Atmospheric delay dynamic space-time modeling and uncertainty quantification method oriented to PPP-RTK

Abstract

The invention discloses a PPP-RTK-oriented atmospheric delay dynamic space-time modeling and uncertainty quantification method. The method comprises the following steps: acquiring atmospheric delay data based on a regional reference station network, introducing a time dimension to construct a dynamic space-time observation window, carrying out space-time modeling on atmospheric delay, and generating atmospheric delay prediction and initial uncertainty information at a position. And then, implementing an uncertainty correction strategy of one-by-one cross validation, and carrying out adaptive correction on the prediction uncertainty by counting the relationship between the error and the initial uncertainty. And finally, the corrected uncertainty is used for atmospheric constraint weighting in PPP-RTK positioning. According to the method, collaborative optimization of atmospheric delay prediction precision and uncertainty is realized through dynamic spatio-temporal joint modeling and epoch-by-epoch cross validation methods, and precision, stability and reliability of PPP-RTK positioning under complex atmospheric conditions and different network scales are improved.

Description

Technical Field

[0001] This invention relates to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, specifically to a method for dynamic spatiotemporal modeling of atmospheric delay and uncertainty quantification for PPP-RTK. Background Technology

[0002] High-precision modeling and reliable uncertainty quantification of regional atmospheric delay correction are core prerequisites for achieving high-quality PPP-RTK positioning services. In a PPP-RTK positioning system, the server estimates ionospheric and tropospheric delays through a regional reference station network and broadcasts atmospheric delay correction information to the user side. This allows users to incorporate atmospheric errors as external constraints into the positioning solution, significantly shortening convergence time and improving positioning accuracy. Currently, among regional atmospheric delay modeling methods, those based on spatial interpolation or spatial statistical theory are widely used due to their relatively mature implementation and strong applicability.

[0003] The existing regional atmospheric delay modeling process typically follows these steps: (1) Perform PPP or PPP-AR calculations based on the regional reference station network to obtain atmospheric delay estimates for each reference station at discrete times; (2) Within a single epoch, perform regional modeling and interpolation on discrete atmospheric delay observations based on the spatial distribution relationship of the reference stations to generate atmospheric delay corrections at the user's location; (3) Provide corresponding uncertainty estimates for the modeling results and introduce the corrections and uncertainties as pseudo-observations into the user-side PPP-RTK positioning calculation; (4) Weight the atmospheric constraints based on the uncertainties to complete the user positioning calculation. The above process constitutes the basic technical framework of the current PPP-RTK regional atmospheric enhancement service.

[0004] While existing regional atmospheric delay modeling methods have improved PPP-RTK positioning performance to some extent, they inevitably suffer from inherent limitations due to idealized assumptions. On the one hand, existing methods primarily focus on spatial modeling, neglecting the continuous evolution of atmospheric delay over time. In cases of enhanced ionospheric activity or significant atmospheric disturbances, this can lead to discontinuities, lags, or abrupt changes in corrections over time, affecting user positioning stability. On the other hand, existing uncertainty estimation methods are typically based on model assumptions or finite residual statistics, which may exhibit systematic biases compared to actual prediction errors.

[0005] When atmospheric delay uncertainty is estimated too optimistically, low-quality or anomalous atmospheric corrections will be given excessive weight, potentially leading to ambiguity fixation anomalies or abrupt changes in positioning results. Conversely, when uncertainty is estimated too conservatively, the constraining effect of atmospheric corrections is insufficient, weakening the convergence speed and accuracy advantages of PPP-RTK positioning. These problems are particularly pronounced in scenarios with enhanced atmospheric activity, uneven distribution of reference stations, or large network scales, making it difficult to simultaneously achieve high accuracy, stability, and reliability in positioning results.

