Method, system and device for correcting tropospheric errors based on beidou satellite signals

Abstract

This application provides a method, system, and device for tropospheric error correction based on BeiDou satellite signals. The method includes: deploying multiple reference stations within a preset coverage area to receive pseudorange and carrier phase observation data from BeiDou satellites, performing gross error elimination and cycle slip detection on the observation data, and constructing an ionospheric-free combined observation equation; combining real-time precise ephemeris and satellite clock bias, calculating the total zenith tropospheric delay of each reference station using precise single-point positioning technology, and obtaining the zenith wet delay using barometric pressure data and an empirical model; further summarizing the wet delay information from multiple reference stations, and establishing a regional wet delay model by combining topographic factors such as altitude, and converting the zenith delay into a tropospheric correction in the satellite line-of-sight direction using a mapping function. This invention can achieve high-precision tropospheric error modeling and correction under high-altitude and complex terrain conditions, and is applicable to power grid inspection, transmission line monitoring, and high-precision positioning services for BeiDou terminals.

Description

Technical Field

[0001] This application relates to the field of BeiDou satellite positioning and correction technology, and in particular to a tropospheric error correction method, system and device based on BeiDou satellite signals. Background Technology

[0002] With the continuous improvement of the BeiDou Navigation Satellite System and the widespread application of high-precision positioning technology in power grid inspection, transmission line monitoring, and smart grid operation and maintenance, the demand for high-precision, real-time satellite positioning services in power grid systems is constantly increasing. Especially in scenarios such as mountainous transmission lines, cross-regional power grid facility inspection, and emergency communication, a high-precision positioning service system is often required, relying on BeiDou satellite signals and a network of ground-based reference stations. However, in high-altitude or complex terrain areas, there are usually significant elevation differences between reference stations, resulting in a marked non-uniformity in the spatial distribution of atmospheric tropospheric delay, which significantly affects the propagation path of satellite signals. If tropospheric errors cannot be effectively modeled and corrected in real time, the stability and accuracy of positioning calculations will be directly reduced, affecting the positioning performance of power grid inspection terminals, drone equipment, and BeiDou communication terminals.

[0003] In related technologies, common network RTK or differential positioning methods typically establish error correction models using relative observation data between reference stations to mitigate the impact of atmospheric errors such as ionospheric and tropospheric errors. However, these methods often rely on the assumption that the atmospheric environment is approximately uniform between reference stations. When reference stations are distributed in mountainous areas with significant elevation differences or complex terrain, this assumption becomes difficult to hold, leading to a decrease in the accuracy of tropospheric error modeling. This, in turn, increases the difficulty of fixing baseline ambiguity and reduces positioning reliability. Summary of the Invention

[0004] In view of this, it is necessary to provide a tropospheric error correction method, system and equipment based on BeiDou satellite signals, which can at least overcome one of the above defects.

[0005] In a first aspect, embodiments of this application provide a tropospheric error correction method based on BeiDou satellite signals, the method comprising:

[0006] Multiple reference stations are deployed within a preset coverage area. Each reference station is used to receive raw pseudorange and carrier phase observation data from BeiDou satellites and to collect air pressure data at the location of each reference station.

[0007] Gross errors were removed and cycle slips were detected in the original pseudorange and carrier phase observation data, and an ionospheric-free combined observation equation was constructed to eliminate the influence of first-order ionospheric delay.

[0008] Obtain real-time precise ephemeris and satellite clock bias;

[0009] Based on the real-time precise ephemeris and the satellite clock difference, precise single-point positioning calculations are performed on each of the reference stations to output the absolute zenith tropospheric total delay and covariance of each of the reference stations. The calculated parameters include zenith tropospheric total delay and digital elevation model data modeled by a random walk model.

[0010] The zenith dry delay of each reference station is calculated based on a preset empirical model and the air pressure data, and the zenith dry delay is subtracted from the total zenith tropospheric delay to obtain the zenith wet delay of each reference station.

[0011] The zenith wet delay of multiple reference stations at the same epoch is aggregated, and a regional wet delay model is established based on the aggregated zenith wet delay and topographic intervention factors. The topographic intervention factors include the elevation information and digital elevation model of each reference station.

[0012] Based on the aforementioned regional wet delay model, a mapping function is applied to map the zenith direction delay to the tropospheric correction in the satellite direction, and then the result is sent to the terminal.

[0013] In one embodiment, the step of performing precise single-point positioning calculations for each of the reference stations based on the real-time precise ephemeris and the satellite clock difference includes:

[0014] Kalman filtering is applied to estimate the state vector of each of the reference stations. The state vector includes the receiver's three-dimensional coordinates, receiver clock error, total zenith tropospheric delay, and carrier phase integer ambiguity at each frequency.

[0015] The carrier phase integer ambiguity is a constant parameter under cycle slip-free observation conditions. If a cycle slip is detected, the corresponding ambiguity parameter is reset.

[0016] In one embodiment, the method further includes:

[0017] The air pressure data is obtained based on the measured values ​​of the meteorological sensors built into each of the base stations or the interpolated estimates of the numerical weather prediction models.

[0018] When calculating the zenith dry delay, the preset empirical model incorporates the latitude and altitude parameters of the reference station to calculate the dry delay component affected by geographical location and gravitational acceleration.

[0019] In one embodiment, establishing a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors includes:

[0020] By applying Kriging interpolation or a multinomial regression method based on station height, discretely distributed wet delay observations from benchmark stations are transformed into a continuous distribution field covering the entire region, wherein the terrain constraint factor of the regional wet delay model includes a digital elevation model.

[0021] The regional wet delay model generates gridded tropospheric correction data according to a preset spatial resolution.

[0022] In one embodiment, the application mapping function maps the zenith direction delay to a tropospheric correction in the satellite direction, including:

[0023] A mapping function is used to map the zenith direction delay into a correction for the satellite line-of-sight direction;

[0024] The correction amount is sent to the terminal via the BeiDou satellite short message communication network;

[0025] In response to the residual of the ionosphere-free combined observation equation exceeding a preset threshold, an abnormal satellite data removal operation is performed.

[0026] In one embodiment, the method further includes:

[0027] The zenith wet delay is converted into columnar water vapor content according to a preset conversion coefficient;

[0028] The columnar water vapor content of multiple reference stations within the preset coverage area is summarized, and regional atmospheric water vapor distribution field data is generated and output using a spatial interpolation method.

[0029] In one embodiment, the method further includes:

[0030] The conversion coefficient is determined based on the weighted average temperature of the atmosphere;

[0031] The atmospheric weighted average temperature is estimated in real time based on the measured surface temperature, air pressure, and water vapor pressure parameters of each of the reference stations and a regression model established based on the historical meteorological statistics of the region, in order to correct the impact of changes in ambient temperature on the accuracy of water vapor conversion.

[0032] In one embodiment, the method further includes:

[0033] Monitor the residuals of combined observations without ionosphere and the model residuals of the wet delay model for the region;

[0034] In response to the fact that the observation residuals of the ionosphere-free combined observations and the model residuals exceed a preset threshold, an anomaly handling process is triggered.

[0035] The anomaly handling process includes: removing satellite observations or base station observations with residual anomalies, adaptively adjusting the process noise and observation weights of the Kalman filter, increasing the update frequency of the regional model, and re-modeling the regional wet delay.

[0036] Secondly, one embodiment of this application provides a tropospheric error correction system based on BeiDou satellite signals, the system comprising:

[0037] The information receiving module is used to receive the raw pseudorange and carrier phase observation data of Beidou satellites from multiple reference stations within a preset coverage area, and to collect the air pressure data and digital elevation model data of the location of each reference station.

[0038] The information processing module is used to perform gross error removal and cycle slip detection on the original pseudorange and carrier phase observation data, and to construct an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay; and to obtain real-time precise ephemeris and satellite clock bias.

