and the current BeiDou coordinates of the station in real time; Step S4: Obtain the visual displacement of the target based on the current pixel coordinates and the initial pixel coordinates of the target; Step S5: Based on the target visual displacement and the preset visual azimuth angle, perform northeast coordinate correction to obtain the target visual northeast displacement; Step S6: Based on the target's visual northeast displacement and the station's initial northeast celestial coordinates, perform visual estimation to obtain the station's current visual northeast celestial coordinates; Step S7: Perform coordinate fusion between the current visual northeast-sky coordinates of the station and the current BeiDou coordinates of the station to obtain the current northeast-sky coordinates of the station.

[0026] In this embodiment, by acquiring the current pixel coordinates of the target and the current BeiDou coordinates of the station in real time, and performing northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle, the target's visual northeast displacement is obtained. Then, the station's current visual northeast celestial coordinates are obtained through visual estimation and fused with the station's current BeiDou coordinates to finally output the station's current northeast celestial coordinates. This embodiment improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional single-reliance on BeiDou positioning, such as insufficient accuracy and susceptibility to interruptions. Only a single reference target needs to be deployed, simplifying the implementation process and reducing deployment costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. Through the effective fusion of visual and BeiDou data, stable and reliable displacement monitoring capabilities are maintained in complex environments, enhancing overall robustness. The output data is compatible with common BeiDou data formats, facilitating direct integration into existing monitoring platforms and enabling widespread application in displacement monitoring of various infrastructures, possessing significant engineering application value.

[0027] In one embodiment, a single-target visual-assisted BeiDou station coordinate monitoring method is provided, suitable for scenarios where only a single reference target needs to be deployed in a stable area, aiming to accurately estimate the station's displacement in the horizontal plane. This embodiment inverts the station displacement by visually observing the pixel changes of the target and fuses it with BeiDou positioning data, significantly improving the horizontal positioning accuracy. Specifically, it includes the following steps: Step S1: System Initialization. Obtain the initial BeiDou coordinates (latitude, longitude, and altitude) of the station, and obtain its initial coordinates in the Northeast Celestial coordinate system through coordinate transformation. Simultaneously, an initial image of the reference target is captured using a visual sensor, and the initial pixel coordinates (x0, y0) of the target center are extracted.

[0028] Step S2: Real-time data acquisition. During the monitoring process, two data points are acquired in real time: first, the pixel coordinates (x1, y1) of the target center in the current image acquired by the visual sensor; and second, the current BeiDou coordinates of the station output by the BeiDou receiver.

[0029] Step S3: Calculate the target visual displacement. Based on the target's current pixel coordinates (x1, y1) and initial pixel coordinates (x0, y0), calculate the target's pixel displacement (Δx, Δy) on the image plane, where Δx = x1 - x0, Δy = y1 - y0.

[0030] Step S4: Convert the pixel displacement into axial displacement in the camera coordinate system.

[0031] It should be noted that the purpose of step S3 is to convert pixel changes in the image into physical displacements in the real world in front of the camera. Using pre-calibrated camera intrinsic parameters (fx, fy) and the approximate object distance Z from the camera's optical center to the reference target, the conversion is performed using the following formula: in,( , This refers to the axial displacement in the camera coordinate system.

[0032] Step S5: Convert the camera coordinate system displacement to an east / north direction displacement in the northeast-northeast coordinate system. It should be noted that since the camera's installation orientation is unknown, coordinate rotation needs to be performed using a preset visual azimuth angle θ (i.e., the angle between the camera's optical axis and true north). The conversion is achieved using the following rotation matrix: This yields the target's visual northeast displacement. .

[0033] Step S6: Visually estimate the station coordinates. Based on the physical principle of relative motion, the observed visual displacement of the target essentially reflects the opposite displacement of the station itself. Therefore, the calculated visual northeast displacement is... relative to the initial northeast celestial coordinates of the station By combining these methods, the current visual estimate of the northeast celestial coordinates of the station can be obtained. ,in , Elevation It remains unchanged.

[0034] Step S7: Coordinate Fusion. Combine the visually estimated current visual northeast-sky coordinates of the station. The current BeiDou coordinates of the station obtained directly from the BeiDou receiver (converted to the Northeast Celestial coordinate system) Perform weighted fusion.

