Deformation monitoring and correcting method and device based on global navigation satellite system

Abstract

The invention provides a deformation monitoring correction method and device based on a global navigation satellite system, and the method comprises the steps: building a double-difference observation equation based on observation data collected by a reference station and a monitoring station, carrying out the Taylor expansion of the double-difference observation equation, converting the double-difference observation equation into a matrix expression, and carrying out the calculation of the matrix expression; establishing a first observation equation aiming at the coordinates of the monitoring station; performing ambiguity integer solution search and fixation on the first observation equation by using an ambiguity search method, determining an ambiguity fixed value in the first observation equation, and determining a second observation equation based on the first observation equation, the ambiguity fixed value and the increased system error nonparametric component; constructing a compensation least square model based on the second observation equation; and determining a target monitoring station coordinate after the monitoring station is corrected based on an extreme value function corresponding to the compensation least square model and the initial approximate coordinate. Through the method, the operability, reliability and accuracy of deformation monitoring are improved.

Description

Technical Field

[0001] The present application relates to the technical field of satellite positioning and deformation monitoring, and in particular to a deformation monitoring and correction method and device based on a global navigation satellite system. Background Art

[0002] In the high-precision positioning of the Global Navigation Satellite System (GNSS), based on the similarity of the observation errors of the base station and the monitoring station, the receiver error and the satellite error can be eliminated by taking a difference, and the path-related errors such as the ionosphere and the troposphere can be weakened to solve the high-precision coordinate time series of the monitoring station; however, there are still non-similarity errors between the base station and the monitoring station, for example, systematic errors such as multipath effect errors. During deformation monitoring, when there is water surface, glass curtain wall or strong reflective surface near the monitoring station, there will be large multipath errors in the observation data, which will seriously affect the accuracy of the GNSS positioning results.

[0003] At present, when using the global navigation satellite system for deformation monitoring, the methods to weaken system errors such as multipath errors mainly include the use of choke antennas and data post-processing filtering. Among them, the choke antenna resists and shields multipath signals from the hardware performance, which will greatly increase the cost of hardware; data post-processing filtering is to smooth the results of baseline solution, and different filtering parameters will produce different filtering results, and the multipath error is not fundamentally separated, which has great limitations and reduces the accuracy of deformation monitoring results. Summary of the invention

[0004] In view of this, the purpose of the present application is to provide a deformation monitoring and correction method and device based on a global navigation satellite system, which separates the similarity errors generated in deformation monitoring by establishing a first observation equation for the monitoring station coordinates and searching for fixed ambiguity, and combines the characteristics of system errors such as multipath errors in deformation monitoring, utilizes the correlation between epochs before and after the error, introduces a non-parametric vector representing the system error, constructs a compensatory least squares estimation model, and separates system errors such as multipath errors in real time, thereby improving the operability and reliability of deformation monitoring, and thereby improving the accuracy of deformation monitoring results.

[0005] The present application provides a deformation monitoring and correction method based on a global navigation satellite system, the method comprising:

[0006] When the target object is deformed by using the reference station and the monitoring station set by the global navigation satellite system, a double difference observation equation is established based on the observation data collected by the reference station and the monitoring station respectively, the double difference observation equation is Taylor expanded and converted into a matrix expression, and a first observation equation for the monitoring station coordinates is established;

[0007] Searching and fixing an ambiguity integer solution for the first observation equation by using an ambiguity search method, determining an ambiguity fixed value in the first observation equation, and determining a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error;

[0008] Based on the second observation equation, construct a compensatory least squares model for the observation value residual in the observation data and the non-parametric component of the systematic error;

[0009] Based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, a target correction number estimate of the monitoring station coordinates is determined to determine the target monitoring station coordinates after the monitoring station is corrected.

[0010] Furthermore, the double difference observation equation is established based on the observation data collected by the reference station and the monitoring station respectively, including:

[0011] Based on the observation data collected by the reference station and the monitoring station, respectively, establishing a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station;

[0012] Determining a single-difference observation equation of the monitoring station relative to the reference station based on the non-difference observation equation of the reference station and the non-difference observation equation of the monitoring station;

[0013] One of the multiple observation satellites is used as a reference satellite, and based on the single-difference observation equation, double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined.

[0014] Furthermore, the double difference observation equation is subjected to Taylor expansion processing and converted into a matrix expression to establish a first observation equation for the monitoring station coordinates, including:

[0015] Using the initial approximate coordinates corresponding to the monitoring station, Taylor expansion calculation is performed on the double difference observation equation to obtain a double difference correction number expression corresponding to the double difference observation equation;

[0016] The double-difference correction number expression is converted into a matrix expression to establish a first observation equation for the monitoring station coordinates.

[0017] Furthermore, the step of searching and fixing an ambiguity integer solution of the first observation equation by using an ambiguity search method, determining an ambiguity fixed value in the first observation equation, and determining a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error, includes:

[0018] Based on the first observation equation, a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate are determined using a preset Kalman filter estimation formula;

[0019] Performing floating-point ambiguity separation on the first correction number estimate and the first covariance matrix respectively, and determining a floating-point ambiguity estimate and a second covariance matrix corresponding to the floating-point ambiguity estimate;

[0020] Determining, based on the floating-point ambiguity estimate and the second covariance matrix, an ambiguity fixed value in the first observation equation using an ambiguity search method;

[0021] The ambiguity fixed value is substituted into the first observation equation, and a non-parametric component of a systematic error is added to determine a second observation equation for the monitoring station coordinates.

[0022] Furthermore, the first observation equation includes a correction vector of the monitoring station coordinates and a first coefficient matrix corresponding thereto, a double difference ambiguity parameter and a second coefficient matrix corresponding thereto, a correction vector of the observation value residual, an observation value residual vector and a weight matrix;

[0023] The method of determining a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate based on the first observation equation using a preset Kalman filter estimation formula includes:

[0024] Determine a gain matrix using a preset first Kalman filter estimation formula based on an initial covariance matrix corresponding to an estimated value of an initial correction number of a preset monitoring station coordinate, the first coefficient matrix, the second coefficient matrix, and the weight matrix;

[0025] Based on the preset initial correction number estimate of the monitoring station coordinates, the gain matrix, the first coefficient matrix, the second coefficient matrix and the observation value residual vector, a first correction number estimate of the monitoring station coordinates is determined using a preset second Kalman filter estimation formula;

[0026] Based on the initial covariance matrix, the gain matrix, the first coefficient matrix and the second coefficient matrix, a first covariance matrix corresponding to the first correction number estimate is determined using a preset third Kalman filter estimation formula.