[0039] The calculation module is used to perform precise single-point positioning calculations on each of the reference stations based on the real-time precise ephemeris and the satellite clock difference, so as to output the absolute zenith tropospheric total delay and covariance of each of the reference stations. The calculation parameters include the zenith tropospheric total delay modeled by a random walk model.

[0040] The model generation module is used to calculate the zenith dry delay of each of the reference stations based on a preset empirical model and the air pressure data, and to subtract the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay of each of the reference stations; to summarize the zenith wet delay of multiple reference stations at the same epoch, and to establish a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors, wherein the topographic intervention factors include the altitude information and digital elevation model of each reference station.

[0041] The tropospheric correction output module is used to map the zenith direction delay to the tropospheric correction in the satellite direction based on the regional wet delay model and apply a mapping function, and then send the correction to the terminal.

[0042] Thirdly, embodiments of this application provide an electronic device, including:

[0043] Processor; and

[0044] The memory stores computer-readable instructions for controlling the processor to execute the tropospheric error correction method based on BeiDou satellite signals as described in the first aspect.

[0045] This application provides a tropospheric error correction method, system, and device based on BeiDou satellite signals. By deploying multiple reference stations within the coverage area and collecting pseudorange and carrier phase observation data from BeiDou satellites, and after gross error removal and cycle slip detection of the observation data, an ionospheric-free combined observation equation is constructed. Real-time precise ephemeris and satellite clock bias are introduced for precise single-point positioning calculations, thereby obtaining stable zenith tropospheric total delay parameters for each reference station. Furthermore, by combining barometric pressure data and empirical models, zenith dry delay and zenith wet delay are separated. A regional wet delay model is constructed using wet delay information from multiple reference stations and terrain intervention factors such as altitude, enabling high-precision tropospheric error modeling even under high-altitude and complex terrain conditions. This effectively improves the stability and reliability of tropospheric error estimation, significantly enhancing the continuity and accuracy of high-precision positioning services in scenarios such as mountain power grid inspection, transmission line monitoring, and BeiDou communication terminal positioning. Attached Figure Description

[0046] Figure 1 This is a schematic flowchart of a tropospheric error correction method based on BeiDou satellite signals provided in an embodiment of this application.

[0047] Figure 2 A schematic diagram of a tropospheric error correction system based on BeiDou satellite signals is provided for one embodiment of this application.

[0048] Figure 3 This is a schematic diagram of the modules of an electronic device provided in an embodiment of this application.

[0049] Explanation of main component symbols

[0050] Detailed Implementation

[0051] 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 a part of the embodiments of this application, and not all of them.

[0052] It should be noted that, in the embodiments of this application, "at least one" refers to one or more, and "more than one" refers to two or more. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the specification of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application.

[0053] It should be noted that in the embodiments of this application, the terms "first," "second," etc., are used only for descriptive purposes and should not be construed as indicating or implying relative importance, nor as indicating or implying order. Features specified as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0054] Based on the embodiments described in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0055] With the continuous improvement of the BeiDou Navigation Satellite System and the widespread application of high-precision positioning technology in power grid inspection, transmission line monitoring, and smart grid operation and maintenance, the demand for high-precision, real-time satellite positioning services in power grid systems is constantly increasing. Especially in scenarios such as mountainous transmission lines, cross-regional power grid facility inspection, and emergency communication, a high-precision positioning service system is often required, relying on BeiDou satellite signals and a network of ground-based reference stations. However, in high-altitude or complex terrain areas, there are usually significant elevation differences between reference stations, resulting in a marked non-uniformity in the spatial distribution of atmospheric tropospheric delay, which significantly affects the propagation path of satellite signals. If tropospheric errors cannot be effectively modeled and corrected in real time, the stability and accuracy of positioning calculations will be directly reduced, affecting the positioning performance of power grid inspection terminals, drone equipment, and BeiDou communication terminals.

[0056] In related technologies, common network RTK or differential positioning methods typically establish error correction models using relative observation data between reference stations to mitigate the impact of atmospheric errors such as ionospheric and tropospheric errors. However, these methods often rely on the assumption that the atmospheric environment is approximately uniform between reference stations. When reference stations are distributed in mountainous areas with significant elevation differences or complex terrain, this assumption becomes difficult to hold, leading to a decrease in the accuracy of tropospheric error modeling. This increases the difficulty of fixing baseline ambiguity and reduces positioning reliability. Therefore, there is an urgent need for a technical solution that can achieve high-precision tropospheric delay estimation and real-time correction under complex terrain conditions to improve the high-precision positioning service capabilities based on BeiDou satellite signals.

[0057] In view of this, the tropospheric error correction method, system, and equipment based on BeiDou satellite signals provided in this application, by deploying multiple reference stations within the coverage area and collecting pseudorange and carrier phase observation data of BeiDou satellites, constructs an ionospheric-free combined observation equation after gross error removal and cycle slip detection of the observation data, and introduces real-time precise ephemeris and satellite clock bias for precise single-point positioning calculation, thereby obtaining stable zenith tropospheric total delay parameters for each reference station; further, by combining barometric pressure data and empirical models to separate zenith dry delay and zenith wet delay, and by using wet delay information from multiple reference stations and terrain intervention factors such as altitude to construct a regional wet delay model, enabling the correction of tropospheric errors at high altitudes and complex terrain. High-precision tropospheric error modeling can still be achieved under complex terrain conditions. Simultaneously, by mapping the zenith delay to a tropospheric correction in the satellite line-of-sight direction using a mapping function, and transmitting this correction to the terminal via the BeiDou short message communication network, real-time correction of user positioning is achieved. Furthermore, by jointly estimating coordinate parameters, receiver clock bias, tropospheric parameters, and ambiguity parameters using Kalman filtering, and combining this with anomaly residual monitoring, adaptive parameter adjustment, and a correction service quality control mechanism, the stability and reliability of tropospheric error estimation can be effectively improved. This significantly enhances the continuity and accuracy of high-precision positioning services in scenarios such as mountain power grid inspection, transmission line monitoring, and BeiDou communication terminal positioning.

[0058] Figure 1 This is a schematic flowchart of a tropospheric error correction method based on BeiDou satellite signals provided in an embodiment of this application. Figure 1 The tropospheric error correction method based on BeiDou satellite signals, as shown, includes at least the following steps: S100: Deploying multiple reference stations within a preset coverage area, each reference station is used to receive raw pseudorange and carrier phase observation data from BeiDou satellites and to collect air pressure data at the location of each reference station; S200: Performing gross error removal and cycle slip detection on the raw pseudorange and carrier phase observation data, and constructing an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay; S300: Obtaining real-time precise ephemeris and satellite clock bias; S400: Performing precise single-point calibration on each reference station based on the real-time precise ephemeris and satellite clock bias. The system performs location calculations to output the absolute zenith tropospheric total delay and covariance for each reference station; S500: Calculates the zenith dry delay for each reference station based on a preset empirical model and barometric pressure data, and subtracts the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay for each reference station; S600: Aggregates the zenith wet delays of multiple reference stations at the same epoch, and establishes a regional wet delay model and a digital elevation model based on the aggregated zenith wet delay and topographic intervention factors; S700: Based on the regional wet delay model, applies a mapping function to map the zenith direction delay to the tropospheric correction in the satellite direction, and sends it to the terminal.

[0059] S100: Multiple reference stations are deployed within a preset coverage area. Each reference station is used to receive raw pseudorange and carrier phase observation data from BeiDou satellites, and to collect air pressure data and digital elevation model data at the location of each reference station.

[0060] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes step S100, which involves setting up multiple reference stations within a preset coverage area. Each reference station is used to receive the raw pseudorange and carrier phase observation data of BeiDou satellites and to collect the air pressure data and digital elevation model data of the location of each reference station.