[0035] It should be noted that the fusion weights can be dynamically adjusted based on the signal-to-noise ratio or accuracy factor of the BeiDou signal. This prioritizes the use of absolute positioning information when the BeiDou signal is strong, while relying on more stable visual relative displacement information when the signal is disrupted. The final output is an optimal current northeast-southeast celestial coordinate for the station. .

[0036] In this embodiment, by weighted fusion of single-target visual displacement inversion and BeiDou positioning data, it is particularly suitable for monitoring scenarios requiring high horizontal accuracy and rapid deployment, without significantly increasing complexity and cost. This effectively improves the planar positioning accuracy and reliability of the station in open environments. The output results are consistent with the general BeiDou data format, facilitating integrated applications.

[0037] In another embodiment, a single-target visual-assisted BeiDou station coordinate monitoring method is provided, which is applicable to situations where only one reference target is set in a stable area. The displacement of the station in the east-north direction in the horizontal plane is estimated by visually observing the image displacement of the target light, and then fused with BeiDou positioning data, aiming to improve the positioning accuracy in the horizontal direction.

[0038] It should be noted that the effective implementation of the single-target visual-assisted BeiDou station coordinate monitoring method provided in this embodiment is based on the following technical premises: a single reference target needs to be fixed at a known and stable northeast-central coordinate position; the initial position of the station is obtained by BeiDou calibration; the camera intrinsic parameters (including focal length and principal point) are known; the initial object distance from the target to the camera can be obtained by laser ranging or GNSS differential; the camera's pitch and roll angles are considered to be known or negligible, for example, by keeping it level through a gimbal.

[0039] First, the system is initialized to obtain the initial BeiDou coordinates of the station and convert them to obtain the initial northeast celestial coordinates of the station. Simultaneously, the center pixel coordinates of the reference target in the initial image are obtained. , During real-time monitoring, the center pixel coordinates of the target in the current image are continuously acquired. , The current BeiDou coordinates of the station are also considered. Based on the current pixel coordinates and the initial pixel coordinates, the two-dimensional pixel displacement of the target on the image plane is calculated. , ),in .

[0040] Subsequently, the pixel displacement is converted into a lateral displacement in the camera coordinate system. It should be noted that this step is based on a pinhole imaging model, utilizing the known object distance Z and camera focal length. Through formula and Calculations are performed. This transformation is based on the assumption that the target plane and image plane are approximately parallel and that the object distance changes little. Next, the camera coordinate system displacement is converted to the northeast-sky coordinate system. It should be noted that this process needs to consider the camera's mounting azimuth angle θ. This is done using the rotation matrix: To achieve the conversion, if the camera is pointed due north, the azimuth angle is zero, which simplifies the calculation. The visually estimated station's current northeast-sky horizontal coordinates are obtained from... and The calculation yielded the result.

[0041] It should be noted that this embodiment mainly estimates horizontal displacement and elevation changes. It requires relying on BeiDou data or assuming the ground is flat.

[0042] Finally, the final coordinates are output using a weighted fusion strategy, as shown in the formula: It should be noted that the fusion weight coefficient w can be dynamically adjusted according to the BeiDou positioning accuracy factor to achieve the optimal fusion effect. This embodiment, under the condition of deploying only a single target, effectively complements visual and BeiDou data, making it particularly suitable for monitoring scenarios requiring high horizontal accuracy and rapid deployment, thus enhancing the system's practicality and cost-effectiveness.

[0043] Further, obtaining the target visual displacement based on the target's current pixel coordinates and initial pixel coordinates includes: Obtain the intrinsic parameter matrix of the visual sensor and the object distance; wherein, the object distance is the straight-line spatial distance between the visual sensor and the target; The target pixel offset is obtained based on the target's current pixel coordinates and initial pixel coordinates; The visual displacement of the target is obtained by performing physical displacement conversion based on the intrinsic parameter matrix of the visual sensor, the object distance, and the target pixel offset.

