A relative ztd-based rtk safety distance determination method and system

Abstract

The present application belongs to the field of GNSS real-time dynamic positioning technology, and discloses a relative ZTD-based RTK safety distance determination method and system. The present application establishes a relative ZTD between a reference point and a rover point, an inter-station spatial distance and a bearing angle calculation system of the rover point relative to the reference point through grid-based spatial unit division; based on the calculated inter-station spatial distance and inter-station relative ZTD, spatial correlation analysis is performed between the rover point and the reference point, and a relative ZTD threshold is determined; bearing partition and direction regression modeling are performed; safety distance inversion and result output are performed. The present application further considers the influence of meteorological conditions such as temperature and humidity on the spatial correlation of ZTD, establishes a meteorological condition-adaptive safety distance model, so that the subsequent positioning server can automatically determine whether RTK positioning can be directly performed according to the position of the rover station.

Description

Technical Field

[0001] This invention belongs to the field of GNSS real-time dynamic positioning technology, and particularly relates to a method and system for determining RTK safe distance based on relative ZTD. Background Technology

[0002] RTK (Real-Time Kinematic) typically uses a base station to send observation correction information to a rover station to mitigate the impact of errors such as satellite clock bias, orbital error, ionospheric delay, and tropospheric delay on the positioning results. When the base station and the rover station are close, the atmospheric delay between the two stations has a strong spatial correlation, and the base station correction information can be well applied to the rover station, resulting in high RTK positioning accuracy and a high success rate in fixing ambiguities. As the distance between the stations increases, the spatial correlation of atmospheric delay, especially tropospheric delay, gradually weakens, and the residual tropospheric error between the rover station and the base station increases, thus affecting positioning accuracy and reliability.

[0003] Zenithal-Tropospheric Delay (ZTD) is a crucial parameter characterizing tropospheric delay. For a base station and a rover within the same region, the difference in ZTD between the two points reflects the spatial differences in tropospheric delay between them. A smaller relative ZTD indicates that the tropospheric states of the two stations are similar, and the base station correction information can be directly used for RTK operations. However, if the relative ZTD exceeds a certain threshold with increasing distance, it indicates an increased risk for direct RTK operations, requiring additional tropospheric delay compensation, network RTK enhancement, or reference station switching. Therefore, determining a safe distance for direct RTK positioning based on historical ZTD data is a critical issue for improving RTK service reliability and operational planning capabilities.

[0004] Existing RTK-related technologies mainly focus on tropospheric delay correction, reference station network interpolation, grid ZTD modeling, or long baseline error compensation. These technologies can improve the accuracy of tropospheric delay estimation to some extent, but in engineering server applications, a safe distance model that can be directly used to determine the operational range is still needed. That is, given the locations of the base station and rover, as well as meteorological conditions, it is necessary to determine whether the rover is within the direct RTK positioning range and to automatically trigger relative ZTD compensation when it is outside the range.

[0005] Furthermore, tropospheric delay is influenced by factors such as regional water vapor, topography, latitude, season, temperature, and humidity, exhibiting significant differences across different regions and directions. Using only a uniform empirical distance or a single circular radius as the RTK operating range is insufficient to represent the directional anisotropy of the safe distance around the reference station, and also fails to accommodate the spatial correlation changes in ZTD caused by variations in temperature and humidity. Therefore, it is necessary to establish a method based on relative ZTD statistical relationships that can invert RTK safe distances according to azimuth and meteorological conditions.

[0006] (1) Invention title: A Short-Range, Large-Elevation-Difference NRTK Tropospheric Delay Correction Method Based on PPP (Publication No. CN115144878A, Publication Date 20221004). This method is designed for network RTK positioning scenarios with short distances but large elevation differences. It estimates the high-precision real-time tropospheric delay at the reference station using the PPP method and combines the tropospheric delay results from multiple reference stations to interpolate or reduce the elevation of the tropospheric delay at the rover's location. Specifically, the method first uses real-time precise ephemeris and observation data to perform PPP calculation to obtain the real-time tropospheric delay of the reference station; then, based on the approximate location of the rover, it uses the tropospheric delay information of surrounding reference stations to calculate the delay correction at the rover's location; finally, it uses this correction for NRTK positioning to reduce the residual tropospheric error under short-range, large-elevation-difference conditions. This method can improve the accuracy of NRTK positioning in complex elevation difference environments.

[0007] (2) Invention Title: An Improved Method and System for Constructing a Real-Time Grid Model of Tropospheric Delay in GNSS (Publication No. CN117669171A, Publication Date 20240308). This method addresses the tropospheric delay correction problem in real-time high-precision GNSS positioning. It constructs a global tropospheric delay elevation normalized grid model using multi-year global ERA5 reanalysis data, and combines it with real-time GNSS ZTD data for elevation normalization and grid horizontal interpolation to generate a real-time global tropospheric delay grid model. Users only need to provide the location and time information of the target point to obtain the ZTD at the target point using the elevation normalized grid model and the real-time grid model. This method can improve the accuracy of obtaining prior or correction values ​​of real-time ZTD and is suitable for tropospheric delay modeling in high-precision GNSS positioning.

[0008] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: (1) Lack of a safe distance determination mechanism for the operating range around the base station. Existing RTK correction schemes focus more on error compensation itself and find it difficult to clearly indicate which rover locations can be directly RTKed and which locations require additional tropospheric delay compensation before the start of the operation.

[0009] (2) The directional anisotropy of the safety distance is not fully expressed. The tropospheric delay is affected by regional water vapor, topography, latitude and longitude and meteorological conditions, and its spatial correlation may be different in different directions. A simple circular radius or a fixed distance threshold is difficult to accurately characterize the real safety boundary.

[0010] (3) There is a lack of statistical methods for determining the relative ZTD threshold that are directly linked to spatial correlation. If only empirical distance or fixed thresholds are used, it is difficult to adapt to the atmospheric conditions of different regions and different years.

