A method and device for modeling and solving a regional tropospheric delay height model
Patent Information
- Application Number
- CN202611552287.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-10-08
- Publication Date
- 2026-11-03
Smart Images
Figure CN123029573A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of data processing technology, and in particular to a method and apparatus for modeling and solving a regional tropospheric delayed elevation model. Background Technology
[0002] In high-precision GNSS deformation monitoring, tropospheric delay is the core error source restricting the accuracy of elevation component calculation. The total zenith delay (ZTD) consists of two parts: the stable dry delay (ZHD) and the time-varying wet delay (ZWD). The wet delay is significantly affected by the vertical distribution of water vapor. In mountainous areas, high dams, and other scenarios with large elevation differences, the elevation difference between stations can reach hundreds to thousands of meters. Traditional general tropospheric correction schemes have obvious adaptation defects: empirical models such as Saastamoinen and GPT are constructed based on the global average atmospheric profile and cannot characterize the nonlinear law of local water vapor decay with elevation exponentially; parameter estimation methods that directly use the complete total zenith delay as the parameter to be estimated will cause strong coupling between elevation parameters and tropospheric delay, ill-conditioned normal equations, and tropospheric residuals are easily absorbed by elevation coordinates, forming systematic offsets; standard mapping functions such as NMF and VMF1 are based on the assumption of horizontal atmospheric stratification. In scenarios with large elevation differences, the difference in the path of satellite signals crossing the troposphere amplifies the mapping error and reduces the success rate of integer ambiguity fixation. Existing mainstream GNSS processing software only provides a general tropospheric estimation module and does not form an end-to-end closed-loop correction process for terrains with large elevation differences, making it difficult to meet the needs of long-term deformation monitoring at the millimeter level.
[0003] Currently, the academic community at home and abroad has carried out a lot of theoretical research on tropospheric errors in GNSS with large elevation differences. Representative results include two core literatures: "Short-time GNSS network solution and its performance in large elevation difference regions with additional tropospheric constraints" published in the Journal of Geodesy and Cartography in 2022 (Jiang Guangwei et al., 2022) and "Tropospheric delay correction model and real-time differential service construction for RTK with large elevation differences" published in the Journal of Wuhan University (Information Science Edition) in 2023 (Yao Yibin et al., 2023). The former confirms that the correlation coefficient between elevation and tropospheric delay can reach over 0.9 under short baseline and large elevation difference environments. Simply relying on measured meteorological sensors to correct ZTD is costly and difficult to deploy in mountainous areas. Simply increasing the observation duration to alleviate parameter coupling will significantly reduce monitoring efficiency. The latter points out that traditional linear elevation correction models cannot match the vertical nonlinear attenuation characteristics of water vapor. Even when using the GPT3 series global empirical models to optimize relative delay, the wet delay residual in large elevation difference areas still remains on the order of 5-10 cm. At the same time, the existing piecewise linear PWL time series parameterization scheme only constrains the time series of independent ZWD for a single station and does not achieve relative wet delay difference dimensionality reduction between benchmark stations, thus failing to weaken the correlation between elevation and tropospheric parameters from the bottom up. In addition, a related study in the journal Frontiers in 2026 shows that existing improved models based on reanalysis meteorological data rely on external meteorological products. The data timeliness and spatial resolution are difficult to adapt to the network monitoring scenario of mountainous areas without meteorological sensor benchmark stations. They do not have offline self-modeling correction capabilities and are difficult to adapt to long-term automated deformation monitoring projects such as dams and mountain roads.
[0004] Domestic patents have also disclosed targeted correction schemes, such as the "A Tropospheric Delay Correction Method Applicable to Short-Distance Large Elevation Difference RTK" published by CN115061167A. This patent calculates the zenith delay of the base station and the rover station respectively based on the global empirical tropospheric model, and completes the RTK solution through the double-difference observation equation, which improves the positioning gross error problem in large elevation difference environment to a certain extent. However, this patented technical solution has several inherent limitations: First, the patent relies entirely on a general empirical model to directly calculate the absolute ZTD, without hard subtraction of the tropospheric main delay from the original GNSS observations. The magnitude of the parameters to be estimated in the observation equation is large, and the strong coupling problem between elevation and tropospheric parameters still exists. Second, the patent only uses a single time-series constant parameter to estimate the tropospheric residual, without introducing piecewise linear PWL time-series modeling and a two-layer constraint mechanism, which cannot suppress parameter oscillations and drifts caused by water vapor time variations, resulting in insufficient stability of ambiguity fixation. Third, the patent can only achieve real-time correction of a single point of the rover station by a single base station, and does not support the construction of a global elevation-delay mapping model using multiple reference stations in the region. It lacks closed-loop constraint logic for model feedback to baseline adjustment, and cannot perform unified high-precision tropospheric delay prediction for any unknown monitoring point in the region. It is only suitable for temporary single-base station RTK operations and does not meet the needs of long-term continuous deformation monitoring in large areas.
[0005] Based on the aforementioned academic literature and patent solutions, it is evident that existing technologies cannot simultaneously achieve four core capabilities: sensorless self-modeling, tropospheric parameter dimensionality reduction and decoupling, nonlinear elevation-delay global modeling, and model closed-loop adjustment constraints. Single improvement methods can only locally alleviate tropospheric errors with large elevation differences and cannot systematically sever the strong coupling relationship between elevation parameters and tropospheric delay. This results in multiple technical shortcomings, including systematic drift in elevation calculation, low ambiguity fixation rate, insufficient accuracy in correcting unknown points in the region, and high hardware deployment and maintenance costs. Summary of the Invention
[0006] To address the aforementioned technical problems, this application discloses a method and apparatus for modeling and solving a regional tropospheric delayed elevation model; the method includes: Based on the elevation information of each reference station in the monitoring area, the air pressure is calculated by the pressure height formula and the zenith dry delay is calculated by combining the Saastamoinen model. A preset fixed constant is used as the prior zenith wet delay. The two are added together to obtain the prior value of the total zenith delay of each reference station. The Niell mapping function is used to project the zenith total delay prior value onto the slant path, and then subtract it from the original GNSS observations to generate residual observations; A double-difference observation model was constructed, which only uses the relative wet delay difference between reference stations as the tropospheric parameter to be estimated. The nodes were divided according to a preset time interval and time constraints were applied. The high-precision relative wet delay difference value was obtained by solving the least squares method in combination with the ambiguity fixing algorithm. The calculated relative wet delay difference value is superimposed back onto the prior value of the total zenith delay to reconstruct the time series of the total absolute zenith delay of each reference station. After averaging the total absolute zenith delay of each station, the elevation difference and the total zenith delay difference of each reference station relative to the selected reference station are calculated. Using the elevation difference as the independent variable and the total zenith delay difference as the dependent variable, a quadratic polynomial model is used for least squares fitting to establish a regional tropospheric delay-elevation model. The elevation of the target point is obtained and its elevation difference relative to the reference station is calculated. The difference is then substituted into the regional tropospheric delay-elevation model to predict the tropospheric delay of the target point. The predicted tropospheric delay is then converted into a virtual observation equation and injected into the baseline double-difference adjustment system to apply strong constraints to the elevation parameters for solution.
[0007] Preferably, the process of calculating the station air pressure using the pressure height formula and solving the zenith dry delay using the Saastamoinen model specifically involves: Using the standard pressure formula From the station elevation Estimating station air pressure ; Based on estimated air pressure The Saastamoinen model is used to calculate the zenith dry delay, and the formula is as follows:
[0008] In the formula The latitude of the base station Elevation of the station is expressed in kilometers; A uniform 0.1m is set as the globally fixed prior zenith wet delay. Superimposed zenith dry delay Obtain the prior value of the total zenith delay for a single station. ; The entire process is calculated solely based on the elevation information of the base station, without the need to deploy actual temperature, humidity, and air pressure meteorological sensors.