[0061] Specifically, each base station is equipped with at least a dual-frequency (or multi-frequency) BeiDou receiver and a high-precision clock to record pseudorange at a uniform sampling rate (e.g., 1Hz or the frequency required for the project). With carrier phase (where subscript) Indicates frequency channel, such as Each base station is equipped with or connected to meteorological sensors, including at least real-time air pressure. (Unit: hPa), Temperature (°C or K) and relative humidity RH are used for subsequent ZHD calculations and ZWD→PWV conversion; if there is no measured air pressure in a local area, the air pressure value can be estimated by interpolation using nearby meteorological stations or numerical weather prediction (NWP); the geographical coordinates (longitude, latitude, normal altitude / altitude) of each reference station must be accurately measured or determined in advance and uploaded together in the data message for subsequent modeling.

[0062] Understandably, the number and distribution of reference stations should meet the required spatial sampling resolution: the larger the coverage area or the stronger the spatial variability of the troposphere, the higher the required density of reference stations; in areas with dramatic elevation differences, priority should be given to increasing the number of stations along the elevation gradient direction to capture altitude dependence; the collection frequency and accuracy of meteorological quantities such as air pressure directly affect the accuracy of ZHD calculation, and it is recommended that the accuracy of air pressure sensors be within ±0.5 hPa to ensure that the ZHD calculation error is controllable; each reference station must ensure that the observation time is synchronized (or record the timestamp and unify it to the same time scale) so that ZTD / ZWD can be summarized by epoch.

[0063] S200: Perform gross error removal and cycle slip detection on the original pseudorange and carrier phase observation data, and construct an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay.

[0064] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes step S200, which involves removing gross errors and detecting cycle slips in the original pseudorange and carrier phase observation data, and constructing an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay.

[0065] Specifically, gross error checks are performed on the original observations: anomalous pseudorange / phase observations are eliminated based on observation residual statistics, signal-to-noise ratio (SNR) thresholds, and satellite geometric forcing conditions. Cycle slip detection and repair are implemented on the carrier phase observations (e.g., continuous phase difference method, differential method, or cycle slip detection based on double difference); if a cycle slip is detected, the epoch of the cycle slip occurrence is recorded, and the corresponding ambiguity parameters are reset or segmented in subsequent filtering. An ionosphere-free (IF) linear combination is constructed for two-frequency observations. (Unit: Hz), construct the IF pseudorange and phase combination as follows:

[0066]

[0067] In the formula Frequency The pseudorange and carrier phase observations (equivalent values ​​in meters or first converted to meters) are used to eliminate the first-order ionospheric delay term.

[0068] Understandably, ionospheric-free combinations can effectively offset the first-order ionospheric delay, but still retain higher-order ionospheric residuals (which may increase during periods of ionospheric activity). Furthermore, the observation noise is amplified after combination (the combined noise is a weighted sum of the original noise). Therefore, when constructing IF observations, the observation weights need to be adjusted, and an adaptive strategy should be adopted during periods of ionospheric activity. The "ambiguity" corresponding to the carrier-phase combination obtained by IF combination is no longer a simple linear integer of the original frequency, but a constant term under the frequency combination (which can be regarded as a constant deviation to be estimated). In PPP, this is usually treated as a parameter to be estimated during filtering.

[0069] S300: Acquires real-time precise ephemeris and satellite clock bias.

[0070] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes, in step S300, acquiring real-time precise ephemeris and satellite clock bias.

[0071] Specifically, the system accesses real-time precise ephemeris and satellite clock bias streams (provided by regional or global precision product providers). At each positioning epoch, precise satellite orbit corrections and clock bias corrections are applied to the observation equations to reduce positioning errors caused by orbit and satellite clock bias. After using precise ephemeris / clock bias, satellite orbit and clock bias can be considered as corrected terms in the Kalman-filtered observation equations, thus focusing the main unknowns in the observation equations on receiver parameters such as receiver clock bias, tropospheric delay, and ambiguity.

[0072] Understandably, introducing precise ephemeris and clock bias can significantly reduce the impact of satellite-end errors on the calculation of parameters such as ZTD, accelerate filter convergence, and improve estimation accuracy. The availability, latency, and quality of real-time precision products will affect the final correction accuracy; therefore, in engineering practice, the availability of precision sources should be monitored and backup source switching should be implemented.

[0073] S400: Based on real-time precise ephemeris and satellite clock bias, perform precise single-point positioning calculations for each reference station to output the absolute zenith tropospheric total delay and covariance of each reference station.

[0074] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes step S400, which involves performing precise single-point positioning calculations on each reference station based on real-time precise ephemeris and satellite clock bias, so as to output the absolute zenith tropospheric total delay and covariance of each reference station. The calculated parameters include the zenith tropospheric total delay modeled by a random walk model.

[0075] Specifically, the Kalman filter state vector is constructed, including:

[0076]

[0077] in The receiver's three-dimensional coordinates (in meters) are given. The receiver clock error (in seconds) Total zenith tropospheric delay (meters) This is the ambiguity constant term under ionospheric non-combination (meter equivalent). The observation equations take the pseudorange and phase of the IF combination as inputs, and the pseudorange and phase observation equations can be expressed as (see S200):

[0078]

[0079]

[0080] in The satellite-receiver geometric distance (m) is given. At the speed of light, For satellite clock bias (s, which has been corrected with precision clock bias or is a known correction term), The tropospheric mapping function used for pseudorange / phase (often the same mapping function can be used) ), For systematic error terms such as multipath, To observe noise; This represents the combined equivalent frequency factor, used to convert combined ambiguities to meters (the equivalent conversion factor used in engineering implementation is explicitly defined). For states... A random walk process noise model is adopted (i.e., the process noise variance of the ZTD in its process noise matrix is ​​non-zero to reflect the characteristics of wet delay changing with time); a smaller process noise or white noise model can be used for coordinates and clock errors; ambiguity is considered constant when there are no cycle slips (process noise is approximately zero), and if a cycle slip is detected, a reset or segmented reassessment is performed. The Kalman filter recursively outputs the current epoch of each reference station. and its covariance matrix This covariance is used for weight allocation and confidence output in subsequent regional modeling.

[0081] Understandably, by As a direct estimate of the filtered state, it can obtain an absolute (non-differential) estimate of tropospheric delay, suitable for scenarios with significant elevation differences between reference stations without relying on the assumption of similar elevations. The random walk model can capture the continuous change of wet delay over time, but its process noise variance needs to be adjusted experimentally or empirically to balance response speed and estimation noise. The output covariance is an important weighting indicator for spatial interpolation and fusion; a smaller covariance indicates a greater contribution of the station's ZTD.

[0082] S500: Calculate the zenith dry delay of each reference station based on the preset empirical model and air pressure data, and subtract the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay of each reference station.

[0083] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes, in step S500, calculating the zenith dry delay of each reference station according to a preset empirical model and air pressure data, and subtracting the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay of each reference station.

[0084] Specifically, the zenith dry delay (ZHD) is calculated using the Saastamoinen type or equivalent empirical formula:

[0085]

[0086] in The air pressure at the station is expressed in hPa. The latitude (in radians) of the station. The station's altitude (units consistent with the formula, commonly kilometers or meters with constant adjustments), constant The unit is m / hPa. (Zenith wet delay) by and The difference is:

[0087]

[0088] Understandably, ZHD is primarily influenced by air pressure and the Earth's gravitational field, and its calculation accuracy depends on the accuracy of air pressure measurements or estimations. If local air pressure observations are unavailable, interpolation from nearby weather stations or NWPs should be prioritized, and their uncertainties should be assessed to evaluate their impact on ZHD. By decomposing ZTD into ZHD and ZWD, most of the predictable static delay (ZHD) can be extracted, allowing subsequent regional wet delay modeling to focus more on the rapidly changing wet delay (ZWD) over time and space, thereby improving the model's sensitivity and accuracy to water vapor fields.