[0011] (4) Temperature and humidity conditions are usually used as explanatory variables, but are not converted into rules for generating safe distances. Existing technologies rarely combine low / medium / high temperature and low / medium / high humidity into independent scenarios, invert safe distances separately, and output decision results. Summary of the Invention

[0012] To overcome the problems existing in related technologies, the present invention discloses an embodiment of a method and system for determining RTK safety distance based on relative ZTD.

[0013] The technical solution is as follows: a method for determining the RTK safe distance based on relative ZTD, including the following steps: S1. By dividing the spatial unit into grids, a calculation system is established for the relative ZTD between the reference point and the movement point, the spatial distance between stations, and the azimuth angle of the movement point relative to the reference point, providing standardized input for subsequent spatial correlation analysis and safety distance inversion. S2. Based on the calculated inter-station spatial distance and inter-station relative ZTD, perform spatial correlation analysis between the flow point and the reference point and determine the relative ZTD threshold. S3. Based on the obtained relative ZTD threshold, perform orientation partitioning and direction regression modeling; S4. Based on the fitting effect of the regression model between the relative ZTD and the inter-station distance, perform the safety distance inversion and output the results.

[0014] In step S1, ERA5 is used to analyze ZTD data with an hourly time resolution; the study area is divided into spatial computing units, and the center point of each grid is used as the reference point. Several points within or around the grid are then analyzed. Grid points serve as movement points; let the reference point be... , No. The flow points are ,in, Indicates latitude, Indicates longitude; The relative ZTD between the reference point and the flow point is defined as follows: ; In the formula, for and Between Each flow point at time [time] The relative absolute value of ZTD For the first Each flow point at time [time] ZTD, ZTD at the reference point at the same time; For each set of reference points and movement points, calculate the spatial distance between stations; use the spherical distance approximation formula: ; ; ; In the formula, The distance between stations. The average radius of the Earth For the first The latitude difference between each migration point and the reference point To obtain the average latitude of the reference point and the movement point, For the first The difference in longitude between each flow point and the reference point. For the first The latitude of each flow point Latitude as the reference point For the first Longitude of each point of movement Longitude as the reference point; Calculate the azimuth angle of the flow point relative to the reference point. , used for subsequent directional sector division; ; In the formula, For the first The azimuth angle of each flow point relative to the reference point, in degrees, ranges from 0° to 360°; the azimuth angle starts at 0° in the due north direction and increases clockwise.

[0015] In step S2, spatial correlation analysis and determination of the relative ZTD threshold include: Spatial correlation analysis was performed on the ZTD time series based on the baseline point and the flow point, for the first... For each flow point, calculate the correlation coefficient between the ZTD time series and the baseline ZTD time series: ; In the formula, For the first ZTD time series correlation coefficient between each flow point and the baseline point For the first Covariance between the ZTD time series at each flow point and the ZTD time series at the baseline point and The first ZTD standard deviation at each flow point and ZTD standard deviation at the benchmark point; Highly correlated regions are selected based on a preset correlation threshold. The flow points are taken as highly correlated samples; the set of highly correlated samples is represented as: ; In the formula, For a highly relevant sample set, Number the movement points. For the correlation coefficient threshold, select... ; Within the highly correlated region, the absolute value of the relative ZTD between each flow point and the reference point is calculated, and statistical analysis is performed on the sample set. Quantiles as relative ZTD thresholds: ; In the formula, The relative ZTD threshold, for Quantiles The time number in the time series. This represents the total length of the time series.

[0016] In step S3, the orientation partitioning and direction regression modeling includes: Centered on the reference point, to The directional range is divided into several equally spaced sectors; the first Each sector is represented as: ; In the formula, For the first Each sector, Number the sectors For the number of sectors, ; Based on the azimuth angle of the flow point relative to the reference point Each flow point is assigned to its corresponding sector; for each sector, a regression model is established between the relative ZTD and the inter-station distance, using a linear model: ; In the formula, For the first The absolute value of the relative ZTD difference between each flow point and the reference point For the first The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; Model parameters and The coefficient of determination was calculated based on the fit of the regression model between relative ZTD and inter-station distance using the least squares method. ; In the formula, As the coefficient of determination, These are the model's predicted values. For the first The relative ZTD sample mean within each sector.

[0017] In step S4, the safe distance inversion includes: When the first When the linear regression model fitting effect between relative ZTD and inter-station distance within a sector meets the requirements, the relative ZTD threshold will be set. Substituting this into the model for that direction, we can deduce the corresponding RTK safety distance: ; In the formula, For the first RTK safety distance in each direction; Given a reference point and a target flow point, calculate the distance between the reference point and the target flow point. and azimuth Determine the sector to which it belongs and compare Safety distance in the corresponding direction If the following conditions are met: ; Then it is determined that the movement point is within the safe distance range in the corresponding direction, and meets the conditions for RTK positioning; if If so, the flow point is determined to be outside the safe distance range.

[0018] Furthermore, regarding the obtained safe distance As temperature and humidity change, the RTK safety distance determination method under temperature and humidity grouping is used to determine the first... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

[0019] Furthermore, the specific methods for determining RTK safety distances under temperature and humidity grouping include: S4.1 Data Foundations and Grid Statistics; S4.2, three-part hierarchical division and nine scene combinations; S4.3 Correlation analysis under various temperature and humidity schemes; S4.4, Calculation of scheme threshold; S4.5, Directional Modeling; S4.6, Safety Distance Inversion and Spatial Representation.