[0044] In this embodiment, by introducing the intrinsic parameter matrix of the visual sensor and a preset object distance, the target pixel offset is accurately converted into the target visual displacement in physical space, achieving efficient and accurate mapping from image pixel coordinates to the northeast-northeast coordinate system. Then, based on this visual displacement and the initial northeast-northeast coordinates of the station, visual estimation is performed, and the result is fused with the station's current BeiDou coordinates to finally output the station's current northeast-northeast coordinates. This embodiment effectively improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional single-reliance on BeiDou positioning which is prone to interruption. Only a single reference target needs to be deployed, simplifying the process and reducing costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. The output data is compatible with the common BeiDou data format, facilitating direct integration into existing monitoring platforms and enabling widespread application in displacement monitoring of various infrastructures.

[0045] Further, the step of performing northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement includes: Obtain the visual orientation rotation matrix based on the preset visual orientation angle; Based on the visual orientation rotation matrix and the target visual displacement, a visual coordinate rotation is performed to obtain the target visual northeast displacement.

[0046] In this embodiment, a visual azimuth rotation matrix is ​​obtained through the preset visual azimuth angle, and the visual displacement of the target is rotated based on this matrix to obtain a precise visual northeast displacement of the target. This embodiment achieves a high-precision, direct mapping from the two-dimensional displacement of the image to the northeast celestial coordinate system, improving the geographic reference consistency of the visual monitoring results. This coordinate correction lays a solid foundation for subsequent visual estimation of the target's visual northeast displacement with the station's initial northeast celestial coordinates, and further coordinate fusion with the station's current BeiDou coordinates, enhancing the reliability and continuity of monitoring in environments where BeiDou signals are blocked or interfered with. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with the common BeiDou data format, facilitating integration into existing monitoring platforms. It can be widely applied to displacement monitoring of various infrastructures.

[0047] Further, the northeast coordinate correction is performed based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement; the process of setting the visual azimuth angle is as follows: Select a fixed reference point within the preset range of the measuring station; Based on this fixed reference point, obtain the reference point pixel coordinates and the reference point northeast-sky coordinates; The theoretical direction vector is obtained based on the reference point's northeast celestial coordinates and the station's initial northeast celestial coordinates. The observation direction vector is obtained based on the reference point pixel coordinates and preset visual sensor intrinsic parameters. The visual azimuth angle is obtained by on-site calibration based on the theoretical direction vector and the observed direction vector.

[0048] In this embodiment, a fixed reference point is selected on-site. Based on the reference point's northeast-sky coordinates and the station's initial northeast-sky coordinates, a theoretical direction vector is obtained. This vector is then combined with the observation direction vector obtained from the reference point's pixel coordinates and the intrinsic parameters of the visual sensor for on-site calibration, accurately obtaining the visual azimuth angle. This embodiment improves the accuracy and reliability of visual azimuth angle acquisition, overcoming reliance on manual measurement or preset angles. A rotation matrix is ​​constructed based on this azimuth angle, accurately converting the target's visual displacement into its northeast-sky visual displacement, ensuring high-precision mapping of visual data to the northeast-sky coordinate system. This provides a precise foundation for subsequent visual estimation and coordinate fusion, enhancing the reliability, accuracy, and continuity of monitoring in environments where BeiDou signals are blocked or interfered with.

[0049] In one embodiment, the visual azimuth angle is defined as the angle between the X-axis of the visual sensor coordinate system (usually corresponding to the horizontal direction of the image) and the east direction (E-axis) of the northeast-northeast (ENU) coordinate system, with the station as the origin, in the horizontal plane, with the counterclockwise direction being positive. The on-site calibration process of the visual azimuth angle includes the following steps: Step S1: Select a reference target point: Select a fixed reference point within the preset range of the station. This point has known, precise northeast celestial coordinates. The reference point can be a pre-deployed measurement control point, a clear and stable fixed feature, or a specially designed target. It must be ensured that the point is within the field of view of the visual sensor and that the image is clear.

[0050] Step S2: Obtain the image coordinates of the reference point: Control the vision sensor to focus on the reference point. Take a picture to acquire its image. Then, use image processing algorithms (such as sub-pixel level circular fitting or feature point extraction algorithms) to accurately obtain the pixel coordinates of the reference point in the image. .

[0051] Step S3: Set the ENU coordinate system offset point and obtain its image coordinates: based on the reference point The coordinates are set at two offset points in the ENU coordinate system: Offset by a predetermined distance Δd (e.g., 10 cm) in the east (E) direction to obtain point Its coordinates are: .