[0089] S600: Aggregates zenith wet delay data from multiple reference stations at the same epoch, and establishes regional wet delay and digital elevation models based on the aggregated zenith wet delay and topographic intervention factors.

[0090] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes step S600, which involves summarizing the zenith wet delay of multiple reference stations at the same epoch, and establishing a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors. The topographic intervention factors include the altitude information of each reference station.

[0091] Specifically, data from all reference stations are collected according to epochs. and its covariance (where subscript) (Indicates the station number). Choose an appropriate spatial interpolation / regression method to establish a continuous regional wet delay field. Common methods include: Kriging: estimating the spatial covariance parameter based on the inter-station semivariance function, using the covariance matrix and observed covariance to perform weighted interpolation and output confidence intervals; and height-based multinomial regression: establishing a system such as... The regression model and fitting coefficients are used, explicitly incorporating altitude as an intervention factor; gridded least squares: a grid is generated according to a preset spatial resolution (e.g., 1km), and the least squares fitting value is calculated for each grid, with a DEM (Digital Elevation Model) introduced as an additional constraint. During interpolation / regression, the covariance of each station is used as a weight: stations with smaller covariance have higher weights. The greater the contribution to the model, the better; abnormal sites can be removed or have their weights reduced. The output regional wet delay model is a spatiotemporal field. It can also generate gridded correction products according to preset spatial resolution.

[0092] Understandably, in areas with significant elevation differences, simple spatial interpolation may introduce highly correlated biases. Introducing altitude (or DEM) as a regression factor can significantly reduce systematic errors caused by topography. The Kriging method performs well when spatial autocorrelation is strong and station density is appropriate, but careful selection of the semivariogram model and separation of temporal correlations are necessary. The update time of the regional model (minutes or less) should be set according to the rate of weather change and engineering requirements; under severe convective weather, it is recommended to increase the update frequency to ensure real-time performance.

[0093] S700: Based on the regional wet delay model, a mapping function is applied to map the zenith delay to the tropospheric correction in the satellite direction, and then the data is sent to the terminal.

[0094] In this embodiment of the application, the tropospheric error correction method based on BeiDou satellite signals includes step S700, which involves applying a mapping function to map the zenith direction delay to the tropospheric correction amount in the satellite direction according to the regional wet delay model, and then sending the correction to the terminal.

[0095] Specifically, for a given satellite at a certain reference station or grid point, the elevation angle... (Units are degrees or radians), using a mapping function. Mapping the zenith wet delay or total zenith delay to the satellite line-of-sight direction:

[0096]

[0097] The above calculations obtained by grid or station The message is sent to the terminal in real time (e.g., RTCMSSR convection layer correction type or customized short message / JSON), and the terminal will perform the localization / resolution process. Subtract from the observations or input as a correction to the local filter.

[0098] Understandably, the choice of mapping function directly affects the accuracy of low elevation angle corrections. Therefore, NMF, VMF1, or NWP-based mapping functions can be used to ensure low-angle accuracy. The distributed tropospheric correction should also carry confidence information (e.g., covariance or uncertainty estimates from the region model) so that the terminal can perform weight adjustments or quality control during fusion calculations. When communication resources are limited, differential compression or gridded representative points can be distributed and interpolated at the terminal to save bandwidth.

[0099] In this embodiment, precise single-point positioning calculations are performed on each reference station based on real-time precise ephemeris and satellite clock bias. This includes: applying Kalman filtering to estimate the state vector of each reference station. The state vector includes the receiver's three-dimensional coordinates, receiver clock bias, total zenith tropospheric delay, and carrier phase integer ambiguity for each frequency. The carrier phase integer ambiguity is treated as a constant parameter under cycle-slip-free observation conditions; if a cycle slip is detected, the corresponding ambiguity parameter is reset.

[0100] Specifically, the discrete-time Kalman filter (or extended / unscented Kalman filter, depending on the degree of nonlinearity) is constructed, and its state vector is represented as:

[0101]

[0102] in The receiver's rectangular coordinates (meters) are used. Receiver clock error (seconds); Total zenith tropospheric delay (meters); The equivalent value of ambiguity under ionosphere-free combination (expressed in meters or period equivalents, and uniformly converted in engineering).

[0103] The state transition and observation equations are respectively in matrix form:

[0104] State transition (process) equations:

[0105]

[0106] Observation equation:

[0107]

[0108] in The state transition matrix (in most implementations, an approximate constant model is used for position coordinates and clock error, and a unit continuation plus random walk term is used for ZTD). The observation matrix is ​​obtained by combining the geometric derivative and the mapping function term. and These represent process noise and observation noise, respectively, with covariance of... , .

[0109] right Using a random walk model, that is, in The ZTD component is approximated with unity gain, and the process noise variance is taken as positive to reflect the characteristics of wet delay changing with time; for coordinates and clock errors, a smaller process noise or white noise model can be used to reflect their slow changing properties; for ambiguity... Under cycle slip-free conditions, near-zero process noise is set (keeping constant). If a cycle slip is detected, the ambiguity state is reset and the estimated covariance is reinitialized at the corresponding epoch.

[0110] The observation equations are refined into pseudorange and carrier phase equations in ionosphere-free combination form:

[0111]

[0112]

[0113] in: The satellite-receiver geometric distance (m); For the speed of light ( m / s); For satellite clock bias (s, which is a known correction term or a small residual after being corrected using precision clock bias); The pseudorange / phase mapping function (often unified as) ); This includes systematic errors such as multipath errors; To observe noise; This is the ionosphere-free combined equivalent frequency factor (used to convert the combined ambiguity to meters for representation in the equation).

[0114] Understandable (Process noise) and (Observation noise) needs to be adjusted according to receiver type, observation quality, and field environment. The process noise of ZTD should not be too low, otherwise the filter cannot track rapid changes in wet delay in time; if it is too high, the estimation noise will increase. It is recommended to adjust parameters through offline experiments or adaptive methods. Ambiguity In the IF combination, this is the combinational constant term; when a cycle slip occurs, the state should be segmented and the cycle slip time recorded within the filter to ensure phase continuity management. The Kalman filter output... The corresponding covariance matrix is ​​an important source of weights for subsequent region fusion / interpolation. The filter should output the covariance of each epoch so that weighted fusion can be performed during spatial interpolation.

[0115] In this embodiment of the application, the method further includes: obtaining air pressure data based on measured values ​​from meteorological sensors built into each reference station or interpolated estimates from numerical weather prediction models. When calculating the zenith dry delay, a preset empirical model incorporates the latitude and altitude parameters of the reference station to calculate the dry delay component affected by geographical location and gravitational acceleration.

[0116] Specifically, the ground air pressure measured directly by the built-in barometric pressure sensor at the base station is given priority. (Unit: hPa); If the base station does not have real-time air pressure observations, spatial interpolation estimation is performed by interpolating data from nearby meteorological stations or by calling numerical weather prediction (NWP) fields. Altitude correction and the exponential / linear relationship between air pressure and altitude should be considered during interpolation. The zenith dry delay (ZHD) is calculated using the Saastamoinen empirical formula:

[0117]

[0118] in The surface pressure of the station (hPa); The latitude (in radians) of the station; The station's altitude (units consistent with constants—usually expressed in kilometers, or adjusted when expressed in meters); constant The unit is m / hPa. The Kalman filter estimates... With the calculated Subtract to obtain the zenith wet delay:

[0119]

[0120] Understandably, the main uncertainty of ZHD comes from air pressure. Measurement or estimation error; air pressure error This will cause ZHD to be approximately The absolute error (in meters) is considered, therefore it is recommended that the accuracy of the barometric pressure sensor be better than ±0.5 hPa or that high-quality interpolation be used and the relevant uncertainty be specified. Latitude and altitude parameters are introduced because the Earth's gravity and static distribution vary with latitude and altitude; the Saastamoinen formula is used... and The items should be revised based on experience; during implementation, the unit's agreement should be explained (e.g., Use km or m to avoid calculation ambiguity. If it is necessary to convert ZWD to columnar water vapor content PWV, empirical relationships can be used. The conversion factor Dependent on atmospheric weighted average temperature (Can be estimated by NWP or regression).