[0009] Preferably, the method for projecting the prior value of the total zenith delay onto the oblique path using the Niell mapping function is as follows: Using satellite elevation angle Call the Niell mapping function for the input parameters ,pass Calculate the tropospheric delay corresponding to the satellite's oblique path; The satellite cutoff elevation angle is preset to 20°. After removing observation data with elevation angles below this threshold, the oblique path tropospheric delay is used to perform interpolation on the raw GNSS observations to generate residual observations.
[0010] Preferably, the step of constructing the double-difference observation model and solving for the relative wet delay difference includes: Establish a double-difference observation equation by performing inter-station difference analysis on the residual observations of the two reference stations:
[0011] In the formula These are double-difference residual observations. It is a double-difference geometric distance. For carrier wavelength, For double-difference integer ambiguity, These are the output values of the Niell mapping function for the two stations, This is the only tropospheric parameter to be estimated between the two stations. To observe noise; The complete observation period was divided into time nodes with a fixed interval of 2 hours, and a piecewise linear PWL model was used to analyze the data. Perform timing parameterization; An a priori constraint with an initial value of 0 and a prior mean error of 0.045m is applied to the first time node of the piecewise linear model, and a spectral density constraint is applied to adjacent time nodes. Noise constraints in the Gauss-Markov process; The least squares method is used to solve the double-difference observation equation, the LAMBDA algorithm is used to search for integer ambiguity, the Ratio test threshold of 3.0 is set to fix the ambiguity, and the relative wet delay difference value corresponding to each time node is output.
[0012] Preferably, the formula for calculating the total absolute zenith delay time series of each reconstructed reference station is as follows:
[0013] The selected reference station does not have a wet delay differential value relative to itself, and the absolute zenith total delay of the reference station is omitted when reconstructing it. item; For all epochs within a complete time series of a single reference station Calculate the arithmetic mean to obtain the average total zenith delay of the reference station; Calculate the elevation difference between the remaining base stations and the reference station. Zenith total delay difference , generated by The fitted sample dataset is composed of these data.
[0014] Preferably, the expression for the quadratic polynomial model is:
[0015] In the formula The elevation difference between the station to be measured and the reference station. This represents the difference in total zenith delay between the station under test and the reference station. The coefficients are to be fitted. All Substitute the samples into the polynomial and solve for the coefficients using the least squares algorithm. The regional tropospheric delay-elevation model was obtained.
[0016] Preferably, the operation of converting the predicted tropospheric delay into a virtual observation equation and injecting it into the baseline double-difference adjustment system includes: Read the elevation of the target point Calculate the elevation difference between the target point and the reference station. ,Will Substituting into the established quadratic polynomial model, the output is the total predicted zenith delay difference between the target point and the reference station. ; Constructing virtual observation equations Set the virtual observation variance to With strong prior constraints, the virtual observation equation is combined with the baseline double-difference observation equation to simultaneously solve the baseline coordinates and tropospheric delay parameters.
[0017] A modeling and solving device for a regional tropospheric delay elevation model, used to execute any of the modeling and solving methods for a regional tropospheric delay elevation model, the device comprising a priori delay calculation unit, a relative wet delay solving unit, an absolute delay reconstruction unit, an elevation delay fitting unit, and a point adjustment correction unit, specifically: The prior delay calculation unit obtains the elevation information of the base station, solves the zenith dry delay by using the pressure height formula and the Saastamoinen model, superimposes the fixed prior wet delay to obtain the zenith total delay prior value, and calls the Niell mapping function to complete the oblique path delay projection and generate residual observation values. The relative wet delay solution unit constructs a double-difference observation equation based on the residual observation values, adopts piecewise linear time series parameterization and applies double-layer constraints, and solves the relative wet delay difference between reference stations through least squares and LAMBDA algorithms. The absolute delay reconstruction unit integrates the relative wet delay difference, zenith dry delay, and a priori wet delay to reconstruct the absolute zenith total delay time series of each reference station. After averaging the time series, it calculates the elevation difference and zenith total delay difference of each station relative to the reference station. The elevation delay fitting unit uses a quadratic polynomial least squares to fit the elevation difference and the total zenith delay difference to generate a regional tropospheric delay-elevation model. The point adjustment and correction unit reads the elevation of the target point, calculates the elevation difference, substitutes it into the model to predict the tropospheric delay, constructs a virtual observation equation with strong variance constraints, and connects it to the baseline double difference adjustment system to complete the coordinate solution.
[0018] A computer device includes a memory and a processor, the memory storing computer-executable instructions, and the processor executing the computer-executable instructions to implement any of the regional tropospheric delay elevation model modeling and solving methods described in the present invention.
[0019] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for modeling and solving a regional tropospheric delay elevation model as described in any one of the claims.
[0020] Compared with the prior art, the technical solution of this application has the following technical effects: This invention calculates the prior value of the total zenith delay based on the elevation of the benchmark station and an atmospheric model. It can complete the main tropospheric delay subtraction of the observation data without the need for supporting meteorological sensing equipment. It can remove stable systematic atmospheric errors in the observation data in advance, simplify the computational burden of the subsequent residual solution process, and allow the subsequent parameter solution to focus only on the small residual components caused by water vapor changes. This reduces the complexity of solving the adjustment equations and improves the automation of the overall data processing flow.
[0021] This invention selects only the relative wet delay difference between reference stations as the tropospheric parameters to be estimated, and uses a piecewise linear time series model and a two-layer constraint mechanism to solve the problem. This can effectively reduce the total number of parameters to be estimated in the observation equation, weaken the correlation between various parameters to be estimated, ensure the stability of the time series parameter solution process, avoid disordered fluctuations in parameters during long-term observation and calculation, ensure the operational stability of the integer ambiguity fixing link, and improve the reliability of baseline observation data solution.
[0022] This invention reconstructs the complete absolute zenith total delay time series of each station by reversing the relative wet delay difference value. Based on the time series averaging process, a sample set of elevation difference and zenith delay difference is constructed. Nonlinear fitting is completed by using a quadratic polynomial, which can accurately establish the corresponding mapping relationship between elevation and tropospheric delay, completely restore the spatial distribution law of water vapor with altitude in the region, and obtain a special correction model adapted to the terrain characteristics of the monitoring area.
[0023] This invention transforms the regional elevation delay model into a virtual observation constraint-integrated baseline adjustment process. By limiting the fluctuation range of tropospheric delay parameters during the adjustment process based on strong constraints, it can limit the absorption of residual tropospheric errors in elevation coordinates, complete tropospheric delay prediction and correction for any target point in the region, unify the vertical calculation benchmark of all monitoring points in the region, and ensure the consistency of coordinate calculation results during long-term continuous monitoring. Attached Figure Description
[0024] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0025] Figure 1 A flowchart illustrating a regional tropospheric delay-elevation modeling method provided in this application embodiment; Figure 2 A flowchart for determining the prior value of the total zenith delay for each reference station, provided for embodiments of this application; Figure 3 A flowchart for converting GNSS observation data into residual observations is provided for embodiments of this application; Figure 4 A flowchart of step S3 provided in the embodiments of this application; Figure 5 A flowchart of step S5 provided in an embodiment of this application; Figure 6 A flowchart of step S7 provided in an embodiment of this application; Figure 7 A schematic diagram of fitting provided for an embodiment of this application; Figure 8 A flowchart illustrating a tropospheric delay calculation method provided in this application embodiment; Figure 9 A block diagram of a regional tropospheric delay-elevation modeling device provided in an embodiment of this application; Figure 10 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation
[0026] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.
[0027] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.
[0028] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.
[0029] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.
[0030] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.
[0031] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.
