A deformation monitoring method based on integration of Beidou GNSS and visual image information

Abstract

The present application relates to the field of satellite navigation and positioning technology, and more particularly to a Beidou GNSS and visual image information fusion deformation monitoring method, comprising: collecting and preliminarily screening the surface periodic images of a monitoring body to determine a time adding period; sub-pixel refining the images in the time adding period, extracting texture and identification features to obtain a visual displacement field; constructing a carrier phase time difference observation equation to eliminate the integer ambiguity, introducing the visual displacement as a priori constraint and jointly solving multiple epochs to obtain optimized coordinates; and combining RTK data to jointly determine the deformation and adjust the real-time static filter. The present application improves the spatial continuity, trigger reliability and adaptability to harsh environments of deformation monitoring, and realizes the technical upgrade from single-point monitoring to full-field millimeter-level high-precision monitoring.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a deformation monitoring method that fuses BeiDou GNSS and visual image information. Background Technology

[0002] Traditional deformation monitoring technologies primarily rely on real-time static filtering algorithms from satellite navigation and positioning systems. These algorithms acquire millimeter-level positioning coordinate sequences by setting process noise parameters to respond to structural deformation. With the increasing sophistication of monitoring requirements, existing technologies are gradually incorporating auxiliary sensing methods such as microelectromechanical systems (MEMS) accelerometers or visual images. MEMS sensors detect local vibrations to trigger encrypted data acquisition, while visual images are used for post-deformation processing verification to improve the timeliness and reliability of monitoring.

[0003] However, the aforementioned existing technologies still have the following shortcomings: (1) MEMS sensors can only acquire local acceleration information at a single point, which cannot reflect the continuous deformation field distribution on the surface of the monitored body. They are also susceptible to environmental vibration interference, which can lead to false triggering and make it difficult to distinguish between real deformation and noise such as wind vibration. (2) Conventional epoch-based differential positioning relies on double-difference observations and requires integer ambiguity fixation. When the number of satellites is small and the observation environment is harsh, cycle slips are likely to occur, which can reduce the accuracy of coordinate change information between epochs or even cause the solution to fail. (3) Existing fusion schemes mostly adopt simple superposition of decision layers, that is, each sensor is solved independently and then logical judgment is performed. They do not achieve deep fusion at the level of original observation data. There is no accurate spatiotemporal registration mechanism between GNSS absolute coordinates and visual relative displacement, which makes it difficult to effectively suppress multipath effects and improve deformation recognition accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a deformation monitoring method that fuses BeiDou GNSS and visual image information, thereby solving the aforementioned problems in the existing technology.

[0005] To achieve the above objectives, this invention provides a deformation monitoring method based on the fusion of BeiDou GNSS and visual image information, comprising the following steps: S1. Based on the visual image acquisition device, periodically acquire images of the surface of the monitored object, perform preliminary screening of the image sequence, and determine the reporting period when a change in the state of the monitored object is detected; S2. The visual image sequence during the reporting period is refined using a sub-pixel fitting algorithm to extract the texture features and artificial marking features of the monitored object surface. The visual displacement field information of the feature points on the structural surface is calculated based on the digital image algorithm. S3. Based on the multi-epoch carrier phase observation values ​​collected by the Beidou receiver during the reporting period, a carrier phase time difference observation equation is constructed to eliminate integer ambiguity parameters and obtain the floating point position change between epochs. A visual relative displacement virtual observation equation is constructed based on visual displacement field information. The object space relative displacement converted from visual displacement field information is introduced into the carrier phase time difference observation equation as a priori constraint. The optimized coordinate sequence and its accuracy information are obtained through multi-epoch joint solution. S4. Calculate the average RTK change information based on the RTK data corresponding to the reporting period. Make a joint judgment based on the RTK change information, the optimized coordinate sequence, and the visual displacement field information to determine the deformation information. Adjust the process noise of the real-time static filter based on the deformation information and perform real-time static filtering.