[0121] In this embodiment, a regional wet delay model is established based on the aggregated zenith wet delay and topographic intervention factors. This includes: applying Kriging interpolation or a multinomial regression method based on station height to convert discretely distributed base station wet delay observations into a continuous distribution field covering the entire region. The topographic constraint factors of the regional wet delay model include a digital elevation model (DEM). The regional wet delay model generates gridded tropospheric correction data according to a preset spatial resolution.

[0122] Specifically, let's assume that at a certain epoch, [the following data was collected]. Wet delay observations and covariance for each reference station: .

[0123] Kriging interpolation prediction form: at the target location The predicted value in (latitude / longitude / projected coordinates) is

[0124]

[0125] in , The inter-station covariance matrix (generated by the semivariance function or covariance model, containing the observation covariance of each station). (diagonal items) This represents the covariance vector between the target point and each station. Kriging can also provide the prediction variance for confidence assessment.

[0126] Polynomial regression based on height can be expressed as:

[0127]

[0128] in For position Elevation at the location (read from DEM). For regression coefficients, The residuals are given. The coefficients are estimated using weighted least squares (the weights are given by the observation covariance).

[0129] A regular grid is generated in the coverage area according to a preset spatial resolution (e.g., 1km × 1km or set according to project needs), and calculations are performed on each grid point. With corresponding confidence levels, a gridded area wet delay product is formed.

[0130] Understandably, the choice between kriging and regression methods depends on site density, regional heterogeneity, and real-time requirements: kriging performs well when sites are dense and spatial autocorrelation can be modeled, but it is computationally expensive; height-based regression methods are robust and computationally simple when sites are sparse but terrain is dominant; in engineering practice, a hybrid approach can be used (first regress to detrend, then krig the residuals). During interpolation / regression, the covariance of each station should be used as a weight to reduce the adverse effects of low-quality sites (high variance) on the model; outliers (such as sites with excessively large covariance or significant deviations) should be removed or processed through iterative reweighting. The output grid should include the estimated value and estimated variance (or confidence level) for each grid point so that downstream terminals can perform quality control and weighted fusion when using corrections; the choice of grid resolution requires a trade-off between accuracy requirements and communication / computation costs.

[0131] In the embodiments of the present application, applying a mapping function to map the zenith delay to the tropospheric correction in the satellite direction includes: using the mapping function to map the zenith delay to the correction in the satellite line-of-sight direction. The correction is sent to the terminal through the Beidou satellite short message communication network. In response to the residual of the ionosphere-free combined observation equation exceeding a preset threshold, an abnormal satellite data rejection operation is performed.

[0132] Specifically, for any satellite observation, given its elevation angle (in radians or degrees) at a certain station / grid point, the correction for mapping the zenith delay to the satellite line-of-sight direction is:

[0133]

[0134] Where is the tropospheric mapping function; common mapping functions include: simple approximation: (high elevation angle approximation); Niell mapping function (NMF): using latitude / season parameterization to improve low elevation angle accuracy; VMF1 based on NWP or measured profile mapping function, which can more accurately reflect the height profile of atmospheric refraction. Pack the of each satellite into a correction message, which can be sent in a standard format (such as the RTCM SSR tropospheric correction message) or a customized compact binary / short message format; the message also includes a timestamp, the target station / grid coordinates, the correction value and the uncertainty, so that the terminal can directly subtract or fuse. Calculate the residual vector in the Kalman filter or observation preprocessing stage. The residual normalization test can use the following criterion:

[0135]

[0136] Where is the residual covariance; if the normalized residual of a single satellite or a certain observation component exceeds a preset threshold (such as the chi-square limit or empirical threshold corresponding to a confidence level of 95%), it is marked as abnormal and the satellite observation is rejected or its weight is reduced, and then the filtering or interpolation calculation is performed again.

[0137] It can be understood that the accuracy of the mapping function directly affects the effect of low elevation angle correction: it is recommended in engineering to adopt different strategies for different elevation angle segments (simple approximation for high angles, NMF / VMF1 or NWP-based mapping for low angles). It is necessary to carry the uncertainty (such as the correction variance) when sending the correction, so that the terminal can perform weight allocation or integrity judgment during fusion; when communication is limited, representative points can be sent and spatial interpolation can be performed at the terminal. The residual test adopts covariance normalization This can be achieved using either the standardized residuals of a single observation (residual divided by its standard deviation) or the threshold can be set at a 95% or 99% confidence level.

[0138] In this embodiment, the method further includes: converting the zenith wet delay into columnar water vapor content according to a preset conversion coefficient; summarizing the columnar water vapor content of multiple reference stations within a preset coverage area; and generating and outputting regional atmospheric water vapor distribution field data using a spatial interpolation method.

[0139] Specifically, this embodiment uses the following linear relationship to convert zenith wet delay (ZWD) into columnar water vapor content (PWV):

[0140]

[0141] in: The columnar water vapor content (unit: millimeters, mm); Zenith wet delay (unit: meters, m); The conversion factor (unit: mm / m) depends on the atmospheric weighted average temperature. and combinations of constant terms. In practice, It can be determined by empirical formulas or regression models; when no empirical coefficients are available, it can be determined by analyzing historical observation data. and Localization obtained by linear regression For each epoch, for each base station The summation of the corresponding confidence levels (obtained from the covariance transformation of ZWD) is denoted as the set. Use the same spatial interpolation / regression procedure as wet delay modeling (e.g., kriging or multinomial regression incorporating the DEM) for... Spatial interpolation is performed to generate a gridded atmospheric water vapor distribution field over the covered area. It also outputs the estimated variance for each grid point to measure confidence. The output format can be a time series grid (e.g., 1km×1km, one frame every 10 minutes) or a list of representative points to be distributed on demand.

[0142] Understandably, the linear form of the formula is a commonly used and numerically stable expression in the field of GNSS atmospheric remote sensing. The accuracy of PWV directly determines its quantitative accuracy; therefore, the method based on fitting local meteorological and historical observations should be given priority. Or determined by analytical expressions based on atmospheric physics The PWV gridded output should simultaneously include observation timestamps, grid coordinates, estimated values, and estimated variances to facilitate further fusion or early warning by downstream meteorological / engineering systems. When communication bandwidth is limited, only representative grids (e.g., key corridors / nodes) and interpolation parameters can be sent. The terminal performs interpolation locally based on the received representative points to obtain local PWV corrections. The unit conversion between PWV and ZWD remains consistent with the numerical values: ZWD is typically expressed in meters (m), while PWV is expressed in millimeters (mm). The order of magnitude is typically from hundreds to thousands (the reciprocal of mm / m) – in engineering, the actual measured regression is used to determine and record the unit.

[0143] In this embodiment of the application, the method further includes: determining the conversion coefficient based on the weighted average atmospheric temperature. The weighted average atmospheric temperature is estimated in real time based on the measured surface temperature, air pressure, and water vapor pressure parameters of each reference station and a regression model established based on historical meteorological statistics of the region, in order to correct for the impact of environmental temperature changes on the accuracy of water vapor conversion.

[0144] Specifically, the conversion factor View as The function of (atmospheric weighted average temperature) can be expressed as:

[0145]

[0146] in The unit is Kelvin (K). Function It can be expressed analytically or in empirical regression form, such as linear or inverse regression models:

[0147]

[0148] in This is a constant obtained through regression of historical observations and assimilated data.