[0027] Further, the step of determining a target correction value estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station to determine the target monitoring station coordinates after the monitoring station is corrected includes:

[0028] Constructing an extreme value function corresponding to the compensated least squares model;

[0029] Derivative calculation is performed on the correction number of the monitoring station coordinates and the non-parametric component of the system error in the extreme value function to determine the correction matrix corresponding to the extreme value function;

[0030] Based on the correction matrix, determining a second correction number estimate of the monitoring station coordinates by matrix calculation as a target correction number estimate;

[0031] The initial approximate coordinates corresponding to the monitoring station are added to the estimated value of the target correction number to obtain an addition result, and the addition result is determined as the coordinates of the target monitoring station after the monitoring station is corrected.

[0032] The embodiment of the present application also provides a deformation monitoring and correction device based on a global navigation satellite system, the device comprising:

[0033] A first observation equation determination module is used to establish a double difference observation equation based on observation data collected by the reference station and the monitoring station respectively when the target object is deformed using the reference station and the monitoring station set by the global navigation satellite system, perform Taylor expansion processing on the double difference observation equation and convert it into a matrix expression, and establish a first observation equation for the coordinates of the monitoring station;

[0034] a second observation equation determination module, configured to search and fix an ambiguity integer solution of the first observation equation by using an ambiguity search method, determine an ambiguity fixed value in the first observation equation, and determine a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error;

[0035] A model building module, for building a compensatory least squares model for the observation value residual in the observation data and the non-parametric component of the system error based on the second observation equation and;

[0036] The coordinate correction module is used to determine the target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, so as to determine the target monitoring station coordinates after the monitoring station is corrected.

[0037] Furthermore, when the first observation equation determination module is used to establish a double-difference observation equation based on the observation data respectively collected by the reference station and the monitoring station, the first observation equation determination module is used to:

[0038] Based on the observation data collected by the reference station and the monitoring station, respectively, establishing a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station;

[0039] Determining a single-difference observation equation of the monitoring station relative to the reference station based on the non-difference observation equation of the reference station and the non-difference observation equation of the monitoring station;

[0040] One of the multiple observation satellites is used as a reference satellite, and based on the single-difference observation equation, double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined.

[0041] Furthermore, when the first observation equation determination module is used to perform Taylor expansion processing on the double difference observation equation and convert it into a matrix expression to establish a first observation equation for the monitoring station coordinates, the first observation equation determination module is used to:

[0042] Using the initial approximate coordinates corresponding to the monitoring station, Taylor expansion calculation is performed on the double difference observation equation to obtain a double difference correction number expression corresponding to the double difference observation equation;

[0043] The double-difference correction number expression is converted into a matrix expression to establish a first observation equation for the monitoring station coordinates.

[0044] Further, when the second observation equation determination module is used to search and fix the ambiguity integer solution of the first observation equation by using the ambiguity search method, determine the ambiguity fixed value in the first observation equation, and determine the second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and the added non-parametric component of the system error, the second observation equation determination module is used to:

[0045] Based on the first observation equation, a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate are determined using a preset Kalman filter estimation formula;

[0046] Performing floating-point ambiguity separation on the first correction number estimate and the first covariance matrix respectively, and determining a floating-point ambiguity estimate and a second covariance matrix corresponding to the floating-point ambiguity estimate;

[0047] Determining, based on the floating-point ambiguity estimate and the second covariance matrix, an ambiguity fixed value in the first observation equation using an ambiguity search method;

[0048] The ambiguity fixed value is substituted into the first observation equation, and a non-parametric component of a systematic error is added to determine a second observation equation for the monitoring station coordinates.

[0049] Furthermore, the first observation equation includes a correction vector of the monitoring station coordinates and a first coefficient matrix corresponding thereto, a double difference ambiguity parameter and a second coefficient matrix corresponding thereto, a correction vector of the observation value residual, an observation value residual vector and a weight matrix;

[0050] When the second observation equation determination module is used to determine the first correction number estimate of the monitoring station coordinates and the first covariance matrix corresponding to the first correction number estimate based on the first observation equation using a preset Kalman filter estimation formula, the second observation equation determination module is used to:

[0051] Determine a gain matrix using a preset first Kalman filter estimation formula based on an initial covariance matrix corresponding to an estimated value of an initial correction number of a preset monitoring station coordinate, the first coefficient matrix, the second coefficient matrix, and the weight matrix;

[0052] Based on the preset initial correction number estimate of the monitoring station coordinates, the gain matrix, the first coefficient matrix, the second coefficient matrix and the observation value residual vector, a first correction number estimate of the monitoring station coordinates is determined using a preset second Kalman filter estimation formula;

[0053] Based on the initial covariance matrix, the gain matrix, the first coefficient matrix and the second coefficient matrix, a first covariance matrix corresponding to the first correction number estimate is determined using a preset third Kalman filter estimation formula.

[0054] Further, when the coordinate correction module is used to determine the target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station to determine the target monitoring station coordinates after the monitoring station is corrected, the coordinate correction module is used to:

[0055] Constructing an extreme value function corresponding to the compensated least squares model;

[0056] Derivative calculation is performed on the correction number of the monitoring station coordinates and the non-parametric component of the system error in the extreme value function to determine the correction matrix corresponding to the extreme value function;

[0057] Based on the correction matrix, determining a second correction number estimate of the monitoring station coordinates by matrix calculation as a target correction number estimate;

[0058] The initial approximate coordinates corresponding to the monitoring station are added to the estimated value of the target correction number to obtain an addition result, and the addition result is determined as the coordinates of the target monitoring station after the monitoring station is corrected.

[0059] An embodiment of the present application also provides an electronic device, including: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the deformation monitoring and correction method based on the global navigation satellite system are performed as described above.

[0060] An embodiment of the present application further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the deformation monitoring and correction method based on the global navigation satellite system are executed as described above.

[0061] The deformation monitoring and correction method and device based on the global navigation satellite system provided in the embodiment of the present application include: when using the base station and the monitoring station set by the global navigation satellite system to monitor the deformation of the target object, based on the observation data collected by the base station and the monitoring station respectively, a double difference observation equation is established, the double difference observation equation is Taylor expanded and converted into a matrix expression, and a first observation equation for the coordinates of the monitoring station is established; the ambiguity integer solution of the first observation equation is searched and fixed by the ambiguity search method, the ambiguity fixed value in the first observation equation is determined, and the second observation equation for the coordinates of the monitoring station is determined based on the first observation equation, the ambiguity fixed value and the added non-parametric component of the system error; based on the second observation equation, a compensating least squares model for the observation value residual and the non-parametric component of the system error in the observation data is constructed; based on the extreme value function corresponding to the compensating least squares model and the initial approximate coordinates corresponding to the monitoring station, the target correction number estimate of the coordinates of the monitoring station is determined to determine the target monitoring station coordinates after the correction of the monitoring station.

