A method, storage medium, and device for tropospheric delay modeling based on multi-source data

Abstract

This invention discloses a method, storage medium, and device for tropospheric delay modeling based on multi-source data. The method includes: estimating first tropospheric delay data using GNSS data processing software and recording the location information and observation time of each GNSS station; calculating second tropospheric delay data based on observation data from each meteorological station and recording the location information and observation time of each meteorological station; constructing a tropospheric delay polynomial model based on the location information of the GNSS stations and the meteorological stations; constructing training samples using the location information of each GNSS station, the first tropospheric delay data, the location information of each meteorological station, and the second tropospheric delay data at the same observation time; optimizing the polynomial parameters of the tropospheric delay polynomial model; and calculating the tropospheric delay data at any specified location using the tropospheric delay polynomial model with the optimal polynomial parameters. This invention achieves high-precision, high-spatiotemporal-resolution tropospheric delay modeling.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and more specifically, to a tropospheric delay modeling method, storage medium, and device based on multi-source data. Background Technology

[0002] Tropospheric delay is the delay in the signal of a Global Navigation Satellite System (GNSS) as it travels through the atmosphere due to atmospheric refraction. It is one of the key error sources limiting the high-precision positioning of GNSS stations. In fields that rely on centimeter- to millimeter-level positioning accuracy, such as precise point positioning, engineering surveying, and geological disaster monitoring, high-precision tropospheric delay modeling is crucial.

[0003] Currently, tropospheric delay modeling methods include: empirical modeling, tropospheric delay modeling methods based on numerical meteorological models, and modeling methods based on GNSS station Zenith Tropospheric Delay (ZTD). Empirical models, such as the Saastamoinen and Hopfield models, are simple in structure and computationally efficient, but their accuracy is relatively low, especially under complex terrain or severe weather conditions. Tropospheric delay modeling methods based on numerical meteorological models can theoretically provide high-precision tropospheric delay errors; however, they rely on large and complex meteorological simulation systems, resulting in long computation times and limitations in practical navigation and positioning applications. The model quality of GNSS Zenith Tropospheric Delay modeling methods depends on high-precision GNSS station ZTD data and the density of GNSS stations. Although high-precision ZTD data can currently be estimated based on GNSS station observations, the high cost of station construction and maintenance results in low GNSS station density and uneven distribution, thus affecting the quality of GNSS station ZTD modeling. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a tropospheric delay modeling method, storage medium, and device based on multi-source data. By fusing high-precision first tropospheric delay data and high spatial resolution second tropospheric delay data, high-precision and high spatiotemporal resolution tropospheric delay modeling is achieved.

[0005] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0006] A tropospheric delay modeling method based on multi-source data includes the following steps:

[0007] Acquire observation data from each GNSS station, combine broadcast ephemeris files and precise ephemeris files, use GNSS data processing software to estimate first tropospheric delay data, and record the location information and observation time of each GNSS station;

[0008] Based on the observation data from each meteorological station, the second tropospheric delay data were calculated according to the Saastamoinen model, and the location information and observation time of each meteorological station were recorded.

[0009] A tropospheric delay polynomial model is constructed based on the location information of GNSS stations and meteorological stations.

[0010] Training samples were constructed using the location information of each GNSS station, the first tropospheric delay data, the location information of each meteorological station, and the second tropospheric delay data under the same observation time.

[0011] The polynomial parameters of the tropospheric delay polynomial model are solved by optimizing the training samples based on Bayesian regularized Helmert variance components, and the optimal polynomial parameters are determined for the corresponding observation time.

[0012] The tropospheric delay polynomial model with optimal polynomial parameters is used to calculate the tropospheric delay data at any specified location.

[0013] Furthermore, the calculation process for the second tropospheric delay data is as follows:

[0014]

[0015] in, Indicates passing through the first m The second tropospheric delay data was calculated from observation data from several weather stations. Indicates the first m The elevation angle of each weather station Indicates the first m Air pressure observed at each weather station Indicates the first m Temperatures observed at each weather station Indicates the first m Water vapor pressure obtained from each weather station , Indicates the first m Relative humidity observed at each weather station Indicates the first m Elevation of each weather station List functions, express The correction function, , Indicates the first m The latitude of each weather station, Indicates based on and List functions.