[0052] Offset by the same preset distance Δd along the north (N) direction, obtain point Its coordinates are: For each point and Images are taken, and their pixel coordinates are precisely obtained using image processing algorithms, denoted as... and .

[0053] Step S4: Calculate the direction vector and visual azimuth angle: Calculate the pixel displacement vector in the east direction: ; Calculate the pixel displacement vector in the north direction: .

[0054] The visual azimuth angle θ is calculated based on the pixel displacement vector in the east direction.

[0055] It should be noted that, ideally, the X-axis of the visual coordinate system should be aligned with the eastward direction of the ENU coordinate system, therefore, this can be achieved through calculation. The angle θ is precisely determined by the angle between the vector and the unit vector pointing east. Specifically, it is calculated using the vector angle formula, preferably using the Math.atan2(dy,dx) function to avoid division by zero errors and to correctly determine the quadrant, where dx and dy are respectively... The X and Y components of a vector.

[0056] In this embodiment, a fixed reference point with known coordinates is selected on-site, and precise offset points along the east and north directions are generated based on this point. The direction vector within the pixel plane is calculated by acquiring the image coordinates of these points, thereby accurately calibrating the visual azimuth angle θ. This embodiment improves the objectivity and accuracy of visual azimuth angle calibration, overcoming the reliance on manual measurement or preset angles. It should be noted that a corresponding visual azimuth rotation matrix can be constructed based on this precisely calibrated visual azimuth angle θ. This rotation matrix can accurately transform (rotate) the target's visual displacement in the image coordinate system to the northeast-northeast coordinate system, obtaining the target's visual northeast displacement. This process achieves high-precision, direct mapping from two-dimensional image displacement to the geographic coordinate system, ensuring the geographic reference consistency of visual data and laying a solid foundation for subsequent effective fusion with BeiDou coordinate data, significantly enhancing the reliability and accuracy of monitoring in complex environments.

[0057] Further, based on the target's visual northeast displacement and the station's initial northeast celestial coordinates, visual estimation is performed to obtain the station's current visual northeast celestial coordinates; including: The current visual eastward coordinates of the station are obtained based on the eastward displacement in the target's visual northeastward displacement and the initial eastward coordinates in the station's initial northeastern celestial coordinates. The current visual north coordinates of the station are obtained based on the north displacement in the target's visual northeast displacement and the initial north coordinates in the station's initial northeast celestial coordinates. The initial celestial coordinates in the initial northeast celestial coordinates of the station are used as the current visual celestial coordinates of the station. The current visual coordinates of the station are obtained from the station's current visual coordinates in the east, north, and celestial directions.

[0058] In this embodiment, the current visual eastward displacement of the target is obtained by superimposing the initial eastward coordinates in the initial northeast celestial coordinates of the station; similarly, the current visual northward coordinates of the station are obtained, while keeping the initial celestial coordinates unchanged, thus obtaining the current visual northeast celestial coordinates of the station. By simplifying the calculation process, the inherent limitation of insufficient celestial observation capability of single-target visual monitoring is effectively solved, improving the efficiency and reliability of displacement estimation. This embodiment maintains high-precision monitoring in the horizontal direction while ensuring stability in the elevation direction, thereby reducing computational complexity and implementation costs. A complete horizontal displacement monitoring system can be established with only a single target, providing an accurate basis for coordinate fusion of visual estimation results and the current BeiDou coordinates of the station, enhancing the continuity and robustness of monitoring in complex environments, and can be widely applied to displacement monitoring of various infrastructures.

[0059] Further, the current visual northeast-sky coordinates and the current BeiDou coordinates of the station are fused to obtain the current northeast-sky coordinates of the station; including: Preset fusion weight coefficients; The current eastward coordinates of the station are obtained by weighted fusion based on the eastward visual coordinates in the current visual northeast-sky coordinates of the station, the eastward BeiDou coordinates in the current BeiDou coordinates of the station, and the fusion weight coefficient. The current north direction coordinates of the station are obtained by weighted fusion based on the north direction visual coordinates in the current visual northeast celestial coordinates of the station, the north direction BeiDou coordinates in the current BeiDou coordinates of the station, and the fusion weight coefficient. The initial coordinates of the celestial direction in the current visual northeast celestial coordinates of the station are taken as the current celestial direction coordinates of the station. The current northeast-sky coordinates of the station are obtained based on the station's current east direction coordinates, current north direction coordinates, and current celestial direction coordinates.