[0006] Furthermore, while traditional uncertainty assessment methods based on leave-one-for-one cross-validation can reflect the overall accuracy level of regional modeling, their assessment results do not directly correspond to the actual PPP-RTK service's "generating correction products based on all reference stations" working mode. This makes it difficult to accurately depict the dynamic changes in atmospheric delay prediction errors over time, limiting its application in real-time or near-real-time PPP-RTK services. Therefore, how to introduce a modeling method capable of jointly characterizing the spatiotemporal evolution of atmospheric delay within the existing PPP-RTK technology framework, and on this basis, achieve adaptive and reliable quantification of uncertainty to improve user-side positioning accuracy and stability, remains a pressing technical problem to be solved. Summary of the Invention

[0007] To address the aforementioned issues, this invention discloses a dynamic spatiotemporal modeling and uncertainty quantification method for atmospheric delay in PPP-RTK. By introducing a dynamic spatiotemporal joint modeling strategy during regional atmospheric delay modeling and combining it with an epoch-by-epoch leave-one-out cross-validation uncertainty correction method, the negative impact of time-varying atmospheric delay characteristics and idealized model assumptions on the reliability of regional correction products is reduced. This improves the stability and consistency of regional atmospheric delay prediction under complex atmospheric conditions and enhances the matching between the atmospheric delay correction uncertainty description and the actual error level, thereby improving the accuracy, stability, and reliability of PPP-RTK positioning solutions.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK includes the following steps:

[0010] Step 1: Obtain the global navigation satellite system observation data of the regional reference station, and combine it with the precise orbit, precise clock error and phase deviation products to perform PPP or PPP-AR calculation on the regional reference station and extract the atmospheric delay observation data of the regional reference station;

[0011] Step 2: Based on the atmospheric delay observation data, introduce time dimension information to construct a dynamic spatiotemporal observation window for atmospheric delay containing multiple epochs, which is used to characterize the continuous variation characteristics of regional atmospheric delay in space and time.

[0012] Step 3: Within the dynamic spatiotemporal observation window, perform dynamic spatiotemporal modeling of the regional atmospheric delay, generate atmospheric delay prediction results at the target location, and simultaneously obtain the initial prediction uncertainty information corresponding to the prediction results;

[0013] Step 4: Based on the leave-one-out cross-validation strategy, perform statistical analysis and correction on the initial prediction uncertainty information to obtain corrected uncertainty information consistent with the actual atmospheric delay error level;

[0014] Step 5: Introduce the atmospheric delay prediction results and their corrected uncertainty information as atmospheric enhancement constraints into the user-side PPP-RTK positioning solution, complete the user positioning solution based on the uncertainty adaptive weighting strategy, and output the user positioning results.

[0015] The specific steps are as follows:

[0016] Step 1. Obtain the global navigation satellite system observation data of the regional reference station, and combine it with precise orbit, precise clock error and phase deviation products to perform PPP or PPP-AR calculation on the regional reference station and extract the atmospheric delay observation data of the regional reference station.

[0017] Based on the raw GNSS observation data from the regional reference station, a precise single-point positioning observation model is established. This model describes the relationship between the observed data, unknown parameters, and observation errors. The unknown parameters include at least the receiver coordinate parameters, receiver clock error parameters, carrier phase ambiguity parameters, and atmospheric delay parameters. The observation error is characterized by a random error term and constrained by the corresponding stochastic model.

[0018] By performing PPP or PPP-AR calculations on the observation model, atmospheric delay estimates for each reference station at different epochs are obtained, which serve as observation input data for subsequent dynamic spatiotemporal modeling.

[0019] Step 2. Based on the atmospheric delay observation data, introduce time dimension information to construct a dynamic spatiotemporal observation window for atmospheric delay containing multiple epochs, which is used to characterize the continuous variation characteristics of regional atmospheric delay in space and time.

[0020] Based on the atmospheric delay observation data of the regional reference station at different epochs obtained in step 1, the region's first... The reference station is at the first The atmospheric delayed observation at each epoch is denoted as:

[0021] ;

[0022] in, Indicates the first Spatial coordinates of each reference station Indicates the corresponding observation epoch time;

[0023] Within a preset time range, select multiple consecutive epochs. The atmospheric delay observations of all reference stations within the corresponding epoch are jointly organized with their spatial locations to form a dynamic spatiotemporal observation window, whose observation data set is represented as follows:

[0024] ;

[0025] in, Indicates the number of regional reference stations. This indicates the number of epochs contained within the dynamic spatiotemporal observation window. The dynamic spatiotemporal observation window is used to describe the joint changes in the spatial distribution and temporal evolution of regional atmospheric delay, and is updated as the epoch progresses, providing a spatiotemporal joint observation data foundation for subsequent dynamic spatiotemporal modeling of regional atmospheric delay.

