Dual residual troposphere delay modeling method and system
By using Vienna mapping function and hierarchical clustering methods, the troposphere delay residuals are calculated and the adaptive latitude banding is performed, the poor space-time adaptability and error characterization problems of troposphere delay modeling in the prior art are solved, and higher precision GNSS positioning and integrity monitoring are achieved.
Patent Information
- Application Number
- CN202510263200.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-06
- Publication Date
- 2025-08-05
AI Technical Summary
The existing troposphere delay modeling methods have poor adaptability to spatial and temporal changes, and cannot accurately characterize residual troposphere delay errors. Fixed standard deviation leads to integrity monitoring errors, and how to improve the convergence speed of PPP positioning and enhance the reliability of GNSS integrity monitoring.
The grid tropospheric delay product provided by the Vienna mapping function is used as the reference value, and adaptive latitude banding is performed through hierarchical clustering, the daily deviation and daily standard deviation and compaction standard deviation and deviation of each latitude band residual are calculated, the residual is standardized and the conservative standard deviation is calculated, and the integrity monitoring is used.
The reliability and applicability of tropospheric delay modeling are improved. Through spatiotemporal feature analysis and standardized processing of error data, the positioning accuracy and stability are enhanced, and the accuracy and integrity monitoring of GNSS positioning are improved.
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Figure CN120428276A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of GNSS satellite navigation systems and enhancement technologies, and in particular to a double residual tropospheric delay modeling method. Background Art
[0002] In Global Navigation Satellite System (GNSS) applications, slant-path tropospheric delay plays a crucial role in GNSS positioning and integrity monitoring. This delay is typically mapped to the zenith, forming the zenith total tropospheric delay (ZTD). ZTD consists of two components: zenith static delay (ZHD) and zenith wet delay (ZWD). To mitigate the impact of tropospheric delay, extensive research has focused on developing empirical models of zenith tropospheric delay. However, these empirical tropospheric delay models still exhibit significant residual ZTD. These residuals exhibit significant geographic and seasonal variations, primarily due to variations in atmospheric water vapor and the spatial distribution of the stations used for model development. This residual ZTD can result in positioning errors of several decimeters, impacting high-precision GNSS applications. Furthermore, residual ZTD can impact GNSS integrity, posing additional challenges for safety-critical applications such as aviation and autonomous driving.
[0003] In precise point positioning (PPP), high-precision tropospheric products and regional tropospheric products based on real-time or near-real-time GNSS measurements are widely used to improve PPP performance. However, in the absence of such high-precision products, an empirical ZTD model is used to initialize the tropospheric state parameters in the Kalman filter, while the residual delay is used to initialize the tropospheric state noise through the empirical standard deviation (STD). In this process, the accuracy of the empirical ZTD model and its standard deviation are crucial. However, the accuracy of the ZTD model varies significantly geographically and seasonally, highlighting the need for spatial and temporal quantitative evaluation to improve GNSS positioning performance.
[0004] In integrity monitoring, residual ZTD is usually incorporated into stochastic models. The Radio Technical Commission for Aeronautics (RTCAMOPS) uses a constant standard deviation of 0.12 meters to represent the unmodeled residual ZTD. However, studies have shown that this constant value is too conservative and fails to take into account spatiotemporal variations. In order to better characterize the residual ZTD, spatiotemporal quantitative evaluation is also crucial for GNSS integrity monitoring. To overcome the above problems, more accurate models and algorithms are needed to improve the correction and accuracy assessment of the tropospheric delay model. Summary of the Invention
[0005] In view of the above-mentioned problems, the present invention is proposed.
[0006] Therefore, the technical problems solved by the present invention are: the existing tropospheric delay modeling method has poor adaptability to spatiotemporal changes, cannot accurately characterize the residual tropospheric delay error, the fixed standard deviation leads to misjudgment of integrity monitoring, and how to improve the PPP positioning convergence speed and enhance the reliability of GNSS integrity monitoring.
[0007] To solve the above technical problems, the present invention provides the following technical solutions: a dual residual tropospheric delay modeling method, comprising calculating the residuals of the tropospheric delay empirical model and performing adaptive latitude zoning through hierarchical clustering; calculating the daily deviation and daily standard deviation of the residuals in each latitude band as well as the compact standard deviation and deviation; standardizing the residuals and calculating the conservative standard deviation, and using the conservative standard deviation for integrity monitoring.