[0062] Compared with the methods of using choke antennas and data post-processing filtering in the prior art, the first observation equation for the monitoring station coordinates is established and the fixed ambiguity is searched to separate the similarity error generated in deformation monitoring. Combined with the characteristics of system errors such as multipath error in deformation monitoring, the correlation between epochs before and after the error is used, a non-parametric vector representing the system error is introduced, and a compensated least squares estimation model is constructed to separate system errors such as multipath error in real time, thereby improving the operability and reliability of deformation monitoring, and thereby improving the accuracy of deformation monitoring results.

[0063] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are specifically cited below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 One of the flow charts of a deformation monitoring and correction method based on a global navigation satellite system provided in an embodiment of the present application;

[0066] FIG. 2( a ) is one of the data result diagrams of a deformation monitoring provided in an embodiment of the present application;

[0067] FIG. 2( b ) is a second diagram of deformation monitoring data results provided by an embodiment of the present application;

[0068] Figure 3 A schematic diagram of the structure of a deformation monitoring and correction device based on a global navigation satellite system provided in an embodiment of the present application;

[0069] Figure 4 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0070] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application usually described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, each other embodiment obtained by those skilled in the art without making creative work belongs to the scope of protection of the present application.

[0071] Research has found that, at present, when using the global navigation satellite system for deformation monitoring, the methods to weaken system errors such as multipath errors mainly include the use of choke antennas and data post-processing filtering. Among them, the choke antenna resists and shields multipath signals from the hardware performance, which will greatly increase the cost of hardware; data post-processing filtering is to smooth the results of baseline solution, and different filtering parameters will produce different filtering results, and the multipath error is not fundamentally separated, which has great limitations, thereby reducing the accuracy of deformation monitoring results.

[0072] It can be seen that in deformation monitoring, since the monitoring station is affected by the surrounding environment, the observed values ​​not only have random errors, but also systematic errors such as multipath errors. This error has a certain correlation with the observation time. Since random errors and systematic errors interfere with each other, it is difficult to quantify and model them, and it is impossible to express them parameterized. Therefore, a non-parametric component representing the systematic error can be introduced to make the observation equation more accurately describe the actual situation of the observed value, and then a semi-parametric model can be constructed to perform compensated least squares estimation. In the case of separating the systematic error, the optimal estimate of the baseline solution can be obtained.

[0073] Based on this, an embodiment of the present application provides a deformation monitoring and correction method based on a global navigation satellite system. By establishing a first observation equation for the monitoring station coordinates and searching for fixed ambiguity, the similarity error generated in deformation monitoring is separated. Combined with the characteristics of system errors such as multipath errors in deformation monitoring, the correlation between epochs before and after the error is utilized, a non-parametric vector representing the system error is introduced, and a compensated least squares estimation model is constructed. System errors such as multipath errors are separated in real time, thereby improving the operability and reliability of deformation monitoring, and thereby improving the accuracy of deformation monitoring results.

[0074] See also Figure 1 , Figure 1 This is a flow chart of a deformation monitoring and correction method based on a global navigation satellite system provided in an embodiment of the present application. Figure 1 As shown in , the deformation monitoring and correction method based on the global navigation satellite system provided in the embodiment of the present application includes:

[0075] S101. When deformation monitoring of a target object is performed using a base station and a monitoring station provided by a global navigation satellite system, a double-difference observation equation is established based on observation data respectively collected by the base station and the monitoring station, the double-difference observation equation is Taylor expanded and converted into a matrix expression, and a first observation equation for the monitoring station coordinates is established.

[0076] It should be noted that the Global Navigation Satellite System (GNSS) is a satellite-based positioning system that can provide geographic location and time information on a global scale. Each satellite continuously sends radio signals containing its position and timestamp to the earth; the GNSS receiver on the ground receives signals from at least four different satellites; the receiver uses the time difference between the arrival of the signals to calculate the distance to each satellite (pseudorange); through trilateration or quadrilateralization (taking into account time errors), the receiver determines its own three-dimensional position (latitude, longitude, altitude) and precise time.

[0077] Among them, the base station is usually set at a known and very precise geographical location; it receives signals from satellites and records the arrival time and other relevant information of these signals; based on its own known position, the base station can calculate the observation error caused by factors such as atmospheric delay and satellite orbit error, and send this error information to the user device or pass it to other stations through the network to improve the user's positioning accuracy.

[0078] The monitoring station is mainly used to measure and record the changes in the spatial position and shape of the monitored object over time, so as to promptly discover and deal with potential safety hazards.

[0079] Here, deformation monitoring refers to the process of accurately measuring and analyzing the changes in the shape, position or volume of structures or natural surfaces (for example, buildings, bridges, dams, slopes, mines and other target objects) over time. Deformation monitoring is essential to ensure the safety, stability and functionality of the target objects.

[0080] In this step, during the specific implementation, first, based on the observation data collected by the reference station and the monitoring station respectively, the non-difference observation equation of the reference station and the non-difference observation equation of the monitoring station are established respectively; then, the single-difference observation equation of the monitoring station relative to the reference station is determined; thereafter, one of the multiple observation satellites is used as the reference satellite, and the double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined; finally, the double-difference observation equation is Taylor expanded and converted into a matrix expression to establish the first observation equation for the monitoring station coordinates.

[0081] In one embodiment of the present application, in a specific implementation, the step of establishing a double difference observation equation based on the observation data collected by the reference station and the monitoring station respectively in step S101 may include:

[0082] S1011. Based on the observation data collected by the reference station and the monitoring station respectively, establish a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station respectively.

[0083] Here, the observation data may include but are not limited to the original non-difference carrier phase observation value (in "weeks"), the original non-difference pseudorange observation value (in "meters"), and the station-satellite geometric distance at the time of signal transmission.

[0084] In the embodiment of the present application, it is assumed that the multiple observation satellites are numbered A, B, ..., F, and taking the observation satellite A as an example, the expression of the non-difference observation equation of the base station for the observation satellite A is as follows.

[0085]

[0086] Among them, "1" represents the base station and "A" represents the observation satellite A; and are the original non-difference carrier phase observation value and the original non-difference pseudorange observation value respectively; λ is the wavelength of the satellite phase observation value; is the geometric distance between the station and the satellite at the time of signal transmission; c is the speed of light in vacuum; t 1 is the receiver clock error; t A is the satellite clock error; is the carrier phase undifference ambiguity; is the tropospheric delay on the signal propagation path; is the ionospheric delay on the signal propagation path; and are other unmodeled errors.

[0087] Taking the observation satellite A as an example, the expression of the non-difference observation equation of the monitoring station for the observation satellite A is as follows.