[0020] In step S4.1, the data foundation and grid statistics include: For each grid cell, calculate the temperature and humidity sequences within that grid cell, and take the 33rd and 67th percentiles of temperature and humidity, respectively, as the basis for classifying them as low, medium, and high levels. ; ; In the formula, It is a temperature sequence. It is a humidity sequence. Temperature series at the 33rd percentile Temperature series at the 67th percentile The humidity sequence is at the 33rd percentile. The humidity sequence is at the 67th percentile. (·)and (·) are the 33rd and 67th percentiles, respectively; In step S4.2, the three-part hierarchical classification and the nine scene combinations include: Based on temperature quantiles, temperatures are divided into three levels: low, medium, and high; based on humidity quantiles, humidity is divided into three levels: low, medium, and high. The combination of temperature and humidity levels forms nine experimental schemes, namely, low temperature and low humidity, low temperature and medium humidity, low temperature and high humidity, medium temperature and medium humidity, medium temperature and high humidity, high temperature and low humidity, high temperature and medium humidity, and high temperature and high humidity, which are respectively denoted as Scheme 1 to Scheme 9. ; ; In the formula, For a moment The corresponding temperature level classification results are used to determine whether the current moment is low, medium, or high. This represents the humidity level classification result corresponding to time t, used to determine whether the humidity level is low, medium, or high at that time. and When combined, they can be used to create different temperature and humidity scenario solutions; In step S4.3, the correlation analysis under each temperature and humidity scheme includes: For the A temperature and humidity scheme was used to filter out highly correlated areas with a correlation coefficient threshold of 0.6, resulting in a set of highly correlated flow points. ; In the formula, For the set of highly correlated flow points, Number the movement points. For the first Under the first scheme ZTD correlation coefficient between each flow point and the baseline point For the first A temperature and humidity scheme; In step S4.4, the scheme threshold calculation includes: For the One approach is to take the 95th percentile of the absolute value of the relative ZTD in the high-relevance region as the relative ZTD threshold under the given temperature and humidity conditions. ; In the formula, For the first The relative ZTD threshold under each temperature and humidity scheme It is the 95th percentile. For the first The flow point at the th _ ... The absolute difference of ZTD relative to the reference point at each time point; In step S4.5, orientation modeling includes: For each temperature and humidity scheme and each direction sector The relationship models between relative ZTD and inter-station distance were fitted respectively; ; In the formula, In the first The temperature and humidity scheme, the first Within the sector of direction, the first The absolute difference of the relative ZTD of each flow point relative to the reference point. For the first Under the first scheme The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; In step S4.6, the safety distance inversion and spatial representation include: The first Substituting the relative ZTD threshold under the first temperature and humidity scheme into the first... The regression model in each direction is used to deduce the RTK safety distance in that direction; ; In the formula, For the first The temperature and humidity scheme, the first Safe distance in each direction.

[0021] Another object of the present invention is to provide an RTK safety distance determination system based on relative ZTD, the system implementing the aforementioned RTK safety distance determination method based on relative ZTD, the system comprising: The data input and spatial unit construction module is used to acquire ZTD data for several consecutive years within the target area. For each set of ZTD data for reference points and mobile points, the spatial distance between stations is calculated. The spatial correlation analysis and threshold determination module is used to perform spatial correlation analysis and determine the relative ZTD threshold based on the calculated inter-station spatial distance. The azimuth partitioning and direction regression modeling module is used to perform azimuth partitioning and direction regression modeling based on the acquired relative ZTD threshold. The safety distance inversion module is used to perform safety distance inversion and output results based on the fitting effect of the regression model between the relative ZTD and the inter-station distance.

[0022] Furthermore, the RTK safe distance determination system based on relative ZTD also includes: The RTK safety distance model building module under different temperature and humidity conditions is used to model the obtained safety distance. As temperature and humidity change, the RTK safety distance determination method under temperature and humidity grouping is used to determine the first... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

[0023] Combining all the above technical solutions, the beneficial effects of this invention are as follows: First, this invention proposes an RTK safety distance determination method based on relative ZTD. By analyzing the spatial correlation of tropospheric delay between the base station and the rover using historical ZTD data, a relative ZTD threshold is determined. Then, by combining inter-station distance and azimuth information, the RTK safety distance in different directions around the base station is retrieved. This addresses the problem that existing RTK technologies mainly focus on tropospheric delay correction and lack pre-operation safety distance determination. Furthermore, this invention considers the impact of meteorological conditions such as temperature and humidity on the spatial correlation of ZTD, establishing a meteorological condition-adaptive safety distance model. This allows the subsequent positioning service to automatically determine whether RTK positioning can be performed directly based on the rover's location, or to invoke the relative ZTD compensation model when the safety distance is exceeded, thereby improving the reliability and service stability of RTK positioning under long baselines or complex meteorological conditions.

[0024] Secondly, this invention can be applied to high-precision positioning scenarios such as CORS base station services, RTK measurement, UAV low-altitude operations, precision agriculture, engineering surveying, and autonomous driving. By determining the safe RTK distance under different directions and temperature and humidity conditions, it can provide a quantitative basis for base station deployment, service radius assessment, and operation distance control, reducing the positioning accuracy degradation and fixation failure caused by tropospheric delay spatial differences, and improving the stability and reliability of RTK services.

[0025] Third, existing RTK safety distances are typically determined based on empirical distances, fixed service radii, or conventional error models, lacking quantitative analysis of the spatial variation characteristics of tropospheric ZTD (Zero-Temperature Difference), and also lacking methods for dynamically retrieving RTK safety distances by combining azimuth, inter-station distance, and temperature and humidity scenarios. This invention constructs a directional partitioning model based on relative ZTD and determines safety distances by combining temperature and humidity scenarios, thus overcoming the problem of existing RTK safety distance determination methods lacking atmospheric spatial difference constraints.

[0026] Fourth, in actual RTK operations, tropospheric wet delay exhibits significant spatiotemporal nonuniformity. Differences in ZTD (Zero-Temperature Delay) under different directions, distances, and meteorological conditions affect ambiguity fixation and positioning accuracy. Existing methods struggle to convert these atmospheric delay differences into safe distances that can be directly used for operational control. This invention establishes relationships between relative ZTD, inter-station distances, azimuth sectors, and temperature and humidity scenarios, transforming complex atmospheric spatial variations into calculable RTK safe distances.