[0060] In this embodiment, by pre-setting a fusion weighting coefficient, the eastward visual coordinates in the current visual northeast-sky coordinates of the station and the eastward BeiDou coordinates in the current BeiDou coordinates of the station are weighted and fused to obtain the station's current eastward coordinates. The northward coordinates are processed in the same way, and the initial sky direction coordinates are used as the station's current sky direction coordinates to finally obtain the station's current northeast-sky coordinates. This embodiment effectively combines the advantages of visual monitoring and BeiDou positioning, improving the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, and overcoming the shortcomings of traditional methods that rely solely on BeiDou positioning. While maintaining high-precision monitoring in the horizontal direction, the stability of the sky direction coordinates is ensured by simplifying elevation processing.

[0061] Please see Figure 2 The present invention also provides a single-target visual-assisted BeiDou station coordinate monitoring system, comprising: The initial calibration module is used to obtain the initial BeiDou coordinates of the station, the northeast celestial coordinates of the target, and the initial pixel coordinates of the target; based on the initial BeiDou coordinates of the station, coordinate transformation is performed to obtain the initial northeast celestial coordinates of the station; The real-time monitoring module is used to monitor and obtain the current pixel coordinates of the target and the current BeiDou coordinates of the station in real time. The visual displacement calculation module is used to obtain the visual displacement of the target based on the current pixel coordinates and the initial pixel coordinates of the target. The northeast coordinate correction module is used to perform northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement. The visual coordinate estimation module is used to perform visual estimation based on the target's visual northeast displacement and the station's initial northeast celestial coordinates to obtain the station's current visual northeast celestial coordinates. The coordinate fusion module is used to fuse the current visual northeast-sky coordinates of the station and the current BeiDou coordinates of the station to obtain the current northeast-sky coordinates of the station.

[0062] In this embodiment, an accurate benchmark is established between the initial northeast-sky coordinates of the station and the initial pixel coordinates of the target through an initial calibration module. The real-time monitoring module synchronously acquires the current pixel coordinates of the target and the current BeiDou coordinates of the station. The visual displacement calculation module obtains the visual displacement of the target based on this, and the northeast coordinate correction module converts it into the target's visual northeast displacement based on a preset visual azimuth angle. The visual coordinate estimation module uses this displacement and the station's initial northeast-sky coordinates to obtain the station's current visual northeast-sky coordinates. Finally, the coordinate fusion module fuses these coordinates with the station's current BeiDou coordinates to output the station's current northeast-sky coordinates. This embodiment achieves effective collaboration between visual and BeiDou data through modular processing, improving monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, and overcoming the shortcomings of traditional single-reliance on BeiDou positioning. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with common BeiDou data formats, facilitating integration and enabling widespread application in displacement monitoring of various infrastructures.

[0063] Furthermore, the visual displacement calculation module is used to obtain the visual displacement of the target based on the current pixel coordinates and the initial pixel coordinates of the target; including: Obtain the intrinsic parameter matrix of the visual sensor and the object distance; wherein, the object distance is the straight-line spatial distance between the visual sensor and the target; The target pixel offset is obtained based on the target's current pixel coordinates and initial pixel coordinates; The visual displacement of the target is obtained by performing physical displacement conversion based on the intrinsic parameter matrix of the visual sensor, the object distance, and the target pixel offset.

[0064] In this embodiment, the visual displacement calculation module, by introducing the intrinsic parameter matrix of the visual sensor and a preset object distance, accurately converts the target pixel offset into the target visual displacement in physical space, achieving efficient and accurate mapping from image pixel coordinates to the northeast-northeast coordinate system. Then, based on this visual displacement and the initial northeast-northeast coordinates of the station, visual estimation is performed, and the result is fused with the station's current BeiDou coordinates to finally output the station's current northeast-northeast coordinates. This embodiment effectively improves the monitoring accuracy and continuity in environments where BeiDou signals are blocked or interfered with, overcoming the shortcomings of traditional single-reliance on BeiDou positioning which is prone to interruption. Only a single reference target needs to be deployed, simplifying the process and reducing costs and complexity, making it particularly suitable for rapid installation and temporary monitoring scenarios. The output data is compatible with the common BeiDou data format, facilitating direct integration into existing monitoring platforms and enabling widespread application in displacement monitoring of various infrastructures.