[0016] Furthermore, the construction process of the tropospheric delayed polynomial model is as follows:

[0017]

[0018] in, This represents a tropospheric delay polynomial model. ~ Represents the polynomial coefficients. This represents the bias correction term in the Saastamoinen model. This indicates the longitude of all GNSS and meteorological stations. This indicates the latitude of all GNSS and meteorological stations. This represents the ellipsoidal height of all GNSS and meteorological stations.

[0019] Furthermore, the process of determining the optimal polynomial parameters is as follows:

[0020] i: Obtain polynomial parameters based on the tropospheric delay polynomial model. and spatial characteristic matrix An observation vector is constructed using first and second tropospheric delay data, where, T Indicates transpose. Indicates measurement deviation. ;

[0021] ii: Introduce a diagonal weight matrix based on corrected variance update to construct an optimization equation for the polynomial parameters. ,in, Represents the regularization parameter. Represents the identity matrix. Indicates the first t The diagonal weight matrix updated based on corrected variance in the next iteration Represents the observation vector. , This represents all first tropospheric delay data at the corresponding observation time. This represents all second tropospheric delay data at the corresponding observation time;

[0022] iii: Input the training samples at the corresponding observation time into the optimization equation of the polynomial parameters and iteratively optimize the polynomial parameters until the total correction variance change under adjacent iterations is less than the threshold, thus obtaining the optimal polynomial parameters.

[0023] Furthermore, the weight update process for each type of station in the diagonal weight matrix is ​​as follows:

[0024]

[0025] in, i This indicates the type of station, which is either a GNSS station or a meteorological station. Indicates the first t The iteration of the iteration i The weight of each monitoring station express The weighting percentage Indicates the first t The iteration of the iteration i Corrected variance of the various stations , Indicates the first i The total number of monitoring stations, l express index, Indicates the prior equivalent sample size. Indicates the first i The initial prior variance of the stations, Indicates the first l The observed values ​​of the first station and the first t The residuals of the calculated values ​​of the tropospheric delayed polynomial model in the next iteration , Indicates the first l Observations from each station Indicates the first l Spatial feature matrix of each station Indicates the first t Polynomial parameters in the next iteration express The weighting percentage.

[0026] Furthermore, the total corrected variance is expressed as:

[0027]

[0028] in, Indicates the first t Total corrected variance over the next iteration.

[0029] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program that causes a computer to execute the tropospheric delay modeling method based on multi-source data.

[0030] Furthermore, the present invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the tropospheric delay modeling method based on multi-source data.

[0031] Compared with existing technologies, the present invention has the following advantages: The tropospheric delay modeling method based on multi-source data of the present invention constructs a tropospheric delay polynomial model through the location information of GNSS stations and meteorological stations, and optimizes the polynomial parameters of the tropospheric delay polynomial model by using high-precision first tropospheric delay data and high spatial resolution second tropospheric delay data. By introducing an adaptive dynamic weight allocation algorithm for Bayesian regularized Helmert variance component estimation, the accuracy difference between the first and second tropospheric delay data is balanced. At the same time, a Saastamoinen model systematic bias correction term is introduced to specifically solve the systematic bias of meteorological stations, effectively overcoming the defects of insufficient spatial resolution of single-source GNSS station models and limited accuracy of single-source meteorological data, thereby constructing a tropospheric delay polynomial model with centimeter-level accuracy. Compared with tropospheric delay models using single-source GNSS station data and single-source meteorological data, the tropospheric delay modeling method of this invention reduces the absolute value of the deviation of the calculated tropospheric delay data by 10% to 40%, and the root mean square error is reduced simultaneously. This effectively solves the problem that insufficient spatial resolution of current GNSS stations and the inadequate use of ground meteorological station observation data affect the quality of tropospheric delay modeling. The tropospheric delay modeling method based on multi-source data of this invention is applicable to various GNSS systems such as GPS, BDS, GLONASS, and GALILEO, and can be widely applied to high-precision navigation and positioning scenarios such as UAVs and vehicle-mounted equipment. Attached Figure Description

[0032] Figure 1 This is a flowchart of the tropospheric delay modeling method based on multi-source data according to the present invention;

[0033] Figure 2 The above is a time series diagram of tropospheric delay data compared to the tropospheric delay modeling method based on multi-source data of the present invention and existing methods;

[0034] Figure 3 This is a time series diagram showing the deviation of tropospheric delay data between the tropospheric delay modeling method based on multi-source data of the present invention and existing methods. Detailed Implementation

[0035] The technical solution of the present invention will be further explained and described below with reference to the accompanying drawings.