[0032] Example 1 describes in detail a method for modeling and solving a regional tropospheric delayed elevation model, such as... Figure 1 As shown, it includes: Based on the elevation information of each reference station in the monitoring area, the air pressure is calculated by the pressure height formula and the zenith dry delay is calculated by combining the Saastamoinen model. A preset fixed constant is used as the prior zenith wet delay. The two are added together to obtain the prior value of the total zenith delay of each reference station. The Niell mapping function is used to project the zenith total delay prior value onto the slant path, and then subtract it from the original GNSS observations to generate residual observations; A double-difference observation model was constructed, which only uses the relative wet delay difference between reference stations as the tropospheric parameter to be estimated. The nodes were divided according to a preset time interval and time constraints were applied. The high-precision relative wet delay difference value was obtained by solving the least squares method in combination with the ambiguity fixing algorithm. The calculated relative wet delay difference value is superimposed back onto the prior value of the total zenith delay to reconstruct the time series of the total absolute zenith delay of each reference station. After averaging the total absolute zenith delay of each station, the elevation difference and the total zenith delay difference of each reference station relative to the selected reference station are calculated. Using the elevation difference as the independent variable and the total zenith delay difference as the dependent variable, a quadratic polynomial model is used for least squares fitting to establish a regional tropospheric delay-elevation model. The elevation of the target point is obtained and its elevation difference relative to the reference station is calculated. The difference is then substituted into the regional tropospheric delay-elevation model to predict the tropospheric delay of the target point. The predicted tropospheric delay is then converted into a virtual observation equation and injected into the baseline double-difference adjustment system to apply strong constraints to the elevation parameters for solution.
[0033] Furthermore, GNSS observation data and elevation information from multiple reference stations within the monitoring area are acquired, and the zenith total delay prior value of each reference station is determined based on a preset atmospheric model, so as to convert the GNSS observation data into residual observation values.
[0034] Specifically, by simultaneously acquiring GNSS observation data and precise elevation information from multiple reference stations within the monitoring area, the zenith total delay (ZTD) prior value, reflecting the average atmospheric state, was first calculated using classical atmospheric models such as Saastamoinen, combined with meteorological parameters such as elevation and air pressure at each station. The GNSS observation data was then subtracted from these prior values to extract the residual observation values. The core purpose of this transformation process is to remove the dominant stationary systematic errors in atmospheric delay, focusing subsequent modeling and solution on the high-frequency residuals that contain the spatiotemporal variation characteristics of water vapor. This not only effectively reduces the difficulty of solving the nonlinear adjustment system but also lays a solid data foundation for subsequently using spatial interpolation algorithms or nonlinear elevation fitting models to accurately capture the spatiotemporal correlation of tropospheric delay.
[0035] A double-difference observation model is constructed based on residual observations, and a piecewise linear model is used to perform time-series parameterization modeling of the relative wet delay difference to be estimated, so as to solve for the relative wet delay difference between each reference station.
[0036] Specifically, after obtaining the residual observations, a double-difference observation model is constructed to effectively eliminate common systematic errors such as satellite clock bias and receiver clock bias, allowing the adjustment system to focus on high-frequency residual information containing water vapor variations. Based on this, a piecewise linear model is used for time-series parameterized modeling of the physical characteristics of the tropospheric wet delay that dynamically changes over time. This involves setting discrete nodes on the time axis and performing linear interpolation between the nodes. This parameterization strategy cleverly balances the stability and dynamism of parameter estimation: on the one hand, it avoids parameter oscillations and rank deficit problems caused by solving each epoch independently; on the other hand, it overcomes the deficiency of treating it as a constant and failing to reflect the dynamic evolution of water vapor. Through the joint solution of this model, the relative wet delay difference values between each reference station can be separated and extracted with high accuracy and low noise, thus providing reliable core data support for the subsequent accurate construction of a regional tropospheric delay-elevation nonlinear model.
[0037] The absolute zenith total delay time series of each reference station is reconstructed based on the relative wet delay difference and the prior value of the zenith total delay. Based on the absolute zenith total delay time series and the elevation information of each reference station, the zenith total delay difference and elevation difference of each reference station relative to the reference station are determined. The reference station is determined from each reference station.
[0038] Specifically, by fusing and reconstructing the relative wet delay difference values obtained from high-precision calculations with the prior values of total zenith delay, the complete time series of absolute total zenith delay for each reference station is effectively recovered, compensating for the deficiency of missing absolute information in the double-difference model. Using selected reference stations as spatial reference benchmarks, the time series of absolute total zenith delay for each station are spatiotemporally aligned and jointly analyzed with their precise elevation information, thereby calculating the absolute total zenith delay difference of each reference station relative to that reference station and its corresponding elevation difference. This process not only establishes the absolute spatial benchmark for regional tropospheric modeling but also directly constructs a core dataset containing high-precision elevation and delay differences, providing an indispensable sample foundation and physical basis for exploring and fitting the nonlinear laws governing tropospheric delay variation with elevation (such as quadratic polynomial models).
[0039] Based on the elevation difference and the total zenith delay difference, a polynomial model is used to fit the data to obtain a regional tropospheric delay-elevation model that characterizes the nonlinear mapping relationship between elevation and tropospheric delay.
[0040] Specifically, by utilizing the high-confidence dataset of elevation difference and total zenith delay difference established in the aforementioned steps, a multinomial model is introduced for nonlinear regression analysis to accurately fit the physical law of tropospheric delay variation with elevation. Since tropospheric atmospheric density decreases nonlinearly with altitude, the multinomial model can effectively capture and characterize this complex spatial correlation, thus overcoming the shortcomings of traditional linear models in fitting accuracy under complex terrain. The resulting regional tropospheric delay-elevation model essentially establishes a precise mapping function from geometric elevation to atmospheric delay. This not only achieves a digital reconstruction of the spatial distribution characteristics of atmospheric delay within the region but also provides crucial mathematical model support for high-precision tropospheric delay interpolation and correction at any non-base station location within the region, improving the vertical accuracy and reliability of satellite positioning solutions.
[0041] This embodiment effectively eliminates the dominant stationary systematic error in atmospheric delay by converting GNSS observation data into residual observations. This allows subsequent modeling to focus on high-frequency residuals that include the spatiotemporal variation characteristics of water vapor, thereby reducing the difficulty of solving the nonlinear adjustment system. Based on this, a double-difference observation model is constructed to eliminate common systematic errors such as satellite clock errors and receiver clock errors. A piecewise linear model is used for parameterized modeling, avoiding parameter oscillations while accurately depicting the dynamic evolution of water vapor, achieving high-precision, low-noise extraction of the relative wet delay difference. Subsequently, the data is recovered through fusion reconstruction. The complete time series of absolute zenith total delay for each reference station compensates for the loss of absolute information in the double-difference model and establishes the absolute spatial benchmark for regional tropospheric modeling. Finally, a polynomial model is used to fit the difference between elevation difference and zenith total delay, effectively capturing the physical law of nonlinear decrease in tropospheric atmospheric density with altitude. This overcomes the deficiency of insufficient accuracy of traditional linear models in complex terrain and establishes an accurate mapping function from geometric elevation to atmospheric delay. It can provide high-precision tropospheric delay interpolation and correction for any non-reference station location in the region, significantly improving the calculation accuracy and reliability of satellite positioning in the vertical direction.
[0042] like Figure 2 The flowchart shown is for determining the prior value of the total zenith delay for each reference station, as provided in this application. Specifically, it includes: Based on the elevation information of each reference station, the station pressure of each reference station is determined using a pre-set atmospheric model: Specifically, since atmospheric pressure decreases with increasing altitude, it is first necessary to convert the standard sea-level pressure to the actual elevation of each reference station. In this embodiment, the preset atmospheric model is as follows:
[0043] Among them, P i Let H be the station pressure of the i-th reference station. i This represents the elevation information of the i-th reference station.
[0044] Based on the station pressure, determine the zenith dry delay corresponding to each reference station: Specifically, the distribution of dry gases (such as nitrogen and oxygen) in the troposphere is relatively stable, and the resulting zenith dry delay (ZHD) is mainly affected by the station's air pressure. After obtaining the station's air pressure P... i Then, the Saastamoinen model was used to calculate the zenith dry delay. The calculation formula is as follows:
[0045] Where, φ iLet be the latitude of the i-th reference station, and z be the satellite zenith distance. This formula fully considers the variation of Earth's gravity with latitude and elevation, and can calculate the zenith delay (in meters) with high accuracy.
[0046] The zenith dry delay is added to the preset prior zenith wet delay to obtain the prior value of the total zenith delay for each reference station.