[0065] Furthermore, the northeast coordinate correction module is used to perform northeast coordinate correction based on the target's visual displacement and a preset visual azimuth angle to obtain the target's visual northeast displacement; including: Obtain the visual orientation rotation matrix based on the preset visual orientation angle; Based on the visual orientation rotation matrix and the target visual displacement, a visual coordinate rotation is performed to obtain the target visual northeast displacement.

[0066] In this embodiment, the northeast coordinate correction module obtains a visual azimuth rotation matrix through the preset visual azimuth angle, and performs visual coordinate rotation on the target's visual displacement based on this matrix, thereby obtaining a precise target visual northeast displacement. This embodiment achieves a high-precision, direct mapping from two-dimensional image displacement to the northeast celestial coordinate system, improving the geographic reference consistency of visual monitoring results. This coordinate correction lays a solid foundation for subsequent visual estimation of the target's visual northeast displacement with the station's initial northeast celestial coordinates, and further coordinate fusion with the station's current BeiDou coordinates, enhancing the reliability and continuity of monitoring in environments where BeiDou signals are blocked or interfered with. Only a single reference target needs to be deployed, simplifying the process, reducing costs and complexity, and the output data is compatible with common BeiDou data formats, facilitating integration into existing monitoring platforms. It can be widely applied to displacement monitoring of various infrastructures.

[0067] Based on the above embodiment of a station displacement monitoring method based on multiple reference targets, another embodiment of the present invention provides a terminal device, which includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements a station displacement monitoring method based on multiple reference targets according to any embodiment of the present invention.

[0068] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to perform the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the terminal device.

[0069] The terminal device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0070] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0071] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A single-target visual-assisted Beidou station coordinate monitoring method, characterized in that, The method comprises the following steps: obtaining initial Beidou coordinates of a station and initial pixel coordinates of a target; performing coordinate conversion based on the initial Beidou coordinates of the station to obtain initial northeast celestial coordinates of the station; real-time monitoring and obtaining current pixel coordinates of the target and current Beidou coordinates of the station; obtaining visual displacement of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target; performing northeast coordinate correction based on the visual displacement of the target and a preset visual azimuth to obtain visual northeast displacement of the target; performing visual estimation based on the visual northeast displacement of the target and the initial northeast celestial coordinates of the station to obtain current visual northeast celestial coordinates of the station; performing coordinate fusion on the current visual northeast celestial coordinates of the station and the current Beidou coordinates of the station to obtain current northeast celestial coordinates of the station.

2. The single-target visual auxiliary Beidou station coordinate monitoring method according to claim 1, characterized in that, The method for obtaining the visual displacement of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target comprises: obtaining an intrinsic matrix of a visual sensor and an object distance, wherein the object distance is a straight-line distance in space between the visual sensor and the target; obtaining a pixel offset of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target; performing physical displacement conversion based on the intrinsic matrix of the visual sensor, the object distance and the pixel offset of the target to obtain the visual displacement of the target.

3. The single-target visual auxiliary Beidou station coordinate monitoring method according to claim 1, characterized in that, The method for performing northeast coordinate correction based on the visual displacement of the target and a preset visual azimuth to obtain visual northeast displacement of the target comprises: obtaining a visual azimuth rotation matrix based on the preset visual azimuth; performing visual coordinate rotation based on the visual azimuth rotation matrix and the visual displacement of the target to obtain the visual northeast displacement of the target.

4. The single-target visual auxiliary Beidou station coordinate monitoring method according to claim 1, characterized in that, In the method for performing northeast coordinate correction based on the visual displacement of the target and a preset visual azimuth to obtain visual northeast displacement of the target, the presetting process of the visual azimuth comprises: selecting a fixed reference point within a preset range of the station; obtaining reference point pixel coordinates and reference point northeast celestial coordinates based on the fixed reference point; obtaining a theoretical direction vector based on the reference point northeast celestial coordinates and the initial northeast celestial coordinates of the station; obtaining an observation direction vector based on the reference point pixel coordinates and a preset visual sensor intrinsic parameter; performing on-site calibration based on the theoretical direction vector and the observation direction vector to obtain the visual azimuth.