[0036] like Figure 1 This is a flowchart of the tropospheric delay modeling method based on multi-source data according to the present invention. The tropospheric delay modeling method includes:

[0037] The observation data of each GNSS station is acquired, and the first tropospheric delay data is estimated by combining the broadcast ephemeris file and the precise ephemeris file with GNSS data processing software. The location information and observation time of each GNSS station are recorded. In one technical solution of the present invention, the GNSS station data processing software used is GAMIT10.71.

[0038] Based on the observation data from each meteorological station, including the observed temperature, air pressure and relative humidity, the second tropospheric delay data were calculated according to the Saastamoinen model, and the location information and observation time of each meteorological station were recorded.

[0039] The calculation process for the second tropospheric delay data in this invention is as follows:

[0040]

[0041] in, Indicates passing through the first m The second tropospheric delay data was calculated from observation data from several weather stations. Indicates the first m The elevation angle of each weather station Indicates the first m Air pressure observed at each weather station Indicates the first m Temperatures observed at each weather station Indicates the first m Water vapor pressure obtained from each weather station , Indicates the first m Relative humidity observed at each weather station Indicates the first m Elevation of each weather station List functions, express The correction function, , Indicates the first m The latitude of each weather station, Indicates based on and List functions.

[0042] A tropospheric delay polynomial model is constructed based on the location information of GNSS stations and meteorological stations:

[0043]

[0044] in, This represents a tropospheric delay polynomial model. ~ Represents the polynomial coefficients. This represents the bias correction term in the Saastamoinen model. This indicates the longitude of all GNSS and meteorological stations. This indicates the latitude of all GNSS and meteorological stations. This represents the ellipsoidal height of all GNSS and meteorological stations.

[0045] Training samples were constructed using the location information of each GNSS station, the first tropospheric delay data, the location information of each meteorological station, and the second tropospheric delay data under the same observation time.

[0046] The polynomial parameters of the tropospheric delay polynomial model are solved by optimizing the training samples based on Bayesian regularized Helmert variance components, and the optimal polynomial parameters are determined for the corresponding observation time; specifically:

[0047] i: Obtain polynomial parameters based on the tropospheric delayed polynomial model and spatial characteristic matrix Observation vectors are constructed using first and second tropospheric delay data. Among them, the spatial feature matrix It contains relevant information from all the GNSS and meteorological stations involved in the measurement. T Indicates transpose. This indicates the measurement deviation. When using a GNSS station to acquire the first tropospheric delay data, the measurement deviation is 0. When using a meteorological station to acquire the second tropospheric delay data, the measurement deviation is 1. , This represents all first tropospheric delay data at the corresponding observation time. This represents all second tropospheric delay data at the corresponding observation time.

[0048] ii: Due to the accuracy difference between the first and second tropospheric delay data, a diagonal weight matrix based on corrected variance update is introduced to construct an optimized solution equation for the polynomial parameters. ,in, Represents the regularization parameter. Represents the identity matrix. Indicates the first t The diagonal weight matrix is ​​updated based on the corrected variance in the next iteration;

[0049] In this invention, the initial weight value for each type of station in the diagonal weight matrix is ​​set as follows:

[0050]

[0051] in, Indicates the first i Initial weights for each monitoring station. Indicates the first i The prior accuracy of the station, when it is a GNSS station. The value range is 0.5~3cm; when it is a weather station, The value range is 2~7cm.

[0052] Based on this, the weight update process for each type of monitoring station is as follows:

[0053]

[0054] in, i This indicates the type of station; it is either a GNSS station or a meteorological station. Indicates the first t The iteration of the iteration i The weight of each monitoring station express The weighting percentage is used to balance stability and responsiveness, and is generally set to 0.8. Indicates the first t The iteration of the iteration i Corrected variance of the various stations , Indicates the first i The total number of monitoring stations, l express index, Indicates the prior equivalent sample size. Indicates the first i The initial prior variance of the stations, Indicates the first l The observed values ​​of the first station and the first t The residuals of the calculated values ​​of the tropospheric delayed polynomial model in the next iteration , Indicates the first l Observations from each station Indicates the first l Spatial feature matrix of each station Indicates the first t Polynomial parameters in the next iteration express The weighting percentage is generally set to 0.2.

