Troposphere delay estimation method for Beidou deformation monitoring of high slope
By introducing constraint factors into the BeiDou deformation monitoring of high slopes and establishing the correlation between delay estimates between adjacent stations, the problem of errors masking the true deformation signal in high slope monitoring was solved, and high-precision deformation monitoring was achieved.
Patent Information
- Application Number
- CN202511583774.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-31
- Publication Date
- 2026-02-03
AI Technical Summary
Existing technologies have failed to effectively establish the spatial constraint relationship between tropospheric delay and elevation between adjacent monitoring stations in high slope environments, resulting in insufficient sensitivity and reliability of the monitoring system. Errors mask the true deformation signals, making it difficult to achieve high-precision monitoring.
By introducing a constraint factor characterizing the correlation between zenith tropospheric delay and station elevation, a virtual observation form is constructed and incorporated into the parameter estimation model. This establishes a strong correlation between delay estimates between adjacent stations and optimizes the parameter estimation process.
It significantly suppresses the delay estimation error caused by uneven vertical atmospheric distribution, clearly separates minute deformation signals, and improves the feasibility and reliability of long-term, stable, and high-precision deformation monitoring in areas with significant elevation differences.
Smart Images
Figure CN121454567A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of BeiDou deformation monitoring technology for high slopes, and in particular to a tropospheric delay estimation method for BeiDou deformation monitoring of high slopes. Background Technology
[0002] The BeiDou Navigation Satellite System, with its high real-time performance and high degree of automation, has become an important means of monitoring slope deformation. However, in high slope monitoring scenarios, BeiDou signal propagation is significantly affected by tropospheric delay errors. Complex terrain can cause drastic changes in atmospheric refraction effects, leading to deviations in the signal propagation path. This has become a key bottleneck restricting the breakthrough of monitoring accuracy to the millimeter or even centimeter level.
[0003] Current methods for correcting tropospheric delay mainly include traditional empirical model correction, numerical meteorological model assistance, and regional modeling techniques. However, they all share a common limitation when dealing with high slope problems: they all estimate or correct the tropospheric delay of each monitoring station as an independent, isolated parameter. This approach stems from the fact that their underlying models or algorithms fail to fully consider and utilize the strong correlation and continuous variation between tropospheric delay and elevation between adjacent stations in high slope environments with large elevation differences. Essentially, they attempt to use models suitable for homogeneous, flat areas to solve complex terrain problems with non-uniform elevations, resulting in a severe mismatch between the model and reality.
[0004] However, this isolated estimation method fails to establish a spatial constraint relationship between tropospheric delay and elevation between adjacent stations. As a result, in high slope environments, the residual tropospheric delay error and the real small deformation signal are highly mixed in frequency domain and magnitude. The error magnitude is even far greater than the slow and small deformation of the slope itself, which seriously masks the real deformation signal. This greatly reduces the sensitivity and reliability of the monitoring system, making it difficult to provide accurate and reliable data support for the stability assessment and disaster early warning of high slopes. Summary of the Invention
[0005] The purpose of this invention is to provide a tropospheric delay estimation method for BeiDou deformation monitoring of high slopes, in order to solve the problem mentioned in the background art that the existing tropospheric delay estimation method adopts an isolated estimation method for each monitoring station and fails to establish a spatial constraint relationship between adjacent monitoring stations, resulting in insufficient sensitivity and reliability of the monitoring system.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for estimating tropospheric delay for BeiDou deformation monitoring of high slopes, comprising the following steps: acquiring observation data, elevation data, and broadcast ephemeris data from a reference station and multiple monitoring stations deployed at different elevations on a high slope; constructing a parameter estimation model and performing initial parameter estimation based on the observation data and the broadcast ephemeris data to obtain initial estimated values including zenith tropospheric delay, integer ambiguity floating-point solution, and coordinates of each station; calculating a constraint factor using the initial estimated value of the zenith tropospheric delay and the corresponding elevation data of the stations; converting the constraint factor into a virtual observation value form and adding it to the parameter estimation model, and performing target parameter estimation through the optimized parameter estimation model; fixing the obtained target estimate of the integer ambiguity to an integer and substituting it back into the optimized parameter estimation model to obtain the target estimates of the zenith tropospheric delay and coordinates of each station.