[0006] In some embodiments of this application, in S1, the initial screening detection of the image sequence includes: inter-frame difference change detection and feature point displacement initial screening detection of the image sequence.

[0007] In some embodiments of this application, in S1, the inter-frame differential change detection includes: performing differential calculation and binarization on adjacent frames, extracting the mask and displacement of the changed region, and when the mask area or displacement exceeds a preset threshold, determining it as abnormal and marking the region of interest.

[0008] In some embodiments of this application, in S1, the initial screening detection of feature point displacement includes: extracting corner features in the region of interest, calculating pixel-level displacement using optical flow; and determining an anomaly when the displacement exceeds a preset displacement threshold for multiple consecutive frames. When both the inter-frame difference change detection and the initial screening of feature point displacement results are abnormal, the reporting period is determined to begin, and BeiDou encrypted data acquisition is triggered synchronously; when multiple consecutive frames are below the threshold, the reporting period is marked to end.

[0009] In some embodiments of this application, in step S2, extracting texture features and artificial marking features from the surface of the monitored object, and calculating the visual displacement field information of the structural surface feature points based on digital image algorithms includes: For areas with natural texture on the surface of the monitored object, digital image algorithms are used to extract speckle feature points. For areas lacking natural texture, artificially coded markers are set as feature points. Feature point matching algorithms are used to establish the correspondence between adjacent frames and determine the initial displacement. The Gauss-Newton iterative algorithm based on inverse combination is used to optimize the initial displacement, optimize the deformation parameters until the correlation coefficient converges, and obtain the displacement coordinates of the feature point on the image plane. By converting image-space displacement into object-space displacement using collinearity equations, and then meshing the object-space displacements of multiple feature points, continuous visual displacement field information of feature points on the structural surface is obtained.

[0010] In some embodiments of this application, in S3, the expression for constructing the carrier phase time difference observation equation is as follows: ; in, For receiver For satellite i in epoch and Carrier phase time difference observations between the two phases. For carrier wavelength, The unit vector in the direction of the line of sight. This is the vector representing the positional change between epochs. To observe noise.

[0011] In some embodiments of this application, in S3, the expression for constructing the virtual observation equation of visual relative displacement based on visual displacement field information is as follows: ; in, It is the relative displacement vector in the object space obtained by converting the visual displacement field information. For Beidou receivers in the historical period and The change in position between them This is the visual observation residual vector.

[0012] In some embodiments of this application, in step S3, obtaining the optimized coordinate sequence and its accuracy information through multi-epoch joint solution includes: Based on the carrier phase time difference observation equation and the visual relative displacement virtual observation equation, the weighted least squares method is used to perform multi-epoch joint solution to obtain the optimized coordinate sequence and its accuracy information.

[0013] In some embodiments of this application, multi-epoch joint solution is performed using the weighted least squares method to obtain the optimized coordinate sequence and its accuracy information, including: Construct a multi-epoch joint observation equation, the expression of which is: ; in, For carrier phase time difference observations The column vector formed The relative displacement vector in the object space The corresponding vector, This is the line-of-sight direction matrix. It is the identity matrix. This is the vector representing the positional change between epochs. This is the carrier phase time difference observation residual vector. The virtual observation residual vector for visual relative displacement; The optimized coordinate sequence is obtained by joint solution through weighted least squares update. : ; in, The weighting matrix is ​​determined based on the accuracy of carrier phase observations. The weight matrix is ​​determined based on the accuracy of visual observation.

[0014] The advantages and beneficial effects of this invention compared to the prior art are: 1. This invention employs visual image frame difference and feature point displacement for initial screening and detection. It obtains continuous visual displacement field information on the surface of the monitored object through a sub-pixel-level digital image correlation algorithm, realizing the expansion from "point monitoring" to "field monitoring". Furthermore, it effectively filters out environmental noise interference by utilizing cross-verification of visual and BeiDou observations, thereby improving the spatial resolution and triggering reliability of deformation monitoring.

