CN117574622A - Troposphere modeling method and device - Google Patents
Troposphere modeling method and device Download PDFInfo
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Abstract
The application discloses a troposphere modeling method, comprising the following steps: setting virtual stations according to the set spatial resolution, and calculating time-varying ZWD of each virtual station according to weather analysis data; according to the space variation characteristic of the troposphere delay of the time-varying ZWD value analysis area calculated by simulation, fitting a variation function; according to the ZWD value and the variation function value of the GNSS observation station, interpolating to calculate the ZWD of the regular lattice points; PPP solution is performed using regular lattice points ZWD. The application also includes an apparatus for implementing the method. The technical scheme of the application solves the problem that the troposphere model in the prior art is low in precision.
Description
Technical Field
The application relates to the technical field of satellite navigation, in particular to a troposphere modeling method and device.
Background
The global satellite system (Global Navigation Satellite System, GNSS) can provide Real-time precision single point location services (Real-Time Precise Point Positioning, RT-PPP) through the predictive precision ephemeris (IGU) provided by the IGS center. In real-time PPP data processing, satellite clock errors and orbit errors can be corrected through precise satellite orbits and clock error products, ionosphere delay can be eliminated by over 90% through double-frequency ionosphere-free combination, troposphere delay can only be corrected through a model, traditional troposphere models are all based on empirical meteorological parameters, the water vapor content of high variation in the atmosphere cannot be considered, and the model precision is difficult to meet the high-precision requirement.
At present, the most commonly used construction method of the high-precision real-time troposphere model is based on ground reference stations such as a land-based network or a Beidou foundation enhancement network, the high-precision troposphere delay correction value is calculated through PPP by fixing station coordinates, the troposphere delay is interpolated to regular lattice points of 1-5 degrees according to the reference station distribution, and the accuracy of the troposphere lattice model constructed in the mode can reach 1-2 cm. In addition, the high-precision troposphere model can be used for optimizing a mathematical model of PPP, the mathematical model comprises a function model and a random model, a pseudo-range observation value and a carrier phase observation value are divided in the function model, troposphere delay is introduced into each group of observation equations to serve as a virtual observation value, and the weight of the troposphere virtual observation value in calculation is increased in the random model, so that optimization is achieved. However, the existing grid models all adopt interpolation grid points based on distance reverse weighting, only distance factors are considered, weights provided in random models are empirical values, high-precision information cannot be provided by fully utilizing troposphere models, the troposphere model precision is influenced by multiple space-time factors such as seasons, latitude, altitude and the like, and real-time performance of the models cannot be embodied by taking the empirical values as weights. In summary, there is also an optimization space in the existing model.
Disclosure of Invention
The application provides a troposphere modeling method and device, which solve the problem that the space-time characteristics of a troposphere are not considered in the existing modeling method.
The embodiment of the application provides a troposphere modeling method, which comprises the following steps:
setting virtual stations according to the set spatial resolution, and calculating tropospheric wet delay (ZWD) of each virtual station according to weather analysis data;
according to the space variation characteristic of the troposphere delay of the time-varying ZWD value analysis area calculated by simulation, fitting a variation function;
according to the ZWD value and the variation function value of the GNSS observation station, interpolating to calculate the ZWD of the regular lattice points;
PPP solution is performed using regular lattice points ZWD.
In one embodiment of the present application, the interpolation method uses Kriging interpolation.
In one embodiment of the application, the space resolution of the weather re-analysis data is 0.25 degrees x 0.25 degrees, the time resolution is hours, and the time-varying ZWD is calculated according to the set time resolution through a GNSS algorithm.
In one embodiment of the present application, unbiased estimation and minimum variance of the estimation error are used as constraints for interpolation.