[0008] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the calculation of the residual of the tropospheric delay empirical model includes taking the grid tropospheric delay product VMF3 of the Vienna Mapping Function Open Access Data Center as a reference value, calculating the tropospheric delay at the VMF3 grid point using the tropospheric delay empirical model UNB3, and subtracting it from the VMF3 reference value to obtain the tropospheric delay residual at each grid point, which is expressed as:
[0009] δ=T ref -T model
[0010] Where δ is the tropospheric delay residual, T ref is the tropospheric delay reference value, T model Estimates calculated for the tropospheric delay model.
[0011] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the adaptive latitude zoning by hierarchical clustering includes treating the tropospheric delay residuals of the same longitude as one sample, obtaining 180 samples, i.e., 180 latitudes, and the correlation coefficient between the tropospheric delay residuals of two latitudes is expressed as:
[0012]
[0013] Among them, r mn is the correlation coefficient between the residuals at the mth latitude and the nth latitude, is the residual of the tropospheric delay at the mth latitude at the ith longitude and the jth day, is the average value of the tropospheric delay residual at the mth latitude. The distance between the residuals of two latitudes is expressed as:
[0014] d mn =1-r mn
[0015] Among them, d mnThe distance between the residuals of the mth latitude and the nth latitude is used as the sample distance indicator of the hierarchical clustering method to perform adaptive latitude zoning, and the samples clustered into one category are regarded as one latitude band.
[0016] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the calculation of the daily deviation and daily standard deviation of the residuals in each latitude band includes sorting the tropospheric delay residuals in each latitude band by date according to the adaptive latitude band, calculating the standard deviation and deviation of the residuals for each day, and obtaining a time series of the residual standard deviation and deviation, which is expressed as:
[0017]
[0018] in, is the residual of the tropospheric delay at the lth latitude at the ith longitude and the jth day, b acc,j is the daily deviation of the residual on day j, σ acc,j is the daily standard deviation of the residual on day j.
[0019] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the compact standard deviation and bias include fitting two periodic functions to obtain the empirical functions of the compact standard deviation and bias, which are expressed as:
[0020]
[0021] Among them, σ acc (DOY) and b acc (DOY) are the tight standard deviation and bias of the fit, DOY is the accumulated day per year, A0, A1, A2, A3, A4 and b0, B1, B2, B3, B4 are the model coefficients.
[0022] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the standardized residual includes standardizing the residual by a compact standard deviation and a bias empirical function according to a fitting periodic function to obtain a standardized tropospheric delay residual, which is expressed as:
[0023]
[0024] Among them, δ norm is the standardized residual.
[0025] As a preferred embodiment of the dual residual tropospheric delay modeling method of the present invention, the calculation of the conservative standard deviation includes enveloping the standardized residual using the Gaussian envelope method to obtain an expansion coefficient, and applying the expansion coefficient to the compact empirical tropospheric delay standard deviation to obtain a conservative empirical tropospheric delay standard deviation, which is expressed as:
[0026] σ int (DOY)=σ acc (DOY)·σ norm +σ acc (DOY) b norm / 3.29
[0027] Among them, σ int (DOY) is the conservative standard deviation, σ norm and b norm is the expansion coefficient, and a conservative empirical standard deviation is used for integrity monitoring.
[0028] Another object of the present invention is to provide a dual residual tropospheric delay modeling system, which can calculate the daily bias and daily standard deviation of the residual in each latitude band through a calculation fitting module, and further calculate the compact standard deviation and deviation to obtain the time series characteristics of the tropospheric delay error, thereby solving the problems of low time resolution and large PPP initialization error of the current model.
[0029] As a preferred solution of the dual residual tropospheric delay modeling system described in the present invention, it includes: a latitude zoning module, a calculation and fitting module, and an integrity monitoring module; the latitude zoning module is used to calculate the residuals of the tropospheric delay empirical model and perform adaptive latitude zoning through hierarchical clustering; the calculation and fitting module is used to calculate the daily deviation and daily standard deviation of the residuals of each latitude band and the compact standard deviation and deviation; the integrity monitoring module is used to standardize the residuals and calculate the conservative standard deviation, and use the conservative standard deviation for integrity monitoring.
[0030] A computer device includes a memory and a processor, wherein the memory stores a computer program, and is characterized in that the processor executes the computer program to implement a step of a dual residual tropospheric delay modeling method.
[0031] A computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of a dual residual tropospheric delay modeling method are implemented.