[0088]

[0089] Among them, "2" represents the monitoring station and "A" represents the observation satellite A; and are the original non-difference carrier phase observation value and the original non-difference pseudorange observation value respectively; λ is the wavelength of the satellite phase observation value; is the geometric distance between the station and the satellite at the time of signal transmission; c is the speed of light in vacuum; t 1 is the receiver clock error; t A is the satellite clock error; is the carrier phase undifference ambiguity; is the tropospheric delay on the signal propagation path; is the ionospheric delay on the signal propagation path; and are other unmodeled errors.

[0090] S1012: Determine a single-difference observation equation of the monitoring station relative to the reference station based on the undifference observation equation of the reference station and the undifference observation equation of the monitoring station.

[0091] In this step, the undifferenced observation equation of the reference station and the undifferenced observation equation of the monitoring station are simultaneously differentiated to determine the single-differenced observation equation of the monitoring station relative to the reference station. The single-differenced observation equation eliminates the satellite clock error in the error parameters contained in the undifferenced observation equation and weakens the tropospheric delay error and ionospheric delay error on the signal transmission path.

[0092] In the embodiment of the present application, taking the example that the observation satellites of the reference station and the monitoring station are both observation satellite A, the expression of the single difference observation equation of the monitoring station relative to the reference station is as follows.

[0093]

[0094] Where Δ is the single difference operator; “A”, “1” and “2” represent satellite A, reference station and monitoring station respectively; and They are single-difference carrier phase observation and single-difference pseudorange observation respectively; is the single difference of the geometric distance between the station and the satellite at the time of signal transmission; Δt 12 is the receiver clock error; is the carrier phase single difference ambiguity; is the single-difference tropospheric delay on the signal propagation path; is the single difference ionospheric delay on the signal propagation path; and are other single-difference unmodeled errors; c is the speed of light in vacuum; λ is the wavelength of the satellite phase observation.

[0095] Furthermore, taking the example that the observation satellites of both the base station and the monitoring station are observation satellite B, the single difference observation equation expression of the monitoring station relative to the base station is as follows.

[0096]

[0097] Where Δ is the single difference operator; "B", "1" and "2" represent satellite B, reference station and monitoring station respectively; and They are single-difference carrier phase observation and single-difference pseudorange observation respectively; is the single difference of the geometric distance between the station and the satellite at the time of signal transmission; Δt 12 is the receiver clock error; is the carrier phase single difference ambiguity; is the single-difference tropospheric delay on the signal propagation path; is the single difference ionospheric delay on the signal propagation path; and are other single-difference unmodeled errors; c is the speed of light in vacuum; λ is the wavelength of the satellite phase observation.

[0098] S1013: Take one of the multiple observation satellites as a reference satellite, and determine double-difference observation equations of the remaining observation satellites relative to the reference satellite based on the single-difference observation equation.

[0099] In this step, one of the multiple observation satellites is used as the reference satellite, and the single-difference observation equations of the remaining observation satellites are simultaneously and differentially matched with the single-difference observation equation of the reference satellite to establish a double-difference observation equation, thereby eliminating the error for the receiver in the error parameters contained in the single-difference observation equation and further weakening the single-difference tropospheric delay error and the single-difference ionospheric delay error.

[0100] In the embodiment of the present application, taking observation satellite A as a reference satellite as an example, the expression of the double difference observation equation of non-reference satellite B relative to reference satellite A is as follows.

[0101]

[0102] Among them, the superscript "A" and "B" represent the reference satellite A and the non-reference satellite B respectively; the subscript "1" represents the reference station; the subscript "2" represents the monitoring station; is the double-difference carrier phase observation value, λ is the wavelength of the satellite phase observation value; is the double-difference pseudorange observation value; is the double difference satellite-to-ground distance; is the carrier phase double difference ambiguity; is the double-difference tropospheric delay error; is the double difference ionospheric delay error; and They are double-difference carrier phase and double-difference pseudorange residual errors respectively.

[0103] In one embodiment of the present application, in a specific implementation, in step S101, the double difference observation equation is subjected to Taylor expansion processing and converted into a matrix expression, and the step of establishing a first observation equation for the monitoring station coordinates may include:

[0104] S1014. Perform Taylor expansion calculation on the double-difference observation equation using the initial approximate coordinates corresponding to the monitoring station to obtain a double-difference correction number expression corresponding to the double-difference observation equation.

[0105] In this step, the double-difference observation equation is Taylor expanded at the initial approximate coordinates corresponding to the preset monitoring station to obtain the double-difference correction number expression corresponding to the double-difference observation equation.

[0106] In the embodiment of the present application, taking the double difference observation equation of the non-reference satellite B relative to the reference satellite A as an example, after Taylor expansion processing, the double difference correction number expression is as follows.

[0107]

[0108] in, and They are the carrier phase double difference correction and pseudorange double difference correction respectively; are the partial derivatives of the approximate satellite-to-earth distance with respect to the corrections of the three coordinate components; dx, dy, dz are the corrections of the monitoring station coordinates; is the approximate satellite-earth double difference distance value; is the double-difference carrier phase observation value; is the double-difference pseudorange observation value; λ is the wavelength of the satellite phase observation value; is the carrier phase double difference ambiguity.

[0109] S1015, converting the double-difference correction number expression into a matrix expression to establish a first observation equation for the monitoring station coordinates.

[0110] In this step, the double difference correction number expression is converted into a matrix expression to establish the first observation equation for the monitoring station coordinates.

[0111] In an embodiment of the present application, the expression of the first observation equation is as follows.

[0112] V=Ax+BN-L,P.

[0113] Among them, x is the correction vector of the monitoring station coordinates; N is the double difference ambiguity parameter; A and B are the first coefficient matrix corresponding to the correction vector of the monitoring station coordinates and the second coefficient matrix corresponding to the double difference ambiguity parameter, respectively; V is the correction vector of the observation residual; L is the observation residual vector; and P is the weight matrix.

[0114] Here, since the carrier phase observation value and the pseudorange observation value are unrelated, the weight matrix may include a first weight matrix corresponding to the carrier phase observation value and a second weight matrix corresponding to the pseudorange observation value.

[0115] In the embodiment of the present application, the expression of the weight matrix is ​​shown as follows.

[0116] P = diag[P car P pse ]

[0117] Among them, P car is the first weight matrix corresponding to the carrier phase observation value, P pse is the second weight matrix corresponding to the pseudorange observation value.

[0118] In an embodiment of the present application, taking the observation satellites as numbered A, B, ..., F, and observation satellite A as a reference satellite as an example, the expression of the first weight matrix corresponding to the carrier phase observation value is as follows.

[0119]

[0120] The superscripts “A, B, …, F” represent observation satellite A, observation satellite B, …, observation satellite F, respectively; is the variance value of the carrier phase observation value of the observed satellite A; the elements on the diagonal of the first weight matrix are the square of the variance value of the carrier phase observation value of the reference satellite plus the square of the variance value of the carrier phase observation value of the non-reference satellite; the elements on the non-diagonal of the first weight matrix are all the square of the variance value of the carrier phase observation value of the reference satellite.