[0027] Fifth, traditional methods typically approximate the RTK service area as a fixed circular region centered on the base station, assuming that the safe distance for the same base station is basically the same in all directions, or simply using a uniform empirical threshold for judgment. This invention recognizes that spatial variations relative to ZTD have directionality and meteorological scene differences. Therefore, it calculates the safe distance separately according to different azimuth sectors and temperature and humidity conditions, overcoming the technical problem of ignoring differences in atmospheric delay direction and scene differences in existing technologies. Attached Figure Description

[0028] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the disclosure of the invention and, together with the description, serve to explain the principles of this disclosure. Figure 1 This is a schematic diagram of the RTK safety distance determination method based on relative ZTD provided in this embodiment of the invention; Figure 2 This is a technical roadmap of the RTK determination method under temperature and humidity grouping provided in the embodiments of the present invention; Figure 3 This is a flowchart of the RTK safety distance determination method based on relative ZTD provided in this embodiment of the invention; Figure 4 This is a schematic diagram of the ZTD spatial correlation coefficient provided by the present invention; Figure 5 This is a schematic diagram of the spatial distribution of the relative ZTD threshold in the study area provided by the present invention; Figure 6 This is a schematic diagram of the safe distances of the reference point in each direction provided by the present invention; Figure 7 This is a schematic diagram of the threshold for temperature and humidity grouping in the research area provided by the present invention; Figure 8 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 1). Figure 9 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 2). Figure 10 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 3). Figure 11 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 4). Figure 12 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 5). Figure 13 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention, which is Scheme 6. Figure 14 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 7). Figure 15 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention (Solution 8). Figure 16 This is a schematic diagram of the safe distance of the reference point in each direction under the temperature and humidity combination provided by the present invention, which is Scheme 9. Detailed Implementation

[0029] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0030] The innovation of this invention lies in the following: This invention conducts ZTD spatial correlation analysis and uses the preset quantiles of the absolute values ​​of relative ZTD in highly correlated regions to determine the threshold for calculating safe distances; at the same time, the azimuth around the base station is divided into multiple sectors, and the relationship model between relative ZTD and inter-station distance in each direction is fitted, and the RTK safe distance in different directions is derived based on the model parameters, thereby forming a safe distance envelope; furthermore, multiple meteorological scenarios are constructed by combining temperature and humidity quantiles to achieve dynamic determination of RTK safe distances under different meteorological conditions.

[0031] This invention proposes a method for retrieving RTK safety distances based on a relative ZTD threshold, including ZTD spatial correlation analysis, relative ZTD threshold determination, azimuth partitioning modeling, and safety distance inversion. This invention uses a preset quantile of the absolute value of the relative ZTD within a highly correlated region as the threshold for calculating the RTK safety distance. This invention divides the 360-degree azimuth around the base station into multiple sectors and independently fits a model of the relationship between relative ZTD and inter-station distances within each sector. This invention derives the safety distance envelope for each direction based on the directional model parameters and the relative ZTD threshold. This invention generates multiple meteorological scenarios based on temperature and humidity quantiles and calculates the relative ZTD threshold and RTK safety distance separately for each scenario.

[0032] Example 1.

[0033] This invention provides a method for determining the safe distance for RTK based on relative ZTD (Zero-Time Tolerance). The method uses multi-year historical ZTD data within a certain area as a basis to calculate the correlation coefficient of the ZTD time series between the base station and surrounding mobile points, identifying high-correlation areas. Within these high-correlation areas, the absolute value of the relative ZTD is extracted, and a relative ZTD threshold is determined using a preset quantile. Subsequently, the 360-degree azimuth surrounding the base station is divided into multiple sectors, and the relationship between relative ZTD and inter-station distance is fitted in each direction. Finally, the safe distance in each direction is inverted based on the relative ZTD threshold to obtain the safe operating range for the mobile station. The technical roadmap is shown below. Figure 1 As shown.

[0034] In one implementation, the scheme further divides temperature and humidity into three levels—low, medium, and high—based on quantiles, forming nine temperature and humidity combination scenarios. For each scenario, a relative ZTD threshold and a safe distance are calculated, thereby outputting a weather-adaptive RTK safe distance. The technology roadmap is as follows: Figure 2 As shown.

[0035] Example 2.

[0036] like Figure 3 As shown, the present invention provides a method for determining RTK safety distance based on relative ZTD, specifically including: S1. By dividing the spatial unit into grids, a calculation system is established for the relative ZTD between the reference point and the movement point, the spatial distance between stations, and the azimuth angle of the movement point relative to the reference point, providing standardized input for subsequent spatial correlation analysis and safety distance inversion. Data input and spatial unit construction: First, multi-year ZTD data for the target region was acquired. ERA5 reanalysis ZTD data from 2021 to 2023 was used, with an hourly time resolution. The study area was divided into spatial computational units, for example, into several... A grid is created, with the center point of each grid serving as a reference point, and several points within or around the grid are then used to define the grid. Grid points serve as movement points. Let the reference point be... , No. The flow points are ,in, Indicates latitude, Indicates longitude; The relative ZTD between the reference point and the flow point is defined as follows: ; In the formula, for and Between Each flow point at time [time] The relative absolute value of ZTD For the first Each flow point at time [time] ZTD, ZTD at the reference point at the same time; For each set of reference points and movement points, calculate the spatial distance between stations; use the spherical distance approximation formula: ; ; ; In the formula, The distance between stations. The average radius of the Earth For the first The latitude difference between each migration point and the reference point To obtain the average latitude of the reference point and the movement point, For the first The difference in longitude between each flow point and the reference point. For the first The latitude of each flow point Latitude as the reference point For the first Longitude of each point of movement Longitude as the reference point; At the same time, calculate the azimuth angle of the flow point relative to the reference point. , used for subsequent directional sector division; ; In the formula, For the first The azimuth angle of each flow point relative to the reference point, in degrees, ranges from 0° to 360°; the azimuth angle starts at 0° in the due north direction and increases clockwise.

[0037] S2. Based on the calculated inter-station spatial distance and inter-station relative ZTD, perform spatial correlation analysis between the flow point and the reference point and determine the relative ZTD threshold. Spatial correlation analysis was performed on the ZTD time series based on the baseline point and the flow point, for the first... For each flow point, calculate the correlation coefficient between the ZTD time series and the baseline ZTD time series: ; In the formula, For the first ZTD time series correlation coefficient between each flow point and the baseline point For the first Covariance between the ZTD time series at each flow point and the ZTD time series at the baseline point and The first ZTD standard deviation at each flow point and ZTD standard deviation at the benchmark point; Highly correlated regions are selected based on a preset correlation threshold. The flow points are taken as highly correlated samples; the set of highly correlated samples is represented as: ; In the formula, For a highly relevant sample set, Number the movement points. For the correlation coefficient threshold, select... ; Within the highly correlated region, the absolute value of the relative ZTD between each flow point and the reference point is calculated, and statistical analysis is performed on the sample set. Quantiles as relative ZTD thresholds: ; In the formula, The relative ZTD threshold is used to characterize the upper limit of the acceptable tropospheric delay difference between the reference point and the flow point while meeting the RTK spatial correlation requirements. for Quantiles The time number in the time series. This represents the total length of the time series.