[0032] Beneficial effects of the present invention: The dual residual tropospheric delay modeling method provided by the present invention adopts the grid tropospheric delay product provided by the Vienna mapping function as a reference value, and calculates the residual of the empirical tropospheric delay model to realize error evaluation of the empirical model, thereby improving the reliability and applicability of the model; by classifying the calculated tropospheric delay residual data according to the principle of the same longitude, calculating the residual correlation coefficient between different latitudes, realizing the spatiotemporal feature analysis of the data, and improving the adaptability of the tropospheric delay correction model; by performing time series analysis on the data of each latitude band, respectively calculating the daily residual standard deviation and deviation, obtaining the time series characteristics of the tropospheric delay error, and improving the accuracy and stability of positioning; by standardizing the calculated residual standard deviation and deviation, the error data can be normalized, thereby improving the adaptability of error modeling. The present invention achieves better results in terms of reliability, adaptability and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without any creative effort. Among them:
[0034] Figure 1 This is an overall flow chart of a dual residual tropospheric delay modeling method provided by the first embodiment of the present invention.
[0035] Figure 2 A diagram showing the standard deviation and bias of the tropospheric delay residual in a certain latitude band of a dual residual tropospheric delay modeling method provided in the second embodiment of the present invention.
[0036] Figure 3 A compact standard deviation and bias and a conservative standard deviation and bias diagram for a dual residual tropospheric delay modeling method provided in the second embodiment of the present invention.
[0037] Figure 4 A diagram showing the envelope results of the tropospheric delay residual limit calculated using the conservative standard deviation and bias of a dual residual tropospheric delay modeling method provided in the second embodiment of the present invention.
[0038] Figure 5 This is a result diagram of positioning enhancement using the compact deviation and standard deviation of a dual residual tropospheric delay modeling method provided by the second embodiment of the present invention.
[0039] Figure 6 This is an overall module diagram of a dual residual tropospheric delay modeling system provided by the third embodiment of the present invention. DETAILED DESCRIPTION
[0040] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.
[0041] Example 1
[0042] Reference Figure 1 , as one embodiment of the present invention, provides a dual residual tropospheric delay modeling method, comprising:
[0043] S1: Calculate the residuals of the empirical model of tropospheric delay and perform adaptive latitude zoning through hierarchical clustering.
[0044] Furthermore, the calculation of the residuals of the empirical model of tropospheric delay involves taking the gridded tropospheric delay product VMF3 of the Vienna Mapping Function Open Access Data Center as a reference value.
[0045] It should be noted that the tropospheric delay at the VMF3 grid point is calculated using the tropospheric delay empirical model UNB3, and the difference between the tropospheric delay at each grid point and the VMF3 reference value is obtained, and the tropospheric delay residual at each grid point is expressed as:
[0046] δ=T ref -T model
[0047] Where δ is the tropospheric delay residual, T ref is the tropospheric delay reference value, T model Estimates calculated for the tropospheric delay model.
[0048] Furthermore, adaptive latitude zoning via hierarchical clustering involves treating the tropospheric delay residuals with the same longitude as one sample.
[0049] It should be noted that for 180 samples, i.e. 180 latitudes, the correlation coefficient between the tropospheric delay residuals at two latitudes is expressed as:
[0050]
[0051] Among them, r mn is the correlation coefficient between the residuals at the mth latitude and the nth latitude, is the residual of the tropospheric delay at the mth latitude at the ith longitude and the jth day, is the average value of the tropospheric delay residual at the mth latitude. The distance between the residuals of two latitudes is expressed as:
[0052] d mn =1-r mn
[0053] Among them, d mn The distance between the residuals of the mth latitude and the nth latitude is used as the sample distance indicator of the hierarchical clustering method to perform adaptive latitude zoning, and the samples clustered into one category are regarded as one latitude band.
[0054] It should also be noted that the hierarchical clustering algorithm calculates the distance between all sample points, constructs an initial distance matrix, treats each sample point as an independent cluster, finds the two nearest clusters and in the current cluster, merges and forms a new cluster, updates the distance matrix, and repeats the iteration until all samples are merged into one cluster or the specified number of clusters is reached, generates a clustering hierarchy tree, and outputs the final cluster division.
[0055] S2: Calculate the daily bias and daily standard deviation of the residuals and the compact standard deviation and bias for each latitude band.
[0056] Furthermore, the calculation of the daily bias and daily standard deviation of the residuals for each latitude band includes the adaptive latitude banding.