[0149] Atmospheric weighted average temperature The real-time estimation employs a hybrid strategy based on surface observations and historical regression models: prioritizing the use of measured surface temperatures from each reference station. (K) air pressure (hPa) and water vapor pressure (hPa). A regression model was established using historical meteorological statistics for the region:

[0150]

[0151] in These are historical regression coefficients, obtained through regression fitting of multi-year survey data or NWP output profile data. If a reference station lacks real-time observations, the regression estimation results or NWP interpolation from neighboring stations are used as the baseline. Alternative estimates. The estimates obtained... Substituting into the above equation, we obtain the localization. Then use the above formula to complete the ZWD→PWV conversion.

[0152] Understandable The temperature, which reflects the atmospheric refractive index-weighted average, has a direct impact on the ZWD→PWV conversion: if estimation deviation If it exists, then it corresponds to The error can be amplified to the error of PWV, therefore, using a hybrid estimation based on measured data and historical regression can significantly reduce the error. Regression coefficients , These are region-dependent parameters and must be determined based on historical meteorological profiles and assimilation data of the coverage area, and periodically recalibrated (e.g., seasonally updated). Under severe convective or extreme weather conditions, The short-term fluctuations may be significant; therefore, the real-time update frequency of the conversion coefficients should be increased, and the result should be simultaneously provided in the output. The PWV confidence interval derived from the uncertainty is used to enable downstream systems to make integrity judgments.

[0153] In this embodiment, the method further includes: monitoring the residuals of the ionosphere-free combined observations and the model residuals of the regional wet delay model. In response to the residuals of the ionosphere-free combined observations and the model residuals exceeding a preset threshold, an anomaly handling process is triggered. The anomaly handling process includes: removing satellite or base station observations with abnormal residuals, adaptively adjusting the process noise and observation weights of the Kalman filter, increasing the update frequency of the regional model, and re-modeling the regional wet delay.

[0154] Specifically, two types of residuals are calculated and monitored in real time: one is the observation residual in Kalman filtering (i.e., the difference between the observation without ionosphere and the observation predicted based on the current state), and the other is the model residual of the regional wet delay model (i.e., the difference between the predicted value of the regional field at the station obtained by interpolation / regression and the actual wet delay at the station). Observation residuals are judged separately based on single-observation normalized residuals and overall innovation: if the normalized residual of a certain satellite or a certain observation component continuously exceeds the preset single-observation threshold (e.g., 3σ), the observation is marked as an anomalous candidate and temporarily removed; if the statistics of overall innovation continuously exceed the global consistency threshold (e.g., the chi-square limit at the 95% significance level), a global or regional anomaly is considered to exist. For model residuals, if the model residual of a certain station or a certain region exceeds the preset model tolerance (judged according to historical residual distribution or multi-station consistency), the observation of that station is downweighted or removed in regional modeling, and the model reconstruction process is triggered. The anomaly handling process is executed in a priority-based manner: first, local rejection and re-filtering are performed; if the anomaly is not alleviated, the Kalman filter process noise is adaptively amplified and / or the observation covariance is adjusted (i.e., Q and R are dynamically changed) to improve the filter's responsiveness to rapid changes; if the quality requirements are still not met, the update time of the regional model is temporarily increased (e.g., shortened from the usual 10 minutes to 1–2 minutes), and the regional wet delay model is re-modeled based on the latest valid observations; after reconstruction, if the anomaly source is found to be systemic (e.g., failure of precise ephemeris, large-scale impact of ionospheric disturbance, or multi-station synchronization anomaly), multi-system fusion or service degradation strategies are further triggered to ensure the availability of the corrected output. All anomaly handling actions should have time windows and rollback rules. For example, if the corresponding observation recovers to normal within a certain number of consecutive epochs after rejection, its weight is automatically restored, and the adaptive adjustment of filter parameters gradually reverts to the default value after the system stabilizes.

[0155] Understandably, this monitoring and anomaly handling mechanism must not only rapidly respond to isolated observation errors (such as multipath errors of a single satellite or sensor failure at a single station), but also identify and address regional or systemic problems (such as ionospheric disturbances, anomalies in precision products, or sudden weather changes), thereby maintaining service stability and integrity while ensuring correction accuracy. Anomaly handling must be tightly integrated with integrity indicators, logging, and alarm systems: each removal or parameter adaptation should generate a traceable event record (including triggering conditions, affected satellites / sites, measures taken, and duration), and push the current correction confidence level or degradation information to the operations and maintenance team and downstream users, so that terminals can adjust weights or select alternative strategies during location fusion. In engineering implementation, configurable ranges should be provided for thresholds and adaptive factors, and continuous optimization should be implemented through offline testing and online evaluation, while retaining channels for manual intervention and rollback to prevent long-term system deviations caused by misjudgments in automated processing.

[0156] The complete workflow of the tropospheric error correction method based on BeiDou satellite signals provided in this application is described below with an exemplary embodiment.

[0157] In this embodiment, the invention is applied to a power transmission line inspection and fault response scenario in a mountainous area. The transmission corridor is approximately 200km long, with significant elevation differences along the route (from 300m to 2400m). The power grid maintenance provider needs to provide real-time meter-level or higher precision positioning services for drone inspections, vehicle-mounted terminals, and manual inspectors, and issue corrections via BeiDou short message / WeChat communication networks. The specific steps of this embodiment are as follows:

[0158] System Deployment and Initial Conditions (S100)

[0159] Specifically, N=30 CORS reference stations will be deployed in the transmission corridor and surrounding pre-defined coverage area (the spacing will be configured according to the terrain and requirements, and appropriately increased along the elevation gradient direction). Each station will be equipped with a dual-frequency BeiDou receiver, a GNSS antenna, a high-precision clock, and a meteorological sensor (for real-time air pressure measurement). Surface temperature (Relative humidity RH). All stations are synchronized to UTC and sample pseudorange at 1Hz (can be changed as needed). With carrier phase .

[0160] The system integrates real-time precise ephemeris and satellite clock difference flow (regional precise or IGS real-time service) and establishes a data aggregation center for real-time calculation and external distribution of corrections.

[0161] It is understandable that deployment density, meteorological sensor accuracy, and observation synchronization directly affect the subsequent ZTD / ZWD accuracy. In engineering practice, it is recommended that the barometric pressure sensor accuracy be ≤ ±0.5 hPa and the sampling frequency be ≥ 1 / 60 Hz (1 time / minute) to meet the ZHD requirements, but real-time measurement data should be given priority.

[0162] Observation preprocessing (S200)

[0163] Specifically, at the data aggregation center, gross error removal (based on SNR and residual statistics) and carrier phase cycle slip detection and repair are performed on the raw observations of each station; an ionospheric-free array (IF) is constructed:

[0164]

[0165] in For two frequencies, This represents the pseudorange and phase at the corresponding frequency.

[0166] Understandably, IF combination can eliminate first-order ionospheric terms but amplifies noise and cannot remove high-order ionospheric residues; therefore, ionospheric activity indicators must be monitored simultaneously during the processing and multi-system fusion strategies must be enabled when necessary.

[0167] Real-time precision single-point positioning (S300–S400)

[0168] Specifically, a Kalman filter is constructed for each station, with the following state vector:

[0169]

[0170] And using the IF pseudorange / phase observation equation:

[0171]

[0172]

[0173] Perform recursive estimation; where: The satellite-receiver geometric distance (m) is given. It is the speed of light. This is for satellite clock bias (corrected by precise ephemeris). Let $\frac{ ... This is a mapping function. This is the ambiguity constant under the IF combination (processed according to equivalent conversion units). To observe noise.

[0174] right Using random walk noise (e.g., a standard deviation of 0.005–0.02 m / s is recommended, adjustable in practice), ambiguity is approximately constant in the absence of cycle slips. If a cycle slip is detected, the corresponding ambiguity state is reset and the covariance is increased before re-estimation. The Kalman filter outputs the ambiguity for each epoch. With covariance matrix .