[0015] 2. This invention uses carrier phase time difference technology to eliminate integer ambiguity parameters, avoiding the risk of ambiguity fixation failure. At the same time, visual relative displacement is introduced as a virtual observation constraint into the joint solution equation. Through weighted least squares, deep fusion of BeiDou and vision at the raw data level is achieved, which effectively suppresses the multipath effect and improves the positioning accuracy and solution success rate in harsh environments.

[0016] 3. This invention constructs a multi-epoch joint observation equation, and performs joint adjustment of the object space relative displacement transformed by visual displacement field and the carrier phase time difference observation value. This achieves accurate registration and information complementarity between Beidou absolute coordinates and visual relative displacement, improves the robustness and reliability of deformation monitoring in complex environments, and ensures the continuity and stability of millimeter-level deformation monitoring.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a flowchart of a deformation monitoring method that fuses BeiDou GNSS and visual image information in an embodiment of the present invention. Detailed Implementation

[0019] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0021] like Figure 1 As shown, this invention provides a deformation monitoring method based on the fusion of BeiDou GNSS and visual image information, comprising the following steps: S1. Based on the visual image acquisition device, periodic images are acquired on the surface of the monitored object. The image sequence is initially screened and detected. When a change in the state of the monitored object is detected, the reporting period is determined.

[0022] Specifically, the initial screening uses a dual judgment strategy of coarse screening by inter-frame difference and fine screening by feature points: First, inter-frame difference operation is performed on adjacent frames. By using gray-scale difference or background difference, the change area mask on the surface of the monitored object is extracted. When the area of ​​the change area exceeds a preset threshold (such as 5%), it is initially determined that deformation may occur and the region of interest is marked. Second, corner points or texture feature points are extracted in the region of interest. The pixel-level displacement of the feature points is calculated using optical flow or template matching algorithm. When the displacement of the feature points in multiple consecutive frames is greater than the preset displacement threshold and the displacement direction conforms to the mechanical characteristics of structural deformation, the feature point displacement is judged to have passed the initial screening. This can effectively filter out environmental interference such as sudden changes in illumination and shadow movement, and avoid false triggers caused by a single threshold judgment.

[0023] S2. The visual image sequence during the reporting period is refined using a subpixel fitting algorithm to extract the texture features and artificial marking features of the monitored object surface. The visual displacement field information of the feature points on the structural surface is calculated based on the digital image algorithm.

[0024] Specifically, the image sequence during the reporting period undergoes sub-pixel level refinement: speckle features are extracted from natural texture areas using the Digital Image Correlation (DIC) algorithm, while artificial markers are placed in texture-deficient areas; after obtaining the initial displacement of integer pixels through feature matching, sub-pixel optimization is performed using inverse combination Gauss-Newton iteration or phase correlation fitting, iterating until the correlation coefficient converges; combined with camera calibration parameters, the image displacement is converted into the actual displacement in the object space through collinearity equations, and continuous visual displacement field information is generated through gridding processing to achieve accurate acquisition of full-field deformation.

[0025] S3. Based on the multi-epoch carrier phase observation values ​​collected by the Beidou receiver during the reporting period, a carrier phase time difference observation equation is constructed to eliminate integer ambiguity parameters and obtain the floating point position change between epochs. A visual relative displacement virtual observation equation is constructed based on visual displacement field information. The object space relative displacement converted from visual displacement field information is introduced into the carrier phase time difference observation equation as a priori constraint. The optimized coordinate sequence and its accuracy information are obtained through multi-epoch joint solution.

[0026] Specifically, Time Differential Carrier Phase (TDCP) technology is used to replace traditional double-difference positioning. The difference between carrier phase observations from adjacent epochs at single stations eliminates integer ambiguity, avoiding cycle slip problems when the number of satellites is insufficient, and directly obtaining the floating-point position change between epochs. Simultaneously, the relative displacement in the object space transformed by the visual displacement field is used as a virtual observation. A visual constraint equation is constructed and introduced into the TDCP observation equation. Through weighted least squares joint solution, high-precision visual relative displacement constrains BeiDou absolute positioning, effectively suppressing multipath effects, improving the solution accuracy and reliability under harsh environments, and outputting optimized coordinate sequences and their covariance accuracy information.