[0055] By combining the prior accuracy and residual sum of squares of corresponding station types, the actual variances of the first and second tropospheric delay data are corrected respectively. Using Bayesian variance estimation, and through dynamic fusion of prior knowledge and training samples, robust correction of the actual variances of the first and second tropospheric delay data is achieved, overcoming the limitations of traditional methods that rely solely on residual sum of squares for variance correction. Furthermore, generally, with fewer GNSS stations, prior knowledge carries higher weight through a prior equivalent sample size, preventing abnormal variance estimation due to insufficient GNSS station numbers. With more meteorological stations, the residual sum of squares accounts for a high proportion, weakening the influence of prior knowledge. Introducing a prior equivalent sample size makes the meteorological station variance estimation closer to the actual data characteristics. This Bayesian fusion logic utilizes real-time information from current observation data while controlling the tropospheric delay polynomial model through prior constraints, making... It is more robust, providing a reliable basis for the dynamic weight update of the station, fundamentally avoiding the phenomenon of overfitting of the tropospheric delay polynomial model due to variance estimation bias, and improving the accuracy and stability of fused tropospheric delay modeling.

[0056] iii: Input the training samples at the corresponding observation time into the optimization equation of the polynomial parameters and iteratively optimize the polynomial parameters until the total correction variance change under adjacent iterations is less than a threshold, thus obtaining the optimal polynomial parameters. In one technical solution of this invention, the threshold is set to 10. -4 .

[0057] In this invention, the total corrected variance is expressed as:

[0058]

[0059] in, Indicates the first t Total corrected variance over the next iteration.

[0060] The tropospheric delay data at any specified location is calculated using a tropospheric delay polynomial model with optimal polynomial parameters. Specifically, the longitude, latitude, and ellipsoidal height of any location within the coverage area of ​​GNSS and meteorological stations are input into the tropospheric delay polynomial model with optimal polynomial parameters to calculate the tropospheric delay data at the corresponding location.

[0061] To verify the effectiveness of the tropospheric delay modeling method based on multi-source data of this invention, observation data from 10 GNSS stations and 40 meteorological stations were selected, and a tropospheric delay polynomial model was constructed using the tropospheric delay modeling method based on multi-source data of this invention. For example... Figure 2Time series plots of tropospheric delay data based on polynomial models from single-source GNSS stations, polynomial models from single-source meteorological stations, and the tropospheric delay polynomial model based on multi-source data of this invention are presented. It can be seen that the tropospheric delay data calculated by the tropospheric delay polynomial model based on multi-source data of this invention has a high degree of consistency with the actual tropospheric delay data and has minimal local deviation. In contrast, the tropospheric delay data calculated by the polynomial models from single-source GNSS stations and single-source meteorological stations have significant differences in trend from the actual tropospheric delay data. This indicates that the tropospheric delay polynomial model based on multi-source data of this invention can achieve high-precision modeling. Figure 3 A comparison of the deviations of tropospheric delay data calculated by the polynomial model based on a single-source GNSS station, the polynomial model based on a single-source meteorological station, and the tropospheric delay polynomial model based on multi-source data of this invention is presented. It can be seen that the deviation of the present invention remains consistently stable within ±0.04m with minimal fluctuations, while the deviation of the polynomial model based on a single-source GNSS station exhibits violent oscillations, and the deviation of the polynomial model based on a single-source meteorological station also shows significant random fluctuations. Table 1 compares the modeling accuracy of the polynomial models based on single-source GNSS stations, the polynomial model based on a single-source meteorological station, and the tropospheric delay polynomial model based on multi-source data of this invention. It can be seen that the absolute value of the deviation of the tropospheric delay data calculated by this invention is reduced by 10%–40%, and the root mean square error is reduced simultaneously. This effectively solves the problem of insufficient spatial resolution of current GNSS stations and the inadequate use of ground meteorological station observation data affecting the quality of tropospheric delay modeling, achieving centimeter-level accuracy in tropospheric delay polynomial model construction. This can enhance the large-scale application capability of high-precision navigation and positioning in fields such as engineering surveying and geological disaster monitoring.

[0062] Table 1. Comparison of modeling accuracy between the tropospheric delay modeling method based on multi-source data of this invention and existing methods (unit: cm)

[0063]

[0064] In one technical solution of the present invention, a computer-readable storage medium is also provided, storing a computer program that enables a computer to execute the tropospheric delay modeling method based on multi-source data of the present invention.