[0007] Optionally, the observation data includes pseudorange observations and carrier phase observations, the elevation data includes the geodetic height component in the geographic coordinate system, and the broadcast ephemeris data includes information on the satellite's orbit.
[0008] Optionally, the step of constructing the parameter estimation model specifically includes: constructing an undifferentiated single-frequency observation equation based on the observation data and the broadcast ephemeris data; linearizing the undifferentiated single-frequency observation equation using the initial coordinates of each station to obtain the error equation between the parameter estimate and the observation value; and constructing a normal equation using the least squares method based on the error equation to perform parameter estimation.
[0009] Optionally, the calculation formula for the undifferentiated single-frequency observation equation is as follows: ; In the formula: and Satellites to receiver The pseudorange observations and carrier phase observations; The distance between the satellite and the receiver; The speed of light; For receiver Clock difference parameters; For satellite clock bias parameters; Wavelength; For tropospheric delay; For mapping functions; For ionospheric delay; and These are the pseudorange hardware delays at the satellite and receiver ends, respectively. and These are the phase hardware delays at the satellite and receiver ends, respectively; For integer ambiguity; and These represent the observation noise and unmodeled error for pseudorange and phase, respectively.
[0010] Optionally, the formula for calculating the constraint factor is: In the formula: Constraint factors; The number of stations involved in the calculation; For the station Estimates of zenith tropospheric delay; For the station The earth is high.
[0011] Optionally, the step of converting the constraint factor into virtual observation form specifically includes: constructing the relationship between the zenith tropospheric delay and the geodetic height for each station, the calculation formula of which is: In the formula: and These are the identifiers for two adjacent stations; The parameters for estimating the zenith tropospheric delay at the station; The geodetic height of the station; As constraint factors; converted to virtual observation equations: ; In the formula: C is the coefficient matrix of the virtual observation equation; W is the virtual observation value; and These are approximate values of the zenith tropospheric delay at stations a and b, calculated using empirical models, respectively. and ...
[0012] Optionally, the optimization steps of the parameter estimation model specifically include: expanding the original observation equation to obtain a new error equation: In the formula: The residual vector of the observed values; C is the coefficient matrix of the original observation equation; W is the coefficient matrix of the virtual observation equation; and W is the constant term of the virtual observation value. The vector of parameters to be estimated includes the coordinates of each station's location, tropospheric delay, and integer ambiguity. Given the observation vector; the new normal equation is constructed from the new error equation as follows: In the formula: This is the transpose of the coefficient matrix of the original observation equation; is the transpose of the coefficient matrix of the virtual observation equation; The weight matrix of the original observations; The weight matrix for virtual observations; The vector of parameters to be estimated; is the observation vector; W is the virtual observation constant term.
[0013] On the other hand, the present invention also provides a tropospheric delay estimation system for BeiDou deformation monitoring of high slopes, comprising: an acquisition module for acquiring observation data, elevation data, and broadcast ephemeris data from a reference station and multiple monitoring stations deployed at different elevations on a high slope; a model building module for constructing a parameter estimation model and performing initial parameter estimation based on the observation data and the broadcast ephemeris data to obtain initial estimated values including zenith tropospheric delay, integer ambiguity floating-point solution, and coordinates of each station; a constraint factor calculation module for calculating constraint factors using the initial estimated value of the zenith tropospheric delay and the elevation data of the corresponding stations; a model optimization module for converting the constraint factors into virtual observation values and adding them to the parameter estimation model, and performing target parameter estimation through the optimized parameter estimation model; and a target parameter estimation module for fixing the obtained target estimate of the integer ambiguity to an integer and substituting it back into the optimized parameter estimation model to obtain target estimates of the zenith tropospheric delay and coordinates of each station.