[0121] Furthermore, the expression of the second weight matrix corresponding to the pseudorange observation value is as follows.

[0122]

[0123] in, is the variance of the pseudorange observations of satellite A. The elements on the diagonal of the second weight matrix are the square of the variance of the pseudorange observations of the reference satellite plus the square of the variance of the pseudorange observations of the non-reference satellite; the elements on the off-diagonal of the second weight matrix are the square of the variance of the pseudorange observations of the reference satellite.

[0124] Here, the variance value of the carrier phase observation value and the variance value of the pseudorange observation value of the observation satellite can be calculated using the satellite altitude angle model, and the expression of the satellite altitude angle model is as follows.

[0125]

[0126] Among them, δ car is the variance of the carrier phase observation; δ pse is the variance of the pseudorange observation; a and b are the constants corresponding to the carrier phase observation respectively; c and d are the constants corresponding to the pseudorange observation respectively, and Ele is the altitude angle of the satellite.

[0127] S102. Use an ambiguity search method to search and fix an ambiguity integer solution for the first observation equation, determine the ambiguity fixed value in the first observation equation, and determine a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and the added non-parametric component of the system error.

[0128] In one implementation of the present application, during specific implementation, step S102 may include:

[0129] S1021. Based on the first observation equation, a preset Kalman filter estimation formula is used to determine a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate.

[0130] In an embodiment of the present application, the first observation equation may include the correction vector of the monitoring station coordinates and its corresponding first coefficient matrix, the double difference ambiguity parameters and its corresponding second coefficient matrix, the correction vector of the observation value residuals, the observation value residual vector and the weight matrix.

[0131] In one implementation of the present application, during specific implementation, step S1021 may include:

[0132] S10211. Based on the initial covariance matrix corresponding to the estimated value of the initial correction number of the preset monitoring station coordinates, the first coefficient matrix, the second coefficient matrix and the weight matrix, a gain matrix is ​​determined using a preset first Kalman filter estimation formula.

[0133] In an embodiment of the present application, the expression of the first Kalman filter estimation formula is as follows.

[0134] K=Q X0 H T [HQ X0 H T +P -1 ] -1 .

[0135] Where K represents the gain matrix; Q X0 Represents the initial covariance matrix corresponding to the estimated value of the initial correction number of the preset monitoring station coordinates; H = [AB], A and B are the first coefficient matrix and the second coefficient matrix respectively; P is the weight matrix.

[0136] S10212. Based on the preset initial correction number estimate of the monitoring station coordinates, the gain matrix, the first coefficient matrix, the second coefficient matrix and the observation value residual vector, determine the first correction number estimate of the monitoring station coordinates using the preset second Kalman filter estimation formula.

[0137] In an embodiment of the present application, the expression of the second Kalman filter estimation formula is as follows.

[0138]

[0139] in, represents the estimated value of the first correction number of the monitoring station coordinates; X 0 represents the estimated value of the initial correction number of the preset monitoring station coordinates; H = [AB], A and B are the first coefficient matrix and the second coefficient matrix respectively; K represents the gain matrix; L is the observation value residual vector.

[0140] S10213. Based on the initial covariance matrix, the gain matrix, the first coefficient matrix and the second coefficient matrix, determine a first covariance matrix corresponding to the first correction number estimate using a preset third Kalman filter estimation formula.

[0141] In this embodiment of the present application, the expression of the third Kalman filter estimation formula is as follows.

[0142]

[0143] in, represents the first covariance matrix corresponding to the first correction number estimate; QX0 represents the initial covariance matrix corresponding to the estimated value of the initial correction number of the preset monitoring station coordinates; H = [AB], A and B are the first coefficient matrix and the second coefficient matrix respectively; K represents the gain matrix.

[0144] S1022. Perform floating-point ambiguity separation on the first correction number estimate and the first covariance matrix respectively to determine a floating-point ambiguity estimate and a second covariance matrix corresponding to the floating-point ambiguity estimate.

[0145] In this step, floating-point ambiguity separation is performed on the first correction number estimate and the first covariance matrix respectively to obtain matrix expressions corresponding to the separated first correction number estimate and the first covariance matrix respectively; then, the floating-point ambiguity estimate in the matrix expression and the second covariance matrix corresponding to the floating-point ambiguity estimate are determined.

[0146] In the embodiment of the present application, the matrix expressions corresponding to the separated first correction number estimate and the first covariance matrix are shown below.

[0147]

[0148] in, represents the estimated value of the first correction; represents the first covariance matrix; Represents a floating point ambiguity estimate; represents the second covariance matrix corresponding to the floating point ambiguity estimate; and They represent the first correction number estimate and the corresponding covariance matrix after floating point ambiguity separation respectively; and They represent the cross-covariance matrices of the first correction number estimate and the floating-point ambiguity estimate after floating-point ambiguity separation.

[0149] S1023. Based on the floating-point ambiguity estimate and the second covariance matrix, determine the ambiguity fixed value in the first observation equation using an ambiguity search method.

[0150] In an embodiment of the present application, the expression of the calculation formula corresponding to the fuzzy search method is as follows.

[0151]

[0152] in, Indicates a fixed value of fuzziness; Represents a floating point ambiguity estimate; represents the second covariance matrix.

[0153] S1024. Substitute the fixed value of ambiguity into the first observation equation, and add a non-parametric component of the system error to determine a second observation equation for the coordinates of the monitoring station.

[0154] In this step, after substituting the fixed value of ambiguity into the first observation equation, the observation value correction residual vector can be calculated based on the observation value residual vector, the fixed value of ambiguity and the second coefficient matrix; then, the second observation equation for the monitoring station coordinates is obtained based on the observation value correction residual vector and the first observation equation, and by adding the non-parametric component of the system error.

[0155] In this step, the influence of system errors such as multipath error on deformation monitoring results is considered. Based on the observation value correction residual vector and the first observation equation, a non-parametric component of system error is introduced, and a semi-parametric model equation is constructed as the second observation equation.

[0156] In an embodiment of the present application, the expression for the observation value correction residual vector calculated based on the observation value residual vector, the ambiguity fixed value and the second coefficient matrix is ​​as follows.

[0157]

[0158] Where L′ is the observation correction residual vector; represents the fixed value of ambiguity; B is the second coefficient matrix; L is the observation residual vector.

[0159] In an embodiment of the present application, the expression of the second observation equation for the monitoring station coordinates is obtained by correcting the residual vector and the first observation equation based on the observation value, and adding the non-parametric component of the system error as shown below.

[0160] V′=Ax+SL′,P.