[0026] Step 3. Within the dynamic spatiotemporal observation window, perform dynamic spatiotemporal modeling of the regional atmospheric delay, generate atmospheric delay prediction results at the target location, and simultaneously obtain the initial prediction uncertainty information corresponding to the prediction results.

[0027] Within the dynamic spatiotemporal observation window constructed in step 2, the regional atmospheric delay observation values ​​are represented as follows:

[0028] ;

[0029] in, Spatial location coordinates, For epochal time; This is the trend term, used to describe the large-scale spatiotemporal variations of regional atmospheric delay; This is a zero-mean random disturbance term used to describe local fluctuations and random errors;

[0030] (1) Expression of the trend term

[0031] The trend term is constructed using a first-order polynomial that incorporates both spatial and temporal dimensions, and its expression is:

[0032] ;

[0033] in, The trend parameter to be estimated is used to characterize the spatial gradient of regional atmospheric delay and its evolution over time; equivalently, the trend basis function vector is defined as:

[0034] ;

[0035] And order Then we have:

[0036] ;

[0037] (2) Spatiotemporal correlation description of random disturbance term

[0038] The random disturbance term It has spatiotemporal correlation, and its correlation is determined by spatial distance. With time interval Jointly determined; in one implementation, a spatially and temporally independent correlation function form can be used:

[0039] ;

[0040] in, For spatially relevant scale parameters, These are time-dependent scale parameters. Representing the Spatiotemporal observations.

[0041] (3) Prediction and solution based on BLUP

[0042] All observation points within the dynamic spatiotemporal observation window and its observed values Construct a trend matrix Based on the spatiotemporal correlation, an observation covariance matrix is ​​constructed. (Its elements are determined by the spatiotemporal distance between observation point pairs); for the target position and target epoch. ,definition:

[0043] ;

[0044] Satisfying the unbiased constraint Under the given conditions, the weight vector is obtained through BLUP. and Lagrange multipliers This allows us to obtain the atmospheric delay prediction value at the target location. It outputs the initial prediction uncertainty information corresponding to the predicted value for uncertainty correction processing in step 4.

[0045] Step 4. Based on the leave-one-out cross-validation strategy, perform statistical analysis and correction on the initial prediction uncertainty information to obtain corrected uncertainty information consistent with the actual atmospheric delay error level.

[0046] Leave-one-out cross-validation is performed epoch-by-epoch along the time dimension: the first epoch... Individual calendar The entire observation data is removed, and the remaining epochal data is used for modeling and prediction in step 3 to obtain the reference station data within that epoch. Predicted value at location And calculate the prediction error:

[0047] ;

[0048] At the same time, the corresponding initial prediction standard deviation is obtained. Based on the summary and Determine the global variance correction factor :

[0049] ;

[0050] Based on this, the initial prediction standard deviation is corrected to obtain the corrected prediction standard deviation:

[0051] ;

[0052] The Used as an uncertainty input in step 5, user-side PPP-RTK atmospheric augmentation positioning.

[0053] Step 5. Introduce the atmospheric delay prediction results and their corrected uncertainty information as atmospheric enhancement constraints into the user-side PPP-RTK positioning solution, complete the user positioning solution based on the uncertainty adaptive weighting strategy, and output the user positioning results.

[0054] The regional atmospheric delay correction obtained in step 3 and the corrected uncertainty information obtained in step 4 are transmitted to the user side. The atmospheric delay correction is introduced into the user-side PPP-RTK positioning solution model as an external constraint. The corresponding constraints are adaptively weighted according to the uncertainty information to complete the user-side PPP-RTK atmospheric enhancement positioning solution and output the user positioning result.