[0057] It should be noted that the tropospheric delay residuals of each latitude band are sorted by date, and the standard deviation and bias of the residuals are calculated for each day to obtain the time series of the residual standard deviation and bias, which can be expressed as:
[0058]
[0059] in, is the residual of the tropospheric delay at the lth latitude at the ith longitude and the jth day, b acc,j is the daily deviation of the residual on day j, σ acc,j is the daily standard deviation of the residual on day j.
[0060] Furthermore, compacting the standard deviation and bias involves fitting them via two periodic functions, respectively.
[0061] It should be noted that the empirical function of the compact standard deviation and bias is expressed as:
[0062]
[0063] Among them, σ acc (DOY) and b acc (DOY) are the tight standard deviation and bias of the fit, DOY is the accumulated day per year, A0, A1, A2, A3, A4 and b0, B1, B2, B3, B4 are the model coefficients.
[0064] S3: Standardize the residuals and calculate the conservative standard deviation, and use the conservative standard deviation for integrity monitoring.
[0065] Furthermore, standardized residuals are included according to the fitted periodic function.
[0066] It should be noted that the residuals are standardized by the compact standard deviation and bias empirical function to obtain the standardized tropospheric delay residuals, which are expressed as:
[0067]
[0068] Among them, δ norm is the standardized residual.
[0069] It should also be noted that the user end uses the residual standard deviation empirical function to correct the empirical tropospheric delay, and uses it to initialize the Kalman filter tropospheric delay state item in precise single-point positioning. The standard deviation is calculated using the empirical standard deviation function, and is used to initialize the Kalman filter tropospheric delay noise item in precise single-point positioning to accelerate positioning convergence.
[0070] Furthermore, the conservative standard deviation is calculated based on the standardized residuals.
[0071] It should be noted that the expansion coefficient is obtained by enveloping the data using the Gaussian envelope method. The expansion coefficient is applied to the compact empirical tropospheric delay standard deviation to obtain the conservative empirical tropospheric delay standard deviation, which is expressed as:
[0072] σ int (DOY)=σ acc (DOY)·σ norm +σ acc (DOY) b norm / 3.29
[0073] Among them, σ int (DOY) is the conservative standard deviation, σ norm and b norm is the expansion coefficient, and a conservative empirical standard deviation is used for integrity monitoring.
[0074] Example 2
[0075] Reference Figure 2-5 , which is an embodiment of the present invention, provides a dual residual tropospheric delay modeling method. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.
[0076] like Figure 2 As shown, the upper sub-figure is the deviation time series and the fitted periodic function, and the lower sub-figure is the standard deviation time series and the fitted periodic function. The periodic changes of the standard deviation and deviation are very obvious, and the fitted periodic function also well characterizes the original time series.
[0077] like Figure 3 As shown, there are obvious differences between the results of different latitude bands, which verifies the effectiveness of the adaptive zoning results. In addition, the conservative standard deviation and deviation are larger than the tight standard deviation and deviation, indicating the effectiveness of the standard deviation and deviation inflation.
[0078] like Figure 4 As shown in the figure, the horizontal axis is the tropospheric delay residual, and the vertical axis is the residual limit. The residual limit can successfully envelop the tropospheric delay residual, indicating that the proposed envelope model is effective.
[0079] like Figure 5 As shown, compared with no constraints and constant value constraints, using the varying standard deviation and bias of the method of the present invention to perform positioning enhancement constraints can effectively accelerate the positioning convergence time and improve the convergence accuracy.
[0080] Example 3
[0081] Reference Figure 6 , as an embodiment of the present invention, provides a dual residual tropospheric delay modeling system, including: a latitude zoning module, a calculation and fitting module, and an integrity monitoring module.
[0082] The latitude zoning module is used to calculate the residuals of the empirical model of tropospheric delay and perform adaptive latitude zoning through hierarchical clustering; the calculation and fitting module is used to calculate the daily bias and daily standard deviation of the residuals of each latitude band as well as the compact standard deviation and deviation; the integrity monitoring module is used to standardize the residuals and calculate the conservative standard deviation, and use the conservative standard deviation for integrity monitoring.
[0083] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.
[0084] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.
[0085] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.
[0086] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having logic gate circuits for implementing logical functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field-programmable gate array (FPGA), etc. It should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention and are not intended to be limiting. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced with equivalents without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications should be encompassed by the claims of the present invention.
[0087] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.