[0038] S3. Based on the obtained relative ZTD threshold, perform orientation partitioning and direction regression modeling; Centered on the reference point, to The azimuth range is divided into several equally spaced sectors; in a preferred embodiment, Divided into There are 1 sector, and the width of each sector is 1. . No. Each sector is represented as: ; In the formula, For the first Each sector, Number the sectors For the number of sectors, ; Based on the azimuth angle of the flow point relative to the reference point Each flow point is assigned to a corresponding sector; for each sector, a regression model is established between the relative ZTD and the inter-station distance. This invention innovatively proposes, in a preferred embodiment, to employ a linear model: ; In the formula, For the first The absolute value of the relative ZTD difference between each flow point and the reference point For the first The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; It can be seen that formula (7) establishes a regression model between relative ZTD and inter-station distance for each sector, which can characterize the spatial gradient characteristics of atmospheric delay with distance in different azimuth directions, avoiding the simple equivalent treatment of ZTD changes in each direction. This model can identify the distance correlation of relative ZTD within each sector, providing a quantitative basis for subsequent judgment on the variation law of RTK error with the increase of reference station distance in this direction. Model parameters and The coefficient of determination was calculated based on the fit of the regression model between relative ZTD and inter-station distance using the least squares method. ; In the formula, As the coefficient of determination, The closer This indicates that the better the linear fit between the relative ZTD and the inter-station distance, the better. These are the model's predicted values. For the first The relative ZTD sample mean within each sector.

[0039] S4. Based on the fitting effect of the regression model between the relative ZTD and the inter-station distance, perform the safety distance inversion and output the results; The innovative proposal of this invention is that when a certain direction model (that is, the direction model established by the aforementioned formula (7)) is established... A linear regression model between relative ZTD and inter-station distance within a sector (used to describe the relationship between relative ZTD and distance in that direction) is used. When the fitting effect meets the requirements, a relative ZTD threshold is set. Substituting this into the model for that direction, we can deduce the corresponding RTK safety distance: ; In the formula, For the first The safe distance for RTK in each direction; Formula (9) can be derived by substituting the preset relative ZTD threshold into the established directional regression model, thus obtaining the maximum inter-station distance that still satisfies the atmospheric delay error constraint in that direction, thereby obtaining the safe distance for each direction. This process converts the spatial variation characteristics of ZTD into distance constraints that can be directly used for reference station selection, operation range delineation and RTK reliability assessment, improving the pertinence and accuracy of safe distance determination.

[0040] Finally, the safe distances in each direction are summed to form a multi-directional safe distance envelope around the reference point. In engineering applications, the above results can serve as a model basis for subsequent positioning server integration or RTK operation range determination.

[0041] Specifically, given a reference point and a work point to be operated, calculate the distance between the reference point and the work point. and azimuth Determine the sector to which it belongs and compare Safety distance in the corresponding direction If the following conditions are met: ; Then it is determined that the movement point is within the safe distance range in the corresponding direction, and meets the conditions for RTK positioning; if If so, the flow point is determined to be outside the safe distance range.

[0042] Example 3.

[0043] This invention provides a method for determining the safe distance in RTK under temperature and humidity grouping. To analyze the safe distance obtained in step S104... Based on ERA5 reanalysis data from 2021 to 2023, this invention constructs RTK safety distance models under different temperature and humidity conditions, taking into account variations in temperature and humidity. Specifically, it utilizes a method for determining RTK safety distances under temperature and humidity groupings by... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

[0044] The data used includes ZTD, temperature, and humidity data, with hourly data preferred for the time resolution. Taking the European region as an example, the study area is divided into several 5°×5° grids. The center point of each grid is selected as the reference point, and the 0.25° grid points within or around the reference point are selected as flow points. The ZTD, temperature, and humidity time series of the reference point and flow points are extracted for the study period. The technical roadmap is as follows. Figure 2 As shown.

[0045] Specifically, it includes: S4.1 Data Foundations and Grid Statistics; First, temperature and humidity statistics were performed on each 5°×5° grid. For each grid, the temperature and humidity sequences within that grid were calculated, and the 33rd and 67th percentiles of temperature and humidity, respectively, were used as the basis for classifying the levels as low, medium, and high.

[0046] ; ; In the formula, It is a temperature sequence. It is a humidity sequence. Temperature series at the 33rd percentile Temperature series at the 67th percentile The humidity sequence is at the 33rd percentile. The humidity sequence is at the 67th percentile. (·)and (·) are the 33rd and 67th percentiles, respectively; S4.2, three-part hierarchical division and nine scene combinations; Based on temperature quantiles, temperatures are divided into three levels: low, medium, and high. Based on humidity quantiles, humidity is divided into three levels: low, medium, and high. Combining these temperature and humidity levels results in nine experimental schemes: low temperature and low humidity, low temperature and medium humidity, low temperature and high humidity, medium temperature and low humidity, medium temperature and medium humidity, medium temperature and high humidity, high temperature and low humidity, high temperature and medium humidity, and high temperature and high humidity, denoted as Scheme 1 to Scheme 9, respectively.

[0047] ; ; In the formula, For a moment The corresponding temperature level classification results are used to determine whether the current moment is low, medium, or high. This represents the humidity level classification result corresponding to time t, used to determine whether the humidity level is low, medium, or high at that time. and When combined, they can be used to create different temperature and humidity scenario solutions; S4.3 Correlation analysis under various temperature and humidity schemes; For each temperature and humidity scheme, time samples belonging to that scheme are extracted, and the ZTD time series correlation coefficient between the baseline point and each flow point is calculated for that scheme. Since the basic correlation coefficient formula has been given in the aforementioned implementation scheme, it will not be repeated here.