[0055] The beneficial effects of this invention are as follows:

[0056] This invention proposes a dynamic spatiotemporal modeling and uncertainty quantification method for atmospheric delay in PPP-RTK. Under complex atmospheric and regional network conditions, by introducing a dynamic spatiotemporal joint modeling strategy in the regional atmospheric delay modeling process, it overcomes to some extent the impact of single-epoch spatial modeling and idealized model assumptions on atmospheric delay prediction performance, improving the stability and consistency of regional atmospheric delay prediction results over time series. Simultaneously, by combining an epoch-wise leave-one-out cross-validation uncertainty correction method, it adaptively corrects the uncertainty of regional atmospheric delay prediction, enabling the uncertainty description to more realistically reflect the actual prediction error level and maintaining the reliability of atmospheric delay correction constraints in user-side positioning solutions. This, in turn, improves the accuracy, stability, and overall reliability of PPP-RTK positioning solutions. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0058] Figure 2 This is a diagram of leave-one-out cross-validation for each epoch.

[0059] Figure 3 This is a comparison chart of the positioning errors of traditional atmospheric modeling methods and dynamic spatiotemporal modeling methods in the east (E), north (N), and elevation (U) directions. Detailed Implementation

[0060] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0061] As shown in the figure, the specific steps of the atmospheric delay dynamic spatiotemporal modeling and uncertainty quantification method for PPP-RTK described in this invention are as follows:

[0062] Step 1. Obtain the global navigation satellite system observation data of the regional reference station, and combine it with precise orbit, precise clock error and phase deviation products to perform PPP or PPP-AR calculation on the regional reference station and extract the atmospheric delay observation data of the regional reference station.

[0063] Based on the raw GNSS observation data from the regional reference station, a precise single-point positioning observation model is established. This model describes the relationship between the observed data, unknown parameters, and observation errors. The unknown parameters include at least the receiver coordinate parameters, receiver clock error parameters, carrier phase ambiguity parameters, and atmospheric delay parameters. The observation error is characterized by a random error term and constrained by the corresponding stochastic model.

[0064] By performing PPP or PPP-AR calculations on the observation model, atmospheric delay estimates for each reference station at different epochs are obtained, which serve as observation input data for subsequent dynamic spatiotemporal modeling.

[0065] Step 2. Based on the atmospheric delay observation data, introduce time dimension information to construct a dynamic spatiotemporal observation window for atmospheric delay containing multiple epochs, which is used to characterize the continuous variation characteristics of regional atmospheric delay in space and time.

[0066] Based on the atmospheric delay observation data of the regional reference station at different epochs obtained in step 1, the region's first... The reference station is at the first The atmospheric delayed observation at each epoch is denoted as:

[0067] ;

[0068] in, Indicates the first Spatial coordinates of each reference station Indicates the corresponding observation epoch time;

[0069] Within a preset time range, select multiple consecutive epochs. The atmospheric delay observations of all reference stations within the corresponding epoch are jointly organized with their spatial locations to form a dynamic spatiotemporal observation window, whose observation data set is represented as follows:

[0070] ;

[0071] in, Indicates the number of regional reference stations. This indicates the number of epochs contained within the dynamic spatiotemporal observation window. The dynamic spatiotemporal observation window is used to describe the joint changes in the spatial distribution and temporal evolution of regional atmospheric delay, and is updated as the epoch progresses, providing a spatiotemporal joint observation data foundation for subsequent dynamic spatiotemporal modeling of regional atmospheric delay.

[0072] Step 3. Within the dynamic spatiotemporal observation window, perform dynamic spatiotemporal modeling of the regional atmospheric delay, generate atmospheric delay prediction results at the target location, and simultaneously obtain the initial prediction uncertainty information corresponding to the prediction results.

[0073] Within the dynamic spatiotemporal observation window constructed in step 2, the regional atmospheric delay observation values ​​are represented as follows:

[0074] ;

[0075] in, Spatial location coordinates, For epochal time; This is the trend term, used to describe the large-scale spatiotemporal variations of regional atmospheric delay; This is a zero-mean random disturbance term used to describe local fluctuations and random errors;

[0076] (1) Expression of the trend term

[0077] The trend term is constructed using a first-order polynomial that incorporates both spatial and temporal dimensions, and its expression is:

[0078] ;

[0079] in, The trend parameter to be estimated is used to characterize the spatial gradient of regional atmospheric delay and its evolution over time; equivalently, the trend basis function vector is defined as:

[0080] ;

[0081] And order Then we have:

[0082] ;

[0083] (2) Spatiotemporal correlation description of random disturbance term

[0084] The random disturbance term It has spatiotemporal correlation, and its correlation is determined by spatial distance. With time interval Jointly determined; in one implementation, a spatially and temporally independent correlation function form can be used:

[0085] ;

[0086] in, For spatially relevant scale parameters, These are time-dependent scale parameters. Representing the Spatiotemporal observations.