Claims
1. A dual residual tropospheric delay modeling method, characterized in that: include: Calculate the residuals of the empirical model of tropospheric delay and perform adaptive latitude zoning through hierarchical clustering; Calculate the daily bias and daily standard deviation of the residuals and the compact standard deviation and bias for each latitude band; Standardize the residuals and calculate the conservative standard deviation, which is then used for integrity monitoring.
2. The dual residual tropospheric delay modeling method according to claim 1, wherein: The calculation of the residual of the empirical model of tropospheric delay includes taking the grid tropospheric delay product VMF3 of the Vienna Mapping Function Open Access Data Center as a reference value, calculating the tropospheric delay at the VMF3 grid point using the empirical model of tropospheric delay UNB3, and subtracting it from the VMF3 reference value to obtain the residual of the tropospheric delay at each grid point, which is expressed as: δ=T ref -T model Where δ is the tropospheric delay residual, T ref is the tropospheric delay reference value, T model Estimates calculated for the tropospheric delay model.
3. The dual residual tropospheric delay modeling method according to claim 2, wherein: The adaptive latitude zoning by hierarchical clustering includes treating the tropospheric delay residuals of the same longitude as one sample, obtaining 180 samples, i.e., 180 latitudes. The correlation coefficient between the tropospheric delay residuals of two latitudes is expressed as: Among them, r mn is the correlation coefficient between the residuals at the mth latitude and the nth latitude, is the residual of the tropospheric delay at the mth latitude at the ith longitude and the jth day, is the average value of the tropospheric delay residual at the mth latitude. The distance between the residuals of two latitudes is expressed as: d mn ＝1-r mn Among them, d mn The distance between the residuals of the mth latitude and the nth latitude is used as the sample distance indicator of the hierarchical clustering method to perform adaptive latitude zoning, and the samples clustered into one category are regarded as one latitude band.
4. The dual residual tropospheric delay modeling method according to claim 3, wherein: The calculation of the daily bias and daily standard deviation of the residuals in each latitude band includes sorting the tropospheric delay residuals in each latitude band by date according to the adaptive latitude band, calculating the standard deviation and deviation of the residuals for each day, and obtaining a time series of the residual standard deviation and deviation, which is expressed as: in, is the residual of the tropospheric delay at the lth latitude at the ith longitude and the jth day, b acc,j is the daily deviation of the residual on day j, σ acc,j is the daily standard deviation of the residual on day j.
5. The dual residual tropospheric delay modeling method according to claim 4, wherein: The compact standard deviation and bias include fitting two periodic functions to obtain the empirical functions of the compact standard deviation and bias, which are expressed as: Among them, σ acc (DOY) and b acc (DOY) are the tight standard deviation and deviation of the fit, DOY is the accumulated day per year, A0, A1, A2, A3, A4 and B0, B1, B2, B3, B4 are the model coefficients.
6. The dual residual tropospheric delay modeling method according to claim 5, wherein: The standardized residual includes standardizing the residual by a compact standard deviation and a bias empirical function according to a fitting periodic function to obtain a standardized tropospheric delay residual, which is expressed as: Among them, δ norm is the standardized residual.
7. The dual residual tropospheric delay modeling method according to claim 6, wherein: The calculation of the conservative standard deviation includes enveloping the standardized residual using the Gaussian envelope method to obtain an expansion coefficient, and applying the expansion coefficient to the compact empirical tropospheric delay standard deviation to obtain a conservative empirical tropospheric delay standard deviation, which is expressed as: s int (DOY)=s acc (DOY)·s norm +s acc (DOY)·b norm / 3.29 Among them, σ int (DOY) is the conservative standard deviation, σ norm and b norm is the expansion coefficient, and a conservative empirical standard deviation is used for integrity monitoring.
8. A system using the dual residual tropospheric delay modeling method according to any one of claims 1 to 7, characterized in that: Including latitude zoning module, calculation and fitting module, and integrity monitoring module; The latitude zoning module is used to calculate the residual of the tropospheric delay empirical model and perform adaptive latitude zoning through hierarchical clustering; The calculation and fitting module is used to calculate the daily deviation and daily standard deviation of the residual in each latitude band and the compact standard deviation and deviation; The integrity monitoring module is used to standardize the residual and calculate the conservative standard deviation, and use the conservative standard deviation to perform integrity monitoring.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the dual residual tropospheric delay modeling method according to any one of claims 1 to 7 are implemented.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the dual residual tropospheric delay modeling method according to any one of claims 1 to 7 are implemented.