[0065] In one technical solution of the present invention, an electronic device is also provided, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the tropospheric delay modeling method based on multi-source data of the present invention.

[0066] In the embodiments disclosed in this application, a computer storage medium may be a tangible medium that may contain or store programs for use by or in conjunction with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of computer storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0067] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0068] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A tropospheric delay modeling method based on multi-source data, characterized in that, Includes the following steps: Acquire observation data from each GNSS station, combine broadcast ephemeris files and precise ephemeris files, use GNSS data processing software to estimate first tropospheric delay data, and record the location information and observation time of each GNSS station; Based on the observation data from each meteorological station, the second tropospheric delay data were calculated according to the Saastamoinen model, and the location information and observation time of each meteorological station were recorded. The calculation process for the second tropospheric delay data is as follows: in, Indicates passing through the first m The second tropospheric delay data was calculated from observation data from several weather stations. Indicates the first m The elevation angle of each weather station Indicates the first m Air pressure observed at each weather station Indicates the first m Temperatures observed at each weather station Indicates the first m Water vapor pressure obtained from each weather station , Indicates the first m Relative humidity observed at each weather station Indicates the first m Elevation of each weather station List functions, express The correction function, , Indicates the first m The latitude of each weather station, Indicates based on and List functions; A tropospheric delay polynomial model is constructed based on the location information of GNSS stations and meteorological stations: in, This represents a tropospheric delay polynomial model. ~ Represents the polynomial coefficients. This represents the bias correction term in the Saastamoinen model. This indicates the longitude of all GNSS and meteorological stations. This indicates the latitude of all GNSS and meteorological stations. This represents the ellipsoidal height of all GNSS and meteorological stations; Training samples were constructed using the location information of each GNSS station, the first tropospheric delay data, the location information of each meteorological station, and the second tropospheric delay data under the same observation time. The polynomial parameters of the tropospheric delay polynomial model are solved by optimizing the training samples based on Bayesian regularized Helmert variance components, and the optimal polynomial parameters are determined for the corresponding observation time. The tropospheric delay polynomial model with optimal polynomial parameters is used to calculate the tropospheric delay data at any specified location.

2. The tropospheric delay modeling method based on multi-source data according to claim 1, characterized in that, The process of determining the optimal polynomial parameters is as follows: i: Obtain polynomial parameters based on the tropospheric delay polynomial model. and spatial characteristic matrix An observation vector is constructed using first and second tropospheric delay data, where, T Indicates transpose. Indicates measurement deviation. ; ii: Introduce a diagonal weight matrix based on corrected variance update to construct an optimization equation for the polynomial parameters. ,in, Represents the regularization parameter. Represents the identity matrix. Indicates the first t The diagonal weight matrix updated based on corrected variance in the next iteration Represents the observation vector. , This represents all first tropospheric delay data at the corresponding observation time. This represents all second tropospheric delay data at the corresponding observation time; iii: Input the training samples at the corresponding observation time into the optimization equation of the polynomial parameters and iteratively optimize the polynomial parameters until the total correction variance change under adjacent iterations is less than the threshold, thus obtaining the optimal polynomial parameters.

3. The tropospheric delay modeling method based on multi-source data according to claim 2, characterized in that, The weight update process for each type of station in the diagonal weight matrix is ​​as follows: in, i This indicates the type of station, which is either a GNSS station or a meteorological station. Indicates the first t The iteration of the iteration i The weight of each monitoring station express The weighting percentage Indicates the first t The iteration of the iteration i Corrected variance of the measurement stations , Indicates the first i The total number of monitoring stations, l express index, Indicates the prior equivalent sample size. Indicates the first i The initial prior variance of the stations, Indicates the first l The observed values ​​of the first station and the first t The residuals of the calculated values ​​of the tropospheric delayed polynomial model in the next iteration , Indicates the first l Observations from each station Indicates the first l Spatial feature matrix of each station Indicates the first t Polynomial parameters in the next iteration express The weighting percentage.

4. The tropospheric delay modeling method based on multi-source data according to claim 3, characterized in that, The total corrected variance is expressed as follows: in, Indicates the first t Total corrected variance over the next iteration.

5. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to execute the tropospheric delay modeling method based on multi-source data as described in any one of claims 1-4.

6. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the tropospheric delay modeling method based on multi-source data as described in any one of claims 1-4.

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