[0161] Among them, V' is the correction vector of the observation residual; S is the non-parametric component of the system error; A is the first coefficient matrix; P is the weight matrix; x is the correction vector of the monitoring station coordinates; L' is the observation correction residual vector.

[0162] S103. Based on the second observation equation, construct a compensatory least squares model for the observation value residuals in the observation data and the non-parametric components of the system error.

[0163] In the embodiment of the present application, the expression of the compensated least squares model is as follows.

[0164] V′ T PV′+αS T RS=min.

[0165] Where R is the regularization matrix of the semi-parametric model; α is the regularization factor; V′ is the correction vector of the observation residual; S is the non-parametric component of the systematic error; and P is the weight matrix.

[0166] Here, the regularization matrix of the semiparametric model is a preset symmetric positive definite matrix; α is the balanced V′ T PV′ and S T The RS parameter can generally be set to 0.1.

[0167] Exemplarily, the regularization matrix can be constructed by the time series method, assuming that the systematic errors (non-parametric components of systematic errors) of adjacent epochs are not much different. At this time, the expression of the regularization matrix (symmetric positive definite matrix) is as follows.

[0168]

[0169] Where n is the number of observations in the observation data.

[0170] S104, determining a target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, so as to determine the target monitoring station coordinates after the monitoring station is corrected.

[0171] In one implementation of the present application, during specific implementation, step S104 may include:

[0172] S1041. Construct an extreme value function corresponding to the compensated least squares model.

[0173] In an embodiment of the present application, the expression of the extreme value function corresponding to the compensated least squares model is as follows.

[0174] Φ=V′ T PV′+αS T RS+2K T (Ax+SL′-V′).

[0175] Among them, Φ is the symbol of the extreme value function; K is the temporary variable of the extreme value function; V′ is the correction vector of the observation residual; S is the non-parametric component of the system error; A is the first coefficient matrix; P is the weight matrix; x is the correction vector of the monitoring station coordinates; L′ is the observation correction residual vector; R is the regularization matrix of the semi-parametric model; α is the regularization factor;

[0176] S1042: Derivative calculation is performed on the correction number of the monitoring station coordinates and the non-parametric component of the system error in the extreme value function to determine a correction matrix corresponding to the extreme value function.

[0177] In the embodiment of the present application, the expression of the correction matrix corresponding to the extreme value function is as follows.

[0178]

[0179] in, is the estimated value of the correction for the monitoring station coordinates; is the estimate of the nonparametric component of the system error; A is the first coefficient matrix; P is the weight matrix; R is the regularization matrix of the semiparametric model; α is the regularization factor; L′ is the residual vector of the observed value correction.

[0180] S1043. Based on the correction matrix, determine a second correction value of the monitoring station coordinates by matrix calculation as a target correction value.

[0181] In this step, by performing matrix calculation on the correction matrix, the expression of the second correction number estimate of the monitoring station coordinates and the estimate of the non-parametric component of the systematic error can be obtained, and then based on the expression, the second correction number estimate of the monitoring station coordinates and the estimate of the non-parametric component of the systematic error can be calculated.

[0182] In the embodiment of the present application, the expressions of the estimated value of the second correction number of the monitoring station coordinates and the estimated value of the non-parametric component of the system error are as follows.

[0183]

[0184] in, is the estimated value of the second correction for the monitoring station coordinates; is the estimate of the nonparametric component of the system error; A is the first coefficient matrix; P is the weight matrix; R is the regularization matrix of the semiparametric model; α is the regularization factor; L′ is the observation value correction residual vector; I is the unit matrix.

[0185] Here, since the purpose of deformation monitoring is to obtain a higher-precision deformation monitoring result, that is, the correction number of the coordinates, the estimated value of the non-parametric component of the system error can be ignored in the precise positioning. It can be understood that the estimated value of the non-parametric component of the system error can also be derived for analysis and research of the system error.

[0186] S1044: Add the initial approximate coordinates corresponding to the monitoring station and the estimated value of the target correction number to obtain an addition result, and determine the addition result as the target monitoring station coordinates after the monitoring station is corrected.

[0187] In this step, the initial approximate coordinates corresponding to the monitoring station are added to the estimated value of the target correction number of the monitoring station coordinates to obtain the target monitoring station coordinates after the monitoring station is corrected.

[0188] For example, please refer to Figure 2(a) and Figure 2(b), where Figure 2(a) is one of the data result diagrams of deformation monitoring provided in the embodiment of the present application, and Figure 2(b) is the second data result diagram of deformation monitoring provided in the embodiment of the present application. Assuming that when the base station and monitoring station set by the global navigation satellite system are used to monitor the deformation of the target object, which is a dam, verification calculations are performed for similarity errors and system errors based on the observation data collected by the base station and the monitoring station respectively.

[0189] As shown in FIG2(a), by establishing a double difference observation equation and performing Taylor expansion on the double difference observation equation and converting it into a matrix expression, a first observation equation for the coordinates of the monitoring station is established, and the ambiguity fixed value in the first observation equation is determined by using the ambiguity search method. By fixing the ambiguity and eliminating the similarity error, the coordinates of the monitoring station can be determined. The RMS values ​​(root mean square) of the position accuracy in the X, Y, and Z directions are 0.032 m, 0.043 m, and 0.022 m, respectively. It can be seen that there are obvious systematic errors in the time series shown in FIG2(a), and they fluctuate around the horizontal axis with time. This is because as the satellite rises and falls in the sky, the satellite signal is reflected by the water surface around the dam, causing a multipath effect and thus leading to systematic errors in the solution results.

[0190] As shown in Figure 2(b), based on the second observation equation with the addition of the nonparametric component of the system error, a compensatory least squares model is constructed, and the coordinates of the monitoring station can be determined by the matrix calculation method of the extreme value function. The RMS values ​​(root mean square) of the point position accuracy in the three directions of X, Y, and Z are 0.005m, 0.008m, and 0.005m, respectively. It can be seen that in the time series shown in Figure 2(b), it basically presents a normal distribution around the horizontal axis, and there is no significant systematic error. The method used in Figure 2(b) is better than the method used in Figure 2(a).

[0191] In this way, the deformation monitoring and correction method based on the global navigation satellite system provided in the embodiment of the present application has certain effectiveness and reliability in eliminating system errors such as multipath errors, and the method is particularly suitable for the field of high-precision GNSS deformation monitoring under static conditions.

[0192] The deformation monitoring and correction method based on the global navigation satellite system provided in the embodiment of the present application establishes a first observation equation for the monitoring station coordinates and searches for fixed ambiguity to separate the similarity error generated in deformation monitoring, and combines the characteristics of system errors such as multipath errors in deformation monitoring, utilizes the correlation between epochs before and after the error, introduces a non-parametric vector representing the system error, constructs a compensatory least squares estimation model, and separates system errors such as multipath errors in real time, thereby improving the operability and reliability of deformation monitoring, and thereby improving the accuracy of deformation monitoring results.