[0087] (3) Prediction and solution based on BLUP

[0088] All observation points within the dynamic spatiotemporal observation window and its observed values Construct a trend matrix Based on the spatiotemporal correlation, an observation covariance matrix is ​​constructed. (Its elements are determined by the spatiotemporal distance between observation point pairs); for the target position and target epoch. ,definition:

[0089] ;

[0090] Satisfying the unbiased constraint Under the given conditions, the weight vector is obtained through BLUP. and Lagrange multipliers This allows us to obtain the atmospheric delay prediction value at the target location. It outputs the initial prediction uncertainty information corresponding to the predicted value for uncertainty correction processing in step 4.

[0091] Step 4. Based on the leave-one-out cross-validation strategy, perform statistical analysis and correction on the initial prediction uncertainty information to obtain corrected uncertainty information consistent with the actual atmospheric delay error level.

[0092] Leave-one-out cross-validation is performed epoch-by-epoch along the time dimension: the first epoch... Individual calendar The entire observation data is removed, and the remaining epochal data is used for modeling and prediction in step 3 to obtain the reference station data within that epoch. Predicted value at location And calculate the prediction error:

[0093] ;

[0094] At the same time, the corresponding initial prediction standard deviation is obtained. Based on the summary and Determine the global variance correction factor :

[0095] ;

[0096] Based on this, the initial prediction standard deviation is corrected to obtain the corrected prediction standard deviation:

[0097] ;

[0098] The Used as an uncertainty input in step 5, user-side PPP-RTK atmospheric augmentation positioning.

[0099] Step 5. Introduce the atmospheric delay prediction results and their corrected uncertainty information as atmospheric enhancement constraints into the user-side PPP-RTK positioning solution, complete the user positioning solution based on the uncertainty adaptive weighting strategy, and output the user positioning results.

[0100] The regional atmospheric delay correction obtained in step 3 and the corrected uncertainty information obtained in step 4 are transmitted to the user side. The atmospheric delay correction is introduced into the user-side PPP-RTK positioning solution model as an external constraint. The corresponding constraints are adaptively weighted according to the uncertainty information to complete the user-side PPP-RTK atmospheric enhancement positioning solution and output the user positioning result.

[0101] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK, characterized in that, include: Step 1: Obtain the global navigation satellite system observation data of the regional reference station, and combine it with the precise orbit, precise clock error and phase deviation products to perform PPP or PPP-AR calculation on the regional reference station and extract the atmospheric delay observation data of the regional reference station; Step 2: Based on the atmospheric delay observation data, introduce time dimension information to construct a dynamic spatiotemporal observation window for atmospheric delay containing multiple epochs, which is used to characterize the continuous variation characteristics of regional atmospheric delay in space and time. Step 3: Within the dynamic spatiotemporal observation window, perform dynamic spatiotemporal modeling of the regional atmospheric delay, generate atmospheric delay prediction results at the target location, and simultaneously obtain the initial prediction uncertainty information corresponding to the prediction results; Step 4: Based on the leave-one-out cross-validation strategy, perform statistical analysis and correction on the initial prediction uncertainty information to obtain corrected uncertainty information consistent with the actual atmospheric delay error level; Step 5: Introduce the atmospheric delay prediction results and their corrected uncertainty information as atmospheric enhancement constraints into the user-side PPP-RTK positioning solution, complete the user positioning solution based on the uncertainty adaptive weighting strategy, and output the user positioning results.

2. The method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK as described in claim 1, characterized in that, Step 1, acquiring atmospheric delay observation data from the regional reference station, includes: Based on the raw GNSS observation data from the regional reference station, a precise single-point positioning observation model is established. This model describes the relationship between the observed data, unknown parameters, and observation errors. The unknown parameters include at least the receiver coordinate parameters, receiver clock error parameters, carrier phase ambiguity parameters, and atmospheric delay parameters. The observation error is characterized by a random error term and constrained by the corresponding stochastic model. By performing PPP or PPP-AR calculations on the observation model, atmospheric delay estimates for each reference station at different epochs are obtained, which serve as observation input data for subsequent dynamic spatiotemporal modeling.