[0027] S4. Calculate the average RTK change information based on the RTK data corresponding to the reporting period. Make a joint judgment based on the RTK change information, the optimized coordinate sequence, and the visual displacement field information to determine the deformation information. Adjust the process noise of the real-time static filter based on the deformation information and perform real-time static filtering.

[0028] This invention employs visual image frame difference and feature point displacement for initial screening and detection. It obtains continuous visual displacement field information on the surface of the monitored object through a sub-pixel level digital image correlation algorithm, realizing the expansion from "point monitoring" to "field monitoring". Furthermore, it utilizes cross-verification of visual and BeiDou observations to effectively filter out environmental noise interference, thereby improving the spatial resolution and triggering reliability of deformation monitoring.

[0029] In some embodiments of this application, in S1, the initial screening detection of the image sequence includes: inter-frame difference change detection and feature point displacement initial screening detection of the image sequence.

[0030] In some embodiments of this application, in S1, the inter-frame differential change detection includes: performing differential calculation and binarization on adjacent frames, extracting the mask and displacement of the changed region, and when the mask area or displacement exceeds a preset threshold, determining it as abnormal and marking the region of interest.

[0031] In some embodiments of this application, in S1, the initial screening detection of feature point displacement includes: extracting corner features in the region of interest, calculating pixel-level displacement using optical flow; and determining an anomaly when the displacement exceeds a preset displacement threshold for multiple consecutive frames. When both the inter-frame difference change detection and the initial screening of feature point displacement results are abnormal, the reporting period is determined to begin, and BeiDou encrypted data acquisition is triggered synchronously; when multiple consecutive frames are below the threshold, the reporting period is marked to end.

[0032] In some embodiments of this application, in step S2, extracting texture features and artificial marking features from the surface of the monitored object, and calculating the visual displacement field information of the structural surface feature points based on digital image algorithms includes: For areas with natural texture on the surface of the monitored object, digital image algorithms are used to extract speckle feature points. For areas lacking natural texture, artificially coded markers are set as feature points. Feature point matching algorithms are used to establish the correspondence between adjacent frames and determine the initial displacement. The Gauss-Newton iterative algorithm based on inverse combination is used to optimize the initial displacement, optimize the deformation parameters until the correlation coefficient converges, and obtain the displacement coordinates of the feature point on the image plane. By converting image-space displacement into object-space displacement using collinearity equations, and then meshing the object-space displacements of multiple feature points, continuous visual displacement field information of feature points on the structural surface is obtained.

[0033] In some embodiments of this application, in S3, the expression for constructing the carrier phase time difference observation equation is as follows: ; in, For receiver For satellite i in epoch and Carrier phase time difference observations between the two phases. For carrier wavelength, The unit vector in the direction of the line of sight. This is the vector representing the positional change between epochs. To observe noise.

[0034] Specifically, Time Differential Carrier Phase (TDCP) technology is employed to perform time difference analysis on multi-epoch carrier phase observations from a single station. This eliminates ambiguity by leveraging the identical integer ambiguity between adjacent epochs, avoiding cycle slip problems and ambiguity fixation failures inherent in traditional double-difference positioning when the number of satellites is insufficient or the observation environment is harsh. By linearizing the geometric distance change, an observation equation containing only inter-epoch position change parameters is established, directly obtaining the position change in floating-point solution form. This provides a reliable BeiDou observation foundation for subsequent fusion with visual information.

[0035] In some embodiments of this application, in S3, the expression for constructing the virtual observation equation of visual relative displacement based on visual displacement field information is as follows: ; in, It is the relative displacement vector in the object space obtained by converting the visual displacement field information. For Beidou receivers in the historical period and The change in position between them This is the visual observation residual vector.