[0048] For the A temperature and humidity scheme was used to filter out highly correlated areas with a correlation coefficient threshold of 0.6, resulting in a set of highly correlated flow points. ; In the formula, For the set of highly correlated flow points, Number the movement points. For the first Under the first scheme ZTD correlation coefficient between each flow point and the baseline point For the first A temperature and humidity scheme; S4.4, Calculation of scheme threshold; Under each temperature and humidity scheme, the absolute value of the relative ZTD between the flow point and the reference point within the highly correlated region is calculated. The definition of relative ZTD has been given in the aforementioned implementation scheme; this section focuses on explaining the threshold calculation method.

[0049] For the One approach is to take the 95th percentile of the absolute value of the relative ZTD in the high-relevance region as the relative ZTD threshold under the given temperature and humidity conditions. ; In the formula, For the first The relative ZTD threshold under a temperature and humidity scheme reflects the upper limit of the relative ZTD difference between the reference point and the flow point under the corresponding temperature and humidity conditions, which can still be considered to have a strong ZTD spatial correlation. It is the 95th percentile. For the first The flow point at the th _ ... The absolute difference of ZTD relative to the reference point at each time point; S4.5, Directional Modeling; Centered on the reference point, the azimuth range from 0° to 360° is divided into 16 equally spaced directional sectors, each sector being 22.5° wide. The calculation methods for inter-station distances and azimuth angles have been given in the aforementioned implementation scheme and will not be repeated here. This invention innovatively proposes that, for each temperature and humidity scheme... and each direction sector We fitted the relationship model (regression model) between relative ZTD and inter-station distance respectively.

[0050] ; In the formula, In the first The temperature and humidity scheme, the first Within the sector of direction, the first The absolute difference of the relative ZTD of each flow point relative to the reference point. For the first Under the first scheme The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; Model parameters can be estimated using the least squares method. By establishing a model of the relationship between relative ZTD and inter-station distance for each sector under each temperature and humidity scheme, the influence of meteorological condition differences and azimuthal spatial differences on atmospheric delay changes can be simultaneously characterized. This model can distinguish the sensitivity of relative ZTD to distance changes under different temperature and humidity combinations, providing a grouped and directional quantitative basis for determining the RTK safety distance under specific meteorological conditions.

[0051] S4.6, Safety Distance Inversion and Spatial Representation.

[0052] The innovative proposal of this invention will... Substituting the relative ZTD threshold under the first temperature and humidity scheme into the first... The regression model in each direction is used to deduce the RTK safety distance in that direction; ; In the formula, For the first The temperature and humidity scheme, the first Safe distance in each direction.

[0053] Through the above calculations, nine sets of safe RTK distances in each direction under different temperature and humidity conditions can be obtained. By... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction can deduce the safe RTK distance under the combined constraints of temperature and humidity conditions and direction. This process transforms the atmospheric delay differences caused by temperature and humidity changes into directly usable distance boundaries, enabling the RTK operating range to be dynamically adjusted according to meteorological conditions and azimuth, thereby improving the precision and reliability of safe distance determination.

[0054] As demonstrated by the above embodiments, the present invention can directly output the RTK safe distance. Compared to schemes that only output tropospheric delay correction, the present invention can provide the distance boundaries around the base station that can be directly located using RTK, facilitating pre-operation planning and real-time determination by the server.

[0055] This invention can describe the azimuth anisotropy of safe distances. It fits the relationship between relative ZTD and distance for each azimuth sector to obtain safe distances in each direction, reflecting directional differences caused by water vapor distribution, geographical location, and atmospheric conditions.

[0056] The threshold determination in this invention is based on statistical evidence. This invention uses a preset quantile of the absolute value of the relative ZTD within a highly correlated region as the threshold, directly linking the safety distance to the spatial correlation of the ZTD, thus avoiding reliance solely on empirical distances.

[0057] This invention can adapt to changes in temperature and humidity. By grouping temperature and humidity separately to retrieve the safety distance, this invention can reflect the trend of shortening RTK safety distance when temperature rises and water vapor activity increases.

[0058] This invention has good scalability. The solution is not limited to a specific region; it can be used to retrain the model using continuous historical ZTD data within the target region to obtain the RTK safety distance for future time periods or business cycles in the corresponding region.

[0059] Example 4.

[0060] This invention provides an RTK safety distance determination system based on relative ZTD, comprising: The data input and spatial unit construction module is used to acquire ZTD data for several consecutive years within the target area. For each set of ZTD data for reference points and mobile points, the spatial distance between stations is calculated. The spatial correlation analysis and threshold determination module is used to perform spatial correlation analysis and determine the relative ZTD threshold based on the calculated inter-station spatial distance. The azimuth partitioning and direction regression modeling module is used to perform azimuth partitioning and direction regression modeling based on the acquired relative ZTD threshold. The safety distance inversion module is used to perform safety distance inversion and output results based on the fitting effect of the regression model between the relative ZTD and the inter-station distance. The RTK safety distance model building module under different temperature and humidity conditions is used to model the obtained safety distance. As temperature and humidity change, the RTK safety distance determination method under temperature and humidity grouping is used to determine the first... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

[0061] Example 5.

[0062] As another embodiment of the present invention, a regional RTK safe distance modeling based on historical ERA5 data is provided; In one embodiment, ERA5 reanalysis data from 2021 to 2023 is used to model the region within Europe, ranging from 10°W to 65°E longitude and 35°N to 60°N latitude. The study area is divided into 75 5° x 5° grids, with the 0.25° grid point at the center of each 5° grid serving as the reference point, and the surrounding 0.25° grid points serving as movement points. Example 1 shows one of the 5° grids. First, calculate the ZTD time series correlation coefficient between each flow point and the baseline point, such as... Figure 4 The ZTD spatial correlation coefficient diagram shows that the flow points with r≥0.6 constitute the high correlation region.