[0014] On the other hand, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method for tropospheric delay estimation for BeiDou deformation monitoring of high slopes.
[0015] On the other hand, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for tropospheric delay estimation for BeiDou deformation monitoring of high slopes.
[0016] Compared with the prior art, the beneficial effects of the present invention are: This application calculates and introduces a constraint factor characterizing the correlation between zenith tropospheric delay and station elevation, and integrates this constraint factor into the overall parameter estimation model in the form of virtual observations, establishing a strong correlation between delay estimates between adjacent stations. This enables the model to effectively utilize prior topographic knowledge, transforming the originally isolated estimation process into a collaborative optimization process, thereby significantly suppressing delay estimation errors caused by uneven vertical atmospheric distribution. Ultimately, it clearly separates minute deformation signals from the strong tropospheric delay background noise, greatly improving the feasibility and reliability of long-term, stable, and high-precision deformation monitoring in areas with significant elevation differences. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the method steps of the present invention.
[0018] Figure 2This is a flowchart of the method of the present invention.
[0019] Figure 3 This is a schematic diagram showing the layout of BeiDou reference stations and monitoring stations in the high slope area of this invention.
[0020] Figure 4 The image shows the NEU coordinate time series before and after adding the constraint factor for the baseline with an elevation difference of approximately 323m.
[0021] Figure 5 This is a comparison chart showing the deformation monitoring accuracy of a baseline with an elevation difference greater than 300m before and after the addition of a constraint factor in the elevation direction according to the present invention.
[0022] Figure 6 This is a schematic diagram of the system structure of the present invention.
[0023] In the diagram: 10 - Acquisition module, 20 - Model building module, 30 - Constraint factor calculation module, 40 - Model optimization module, 50 - Target parameter estimation module. Detailed Implementation
[0024] The present invention will now be clearly and completely described in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.
[0025] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be used interchangeably where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0026] Those skilled in the art will understand that, unless explicitly stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of this application means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.
[0027] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.
[0028] It should be understood that the sequence number and size of each step in this embodiment do not imply the order of execution. The execution order of each process is determined by its function and internal logic, and should not constitute any limitation on the implementation process of this application embodiment.
[0029] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0030] Please refer to Figures 1-5 This invention discloses a method for estimating tropospheric delay for BeiDou deformation monitoring of high slopes. The method includes the following steps: acquiring observation data, elevation data, and broadcast ephemeris data from a reference station and multiple monitoring stations deployed at different elevations on the high slope; constructing a parameter estimation model and performing initial parameter estimation based on the observation data and broadcast ephemeris data to obtain initial estimates including zenith tropospheric delay, integer ambiguity floating-point solutions, and coordinates of each station; calculating constraint factors using the initial estimates of the zenith tropospheric delay and the corresponding station elevation data; converting the constraint factors into virtual observation values and adding them to the parameter estimation model; and estimating target parameters using the optimized parameter estimation model; fixing the obtained integer ambiguity target estimates to integers and substituting them back into the optimized parameter estimation model to obtain target estimates of the zenith tropospheric delay and coordinates of each station.
[0031] Specifically, the deformation monitoring area in this embodiment is a high slope area with a slope height difference of more than 300m. The base station is set up at the bottom of the high slope, and the monitoring stations are set up on the slopes at all levels.
[0032] The data processing strategy for BeiDou deformation monitoring is shown in Table 1: Table 1: Data processing strategy for BeiDou deformation monitoring.