[0047] Specifically, due to the highly spatiotemporal variability of water vapor distribution in the troposphere, it is difficult to accurately obtain the real-time zenith wet delay (ZWD) without actual meteorological sensors (such as microwave radiometers). Therefore, this embodiment introduces an empirically preset a priori zenith wet delay value (for example, typically set between 0.10m and 0.15m in temperate regions, or set according to local historical climate averages; preferably, the preset a priori zenith wet delay ZWD in this embodiment is...). prior =0.1m), the prior value of the total zenith delay for each reference station ( Calculated using the following formula:
[0048] Through the above steps, without relying on real-time temperature and humidity observation data from each reference station, the a priori value of the total zenith delay can be quickly and stably estimated using elevation information and classical atmospheric models, laying a reliable foundation for extracting high-precision tropospheric residual observation values from GNSS observation data.
[0049] By determining the station air pressure using a pre-set atmospheric model based on the elevation information of each reference station, the physical law that atmospheric pressure decreases with increasing altitude is fully considered, achieving accurate conversion of standard sea-level air pressure to actual elevation position. On this basis, the station air pressure is used to determine the zenith dry delay, fully considering the variation of Earth's gravity with latitude and elevation, enabling high-precision calculation of the zenith dry delay caused by relatively stable dry gas distribution. Subsequently, the zenith dry delay is added to the pre-set a priori zenith wet delay to obtain the a priori value of the total zenith delay. Without relying on real-time temperature and humidity observation data from each reference station, the a priori value of the total zenith delay can be quickly and stably estimated using elevation information and classical atmospheric models, laying a reliable foundation for extracting high-precision tropospheric residual observation values from GNSS observation data.
[0050] like Figure 3 The diagram shown is a flowchart for converting GNSS observation data into residual observations, as provided in this application. The flowchart specifically includes: The zenith total delay prior value is projected onto the satellite signal direction using a preset mapping function to obtain the oblique path tropospheric delay of each reference station in the corresponding satellite signal direction.
[0051] Specifically, since GNSS satellite signals do not arrive at the receiver at the zenith direction but rather pass through the troposphere at a certain zenith distance, it is necessary to convert the zenith delay into a slant-path tropospheric delay along the signal propagation path. In this embodiment, the preset mapping function can be the widely used Niell mapping function (NMF) or Vienna mapping function (VMF1). The formula for calculating the slant-path tropospheric delay (L) is as follows:
[0052] Among them, L i θ represents the slant path tropospheric delay corresponding to the i-th reference station; M(θ) is the NMF mapping function related to the satellite elevation angle θ.
[0053] The residual observation values are obtained by subtracting the corresponding tropospheric delay from the GNSS observation data of each reference station.
[0054] Specifically, the calculated slant path tropospheric delay is subtracted from the original GNSS observation data:
[0055] in, Let i be the residual observation value of the i-th reference station. This represents the GNSS observation data corresponding to the i-th reference station.
[0056] Through the above subtraction operation, the portion of the original GNSS observation data correctly described by classical atmospheric models (such as the Saastamoinen model) is subtracted. The remaining residual observation values mainly include the error of the prior wet delay, the residual of the nonlinear variation of water vapor with elevation, and observation noise. This provides clean and reliable input data for the subsequent construction of a double-difference observation model and the high-precision calculation of the relative wet delay difference value.
[0057] By using a preset mapping function to project the prior value of the total zenith delay to the direction of the satellite signal, the actual propagation path of the GNSS satellite signal through the troposphere at a certain zenith distance is fully considered, achieving a precise conversion from zenith delay to oblique path tropospheric delay. Based on this, the corresponding oblique path tropospheric delay is subtracted from the GNSS observation data of each reference station to obtain residual observation values. This effectively removes the part of the original GNSS observation data that is correctly described by the classical atmospheric model, so that the remaining residual observation values mainly include the error of the prior wet delay, the residual of water vapor nonlinear variation with elevation, and observation noise. This provides clean and reliable input data for constructing a double-difference observation model and solving the relative wet delay difference value with high precision.
[0058] like Figure 4As shown, a double-difference observation model is constructed based on residual observations, and a piecewise linear model is used to perform time-series parameterized modeling of the relative wet delay difference to be estimated, so as to solve for the relative wet delay difference between each reference station. Specifically: For any two reference stations, the residual observations are differentially analyzed between stations to construct a double-difference observation equation that includes the double-difference geometric distance, double-difference integer ambiguity, and relative wet delay difference.
[0059] Specifically, to eliminate common errors such as clock bias at the base stations, any two base stations (denoted as base station i and base station j) within the monitoring area are selected to form a baseline. The residual observation values of each base station obtained in the preceding steps are then differentiald between stations to eliminate clock bias errors at the satellite end, thus constructing a double-difference observation equation. The mathematical expression of this double-difference observation equation is as follows:
[0060] in, The residual observations are obtained by subtracting the residual observations of reference station B from the residual observations of reference station A. λ is the double-difference geometric distance (the distance difference between the satellite and two reference stations, calculated from the coordinates of the reference stations and the satellite ephemeris); λ is the carrier wavelength. The ambiguity is a double-difference integer ambiguity. Let be the relative wet delay difference between reference station i and reference station j; This is double-difference observation noise.
[0061] The observation period is divided into multiple time nodes according to a preset time interval, and the relative wet delay difference value is parameterized into the parameter to be estimated at each time node using a piecewise linear model.
[0062] Specifically, considering that GNSS observation periods are typically as long as 24 hours and that atmospheric water vapor changes drastically under large elevation differences, this embodiment employs a piecewise linear model (PWL) to parameterize the relative wet delay difference value over time. The 24-hour observation period is divided into preset time intervals (e.g., 2 hours), resulting in a total of 13 time nodes. At each time node, an independent relative wet delay difference value is assigned. As parameters to be estimated, the parameter values between two adjacent time points are obtained through linear interpolation. This parameterization method ensures the model's accuracy in fitting the spatiotemporal variations of water vapor while avoiding the problem of too many parameters caused by epoch-by-epoch estimation.
[0063] Furthermore, the piecewise linear model employs a piecewise linear approximation strategy, allowing the ZTD to change linearly between preset time nodes. If the time period is divided into n intervals, the PWL model needs to estimate n+1 ZTD parameters (including the first and last nodes), and its mathematical expression is:
[0064] in This is a time interval index within a time period. For the first The time span of each interval.
[0065] Prior constraints are applied to the first time node of the piecewise linear model, and process noise constraints are applied to adjacent time nodes.
[0066] Specifically, in order to ensure the numerical stability of the parameter estimates and prevent parameter drift during long-term solutions, external constraints need to be imposed on the piecewise linear model: (1) For the first time node (i.e., the 0th hour node) Apply a loose prior constraint, setting its initial value to 0, and set the prior standard error (square root of variance) to 0.045 meters.
[0067] (2) For two adjacent time nodes (such as the i-th and i+1-th nodes) Gauss-Markov process noise constraints are applied. In this embodiment, the process noise spectral density (q) is taken as an empirical value of 1×10⁻⁶. -6 m / s. This means that within a 2-hour node interval (Δt = 7200 s), the allowable standard deviation of parameter variation is approximately sqrt(q × Δt) ≈ 2.7 mm. This tight constraint effectively limits abrupt changes in water vapor parameters between adjacent nodes and is crucial for ensuring parameter stability under scenarios with large elevation differences.
[0068] By solving the double-difference observation equations using least squares and fixing the integer ambiguity, the relative wet delay difference values corresponding to each reference station are obtained.
[0069] Specifically, after constructing the double-difference observation equations and parameter constraints, the least squares method is used to assemble and iteratively solve the double-difference observation equations. During the solution process, the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) algorithm is used to search for and fix integer ambiguities, and the reliability of the fixed solution is confirmed through a ratio test (the threshold is usually set to 3.0). Once the ambiguities are successfully fixed, a high-precision baseline vector and the baseline at each time point can be obtained. The posterior estimate is obtained, thus providing a high-precision relative wet delay difference for subsequent reconstruction of the absolute zenith total delay time series.