3. The method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK as described in claim 1, characterized in that, Step 2, which involves constructing a dynamic spatiotemporal observation window, includes: Based on the atmospheric delay observation data of the regional reference station at different epochs obtained in step 1, the region's first... The reference station is at the first The atmospheric delayed observation at each epoch is denoted as: ； in, Indicates the first Spatial coordinates of each reference station Indicates the corresponding observation epoch time; Within a preset time range, select multiple consecutive epochs. The atmospheric delay observations of all reference stations within the corresponding epoch are jointly organized with their spatial locations to form a dynamic spatiotemporal observation window, whose observation data set is represented as follows: ； in, Indicates the number of regional reference stations. This indicates the number of epochs contained within the dynamic spatiotemporal observation window. The dynamic spatiotemporal observation window is used to describe the joint changes in the spatial distribution and temporal evolution of regional atmospheric delay, and is updated as the epoch progresses, so as to provide a spatiotemporal joint observation data basis for subsequent dynamic spatiotemporal modeling of regional atmospheric delay.

4. The method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK as described in claim 1, characterized in that, Step 3, the dynamic spatiotemporal modeling of the regional atmospheric delay, includes: Within the dynamic spatiotemporal observation window constructed in step 2, the regional atmospheric delay observation values ​​are represented as follows: ； in, Spatial location coordinates, For epochal time; This is the trend term, used to describe the large-scale spatiotemporal variations of regional atmospheric delay; This is a zero-mean random disturbance term used to describe local fluctuations and random errors; (1) Expression of the trend term The trend term is constructed using a first-order polynomial that incorporates both spatial and temporal dimensions, and its expression is: ； in, The trend parameter to be estimated is used to characterize the spatial gradient of regional atmospheric delay and its evolution over time; equivalently, the trend basis function vector is defined as: ； And order Then we have: ； (2) Spatiotemporal correlation description of random disturbance term The random disturbance term It has spatiotemporal correlation, and its correlation is determined by spatial distance. With time interval Jointly determined; in one implementation, a spatially and temporally independent correlation function is used: ； in, For spatially relevant scale parameters, For time-dependent scale parameters; Representing the One spatiotemporal observation value; (3) Prediction and solution based on BLUP All observation points within the dynamic spatiotemporal observation window and its observed values Construct a trend matrix Based on the spatiotemporal correlation, an observation covariance matrix is ​​constructed. For target location and target epoch ,definition: ； Satisfying the unbiased constraint Under the given conditions, the weight vector is obtained through BLUP. and Lagrange multipliers This allows us to obtain the atmospheric delay prediction value at the target location. It outputs the initial prediction uncertainty information corresponding to the predicted value for uncertainty correction processing in step 4.

5. The atmospheric delay dynamic spatiotemporal modeling and uncertainty quantification method for PPP-RTK as described in claim 1, characterized in that, Step 4, which involves uncertainty quantification based on leave-one-out cross-validation, includes: Leave-one-out cross-validation is performed epoch-by-epoch along the time dimension: the first epoch... Individual calendar The entire observation data is removed, and the remaining epochal data is used for modeling and prediction in step 3 to obtain the reference station data within that epoch. Predicted value at location And calculate the prediction error: ； At the same time, the corresponding initial prediction standard deviation is obtained. Based on the summary and Determine the global variance correction factor : ； Based on this, the initial prediction standard deviation is corrected to obtain the corrected prediction standard deviation: ； The Used as an uncertainty input in step 5, user-side PPP-RTK atmospheric augmentation positioning.

6. The method for dynamic spatiotemporal modeling and uncertainty quantification of atmospheric delay for PPP-RTK as described in claim 1, characterized in that, Step 5, the user-side PPP-RTK atmospheric enhancement positioning based on atmospheric uncertainties, includes: The regional atmospheric delay correction obtained in step 3 and the corrected uncertainty information obtained in step 4 are transmitted to the user side. The atmospheric delay correction is introduced into the user-side PPP-RTK positioning solution model as an external constraint. The corresponding constraints are adaptively weighted according to the uncertainty information to complete the user-side PPP-RTK atmospheric enhancement positioning solution and output the user positioning result.

Images