[0175] It is understandable that the process noise and observation noise matrices The settings will affect the convergence speed and smoothness of the filter; during severe weather or periods of ionospheric disturbance, these parameters need to be dynamically adjusted (see the anomaly handling section).

[0176] Dry and wet separation (S500)

[0177] Specifically, the zenith dry delay (ZHD) is calculated using Saastamoinen's empirical formula:

[0178]

[0179] in The reference station pressure is (hPa). Latitude (radians) Altitude (units must match a constant, usually in km or m with constant adjustment). Estimated by Kalman filtering. deduct get : .

[0180] It is understandable that ZHD accuracy is significantly affected by air pressure accuracy; if local air pressure is missing, NWP or neighboring station interpolation is used and its uncertainty is included in the total covariance.

[0181] Regional wet delay modeling and meshing (S600)

[0182] Specifically, the same epoch will include all stations In summary, a continuous field is generated using modeling methods with height constraints, such as first detrending using multinomial regression (including the DEM elevation term), and then using Kriging interpolation of the residuals:

[0183] Example of a regression model: ;

[0184] Kriging is applied to the residuals to obtain the prediction variance. A gridded wet delay field is generated at a preset resolution (1km × 1km in the example). And derive the estimated variance for each grid point.

[0185] Understandably, a finer resolution is used along critical routes (e.g., within ±2km of the transmission corridor), with grids and weights guided by station covariance, and outlier stations can be downweighted or removed during modeling.

[0186] Mapping and correction distribution (S700)

[0187] Specifically, satellite observations for each grid point or base station are based on their elevation angle. Using mapping functions Calculate line-of-sight correction:

[0188]

[0189] Recommended mapping function: Niell mapping function (NMF) or VMF1 based on NWP; available for high elevation angles. Approximately. The correction value and corresponding uncertainty of each satellite are packaged in a standard format (e.g., RTCMSSR or customized short message) and sent to drones, vehicle terminals, and maintenance personnel via BeiDou short message service. The terminal directly subtracts the correction or uses it as an input for observation weights during local positioning calculation.

[0190] Understandably, the transmitted content should include timestamps, satellite identifiers, correction values ​​and variances, grid / site identifiers, and quality of service levels, so that the terminal can perform fusion and integrity determination; when communication is restricted, representative points can be sent and interpolated internally by the terminal.

[0191] PWV calculations and meteorological products (parallel processing)

[0192] Specifically, adopt Each station Convert to PWV, conversion factor Estimated atmospheric weighted average temperature Decision (e.g.) (Empirical form). Based on the station PWV, the same spatial interpolation is performed to generate regional PWV grids for meteorological departments to use for short-term severe convective weather warnings.

[0193] Understandably, PWV products can be used as a meteorological reference for inspection and emergency dispatch. If a rapid increase in PWV is detected, it will trigger inspection delays or drone return.

[0194] Residual monitoring and anomaly handling (parallel monitoring)

[0195] Specifically, real-time computing observation innovation Its covariance And calculate the single-observation normalized residuals and chi-square statistic. If single observation or If the chi-square value exceeds 95%, exception handling will be triggered.

[0196] Anomaly handling is performed sequentially: local removal of anomalous satellites / observations → adaptive amplification of process noise (e.g.) Multiply ) and / or increase the variance of the observed parts →Re-filter →If there is a regional anomaly, increase the model update frequency (e.g., shorten from 10 minutes to 1–2 minutes) and remodel →If it still cannot be recovered, trigger multi-system fusion or service degradation (introduce GPS / Galileo data or provide degradation correction).

[0197] Understandably, anomaly handling should generate complete logs and send integrity and confidence information to the operations / maintenance end / terminal; after recovery, parameters should be automatically rolled back and a manual intervention channel should be retained to verify the rationality of the automation strategy.

[0198] Figure 2 This is a schematic diagram of a tropospheric error correction system module based on BeiDou satellite signals provided in one embodiment of this application. Figure 2The tropospheric error correction system 10 based on BeiDou satellite signals shown includes at least the following components: an information receiving module 11, an information processing module 12, a calculation module 13, a model generation module 14, and a tropospheric correction output module 15.

[0199] In this embodiment, the information receiving module 11 is used to receive raw pseudorange and carrier phase observation data of BeiDou satellites from multiple reference stations within a preset coverage area, and to collect air pressure data at the location of each reference station. (See also the attached document for details.) Figure 1 The details and their corresponding descriptions are not repeated here.

[0200] In this embodiment, the information processing module 12 is used to perform gross error removal and cycle slip detection on the original pseudorange and carrier phase observation data, and to construct an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay; and to obtain real-time precise ephemeris and satellite clock bias. For details, please refer to [link to relevant documentation]. Figure 1 The details and their corresponding descriptions are not repeated here.

[0201] In this embodiment, the calculation module 13 is used to perform precise single-point positioning calculations for each reference station based on real-time precise ephemeris and satellite clock bias, so as to output the absolute zenith tropospheric total delay and covariance of each reference station. The calculation parameters include the zenith tropospheric total delay modeled using a random walk model; please refer to the documentation for details. Figure 1 The details and their corresponding descriptions are not repeated here.

[0202] In this embodiment, the model generation module 14 is used to calculate the zenith dry delay of each reference station based on a preset empirical model and air pressure data, and subtract the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay; it summarizes the zenith wet delays of multiple reference stations at the same epoch, and establishes a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors. The topographic intervention factors include the altitude information of each reference station; please refer to the details for further information. Figure 1 The details and their corresponding descriptions are not repeated here.

[0203] In this embodiment, the tropospheric correction output module 15 is used to map the zenith direction delay to the tropospheric correction in the satellite direction using a mapping function based on the regional wet delay model. Please refer to the following for details. Figure 1 The details and their corresponding descriptions are not repeated here.

[0204] Figure 3 This is an electronic device 20 provided in one embodiment of this application. For example... Figure 3 As shown, the electronic device 20 includes at least the following components: a processor 21 and a memory 22.

[0205] In this embodiment, the memory 22 is used to store executable instructions of the processor 21, which, when configured to execute instructions, implement... Figure 1 The diagram shows a tropospheric error correction method based on BeiDou satellite signals.

[0206] In one embodiment of this application, the program operating in the electronic device 20 may be a program that controls a central processing unit (CPU) or similar device to achieve the functions of the above-described embodiments of the present invention (a program that enables the computer to function). The information processed by these devices is then temporarily stored in random access memory (RAM) during processing, and subsequently stored in various ROMs such as read-only memory (Flash ROM) and hard disk drives (HDDs), and read, corrected, and written by the CPU as needed.

[0207] It should be noted that a portion of the electronic device 20 described above can also be implemented using a computer. In this case, the program for implementing the control function can be recorded on a computer-readable recording medium, and the program recorded on the recording medium can be read into the computer and executed.

[0208] It should be noted that the term "computer" as used here refers to a computer built into electronic device 20, employing hardware including an operating system and peripheral devices. Furthermore, "computer-readable recording media" refers to removable media such as floppy disks, magneto-optical disks, ROMs, and CD-ROMs, as well as storage devices such as hard drives built into the computer.

[0209] Furthermore, a "computer-readable recording medium" can include: a medium that dynamically stores a program for a short period of time, such as a communication line used when transmitting a program via a network such as the Internet or a communication line such as a telephone line; or a medium that stores a program for a fixed period of time, such as volatile memory inside a computer that serves as a server or client in this case. In addition, the aforementioned program can be a program used to implement the above-mentioned functions, or it can be a program that can implement the above-mentioned functions by combining with programs already recorded in the computer.