[0063] Secondly, calculate the absolute value of the relative ZTD within the highly correlated region, and take the 95th percentile as the relative ZTD threshold. For example... Figure 5 The schematic diagram of the spatial distribution of relative ZTD thresholds in the study area is shown. The relative ZTD threshold ranges from 0.0189m to 0.0291m.

[0064] Subsequently, the 360-degree azimuth around the benchmark point was divided into 16 directions, each with a width of 22.5 degrees. A linear relationship between the relative ZTD and the inter-station distance was fitted for each direction, and the safe distance for that direction was inverted based on the relative ZTD threshold. The safe distances for each direction of a benchmark point within one grid are shown below. Figure 6 A schematic diagram of the safe distances in each direction from the reference point is shown. In the model fitting results, the maximum coefficient of determination R² was 0.994, the minimum was 0.852, and the mean was 0.971; the maximum spatial variation rate of the relative ZTD was 0.2265 mm / km, the minimum was 0.1319 mm / km, and the mean was 0.1669 mm / km. These results indicate that the relative ZTD has a good linear relationship with the inter-station distance and can be used to invert the RTK safety distance.

[0065] Example 6.

[0066] As another embodiment of the present invention, a safe distance inversion under temperature and humidity grouping is provided; The average temperature and humidity of the reference point and the flow point within each 5-degree by 5-degree grid are taken, and then divided into three levels (low, medium, and high) according to the 33rd and 67th percentiles, forming nine temperature and humidity combination schemes: Table 1 Temperature and Humidity Combination Scheme

[0067] Correlation analysis, threshold determination, and safety distance inversion were performed on nine sets of scenarios respectively. The relative ZTD thresholds for each scheme are as follows: Figure 7 The threshold diagram for temperature and humidity grouping in the study area is shown below; Safety distances of the reference point in various directions under different temperature and humidity combinations Figure 8 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 1. Figure 9 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 2. Figure 10 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 3. Figure 11 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 4. Figure 12 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 5. Figure 13 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 6. Figure 14 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 7. Figure 15 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 8. Figure 16 This is a schematic diagram showing the safe distances of the reference point in various directions under the temperature and humidity combination of Scheme 9. Experimental results show that the RTK safe distance generally decreases with increasing temperature and humidity, with temperature being the dominant factor and humidity having a relatively weak impact. Under high-temperature conditions, the spatial correlation decay of relative ZTD is more pronounced, resulting in a shorter safe distance, and the server needs to compensate through relative ZTD.

[0068] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for determining a safety distance of RTK based on relative ZTD, characterized in that, The method includes the following steps: S1. By dividing the spatial unit into grids, a calculation system is established for the relative ZTD between the reference point and the movement point, the spatial distance between stations, and the azimuth angle of the movement point relative to the reference point, providing standardized input for subsequent spatial correlation analysis between stations and safety distance inversion. S2. Based on the calculated inter-station spatial distance and inter-station relative ZTD, perform spatial correlation analysis between the flow point and the reference point and determine the relative ZTD threshold. S3. Based on the obtained relative ZTD threshold, perform orientation partitioning and direction regression modeling; S4. Based on the fitting effect of the regression model between the relative ZTD and the inter-station distance, perform the safety distance inversion and output the results.

2. The RTK safety distance determination method based on relative ZTD according to claim 1, characterized in that, In step S1, ERA5 is used to analyze ZTD data with an hourly time resolution; the study area is divided into spatial computing units, and the center point of each grid is used as the reference point. Several points within or around the grid are then analyzed. Grid points serve as movement points; let the reference point be... , No. The flow points are ,in, Indicates latitude, Indicates longitude; The relative ZTD between the reference point and the flow point is defined as follows: ； wherein is between the relative ZTD absolute value at time is the ZTD at time is the ZTD of the reference point at the same time;​​​ For each set of reference points and movement points, calculate the spatial distance between stations; use the spherical distance approximation formula: ； ； ； In the formula, The distance between stations. The average radius of the Earth For the first The latitude difference between each migration point and the reference point To obtain the average latitude of the reference point and the movement point, For the first The difference in longitude between each flow point and the reference point. For the first The latitude of each flow point Latitude as the reference point For the first Longitude of each point of movement Longitude as the reference point; Computing an azimuth angle of a flow point relative to a reference point for subsequent azimuth sector division; ； In the formula, For the first The azimuth angle of each flow point relative to the reference point, in degrees, ranges from 0° to 360°; the azimuth angle starts at 0° in the due north direction and increases clockwise.

3. The relative ZTD-based RTK safety distance determination method of claim 2, wherein, In step S2, spatial correlation analysis and determination of the relative ZTD threshold include: The spatial correlation analysis is performed based on the ZTD time series of the reference points and the ZTD time series of the flow points. For the first flow point, the correlation coefficient between the ZTD time series of the flow point and the ZTD time series of the reference points is calculated: r = corr(ZTDref, ZTDflow) ； wherein is the ZTD time series correlation coefficient between the first flowing point and the reference point, is the ZTD time series correlation coefficient between the first flowing point and the reference point, and are the ZTD standard deviation of the first flowing point and the reference point, respectively. Screening the high correlation region with a preset correlation threshold value, taking the flow point as the high correlation sample; the high correlation sample set is represented as: ； In the formula, is a high correlation sample set, is a flow point number, is a correlation coefficient threshold, selected ; In the high-correlation area, the absolute value of relative ZTD between each flow point and the reference point is calculated, and statistical analysis is performed on the sample set to take Quantile as the threshold of relative ZTD: ； wherein is a relative ZTD threshold, is quantile, is a time series sampling time index number, is a total number of sampling times.

4. The relative ZTD-based RTK safety distance determination method of claim 3, wherein, In step S3, the orientation partitioning and direction regression modeling includes: Centered on the reference point, to The directional range is divided into several equally spaced sectors; the first Each sector is represented as: ； In the formula, For the first Each sector, Number the sectors For the number of sectors, ; Based on the azimuth angle of the flow point relative to the reference point Each flow point is assigned to its corresponding sector; for each sector, a regression model is established between the relative ZTD and the inter-station distance, using a linear model: ； In the formula, For the first The absolute value of the relative ZTD difference between each flow point and the reference point For the first The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; Model parameters and The coefficient of determination was calculated based on the fit of the regression model between relative ZTD and inter-station distance using the least squares method. ； In the formula, As the coefficient of determination, These are the model's predicted values. For the first The relative ZTD sample mean within each sector.