[0070] By constructing a double-difference observation equation through inter-station differencing of residual observations for any two reference stations, common systematic errors such as satellite clock bias and receiver clock bias are effectively eliminated, allowing the adjustment system to focus on high-frequency residual information containing water vapor variations. Based on this, the observation period is divided into multiple time nodes according to a preset time interval, and a piecewise linear model is used to time-series parameterize the relative wet delay difference values. This ensures the model's fitting accuracy to the spatiotemporal variations of water vapor while avoiding the problem of excessive parameters caused by epoch-by-epoch estimation. Simultaneously, prior constraints are applied to the first time node, and Gauss-Markov process noise constraints are applied to adjacent time nodes, effectively limiting abrupt changes in water vapor parameters between adjacent nodes and preventing parameter drift during long-term time-series calculations, thus ensuring the numerical stability of parameter estimation in scenarios with large elevation differences. Finally, by fixing integer ambiguities through least-squares solution and the LAMBDA algorithm, high-precision baseline vectors and posterior estimates of the relative wet delay difference values at each time node are obtained, providing high-precision core data support for subsequent reconstruction of the absolute zenith total delay time series.
[0071] like Figure 5 The diagram shows the reconstruction of the absolute zenith total delay time series for each reference station based on the relative wet delay difference and the prior value of the zenith total delay. Based on the absolute zenith total delay time series and the elevation information of each reference station, the zenith total delay difference and elevation difference of each reference station relative to the reference station are determined. The reference station is determined from among the reference stations, specifically as follows: The relative wet delay difference, zenith dry delay, and prior zenith wet delay are superimposed to reconstruct the absolute zenith total delay time series for each reference station.
[0072] To obtain the independent tropospheric state of each reference station, one reference station is selected from multiple reference stations within the monitoring area as a reference station, denoted as reference station A. For any reference station i to be measured, the reconstruction formula for its absolute zenith total delay (ZTD) is as follows:
[0073] Among them, ZTD i (t) represents the absolute zenith total delay of reference station i at time t; The calculated relative wet delay difference between reference station i and reference station A; ZHD i (t) represents the zenith delay of reference station i at time t; ZWD prior The a priori zenith wet delay.
[0074] That is, the absolute zenith total delay of the reference station i = its own zenith dry delay + its own prior zenith wet delay + the relative wet delay difference between the station and the reference station A. After superimposing the three, the absolute quantity can be recovered from the relative quantity.
[0075] Similarly, the absolute zenith total delay of reference station A itself is:
[0076] Since the relative wet delay difference of reference station A is always zero (i.e. Therefore, no correction term needs to be added in the reconstruction formula of reference station A.
[0077] The absolute zenith total delay time series is averaged to obtain the average zenith total delay for each reference station.
[0078] Specifically, since GNSS observation data typically contains high-frequency noise such as multipath effects, directly using the ZTD value of a single epoch for subsequent elevation fitting will introduce significant errors. Therefore, this embodiment performs mean averaging on the reconstructed absolute zenith total delay time series.
[0079] If the observation period is T and the sampling interval is Δt, then the average total zenith delay of the reference station i to be measured is... The calculation is as follows:
[0080] Where M is the total number of epochs within the observation period, t k This represents the time corresponding to the k-th epoch. The mean... This represents the average level of atmospheric tropospheric delay over base station i during the observation period.
[0081] A reference station is selected from each base station, and the difference between the elevation information of each base station and the elevation information of the reference station is determined to obtain the elevation difference.
[0082] Specifically, to quantify the impact of topographic relief on tropospheric delay, precise elevation information was obtained from each reference station. Let the elevation of reference station A be h. A The elevation of the reference station i to be measured is h i Calculate the elevation difference Δh between the base station i and the reference station A. i Δh i =h i -h A .
[0083] The zenith total delay difference is determined based on the difference between the average zenith total delay corresponding to each base station and the average zenith total delay corresponding to the reference station.
[0084] Specifically, the difference between the average total zenith delay of the base station i and the average total zenith delay of the reference station A is calculated to obtain the total zenith delay difference ΔZTD; Through the above steps, a dataset {(Δh)} containing multiple sets of valid data points was constructed. i ,ΔZTD iA )}.
[0085] By superimposing and reconstructing the relative wet delay difference, zenith dry delay, and prior zenith wet delay, the complete time series of absolute zenith total delay for each reference station was effectively recovered, compensating for the loss of absolute information in the double-difference model and achieving accurate recovery from relative to absolute values. Based on this, the absolute zenith total delay time series was averaged, effectively suppressing the interference of high-frequency noise such as multipath effects on subsequent elevation fitting, and obtaining stable data representing the average level of atmospheric tropospheric delay during the observation period. Subsequently, by determining reference stations and calculating the elevation difference between each reference station and the reference station, as well as the average zenith total delay difference, a core dataset containing multiple sets of valid data points was constructed. This provides an indispensable sample foundation and physical basis for subsequent exploration and fitting of the nonlinear law of tropospheric delay variation with elevation.
[0086] like Figure 6 The model shown uses a polynomial model to fit data based on the elevation difference and the total zenith delay difference to obtain a regional tropospheric delay-elevation model that characterizes the nonlinear mapping relationship between elevation and tropospheric delay. Specifically: Using elevation difference as the independent variable and total zenith delay difference as the dependent variable, a quadratic polynomial model was used for data fitting.
[0087] Specifically, a quadratic polynomial fitting model is constructed using the elevation difference Δh between each base station and the reference station as the independent variable and the total zenith delay difference ΔZTD as the dependent variable. The mathematical expression of this model is as follows: ΔZTD = a × Δh 2 +b×Δh+c, where ΔZTD is the total zenith delay difference between the base station and the reference station; Δh is the elevation difference between the base station and the reference station; a is the quadratic coefficient, used to characterize the nonlinear curvature of the delay as a function of elevation; b is the linear coefficient (unit: mm / m), used to characterize the linear vertical gradient of the base station; and c is the constant term.
[0088] Solving for the fitting coefficients of the quadratic polynomial model yields the regional tropospheric delay-elevation model.
[0089] Specifically, the n sets of valid data points (Δh) will be obtained i ,ΔZTD iSubstituting the above quadratic polynomial model, the least squares method is used to construct the error equation and solve for the fitting coefficients a, b, and c. The fitting result is: coefficient a = -0.0003 mm / m 2 b = -2.5 mm / m, c = 1.5 mm; the root mean square residual (RMS) of the fitting is 1.8 mm. The tropospheric delay-elevation model in this region can accurately reflect the changing pattern that the higher the elevation, the smaller the tropospheric delay, and the gradual slowing down of the delay decay rate.
[0090] like Figure 7 As shown in the figure, the blue dots represent measured sample data points obtained from the regional reference station, the red lines represent the linear fitting results, and the green lines represent the quadratic polynomial fitting curve used in this application. It can be observed that the measured data exhibits a non-linear trend, and the quadratic polynomial fitting curve better matches the distribution characteristics of the measured data points. Compared to the linear fitting method, it better captures the non-linear correlation between the elevation difference and the tropospheric delay difference, verifying the rationality of using a quadratic polynomial to construct the regional tropospheric delay elevation model.
[0091] By using a quadratic polynomial model with elevation difference as the independent variable and total zenith delay difference as the dependent variable for data fitting, the physical law of nonlinear decrease in tropospheric atmospheric density with altitude was effectively captured, overcoming the shortcomings of traditional linear models in terms of insufficient accuracy under complex terrain. Based on this, the fitting coefficients of the quadratic polynomial model were solved to obtain a regional tropospheric delay-elevation model. The root mean square of the fitting residual was only 1.8 mm, accurately reflecting the changing law that the tropospheric delay decreases with increasing elevation and the delay decay rate gradually slows down. Finally, an accurate mapping function from geometric elevation to atmospheric delay was established, providing key mathematical model support for high-precision tropospheric delay interpolation and correction at any non-base station location in the region, significantly improving the calculation accuracy and reliability of satellite positioning in the vertical direction.