5. The single-target visual auxiliary Beidou station coordinate monitoring method according to claim 1, characterized in that, The method for performing visual estimation based on the visual northeast displacement of the target and the initial northeast celestial coordinates of the station to obtain current visual northeast celestial coordinates of the station comprises: obtaining current visual east direction coordinates of the station based on an east direction displacement amount in the visual northeast displacement of the target and an east direction initial coordinate in the initial northeast celestial coordinates of the station; obtaining current visual north direction coordinates of the station based on a north direction displacement amount in the visual northeast displacement of the target and a north direction initial coordinate in the initial northeast celestial coordinates of the station; taking a celestial direction initial coordinate in the initial northeast celestial coordinates of the station as current visual celestial direction coordinates of the station; obtaining the current visual northeast celestial coordinates of the station based on the current visual east direction coordinates of the station, the current visual north direction coordinates of the station and the current visual celestial direction coordinates of the station.

6. The single-target visual auxiliary Beidou station coordinate monitoring method according to claim 1, characterized in that, The method for performing coordinate fusion on the current visual northeast celestial coordinates of the station and the current Beidou coordinates of the station to obtain current northeast celestial coordinates of the station comprises: presetting a fusion weight coefficient; fusing the east direction visual coordinate in the current visual northeast celestial coordinate of the station, the east direction Beidou coordinate in the current Beidou coordinate of the station and the fusion weight coefficient to obtain the current east direction coordinate of the station; fusing the north direction visual coordinate in the current visual northeast celestial coordinate of the station, the north direction Beidou coordinate in the current Beidou coordinate of the station and the fusion weight coefficient to obtain the current north direction coordinate of the station; taking the initial coordinate of the sky direction in the current visual northeast celestial coordinate of the station as the current sky direction coordinate of the station; obtaining the current northeast celestial coordinate of the station based on the current east direction coordinate of the station, the current north direction coordinate of the station and the current sky direction coordinate of the station.

7. A single-target visual auxiliary Beidou station coordinate monitoring system, characterized in that, comprising: an initial calibration module, configured to obtain initial Beidou coordinates of a station, northeast celestial coordinates of a target and initial pixel coordinates of the target; performing coordinate conversion based on the initial Beidou coordinates of the station to obtain initial northeast celestial coordinates of the station; a real-time monitoring module, configured to monitor and obtain current pixel coordinates of the target and current Beidou coordinates of the station in real time; a visual displacement solving module, configured to obtain visual displacement of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target; a northeast coordinate correction module, configured to perform northeast coordinate correction based on the visual displacement of the target and a preset visual azimuth to obtain visual northeast displacement of the target; a visual coordinate estimation module, configured to perform visual estimation based on the visual northeast displacement of the target and the initial northeast celestial coordinates of the station to obtain current visual northeast celestial coordinates of the station; a coordinate fusion module, configured to perform coordinate fusion on the current visual northeast celestial coordinates of the station and the current Beidou coordinates of the station to obtain current northeast celestial coordinates of the station.

8. The single-target visual auxiliary Beidou station coordinate monitoring system according to claim 7, characterized in that, the visual displacement solving module, configured to obtain visual displacement of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target; comprising: obtaining an intrinsic matrix of a visual sensor and an object distance; wherein the object distance is a spatial straight-line distance between the visual sensor and the target; obtaining a pixel offset of the target based on the current pixel coordinates of the target and the initial pixel coordinates of the target; performing physical displacement conversion based on the intrinsic matrix of the visual sensor, the object distance and the pixel offset of the target to obtain the visual displacement of the target.

9. The single-target visual auxiliary Beidou station coordinate monitoring system according to claim 7, characterized in that, the northeast coordinate correction module, configured to perform northeast coordinate correction based on the visual displacement of the target and a preset visual azimuth to obtain visual northeast displacement of the target; comprising: obtaining a visual azimuth rotation matrix based on the preset visual azimuth; performing visual coordinate rotation based on the visual azimuth rotation matrix and the visual displacement of the target to obtain the visual northeast displacement of the target.

10. A terminal device, comprising: a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, when the computer program is executed by the processor, a single-target visual auxiliary Beidou station coordinate monitoring method according to any one of claims 1-6 is implemented.

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