[0033] Model or parameters Processing strategy Observations BDS B1I Astrology Beidou Broadcast Ephemeris Sampling interval 30s Solving the time period length 12h Meteorological parameters GPT model Initial value of zenith tropospheric delay Saastamoinen model PCO / PCV Model correction (igs20.atx) Tropospheric Delayed Projection Function GMF model Ambiguity fixing method Rounding method Parameter estimation methods Least Squares Tropospheric parameter estimation strategy Piecewise constant estimation This application calculates and introduces a constraint factor characterizing the correlation between zenith tropospheric delay and station elevation, and integrates this constraint factor into the overall parameter estimation model in the form of virtual observations, establishing a strong correlation between delay estimates between adjacent stations. This enables the model to effectively utilize prior topographic knowledge, transforming the originally isolated estimation process into a collaborative optimization process, thereby significantly suppressing delay estimation errors caused by uneven vertical atmospheric distribution. Ultimately, it clearly separates minute deformation signals from the strong tropospheric delay background noise, greatly improving the feasibility and reliability of long-term, stable, and high-precision deformation monitoring in areas with significant elevation differences.
[0034] In some embodiments, the observation data includes pseudorange observations and carrier phase observations, the elevation data includes the geodetic height component in the geographic coordinate system, and the broadcast ephemeris data includes information on the satellite's orbit.
[0035] In some embodiments, the step of constructing the parameter estimation model specifically includes: constructing an undifferentiated single-frequency observation equation based on the observation data and the broadcast ephemeris data; linearizing the undifferentiated single-frequency observation equation using the initial coordinates of each station to obtain the error equation between the parameter estimate and the observation value; and constructing a normal equation using the least squares method based on the error equation to perform parameter estimation.
[0036] This application employs non-differenced single-frequency observation equations and supplements them with linearization and least squares methods to construct a parameter estimation model. This ensures that the entire high-precision processing flow can be built on a solid foundation of computational efficiency and feasibility. This allows the complex tropospheric delay correction algorithm to run smoothly on conventional engineering computing equipment without relying on supercomputing resources, thereby meeting the stringent requirements of field monitoring stations for real-time or near-real-time data processing.
[0037] In some embodiments, the calculation formula for the non-differenced single-frequency observation equation is as follows: ; In the formula: and Satellites to receiver The pseudorange observations and carrier phase observations; The distance between the satellite and the receiver; The speed of light; For receiver Clock difference parameters; For satellite clock bias parameters; Wavelength; For tropospheric delay; For mapping functions; For ionospheric delay; and These are the pseudorange hardware delays at the satellite and receiver ends, respectively. and These are the phase hardware delays at the satellite and receiver ends, respectively; For integer ambiguity; and These represent the observation noise and unmodeled error for pseudorange and phase, respectively.
[0038] Furthermore, satellite to receiver pseudorange observations Represented by station coordinates and satellite coordinates: ;in, and These are the spatial rectangular coordinates of the satellite and the station, respectively. The initial coordinates of the station are used. Linearizing the above equation, the resulting error equation between the parameter estimates and the observed values is: ;in, The residual vector of the observed values; It is a coefficient matrix; Let be the vector of parameters to be estimated, containing the station location coordinates, tropospheric delay, and integer ambiguity. The normal equation is constructed from the error equation as follows: ;in, Let be the weight matrix of the observations. Solving the formula yields the vector of parameters to be determined. .
[0039] This application transforms the complex physical process of satellite observation into a computable least-squares adjustment model. By establishing and linearizing the non-differenced single-frequency observation equation, it systematically parameterizes various error sources, such as geometric distance, clock error, tropospheric and ionospheric delay, and ambiguity. This abstracts the practical engineering problem into a standard mathematical optimization problem, laying a solid algorithmic foundation for the final high-precision solution of the key parameter, zenith tropospheric delay, and ensuring the rigor and feasibility of the entire method.
[0040] In some embodiments, the constraint factor is calculated using the following formula: In the formula: Constraint factors; The number of stations involved in the calculation; For the station Estimates of zenith tropospheric delay; For the station The earth is high.