[0092] This embodiment further provides a method for calculating tropospheric delay, such as Figure 8 As shown, it specifically includes: Obtain the target elevation of the target location.
[0093] The target elevation is input into the regional tropospheric delay-elevation model obtained by the above method, and the tropospheric delay corresponding to the target location is calculated.
[0094] Specifically, in this embodiment, an elevation of h is selected within the monitoring area. C The unknown monitoring point C, with a depth of 1200m, is used as the target location for calculation and compensation.
[0095] Calculate the elevation of monitoring point C relative to reference station A (h). A The elevation difference Δh = 820m) C Δh C=h C -h A =1200−820=380m, then Δh C Substituting 380m into the aforementioned quadratic polynomial fitting model, the tropospheric delay ΔZTD corresponding to monitoring point C is calculated. C : ΔZTD C =a×Δh 2 +b×Δh+c=−0.0003×380 2 +(-2.5)×380+1.5≈-0.992m.
[0096] In a preferred embodiment, after obtaining the tropospheric delay at monitoring point C, it is incorporated into the baseline calculation process between monitoring point C and reference station A. A virtual observation equation is constructed in the GNSS baseline adjustment system. The calculated ΔZTD is then used... C This constraint is incorporated into the virtual observation equation as a strong prior constraint. This constraint defines a baseline value for the tropospheric delay difference between the two stations, and the adjustment calculation is only slightly modified based on this baseline.
[0097] In this scheme, the tropospheric delay ΔZTD of monitoring point C relative to reference station A has been calculated using a quadratic polynomial model. C =-991.82mm. This value does not come from satellite observations but from model predictions; therefore, it is prior information. To incorporate this prior information into the adjustment system, the following virtual observation equation is constructed:
[0098] Among them, ΔZTD C For tropospheric delay; Let ε be the tropospheric delay parameter to be estimated in the adjustment system; ε is the residual of the virtual observation. This scheme employs strong constraints, that is, assigning a very small variance (e.g., 0.001) to the virtual observation equation. 2 mm 2 This causes the tropospheric delay parameter of monitoring point C in the adjustment calculation to be "locked" at the ΔZTD given by the model. C In the vicinity, only minor adjustments are permitted.
[0099] By obtaining the target elevation of the target location and inputting it into the regional tropospheric delay-elevation model, the tropospheric delay corresponding to the target location is calculated. This achieves high-precision prediction of tropospheric delay for any non-reference station location within the region. This lays the foundation for the subsequent adjustment system of GNSS baseline calculation to introduce the tropospheric delay into the form of a strong prior constraint, thereby effectively limiting the reference value of the tropospheric delay difference between two stations and significantly improving the calculation accuracy and reliability of satellite positioning in the vertical direction.
[0100] Example 2 verifies the specific implementation of this application. Specifically, a construction control network needs to be established for a mountainous highway under construction. The elevation range of the survey area is from 800 meters to 1500 meters, with a total elevation difference of 700 meters, and the baseline length of the control network is between 3 and 8 kilometers. Static observation is conducted using four domestically produced dual-frequency GNSS receivers for a duration of 24 hours. This example is achieved through the following steps: Four points with known high-precision coordinates (better than 3 mm) were selected as reference stations within the survey area. The selection criteria were as follows: two near the foot of the mountain (elevations 820 m and 850 m), one on the mountainside (elevation 1150 m), and one on the summit (elevation 1480 m). This ensured that the sky above each reference station was clear and that they were largely visible to each other. This high-low grid layout aimed to provide sufficient elevation span data for the subsequent construction of the regional tropospheric delay-elevation model.
[0101] RINEX format observation data from each reference station were imported into the GNSS data processing software platform. Data quality checks were performed, and cycle slip detection and repair were conducted using the MW (Melbourne-Wübbena) and LG (L geometry-free) arrays. The satellite cutoff elevation angle was uniformly set to 20° to reduce multipath effects, and the data sampling interval was set to 30 seconds.
[0102] For the baselines between various reference stations (e.g., reference station A at the foot of the mountain and reference station B at the summit), perform the following operations: Using the Saastamoinen model and the standard pressure formula (P) i =1013.25×exp(-H i / 8434), based on the elevations of the two stations, the station air pressure was estimated, and the zenith dry delay (ZHD) of each reference station was calculated. A and ZHD B ).
[0103] Based on long-term meteorological observation data for this region, the zenith wet delay prior value was uniformly set to 0.1 m. The total zenith delay prior value (ZTD) for each reference station is as follows. A =ZHD A +0.1, ZTD B =ZHD B +0.1.
[0104] The NMF mapping function is used to convert the zenith delay into the slant path tropospheric delay of the satellite signal propagation direction (formula: L=M(θ)·ZTD). From the original carrier phase and pseudorange observations, the ZHD corresponding to reference station A is subtracted respectively. A +0.1m) and the corresponding (ZHD) of base station B BThe oblique path tropospheric delay corresponding to +0.1m. After this processing step, only a very small residual wet delay and observation noise remain in the observation values.
[0105] A double-difference observation model was constructed based on residual observations. Since the observation period lasted 24 hours, a piecewise linear model (PWL) was used to perform time-series parameterization modeling of the relative wet delay difference to be estimated. Considering the parameter stability in mountainous scenarios with large elevation differences, the node interval was set to 2 hours, resulting in a total of 13 nodes throughout the entire period.
[0106] In parameter estimation, the parameter to be estimated is set as a single relative wet delay difference ΔδZWD between the two stations. AB A relaxed prior constraint is applied to the first node (initial value is 0, prior mean error is 0.045m); Gauss-Markov stochastic process constraints are applied to adjacent nodes, with the process noise spectral density taking a minimum empirical value (1×10). -6 m 2 / s) to prevent parameter drift.
[0107] The least squares method was used to assemble and solve the double-difference observation equations. The LAMBDA algorithm was employed for integer ambiguity search and fixation, and the reliability of the fixed solution was confirmed through a ratio test (threshold set to 3.0). After the solution was completed, the relative wet delay difference (ΔδZWD) between each reference station was obtained. AB The posterior estimate of ).
[0108] Using base station A at the foot of the mountain (elevation 820m) as the reference station, the calculated relative wet delay difference (ΔδZWD) is superimposed with the prior zenith wet delay (0.1m) and zenith dry delay (ZHD) to reconstruct the absolute zenith total delay time series for each base station. Due to sufficient observation time, the average value of each series is taken.
[0109] The total zenith delay difference (ΔZTD) and elevation difference (Δh) of each reference station relative to reference station A were determined. Scatter plot analysis revealed a slight nonlinear concave characteristic when the elevation difference exceeded 300m. Therefore, a quadratic polynomial model (ΔZTD = a·Δh) was adopted. 2 The data was fitted using the formula +b·Δh+c. The fitted coefficient was a = -0.0003 mm / m. 2 With b=-2.5mm / m and c=1.5mm, the root mean square residual (RMS) of the fitting is 1.8mm, and a regional tropospheric delay-elevation model characterizing the nonlinear mapping relationship between elevation and tropospheric delay is successfully obtained.
[0110] An unknown monitoring point C with an elevation of 1200m within the survey area was selected for compensation calculation. The elevation difference of monitoring point C relative to the reference station A was calculated to be 380m. Substituting this into the above quadratic polynomial fitting model, the corresponding tropospheric delay of -0.992m was obtained.
[0111] During the baseline calculation process between monitoring point C and reference station A, the calculated tropospheric delay is written into the virtual observation equation in the form of a strong prior constraint, limiting the benchmark value of the tropospheric delay difference between the two stations. This fundamentally deprives the elevation coordinates of the degree of freedom to absorb the tropospheric delay residual, thus avoiding distortion of the elevation parameters.
[0112] Comparing the traditional direct estimation ZTD scheme with the scheme in this embodiment, the results show that the elevation direction error of the scheme in this embodiment is reduced from ±15mm to ±6mm, and the accuracy is improved by 60%; the ambiguity fixation rate is improved from 78% to 95%, and the time series of elevation calculation results is smoother and there is no systematic drift.