[0210] It is understood that the tropospheric error correction method, system, and equipment based on BeiDou satellite signals provided in this application, by deploying multiple reference stations within the coverage area and collecting pseudorange and carrier phase observation data of BeiDou satellites, constructs an ionospheric-free combined observation equation after gross error removal and cycle slip detection of the observation data, and introduces real-time precise ephemeris and satellite clock bias for precise single-point positioning calculation, thereby obtaining stable zenith tropospheric total delay parameters for each reference station; further, by combining barometric pressure data and empirical models to separate zenith dry delay and zenith wet delay, and by using wet delay information from multiple reference stations and topographic intervention factors such as altitude to construct a regional wet delay model, thus enabling the correction of tropospheric errors at high sea levels. Even under complex terrain conditions, it can achieve high-precision tropospheric error modeling; at the same time, by mapping the zenith delay to the tropospheric correction in the satellite line-of-sight direction through a mapping function and sending it to the terminal via the BeiDou short message communication network, it can realize real-time correction of user positioning calculation; in addition, by jointly estimating coordinate parameters, receiver clock error, tropospheric parameters and ambiguity parameters through Kalman filtering, and combining anomaly residual monitoring, adaptive parameter adjustment and correction service quality control mechanism, it can effectively improve the stability and reliability of tropospheric error estimation, and significantly improve the continuity and accuracy of high-precision positioning services in scenarios such as mountain power grid inspection, transmission line monitoring and BeiDou communication terminal positioning.

[0211] Those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application fall within the scope of protection claimed in this application.

Claims

1. A tropospheric error correction method based on BeiDou satellite signals, characterized in that, The method includes: Multiple reference stations are deployed within a preset coverage area. Each reference station is used to receive raw pseudorange and carrier phase observation data from BeiDou satellites and to collect air pressure data and digital elevation model data at the location of each reference station. Gross errors were removed and cycle slips were detected in the original pseudorange and carrier phase observation data, and an ionospheric-free combined observation equation was constructed to eliminate the influence of first-order ionospheric delay. Obtain real-time precise ephemeris and satellite clock bias; Based on the real-time precise ephemeris and the satellite clock difference, precise single-point positioning calculations are performed on each of the reference stations to output the absolute zenith tropospheric total delay and covariance of each of the reference stations. The calculated parameters include the zenith tropospheric total delay modeled by a random walk model. The zenith dry delay of each reference station is calculated based on a preset empirical model and the air pressure data, and the zenith dry delay is subtracted from the total zenith tropospheric delay to obtain the zenith wet delay of each reference station. The zenith wet delay of multiple reference stations at the same epoch is aggregated, and a regional wet delay model is established based on the aggregated zenith wet delay and topographic intervention factors. The topographic intervention factors include the elevation information and digital elevation model of each reference station. Based on the aforementioned regional wet delay model, a mapping function is applied to map the zenith direction delay to the tropospheric correction in the satellite direction, and then the result is sent to the terminal.

2. The tropospheric error correction method based on BeiDou satellite signals according to claim 1, characterized in that, The step of performing precise single-point positioning calculations for each of the reference stations based on the real-time precise ephemeris and the satellite clock difference includes: Kalman filtering is applied to estimate the state vector of each of the reference stations. The state vector includes the receiver's three-dimensional coordinates, receiver clock error, total zenith tropospheric delay, and carrier phase integer ambiguity at each frequency. The carrier phase integer ambiguity is a constant parameter under cycle slip-free observation conditions. If a cycle slip is detected, the corresponding ambiguity parameter is reset.

3. The tropospheric error correction method based on BeiDou satellite signals according to claim 2, characterized in that, The method further includes: The air pressure data is obtained based on the measured values ​​of the meteorological sensors built into each of the base stations or the interpolated estimates of the numerical weather prediction models. When calculating the zenith dry delay, the preset empirical model incorporates the latitude and altitude parameters of the reference station to calculate the dry delay component affected by geographical location and gravitational acceleration.

4. The tropospheric error correction method based on BeiDou satellite signals according to claim 3, characterized in that, The process of establishing a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors includes: By applying Kriging interpolation or a multinomial regression method based on station height, discretely distributed wet delay observations from benchmark stations are transformed into a continuous distribution field covering the entire region, wherein the terrain constraint factor of the regional wet delay model includes a digital elevation model. The regional wet delay model generates gridded tropospheric correction data according to a preset spatial resolution.

5. The tropospheric error correction method based on BeiDou satellite signals according to claim 4, characterized in that, The application mapping function maps the zenith direction delay to a tropospheric correction in the satellite direction, including: A mapping function is used to map the zenith direction delay into a correction for the satellite line-of-sight direction; The correction amount is sent to the terminal via the BeiDou satellite short message communication network; In response to the residual of the ionosphere-free combined observation equation exceeding a preset threshold, an abnormal satellite data removal operation is performed.

6. The tropospheric error correction method based on BeiDou satellite signals according to claim 1, characterized in that, The method further includes: The zenith wet delay is converted into columnar water vapor content according to a preset conversion coefficient; The columnar water vapor content of multiple reference stations within the preset coverage area is summarized, and regional atmospheric water vapor distribution field data is generated and output using a spatial interpolation method.

7. The tropospheric error correction method based on BeiDou satellite signals according to claim 6, characterized in that, The method further includes: The conversion coefficient is determined based on the weighted average temperature of the atmosphere; The atmospheric weighted average temperature is estimated in real time based on the measured surface temperature, air pressure, and water vapor pressure parameters of each of the reference stations and a regression model established based on the historical meteorological statistics of the region, in order to correct the impact of changes in ambient temperature on the accuracy of water vapor conversion.

8. The tropospheric error correction method based on BeiDou satellite signals according to claim 1, characterized in that, The method further includes: Monitor the residuals of combined observations without ionosphere and the model residuals of the wet delay model for the region; In response to the fact that the observation residuals of the ionosphere-free combined observations and the model residuals exceed a preset threshold, an anomaly handling process is triggered. The anomaly handling process includes: removing satellite observations or base station observations with residual anomalies, adaptively adjusting the process noise and observation weights of the Kalman filter, increasing the update frequency of the regional model, and re-modeling the regional wet delay.

9. A tropospheric error correction system based on BeiDou satellite signals, characterized in that, The system includes: The information receiving module is used to receive the raw pseudorange and carrier phase observation data of Beidou satellites from multiple reference stations within a preset coverage area, and to collect the air pressure data and digital elevation model data of the location of each reference station. The information processing module is used to perform gross error removal and cycle slip detection on the original pseudorange and carrier phase observation data, and to construct an ionospheric-free combined observation equation to eliminate the influence of first-order ionospheric delay; and to obtain real-time precise ephemeris and satellite clock bias. The calculation module is used to perform precise single-point positioning calculations on each of the reference stations based on the real-time precise ephemeris and the satellite clock difference, so as to output the absolute zenith tropospheric total delay and covariance of each of the reference stations. The calculation parameters include the zenith tropospheric total delay modeled by a random walk model. The model generation module is used to calculate the zenith dry delay of each of the reference stations based on a preset empirical model and the air pressure data, and to subtract the zenith dry delay from the total zenith tropospheric delay to obtain the zenith wet delay of each of the reference stations; to summarize the zenith wet delay of multiple reference stations at the same epoch, and to establish a regional wet delay model based on the summarized zenith wet delay and topographic intervention factors, wherein the topographic intervention factors include the altitude information and digital elevation model of each reference station. The tropospheric correction output module is used to map the zenith direction delay to the tropospheric correction in the satellite direction based on the regional wet delay model and apply a mapping function, and then send the correction to the terminal.

10. An electronic device, characterized in that, include: processor; as well as A memory having computer-readable instructions stored thereon for controlling the processor to execute the tropospheric error correction method based on BeiDou satellite signals as described in any one of claims 1 to 8.

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