[0041] This application introduces constraint factors to achieve adaptive learning and quantification of local atmospheric characteristics. It can automatically capture the real-time relationship between tropospheric delay and elevation within the monitoring area using the initial solution results of the model. This makes the constraints finally applied to the model no longer rigid theoretical values or global model parameters, but an optimization factor that dynamically reflects the actual atmospheric conditions at that time and place. This greatly improves the pertinence and effectiveness of the constraints, makes the model optimization more in line with the specific monitoring environment, and greatly improves the monitoring accuracy.
[0042] In some embodiments, the step of converting the constraint factor into a virtual observation form specifically includes: constructing the relationship between the zenith tropospheric delay and the geodetic height for each station, the calculation formula of which is: In the formula: and These are the identifiers for two adjacent stations; The parameters for estimating the zenith tropospheric delay at the station; The geodetic height of the station; As constraint factors; converted to virtual observation equations: ; In the formula: C is the coefficient matrix of the virtual observation equation; W is the virtual observation value; and These are approximate values of the zenith tropospheric delay at stations a and b, calculated using empirical models, respectively. and ...
[0043] This application constructs a relationship between zenith tropospheric delay and geodetic height between adjacent stations as a constraint factor and converts it into a virtual observation equation. Without changing the core architecture of the original adjustment algorithm, it enhances the stability of the model at the lowest cost. Furthermore, by introducing additional observation information that conforms to physical laws, it effectively improves the strength of the solution results and the ability to resist interference from poor observation data.
[0044] In some embodiments, the optimization step of the parameter estimation model specifically includes: expanding the original observation equation to obtain a new error equation: In the formula: The residual vector of the observed values; C is the coefficient matrix of the original observation equation; W is the coefficient matrix of the virtual observation equation; and W is the constant term of the virtual observation value. The vector of parameters to be estimated includes the coordinates of each station's location, tropospheric delay, and integer ambiguity. Given the observation vector; the new normal equation is constructed from the new error equation as follows: In the formula: This is the transpose of the coefficient matrix of the original observation equation; is the transpose of the coefficient matrix of the virtual observation equation; The weight matrix of the original observations; The weight matrix for virtual observations; The vector of parameters to be estimated; is the observation vector; W is the virtual observation constant term.
[0045] This application introduces constraint factors to construct new normal equations to optimize the parameter estimation model, providing a clear algorithmic loop for the entire optimization process. It effectively integrates the relationship between the zenith tropospheric delay and geodetic height of each station with the initial model, greatly improving the feasibility and reliability of long-term, stable, and high-precision deformation monitoring in areas with significant elevation differences.
[0046] In some embodiments, the step of fixing the target estimate of the obtained integer ambiguity to an integer and then substituting it back into the optimized parameter estimation model specifically includes: re-estimating the parameters through the optimized parameter estimation model to estimate the troposphere, the floating-point solution of the ambiguity, and the station position parameters; fixing the ambiguity and substituting it back into the observation equations to obtain the fixed solution of the equation set.
[0047] Please refer to Figure 6 On the other hand, the present invention also provides a tropospheric delay estimation system for BeiDou deformation monitoring of high slopes, comprising: an acquisition module for acquiring observation data, elevation data, and broadcast ephemeris data from a reference station and multiple monitoring stations deployed at different elevations on a high slope; a model building module for constructing a parameter estimation model and performing initial parameter estimation based on the observation data and the broadcast ephemeris data to obtain initial estimated values including zenith tropospheric delay, integer ambiguity floating-point solution, and coordinates of each station; a constraint factor calculation module for calculating constraint factors using the initial estimated value of zenith tropospheric delay and the elevation data of the corresponding stations; a model optimization module for converting the constraint factors into virtual observation values and adding them to the parameter estimation model, and performing target parameter estimation through the optimized parameter estimation model; and a target parameter estimation module for fixing the obtained target estimate of integer ambiguity to an integer and substituting it back into the optimized parameter estimation model to obtain target estimates of zenith tropospheric delay and coordinates of each station.