[0113] Furthermore, this application pertains to a high arch dam with a height of 120 meters and a height difference of approximately 300 meters between the mountains on both sides of the reservoir. A GNSS automated deformation monitoring system needs to be established to continuously monitor the dam body and the reservoir bank near the dam, with a sampling interval of 60 seconds, requiring an elevation monitoring accuracy of ±2 mm.
[0114] Six benchmark stations were deployed along both banks of the dam, with elevations ranging from near the reservoir bottom (400 meters) to the dam crest (720 meters). Two stations were located on the dam crest, two on the dam abutments, and one each at the foot of the mountains on both banks. Monitoring points were placed on the dam surface and key reservoir bank sections to ensure sufficient spatial spacing between the benchmark stations, providing data support for constructing a high-precision regional tropospheric delay-elevation model.
[0115] Residual observations from each benchmark station were collected using a continuous operation mode. To address the extremely high accuracy and stability requirements of dam deformation monitoring, a piecewise linear model (PWL) was employed in the parameter estimation stage, with the node intervals reduced to 30 minutes and the process noise spectral density tightened to 5 × 10⁻⁶. -7 m 2 / s, to obtain high-precision relative wet delay difference values (ΔδZWD) between each reference station.
[0116] Using the dam crest benchmark station (elevation 720 meters) as the reference station, the a priori values of the relative wet delay difference obtained by calculation are superimposed with the a priori zenith wet delay and zenith dry delay to reconstruct the absolute zenith total delay time series of each benchmark station.
[0117] The total zenith delay difference (ΔZTD) and elevation difference (Δh) of each base station relative to the reference station were determined. Since dam deformation monitoring needs to address dynamic changes in the atmospheric environment, this embodiment constructs a three-dimensional spatiotemporal grid model of "elevation difference-time-delay": every 30 minutes, the instantaneous ΔZTD and Δh of all base stations are used for data fitting to obtain a regional tropospheric delay-elevation model (quadratic polynomial model coefficients a(t), b(t), c(t)) representing the nonlinear mapping relationship between elevation and tropospheric delay. A total of 48 sets of model parameters are generated per day, organized into a two-dimensional spatiotemporal grid according to time (t) - elevation difference (Δh).
[0118] For unknown monitoring points on the dam surface, their elevation will change in real time at the millimeter level due to factors such as water pressure; the system reads the current time t, obtains the real-time elevation h(t) of the monitoring point, and calculates the current elevation difference Δh(t) = h(t) - 720.
[0119] In a pre-generated spatiotemporal grid, bilinear interpolation is performed based on time t and elevation difference Δh(t) to extract the most accurate tropospheric delay ΔZTD(t, Δh) at the current moment. This tropospheric delay is written into the virtual observation equation as a strong prior constraint and applied to the real-time epoch-by-epoch solution of this monitoring point, thereby fundamentally depriving the elevation coordinates of the degrees of freedom that absorb the tropospheric delay residual.
[0120] After three consecutive months of operation, compared with high-precision leveling results, the internal consistency accuracy and external verification accuracy of this embodiment in the GNSS elevation direction are both better than ±2 mm. Throughout the entire monitoring period, no seasonal elevation drift phenomenon common in traditional methods was observed, indicating that this embodiment successfully isolated the seasonal variation of tropospheric delay, ensuring extremely high reliability of dam deformation monitoring.
[0121] Example 3 describes in detail a modeling and solving device for a regional tropospheric delayed elevation model, such as... Figure 9 As shown, specifically: The prior value determination unit acquires GNSS observation data and elevation information from multiple reference stations within the monitoring area, and determines the zenith total delay prior value of each reference station based on a preset atmospheric model, so as to convert the GNSS observation data into residual observation values. The relative wet delay calculation unit constructs a double-difference observation model based on the residual observations, and uses a piecewise linear model to perform time-series parameterized modeling of the relative wet delay difference to be estimated, so as to calculate the relative wet delay difference between each reference station. The delay difference determination unit reconstructs the absolute zenith total delay time series of each reference station based on the relative wet delay difference value and the prior value of the zenith total delay, and determines the zenith total delay difference and elevation difference of each reference station relative to the reference station based on the absolute zenith total delay time series and the elevation information of each reference station; wherein, the reference station is determined from each reference station. The elevation fitting model acquisition unit uses a polynomial model to fit data based on the elevation difference and the total zenith delay difference, in order to obtain a regional tropospheric delay-elevation model that characterizes the nonlinear mapping relationship between elevation and tropospheric delay.
[0122] In some optional implementations, the prior value of the total zenith delay for each reference station is determined based on a pre-defined atmospheric model, including: Based on the elevation information of each reference station, the station air pressure of each reference station is determined using a pre-set atmospheric model; Based on the station air pressure, determine the zenith dry delay corresponding to each reference station; The zenith dry delay is added to the preset prior zenith wet delay to obtain the prior value of the total zenith delay for each reference station.
[0123] In some alternative implementations, GNSS observation data is converted into residual observations, including: The zenith total delay prior value is projected onto the satellite signal direction using a preset mapping function to obtain the slant path tropospheric delay of each reference station in the corresponding satellite signal direction; The residual observation values are obtained by subtracting the corresponding tropospheric delay from the GNSS observation data of each reference station.
[0124] In some optional implementations, a double-difference observation model is constructed based on the residual observations, and a piecewise linear model is used to perform time-series parameterized modeling of the relative wet delay difference to be estimated, in order to solve for the relative wet delay difference between each reference station, including: For any two reference stations, the residual observations are differentially analyzed between stations to construct a double-difference observation equation that includes double-difference geometric distance, double-difference integer ambiguity, and relative wet delay difference. The observation period is divided into multiple time nodes according to a preset time interval, and the relative wet delay difference is parameterized into the parameters to be estimated at each time node using a piecewise linear model. Prior constraints are applied to the first time node of the piecewise linear model, and process noise constraints are applied to adjacent time nodes; By solving the double-difference observation equations using least squares and fixing the integer ambiguity, the relative wet delay difference values corresponding to each reference station are obtained.
[0125] In some alternative implementations, determining the total zenith delay difference and elevation difference between each reference station and the reference station includes: The relative wet delay difference, zenith dry delay, and prior zenith wet delay are superimposed to reconstruct the absolute zenith total delay time series for each reference station. The absolute zenith total delay time series is averaged to obtain the average zenith total delay for each reference station. From each base station, a reference station is determined, and the difference between the elevation information of each base station and the elevation information of the reference station is determined to obtain the elevation difference; The zenith total delay difference is determined based on the difference between the average zenith total delay corresponding to each base station and the average zenith total delay corresponding to the reference station.
[0126] In some alternative implementations, the regional tropospheric delay-elevation model is obtained in the following ways: Using elevation difference as the independent variable and total zenith delay difference as the dependent variable, a quadratic polynomial model was used for data fitting. Solving for the fitting coefficients of the quadratic polynomial model yields the regional tropospheric delay-elevation model.
[0127] This application also provides a tropospheric delay calculation apparatus, which includes: The elevation acquisition unit is used to acquire the target elevation of the target location. The delay calculation unit is used to input the target elevation into the regional tropospheric delay-elevation model obtained by the above method, and calculate the tropospheric delay corresponding to the target location.
[0128] In this embodiment, a regional tropospheric delay-elevation modeling device is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above-mentioned functions.
[0129] like Figure 10 As shown in the diagram, this application provides a structural schematic diagram of a computer device, as follows: Figure 10As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 10 Take a processor 10 as an example.
[0130] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.
[0131] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.
[0132] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.
[0133] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.
[0134] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.
[0135] This application also provides a computer-readable storage medium. The methods described in this application can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code downloaded over a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the methods shown in the above embodiments are implemented.