5. The RTK safety distance determination method based on relative ZTD according to claim 4, characterized in that, In step S4, the safe distance inversion includes: When the first When the linear regression model fitting effect between relative ZTD and inter-station distance within a sector meets the requirements, the relative ZTD threshold will be set. Substituting this into the model for that direction, we can deduce the corresponding RTK safety distance: ； In the formula, For the first RTK safety distance in each direction; Given a reference point and a target flow point, calculate the distance between the reference point and the target flow point. and azimuth Determine the sector to which it belongs and compare Safety distance in the corresponding direction If the following conditions are met: ； Then it is determined that the movement point is within the safe distance range in the corresponding direction, and meets the conditions for RTK positioning; if If so, the flow point is determined to be outside the safe distance range.

6. The RTK safety distance determination method based on relative ZTD according to claim 5, characterized in that, Regarding the obtained safe distance As temperature and humidity change, the RTK safety distance determination method under temperature and humidity grouping is used to determine the first... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

7. The RTK safety distance determination method based on relative ZTD according to claim 6, characterized in that, The specific methods for determining RTK safety distance under temperature and humidity grouping include: S4.1 Data Foundations and Grid Statistics; S4.2, three-part hierarchical division and nine scene combinations; S4.3 Correlation analysis under various temperature and humidity schemes; S4.4, Calculation of scheme threshold; S4.5, Directional Modeling; S4.6, Safety Distance Inversion and Spatial Representation.

8. The RTK safety distance determination method based on relative ZTD according to claim 7, characterized in that, In step S4.1, the data foundation and grid statistics include: For each grid cell, calculate the temperature and humidity sequences within that grid cell, and take the 33rd and 67th percentiles of temperature and humidity, respectively, as the basis for classifying them as low, medium, and high levels. ； ； In the formula, It is a temperature sequence. It is a humidity sequence. Temperature series at the 33rd percentile Temperature series at the 67th percentile The humidity sequence is at the 33rd percentile. The humidity sequence is at the 67th percentile. (·)and (·) are the 33rd and 67th percentiles, respectively; In step S4.2, the three-part hierarchical classification and the nine scene combinations include: Based on temperature quantiles, temperatures are divided into three levels: low, medium, and high; based on humidity quantiles, humidity is divided into three levels: low, medium, and high. The combination of temperature and humidity levels forms nine experimental schemes, namely, low temperature and low humidity, low temperature and medium humidity, low temperature and high humidity, medium temperature and medium humidity, medium temperature and high humidity, high temperature and low humidity, high temperature and medium humidity, and high temperature and high humidity, which are respectively denoted as Scheme 1 to Scheme 9. ； ； In the formula, For a moment The corresponding temperature level classification results are used to determine whether the current moment is low, medium, or high. This represents the humidity level classification result corresponding to time t, used to determine whether the humidity level is low, medium, or high at that time. and When combined, they can be used to create different temperature and humidity scenario solutions; In step S4.3, the correlation analysis under each temperature and humidity scheme includes: For the A temperature and humidity scheme was used to filter out highly correlated areas with a correlation coefficient threshold of 0.6, resulting in a set of highly correlated flow points. ； In the formula, For the set of highly correlated flow points, Number the movement points. For the first Under the first scheme ZTD correlation coefficient between each flow point and the baseline point For the first A temperature and humidity scheme; In step S4.4, the scheme threshold calculation includes: For the One approach is to take the 95th percentile of the absolute value of the relative ZTD in the high-relevance region as the relative ZTD threshold under the given temperature and humidity conditions. ； In the formula, For the first The relative ZTD threshold under each temperature and humidity scheme It is the 95th percentile. For the first The flow point at the th _ ... The absolute difference of ZTD relative to the reference point at each time point; In step S4.5, orientation modeling includes: For each temperature and humidity scheme and each direction sector The relationship models between relative ZTD and inter-station distance were fitted respectively; ； In the formula, In the first The temperature and humidity scheme, the first Within the sector of direction, the first The absolute difference of the relative ZTD of each flow point relative to the reference point. For the first Under the first scheme The relative ZTD spatial rate of change in each direction For the intercept term, This is the random error term; In step S4.6, the safety distance inversion and spatial representation include: The first Substituting the relative ZTD threshold under the first temperature and humidity scheme into the first... The regression model in each direction is used to deduce the RTK safety distance in that direction; ； In the formula, For the first The temperature and humidity scheme, the first Safe distance in each direction.

9. A RTK safety distance determination system based on relative ZTD, characterized in that, The system implements the RTK safety distance determination method based on relative ZTD as described in any one of claims 1-8, and the system includes: The data input and spatial unit construction module is used to acquire ZTD data for several consecutive years within the target area. For each set of ZTD data for reference points and mobile points, the spatial distance between stations is calculated. The spatial correlation analysis and threshold determination module is used to perform spatial correlation analysis and determine the relative ZTD threshold based on the calculated inter-station spatial distance. The azimuth partitioning and direction regression modeling module is used to perform azimuth partitioning and direction regression modeling based on the acquired relative ZTD threshold. The safety distance inversion module is used to perform safety distance inversion and output results based on the fitting effect of the regression model between the relative ZTD and the inter-station distance.

10. The RTK safety distance determination system based on relative ZTD according to claim 9, characterized in that, The RTK safe distance determination system based on relative ZTD also includes: The RTK safety distance model building module under different temperature and humidity conditions is used to model the obtained safety distance. As temperature and humidity change, the RTK safety distance determination method under temperature and humidity grouping is used to determine the first... Substituting the relative ZTD threshold corresponding to the temperature and humidity scheme into the first... The regression model in each direction is used to deduce the safe distance for RTK under the combined constraints of temperature and humidity conditions and direction, so that the RTK operation range can be dynamically adjusted according to meteorological conditions and azimuth, and the safe distance can be determined in a refined manner.

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