[0193] See also Figure 3 , Figure 3 This is a schematic diagram of the structure of a deformation monitoring and correction device based on a global navigation satellite system provided in an embodiment of the present application. Figure 3 As shown in , the device 300 includes:

[0194] A first observation equation determination module 310 is used to establish a double difference observation equation based on the observation data collected by the reference station and the monitoring station respectively when the target object is deformed using the reference station and the monitoring station set by the global navigation satellite system, perform Taylor expansion processing on the double difference observation equation and convert it into a matrix expression, and establish a first observation equation for the monitoring station coordinates;

[0195] a second observation equation determination module 320, configured to search and fix an ambiguity integer solution of the first observation equation by using an ambiguity search method, determine an ambiguity fixed value in the first observation equation, and determine a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error;

[0196] A model building module 330 is used to build a compensatory least squares model for the observation value residual in the observation data and the non-parametric component of the system error based on the second observation equation;

[0197] The coordinate correction module 340 is used to determine the target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, so as to determine the target monitoring station coordinates after the monitoring station is corrected.

[0198] Further, when the first observation equation determination module 310 is used to establish a double difference observation equation based on the observation data respectively collected by the reference station and the monitoring station, the first observation equation determination module 310 is used to:

[0199] Based on the observation data collected by the reference station and the monitoring station, respectively, establishing a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station;

[0200] Determining a single-difference observation equation of the monitoring station relative to the reference station based on the non-difference observation equation of the reference station and the non-difference observation equation of the observation station;

[0201] One of the multiple observation satellites is used as a reference satellite, and based on the single-difference observation equation, double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined.

[0202] Furthermore, when the first observation equation determination module 310 is used to perform Taylor expansion processing on the double difference observation equation and convert it into a matrix expression to establish the first observation equation for the monitoring station coordinates, the first observation equation determination module 310 is used to:

[0203] Using the initial approximate coordinates corresponding to the monitoring station, Taylor expansion calculation is performed on the double difference observation equation to obtain a double difference correction number expression corresponding to the double difference observation equation;

[0204] The double-difference correction number expression is converted into a matrix expression to establish a first observation equation for the monitoring station coordinates.

[0205] Further, when the second observation equation determination module 320 is used to search and fix the ambiguity integer solution of the first observation equation by using the ambiguity search method, determine the ambiguity fixed value in the first observation equation, and determine the second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and the added system error non-parametric component, the second observation equation determination module 320 is used to:

[0206] Based on the first observation equation, a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate are determined using a preset Kalman filter estimation formula;

[0207] Performing floating-point ambiguity separation on the first correction number estimate and the first covariance matrix respectively, and determining a floating-point ambiguity estimate and a second covariance matrix corresponding to the floating-point ambiguity estimate;

[0208] Determining, based on the floating-point ambiguity estimate and the second covariance matrix, an ambiguity fixed value in the first observation equation using an ambiguity search method;

[0209] The ambiguity fixed value is substituted into the first observation equation, and a non-parametric component of a systematic error is added to determine a second observation equation for the monitoring station coordinates.

[0210] Furthermore, the first observation equation includes a correction vector of the monitoring station coordinates and a first coefficient matrix corresponding thereto, a double difference ambiguity parameter and a second coefficient matrix corresponding thereto, a correction vector of the observation value residual, an observation value residual vector and a weight matrix;

[0211] When the second observation equation determination module 320 is used to determine the first correction number estimate of the monitoring station coordinates and the first covariance matrix corresponding to the first correction number estimate based on the first observation equation using a preset Kalman filter estimation formula, the second observation equation determination module 320 is used to:

[0212] Determine a gain matrix using a preset first Kalman filter estimation formula based on an initial covariance matrix corresponding to an estimated value of an initial correction number of a preset monitoring station coordinate, the first coefficient matrix, the second coefficient matrix, and the weight matrix;

[0213] Based on the preset initial correction number estimate of the monitoring station coordinates, the gain matrix, the first coefficient matrix, the second coefficient matrix and the observation value residual vector, a first correction number estimate of the monitoring station coordinates is determined using a preset second Kalman filter estimation formula;

[0214] Based on the initial covariance matrix, the gain matrix, the first coefficient matrix and the second coefficient matrix, a first covariance matrix corresponding to the first correction number estimate is determined using a preset third Kalman filter estimation formula.

[0215] Further, when the coordinate correction module 340 is used to determine the target correction number estimate value of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station to determine the target monitoring station coordinates after the monitoring station is corrected, the coordinate correction module 340 is used to:

[0216] Constructing an extreme value function corresponding to the compensated least squares model;

[0217] Derivative calculation is performed on the correction number of the monitoring station coordinates and the non-parametric component of the system error in the extreme value function to determine the correction matrix corresponding to the extreme value function;

[0218] Based on the correction matrix, determining a second correction number estimate of the monitoring station coordinates by matrix calculation as a target correction number estimate;

[0219] The initial approximate coordinates corresponding to the monitoring station are added to the estimated value of the target correction number to obtain an addition result, and the addition result is determined as the coordinates of the target monitoring station after the monitoring station is corrected.

[0220] The deformation monitoring and correction device based on the global navigation satellite system provided in the embodiment of the present application establishes a first observation equation for the monitoring station coordinates and searches for fixed ambiguity to separate the similarity error generated in deformation monitoring, and combines the characteristics of system errors such as multipath errors in deformation monitoring, utilizes the correlation between epochs before and after the error, introduces a non-parametric vector representing the system error, constructs a compensatory least squares estimation model, and separates system errors such as multipath errors in real time, thereby improving the operability and reliability of deformation monitoring, and thereby improving the accuracy of deformation monitoring results.

[0221] See also Figure 4 , Figure 4This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. Figure 4 As shown in , the electronic device 400 includes a processor 410 , a memory 420 and a bus 430 .

[0222] The memory 420 stores machine-readable instructions executable by the processor 410. When the electronic device 400 is running, the processor 410 communicates with the memory 420 via the bus 430. When the machine-readable instructions are executed by the processor 410, the above-mentioned Figure 1 The specific implementation of the steps of the deformation monitoring and correction method based on the global navigation satellite system in the method embodiment shown can be found in the method embodiment, which will not be repeated here.

[0223] The present application also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the computer program can execute the above-mentioned Figure 1 The specific implementation of the steps of the deformation monitoring and correction method based on the global navigation satellite system in the method embodiment shown can be found in the method embodiment, which will not be repeated here.

[0224] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0225] In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of devices or units can be electrical, mechanical or other forms.