[0136] This application can complete the preprocessing of tropospheric prior errors based on the elevation data of the benchmark station, improve the stability of the solution by reducing the dimensionality of parameters, construct a regional dedicated delayed elevation model using a quadratic polynomial, and optimize the adjustment process with the help of virtual observation constraints, so as to realize the systematic correction of tropospheric errors in areas with large elevation differences and support the long-term high-precision GNSS deformation monitoring work in the region.
[0137] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter changes made to these embodiments within the spirit and principles of the present invention, without departing from the principles and spirit of the present invention, through conventional substitutions or to achieve the same function, fall within the scope of protection of the present invention.
Claims
1. A method for modeling and solving a regional tropospheric delay elevation model, characterized in that, include: Based on the elevation information of each reference station in the monitoring area, the air pressure is calculated by the pressure height formula and the zenith dry delay is calculated by combining the Saastamoinen model. A preset fixed constant is used as the prior zenith wet delay. The two are added together to obtain the prior value of the total zenith delay of each reference station. The Niell mapping function is used to project the total zenith delay prior value onto the slant path, and then subtract it from the original GNSS observations to generate residual observations; A double-difference observation model was constructed, which only uses the relative wet delay difference between reference stations as the tropospheric parameter to be estimated. The nodes were divided according to a preset time interval and time constraints were applied. The high-precision relative wet delay difference value was obtained by solving the least squares method in combination with the ambiguity fixing algorithm. The calculated relative wet delay difference value is superimposed back onto the prior value of the total zenith delay to reconstruct the time series of the total absolute zenith delay of each reference station. After averaging the total absolute zenith delay of each station, the elevation difference and the total zenith delay difference of each reference station relative to the selected reference station are calculated. Using the elevation difference as the independent variable and the total zenith delay difference as the dependent variable, a quadratic polynomial model is used for least squares fitting to establish a regional tropospheric delay-elevation model. The elevation of the target point is obtained and its elevation difference relative to the reference station is calculated. The difference is then substituted into the regional tropospheric delay-elevation model to predict the tropospheric delay of the target point. The predicted tropospheric delay is then converted into a virtual observation equation and injected into the baseline double-difference adjustment system to apply strong constraints to the elevation parameters for solution.
2. The method for modeling and solving a regional tropospheric delay elevation model according to claim 1, characterized in that, The process of calculating the station air pressure using the pressure height formula and solving the zenith dry delay using the Saastamoinen model is as follows: Using the standard pressure formula From the station elevation Estimating station air pressure ; Based on estimated air pressure The Saastamoinen model is used to calculate the zenith dry delay, and the formula is as follows: In the formula The latitude of the base station Elevation of the station is expressed in kilometers; A uniform 0.1m is set as the globally fixed prior zenith wet delay. Superimposed zenith dry delay Obtain the prior value of the total zenith delay for a single station. ; The entire process is calculated solely based on the elevation information of the base station, without the need to deploy actual temperature, humidity, and air pressure meteorological sensors.
3. The method for modeling and solving a regional tropospheric delay elevation model according to claim 2, characterized in that, The method for projecting the zenith total delay prior value onto the slant path using the Niell mapping function is as follows: Using satellite elevation angle Call the Niell mapping function for the input parameters ,pass Calculate the tropospheric delay corresponding to the satellite's oblique path; The satellite cutoff elevation angle is preset to 20°. After removing observation data with elevation angles below this threshold, the oblique path tropospheric delay is used to perform interpolation on the raw GNSS observations to generate residual observations.
4. The method for modeling and solving a regional tropospheric delay elevation model according to claim 3, characterized in that, The steps for constructing the double-difference observation model and solving for the relative wet delay difference include: Establish a double-difference observation equation by performing inter-station difference analysis on the residual observations of the two reference stations: In the formula These are double-difference residual observations. It is a double-difference geometric distance. For carrier wavelength, For double-difference integer ambiguity, These are the output values of the Niell mapping function for the two stations, This is the only tropospheric parameter to be estimated between the two stations. To observe noise; The complete observation period was divided into time nodes with a fixed interval of 2 hours, and a piecewise linear PWL model was used to analyze the data. Perform timing parameterization; An a priori constraint with an initial value of 0 and a prior mean error of 0.045m is applied to the first time node of the piecewise linear model, and a spectral density constraint is applied to adjacent time nodes. Noise constraints on the Gauss-Markov process; The least squares method is used to solve the double-difference observation equation, the LAMBDA algorithm is used to search for integer ambiguity, the Ratio test threshold of 3.0 is set to fix the ambiguity, and the relative wet delay difference value corresponding to each time node is output.
5. The method for modeling and solving a regional tropospheric delay elevation model according to claim 4, characterized in that, The formula for calculating the total absolute zenith delay time series of each reconstructed reference station is as follows: The selected reference station does not have a wet delay differential value relative to itself, and the absolute zenith total delay of the reference station is omitted when reconstructing it. item; For all epochs within a complete time series of a single reference station Calculate the arithmetic mean to obtain the average total zenith delay of the reference station; Calculate the elevation difference between the remaining base stations and the reference station. Zenith total delay difference , generated by The fitted sample dataset is composed of these data.
6. The method for modeling and solving a regional tropospheric delay elevation model according to claim 5, characterized in that, The expression for the quadratic polynomial model is: In the formula The elevation difference between the station to be measured and the reference station. This represents the difference in total zenith delay between the station under test and the reference station. The coefficients are to be fitted. All Substitute the samples into the polynomial and solve for the coefficients using the least squares algorithm. The regional tropospheric delay-elevation model was obtained.
7. The method for modeling and solving a regional tropospheric delay elevation model according to claim 6, characterized in that, The operation of converting the predicted tropospheric delay into a virtual observation equation and injecting it into the baseline double-difference adjustment system includes: Read the elevation of the target point Calculate the elevation difference between the target point and the reference station. ,Will Substituting into the established quadratic polynomial model, the output is the total predicted zenith delay difference between the target point and the reference station. ; Constructing virtual observation equations Set the virtual observation variance to With strong prior constraints, the virtual observation equation is combined with the baseline double-difference observation equation to simultaneously solve the baseline coordinates and tropospheric delay parameters.
8. A modeling and solving device for a regional tropospheric delay elevation model, characterized in that, The apparatus for performing a regional tropospheric delay elevation model modeling and solving method according to any one of claims 1 to 7, the apparatus comprising a priori delay calculation unit, a relative wet delay solving unit, an absolute delay reconstruction unit, an elevation delay fitting unit, and a point adjustment correction unit, specifically: The prior delay calculation unit obtains the elevation information of the base station, solves the zenith dry delay by using the pressure height formula and the Saastamoinen model, superimposes the fixed prior wet delay to obtain the zenith total delay prior value, and calls the Niell mapping function to complete the oblique path delay projection and generate residual observation values. The relative wet delay solution unit constructs a double-difference observation equation based on the residual observation values, adopts piecewise linear time series parameterization and applies double-layer constraints, and solves the relative wet delay difference between reference stations through least squares and LAMBDA algorithms. The absolute delay reconstruction unit integrates the relative wet delay difference, zenith dry delay, and a priori wet delay to reconstruct the absolute zenith total delay time series of each reference station. After averaging the time series, it calculates the elevation difference and zenith total delay difference of each station relative to the reference station. The elevation delay fitting unit uses a quadratic polynomial least squares to fit the elevation difference and the total zenith delay difference to generate a regional tropospheric delay-elevation model. The point adjustment and correction unit reads the elevation of the target point, calculates the elevation difference, substitutes it into the model to predict the tropospheric delay, constructs a virtual observation equation with strong variance constraints, and connects it to the baseline double difference adjustment system to complete the coordinate solution.
9. A computer device, characterized in that, The system includes a memory and a processor, wherein the memory stores computer-executable instructions, and the processor executes the computer-executable instructions to implement the regional tropospheric delay elevation model modeling and solving method according to any one of claims 1 to 7.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for modeling and solving a regional tropospheric delayed elevation model as described in any one of claims 1 to 7.
Citation Information
Patent Citations
Troposphere delay correction method suitable for short-distance large-height-difference RTK
CN115061167A