[0048] Specifically, the baseline repeatability is used as the evaluation index for deformation monitoring accuracy, and its formula is: ; in, These are the values of each component of the baseline in the solution for each time period; It is the variance of the corresponding component; This is the weighted average of the corresponding baseline components; For the corresponding repetition.
[0049] like Figure 4 The image shows the time series coordinates of a baseline with an elevation difference of approximately 323m before and after the addition of a constraint factor. It can be seen that there is no significant difference in the time series coordinates of the plane before and after adding the constraint factor, while the time series coordinates of the elevation direction show a larger difference. Before adding the constraint factor, the range of the U-direction coordinate variation was -20.8mm to 25.0mm, with a deformation monitoring accuracy of 9.0mm. After adding the constraint factor, the range of variation was -12.7mm to 15.7mm, with a deformation monitoring accuracy of 6.2mm.
[0050] like Figure 5 As shown, to more clearly illustrate the advantages of the tropospheric delay estimation method for BeiDou deformation monitoring of high slopes described in this invention compared to previous techniques in environments with large elevation differences, the elevation deformation monitoring accuracy of baselines with elevation differences greater than 300m is compared before and after the addition of a constraint factor. The horizontal axis in the figure represents the baseline elevation difference, which increases sequentially from left to right. It can be seen that before adding the constraint factor, the average accuracy of deformation monitoring was 9.8mm, while after adding the constraint factor, the average accuracy of deformation monitoring was 7.9mm, representing an average improvement of 19%.
[0051] The estimated unit weight error (Sigma) is a core and globally significant statistic in BeiDou data processing. It measures the overall quality of the observations and their correction models, reflecting the degree of agreement between the observations and the adjustment model. It is a key parameter for evaluating the reliability of BeiDou data solution results. Sigma is obtained by inverse calculation from the residuals after adjustment, and its formula is as follows: ; in, The residual vector of the observed values; For the power formation; , where represents the degrees of freedom, indicating redundant observations.
[0052] Table 2 shows the Sigma statistics before and after adding constraint factors: Table 2: Sigma statistics before and after adding constraint factors (unit: mm).
[0053] Before adding constraint factors After adding constraint factors Minimum 1.299 1.274 Maximum value 2.956 2.850 average value 1.667 1.637 Root Mean Square 1.707 1.677 Standard deviation 3.690E-01 3.636E-01 The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes described in this invention can effectively improve the deformation monitoring accuracy of the baseline with an elevation difference of more than 300m in the deformation monitoring environment of high slopes.
[0054] On the other hand, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method for tropospheric delay estimation for BeiDou deformation monitoring of high slopes.
[0055] On the other hand, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for tropospheric delay estimation for BeiDou deformation monitoring of high slopes.
[0056] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0057] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, database, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.
[0058] The above are merely embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention's specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.
Claims
1. A method for estimating tropospheric delay for BeiDou deformation monitoring of high slopes, characterized by the following steps: include: Acquire observation data, elevation data, and broadcast ephemeris data from benchmark stations and multiple monitoring stations deployed at different elevations on the high slope; Based on the observation data and the broadcast ephemeris data, a parameter estimation model is constructed and initial parameter estimation is performed to obtain initial estimated values including zenith tropospheric delay, integer ambiguity floating-point solution and coordinates of each station. Using the initial estimate of the zenith tropospheric delay and the corresponding station elevation data, the constraint factor is calculated; The constraint factors are converted into virtual observations and added to the parameter estimation model. The target parameters are then estimated using the optimized parameter estimation model. After fixing the target estimate of the integer ambiguity to an integer, it is substituted back into the optimized parameter estimation model to obtain the target estimate of the zenith tropospheric delay and the coordinates of each station.
2. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 1, characterized in that, The observation data includes pseudorange observations and carrier phase observations; the elevation data includes the geodetic height component in the geographic coordinate system; and the broadcast ephemeris data includes information on the satellite's orbit.
3. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 1, characterized in that, The steps for constructing the parameter estimation model specifically include: Based on the observation data and the broadcast ephemeris data, an unequal single-frequency observation equation is constructed. The non-difference single-frequency observation equation is linearized using the initial coordinates of each station to obtain the error equation between the parameter estimate and the observed value. Based on the error equation, the least squares method is used to construct the normal equation for parameter estimation.
4. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 3, characterized in that, The calculation formula for the non-differenced single-frequency observation equation is as follows: ； ； In the formula: and Satellites to receiver The pseudorange and carrier phase observations; The distance between the satellite and the receiver; The speed of light; For receiver Clock difference parameters; For satellite clock bias parameters; Wavelength; For tropospheric delay; For mapping functions; For ionospheric delay; and These are the pseudorange hardware delays at the satellite and receiver ends, respectively. and These are the phase hardware delays at the satellite and receiver ends, respectively; For integer ambiguity; and These represent the observation noise and unmodeled error for pseudorange and phase, respectively.
5. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 1, characterized in that, The formula for calculating the constraint factor is as follows: ； In the formula: Constraint factors; The number of stations involved in the calculation; For the station The estimated zenith tropospheric delay; For the station The earth is high.
6. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 1, characterized in that, The step of converting the constraint factor into virtual observations specifically includes: The relationship between the zenith tropospheric delay and geodetic height at each station is established using the following formula: ； In the formula: and These are the identifiers for two adjacent stations; The parameters for estimating the zenith tropospheric delay at the station; The geodetic height of the station; Constraint factors; Convert to virtual observation equations: ； ； In the formula: C is the coefficient matrix of the virtual observation equation; W is the virtual observation value; and These are approximate values of the zenith tropospheric delay at stations a and b, calculated using empirical models, respectively. and ...
7. The tropospheric delay estimation method for BeiDou deformation monitoring of high slopes according to claim 6, characterized in that, The optimization steps of the parameter estimation model specifically include: Extending the original observation equation, we obtain the new error equation as follows: ； In the formula: The residual vector of the observed values; C is the coefficient matrix of the original observation equation; W is the coefficient matrix of the virtual observation equation; and W is the constant term of the virtual observation value. The vector of parameters to be estimated includes the coordinates of each station's location, tropospheric delay, and integer ambiguity. A vector of observations; The new normal equation is constructed from the new error equation as follows: ； In the formula: This is the transpose of the coefficient matrix of the original observation equation; is the transpose of the coefficient matrix of the virtual observation equation; The weight matrix of the original observations; The weight matrix for virtual observations; The vector of parameters to be estimated; is the observation vector; W is the virtual observation constant term.
8. A tropospheric delay estimation system for BeiDou deformation monitoring of high slopes, characterized in that, include: The acquisition module is used to acquire observation data, elevation data, and broadcast ephemeris data from benchmark stations and multiple monitoring stations located at different elevations on the high slope. The model building module is used to build a parameter estimation model and perform initial parameter estimation based on the observation data and the broadcast ephemeris data, so as to obtain initial estimated values including zenith tropospheric delay, integer ambiguity floating-point solution and coordinates of each station. The constraint factor calculation module is used to calculate the constraint factor using the initial estimate of the zenith tropospheric delay and the corresponding station elevation data; The model optimization module is used to convert the constraint factors into virtual observations and add them to the parameter estimation model, and then use the optimized parameter estimation model to estimate the target parameters. The target parameter estimation module is used to fix the target estimate of the obtained integer ambiguity to an integer and then substitute it back into the optimized parameter estimation model to obtain the target estimate of the zenith tropospheric delay and the coordinates of each station.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the tropospheric delay estimation method for BeiDou deformation monitoring of high slopes as described in any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the tropospheric delay estimation method for BeiDou deformation monitoring of high slopes as described in any one of claims 1 to 7.