[0036] Specifically, the relative displacement in the object space converted from the visual displacement field is used as a virtual observation value. A virtual observation equation for visual relative displacement is constructed to establish a mathematical relationship between visual observation and the position change of the BeiDou receiver. By introducing high-precision visual relative displacement as a priori constraint into the carrier phase time difference observation equation, deep fusion of BeiDou absolute positioning and visual relative measurement at the raw data level is achieved. Visual observation is used to constrain the degrees of freedom of BeiDou solution, effectively suppressing multipath effects and improving solution robustness.

[0037] In some embodiments of this application, in step S3, obtaining the optimized coordinate sequence and its accuracy information through multi-epoch joint solution includes: Based on the carrier phase time difference observation equation and the visual relative displacement virtual observation equation, the weighted least squares method is used to perform multi-epoch joint solution to obtain the optimized coordinate sequence and its accuracy information.

[0038] Based on the carrier phase time difference observation equation and the visual relative displacement virtual observation equation, multi-epoch joint solution is performed using factor graph optimization or Kalman filtering. By constructing a joint state space containing multi-epoch observation information, the high short-term accuracy of visual displacement and the long-term stability of BeiDou carrier phase are complemented and fused to globally optimize and estimate the coordinate sequence, and output the accuracy information covariance matrix, thereby achieving high accuracy and continuous reliability of deformation monitoring in complex environments.

[0039] In some embodiments of this application, multi-epoch joint solution is performed using the weighted least squares method to obtain the optimized coordinate sequence and its accuracy information, including: Construct a multi-epoch joint observation equation, the expression of which is: ; in, For carrier phase time difference observations The column vector formed The relative displacement vector in the object space The corresponding vector, This is the line-of-sight direction matrix. It is the identity matrix. This is the vector representing the positional change between epochs. This is the carrier phase time difference observation residual vector. The virtual observation residual vector for visual relative displacement; The optimized coordinate sequence is obtained by joint solution through weighted least squares update. : ; in, The weighting matrix is ​​determined based on the accuracy of carrier phase observations. The weight matrix is ​​determined based on the accuracy of visual observation.

[0040] Specifically, a multi-epoch joint observation equation is constructed to unify the carrier phase time difference observations and the visual relative displacement virtual observations into the same state space. The designed matrix includes a line-of-sight matrix and an identity matrix. Joint adjustment is performed using the weighted least squares method, and the weight matrix is ​​adaptively weighted according to the accuracy characteristics of the two observations. The equations are solved to obtain an optimized coordinate sequence, ensuring that the solution simultaneously satisfies the geometric constraints of BeiDou observations and the visual displacement constraints, thus obtaining the statistically optimal deformation estimate.

[0041] This invention employs carrier phase time difference technology to eliminate integer ambiguity parameters, avoiding the risk of ambiguity fixation failure. At the same time, visual relative displacement is introduced as a virtual observation constraint into the joint solution equation. Through weighted least squares, deep fusion of BeiDou and vision is achieved at the raw data level, effectively suppressing multipath effects and improving positioning accuracy and solution success rate in harsh environments.

[0042] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A deformation monitoring method that fuses BeiDou GNSS and visual image information, characterized in that, Includes the following steps: S1. Based on the visual image acquisition device, periodically acquire images of the surface of the monitored object, perform preliminary screening of the image sequence, and determine the reporting period when a change in the state of the monitored object is detected; S2. The visual image sequence during the reporting period is refined using a sub-pixel fitting algorithm to extract the texture features and artificial marking features of the monitored object surface. The visual displacement field information of the feature points on the structural surface is calculated based on the digital image algorithm. S3. Based on the multi-epoch carrier phase observation values ​​collected by the Beidou receiver during the reporting period, a carrier phase time difference observation equation is constructed to eliminate integer ambiguity parameters and obtain the floating-point position change between epochs. A visual relative displacement virtual observation equation is constructed based on visual displacement field information. The object space relative displacement converted from visual displacement field information is introduced into the carrier phase time difference observation equation as a priori constraint. The optimized coordinate sequence and its accuracy information are obtained through multi-epoch joint solution. S4. Calculate the average RTK change information based on the RTK data corresponding to the reporting period. Make a joint judgment based on the RTK change information, the optimized coordinate sequence, and the visual displacement field information to determine the deformation information. Adjust the process noise of the real-time static filter based on the deformation information and perform real-time static filtering.

2. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 1, characterized in that, In step S1, the initial screening detection of the image sequence includes: inter-frame difference change detection and feature point displacement initial screening detection of the image sequence.

3. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 2, characterized in that, In step S1, the inter-frame differential change detection includes: performing differential calculation and binarization on adjacent frames, extracting the mask and displacement of the changed region, and determining it as an anomaly and marking the region of interest when the mask area or displacement exceeds a preset threshold.

4. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 3, characterized in that, In step S1, the initial screening detection of feature point displacement includes: extracting corner features in the region of interest and calculating pixel-level displacement using optical flow; when the displacement of multiple consecutive frames exceeds a preset displacement threshold, it is determined to be abnormal. When both the inter-frame difference change detection and the initial screening of feature point displacement results are abnormal, the reporting period is determined to begin, and BeiDou encrypted data acquisition is triggered synchronously; when multiple consecutive frames are below the threshold, the reporting period is marked to end.

5. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 4, characterized in that, In step S2, the texture features and artificial marking features of the monitored object's surface are extracted, and the visual displacement field information of the structural surface feature points is calculated based on digital image algorithms, including: For areas with natural texture on the surface of the monitored object, digital image algorithms are used to extract speckle feature points. For areas lacking natural texture, artificially coded markers are set as feature points. Feature point matching algorithms are used to establish the correspondence between adjacent frames and determine the initial displacement. The Gauss-Newton iterative algorithm based on inverse combination is used to optimize the initial displacement, optimize the deformation parameters until the correlation coefficient converges, and obtain the displacement coordinates of the feature point on the image plane. By converting image-space displacement into object-space displacement using collinearity equations, and then meshing the object-space displacements of multiple feature points, continuous visual displacement field information of feature points on the structural surface is obtained.

6. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 5, characterized in that, In S3, the expression for constructing the carrier phase time difference observation equation is as follows: ； in, For receiver For satellite i in epoch and Carrier phase time difference observations between the two phases. For carrier wavelength, The unit vector in the direction of the line of sight. This is the vector representing the positional change between epochs. To observe noise.

7. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 6, characterized in that, In step S3, the expression for constructing the virtual observation equation of visual relative displacement based on the visual displacement field information is as follows: ； in, It is the relative displacement vector in the object space obtained by converting the visual displacement field information. For Beidou receivers in the historical period and The change in position between them This is the visual observation residual vector.

8. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 7, characterized in that, In step S3, the optimized coordinate sequence and its accuracy information obtained through multi-epoch joint solution include: Based on the carrier phase time difference observation equation and the visual relative displacement virtual observation equation, the weighted least squares method is used to perform multi-epoch joint solution to obtain the optimized coordinate sequence and its accuracy information.

9. The deformation monitoring method based on the fusion of BeiDou GNSS and visual image information according to claim 8, characterized in that, The optimized coordinate sequence and its accuracy information obtained by performing multi-epoch joint solution using the weighted least squares method include: Construct a multi-epoch joint observation equation, the expression of which is: ； in, For carrier phase time difference observations The column vector formed The relative displacement vector in the object space The corresponding vector, This is the line-of-sight direction matrix. It is the identity matrix. This is the vector representing the positional change between epochs. The carrier phase time difference observation residual vector, The virtual observation residual vector for visual relative displacement; The optimized coordinate sequence is obtained by joint solution through weighted least squares update. : ； in, The weighting matrix is ​​determined based on the accuracy of carrier phase observations. The weight matrix is ​​determined based on the accuracy of visual observation.

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