[0226] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0227] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0228] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that is executable by a processor. Based on this understanding, the technical solution of the present application can essentially be embodied in the form of a software product, or in other words, the part that contributes to the prior art or the part of the technical solution. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0229] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present application, which are used to illustrate the technical solutions of the present application, rather than to limit them. The protection scope of the present application is not limited thereto. Although the present application is described in detail with reference to the above-mentioned embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-mentioned embodiments within the technical scope disclosed in the present application, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A deformation monitoring and correction method based on a global navigation satellite system, characterized in that: The method comprises: When the target object is deformed by using the reference station and the monitoring station set by the global navigation satellite system, a double difference observation equation is established based on the observation data collected by the reference station and the monitoring station respectively, the double difference observation equation is Taylor expanded and converted into a matrix expression, and a first observation equation for the monitoring station coordinates is established; Searching and fixing an ambiguity integer solution for the first observation equation by using an ambiguity search method, determining an ambiguity fixed value in the first observation equation, and determining a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error; Based on the second observation equation, construct a compensatory least squares model for the observation value residual in the observation data and the non-parametric component of the systematic error; Based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, a target correction number estimate of the monitoring station coordinates is determined to determine the target monitoring station coordinates after the monitoring station is corrected.

2. The method according to claim 1, characterized in that: The double difference observation equation is established based on the observation data collected by the reference station and the monitoring station respectively, including: Based on the observation data collected by the reference station and the monitoring station, respectively, establishing a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station; Determining a single-difference observation equation of the monitoring station relative to the reference station based on the non-difference observation equation of the reference station and the non-difference observation equation of the monitoring station; One of the multiple observation satellites is used as a reference satellite, and based on the single-difference observation equation, double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined.

3. The method according to claim 1, characterized in that The step of performing Taylor expansion processing on the double difference observation equation and converting it into a matrix expression to establish a first observation equation for the monitoring station coordinates includes: Using the initial approximate coordinates corresponding to the monitoring station, Taylor expansion calculation is performed on the double difference observation equation to obtain a double difference correction number expression corresponding to the double difference observation equation; The double-difference correction number expression is converted into a matrix expression to establish a first observation equation for the monitoring station coordinates.

4. The method according to claim 1, characterized in that: The step of searching and fixing the ambiguity integer solution of the first observation equation by using the ambiguity search method, determining the ambiguity fixed value in the first observation equation, and determining the second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and the added non-parametric component of the system error, comprises: Based on the first observation equation, a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate are determined using a preset Kalman filter estimation formula; Performing floating-point ambiguity separation on the first correction number estimate and the first covariance matrix respectively, and determining a floating-point ambiguity estimate and a second covariance matrix corresponding to the floating-point ambiguity estimate; Determining, based on the floating-point ambiguity estimate and the second covariance matrix, an ambiguity fixed value in the first observation equation using an ambiguity search method; The ambiguity fixed value is substituted into the first observation equation, and a non-parametric component of a systematic error is added to determine a second observation equation for the monitoring station coordinates.

5. The method according to claim 4, characterized in that The first observation equation includes a correction vector of the monitoring station coordinates and a first coefficient matrix corresponding thereto, a double difference ambiguity parameter and a second coefficient matrix corresponding thereto, a correction vector of the observation value residual, an observation value residual vector and a weight matrix; The method of determining a first correction number estimate of the monitoring station coordinates and a first covariance matrix corresponding to the first correction number estimate based on the first observation equation using a preset Kalman filter estimation formula includes: Determine a gain matrix using a preset first Kalman filter estimation formula based on an initial covariance matrix corresponding to an estimated value of an initial correction number of a preset monitoring station coordinate, the first coefficient matrix, the second coefficient matrix, and the weight matrix; Based on the preset initial correction number estimate of the monitoring station coordinates, the gain matrix, the first coefficient matrix, the second coefficient matrix and the observation value residual vector, a first correction number estimate of the monitoring station coordinates is determined using a preset second Kalman filter estimation formula; Based on the initial covariance matrix, the gain matrix, the first coefficient matrix and the second coefficient matrix, a first covariance matrix corresponding to the first correction number estimate is determined using a preset third Kalman filter estimation formula.

6. The method according to claim 1, characterized in that The step of determining a target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station to determine the target monitoring station coordinates after the monitoring station is corrected includes: Constructing an extreme value function corresponding to the compensated least squares model; Derivative calculation is performed on the correction number of the monitoring station coordinates and the non-parametric component of the system error in the extreme value function to determine the correction matrix corresponding to the extreme value function; Based on the correction matrix, determining a second correction number estimate of the monitoring station coordinates by matrix calculation as a target correction number estimate; The initial approximate coordinates corresponding to the monitoring station are added to the estimated value of the target correction number to obtain an addition result, and the addition result is determined as the coordinates of the target monitoring station after the monitoring station is corrected.

7. A deformation monitoring and correction device based on a global navigation satellite system, characterized in that: The device comprises: A first observation equation determination module is used to establish a double difference observation equation based on observation data collected by the reference station and the monitoring station respectively when the target object is deformed using the reference station and the monitoring station set by the global navigation satellite system, perform Taylor expansion processing on the double difference observation equation and convert it into a matrix expression, and establish a first observation equation for the coordinates of the monitoring station; a second observation equation determination module, configured to search and fix an ambiguity integer solution of the first observation equation by using an ambiguity search method, determine an ambiguity fixed value in the first observation equation, and determine a second observation equation for the monitoring station coordinates based on the first observation equation, the ambiguity fixed value and an added non-parametric component of a systematic error; A model building module, used for building a compensatory least squares model for the observation value residual in the observation data and the non-parametric component of the system error based on the second observation equation; The coordinate correction module is used to determine the target correction number estimate of the monitoring station coordinates based on the extreme value function corresponding to the compensated least squares model and the initial approximate coordinates corresponding to the monitoring station, so as to determine the target monitoring station coordinates after the monitoring station is corrected.

8. The device according to claim 7, characterized in that When the first observation equation determination module is used to establish a double difference observation equation based on the observation data collected by the reference station and the monitoring station respectively, the first observation equation determination module is used to: Based on the observation data collected by the reference station and the monitoring station, respectively, establishing a non-difference observation equation of the reference station and a non-difference observation equation of the monitoring station; Determining a single-difference observation equation of the monitoring station relative to the reference station based on the non-difference observation equation of the reference station and the non-difference observation equation of the monitoring station; One of the multiple observation satellites is used as a reference satellite, and based on the single-difference observation equation, double-difference observation equations of the remaining observation satellites relative to the reference satellite are determined.

9. An electronic device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate through the bus, and the machine-readable instructions are executed by the processor when running to execute the steps of the deformation monitoring and correction method based on the global navigation satellite system as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the deformation monitoring and correction method based on the global navigation satellite system as claimed in any one of claims 1 to 6 are executed.

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