The embodiment of the application also provides a troposphere modeling device, which is used for realizing the method according to any one embodiment of the application, and the device comprises:
the acquisition module is used for setting virtual stations according to the set spatial resolution and calculating the ZWD of each virtual station according to the weather analysis data;
the fitting module is used for analyzing the spatial variation characteristics of the troposphere delay of the region according to the time-varying ZWD value calculated by simulation and fitting a variation function;
the determining module is used for interpolating and calculating the ZWD of the regular lattice points according to the ZWD value and the variation function value of the GNSS observation station;
and the resolving module is used for PPP resolving by using the rule lattice point ZWD.
The embodiments also provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method as described in any of the embodiments of the present application.
The embodiment of the application also provides electronic equipment, which comprises a memory, a processor and a computer program stored on the memory and capable of being executed by the processor, wherein the processor executes the computer program to realize the method according to any embodiment of the application.
The above-mentioned at least one technical scheme that this application embodiment adopted can reach following beneficial effect:
the invention provides a method for constructing a high-precision tropospheric grid model taking space-time characteristics into consideration, interpolation is carried out by a Kriging method, wherein the Kriging is an optimal linear unbiased estimation method, and two criteria of unbiased estimation and minimum variance of estimation errors are required to be met simultaneously. The method provides high-precision delay correction values and simultaneously provides precision information of a model, the high-precision delay correction values are introduced into a function model as virtual observables, and the model precision information provides reference information for the virtual observables in a random model, so that the PPP function model and the random model are optimized simultaneously.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute an undue limitation to the application. In the drawings:
FIG. 1 is a flow chart of an embodiment of a tropospheric modeling method of the present application;
FIG. 2 is a flow chart of a tropospheric spatiotemporal character analysis;
FIG. 3 is an example of a theoretical model of variation function;
FIG. 4 is a schematic diagram of a model of convection Cheng Gewang;
FIG. 5 illustrates a tropospheric modeling apparatus embodiment of the present application;
fig. 6 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For the purposes, technical solutions and advantages of the present application, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments of the present application and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
According to the technical scheme, virtual stations are set according to the set resolution, ZWD distribution is obtained, then a dead ZWD space variation function is obtained through fitting, lattice points are built, ZWD values of the lattice points are obtained, and then a PPP function model is calculated. However, in the prior art, the troposphere delay is directly interpolated to a regular grid point of 1 DEG or 5 DEG, a troposphere grid model is constructed in the way, the interpolation is based on distance reverse interpolation, only distance factors are considered, and the Kriging interpolation is adopted, so that the space-time correlation between two points is estimated while the distance is considered.
Fig. 1 is a flowchart of an embodiment of a tropospheric modeling method of the present application.
The application provides a troposphere grid model construction method taking space-time characteristics into consideration, which calculates a variation value of a ZWD in a region by using weather re-analysis data (spatial resolution 0.25 degrees x 0.25 degrees, time resolution 1 hour) of ERA5 provided by a European middle weather forecast center (European Centre for MediumRange Weather Forecasts, ECMWF). The method comprises the following steps:
step 110, calculating a time-varying ZWD value according to the weather re-analysis data.
In one embodiment, first, a latitude range of 0 ° to 60 ° is divided into 4 latitude bands at 15 ° intervals, and in view of the weather re-analysis data spatial resolution of ERA5 being 0.25 ° x 0.25 ° and the time resolution being hour, a virtual station is set at the spatial resolution of 0.25 ° in each latitude band, as GNSS software input, the zenith tropospheric delay (Troposphere Zenith Delay, ZTD) and the tropospheric dry delay (Troposphere Zenith Hydrostatic Delay, ZHD) of each latitude band virtual station are calculated by GNSS calculation software at the set time resolution (e.g., set between hours and months) for a long period of time, and the time-varying ZWD is calculated by differencing. I.e.
ZWD(t)＝ZTD(t)–ZHD(t)
Wherein t represents time.
The "virtual station" here is defined in terms of the distribution of longitude, latitude, and altitude in the weather analysis data, and the extracted data is used as input data of the GNSS software.
It should also be noted that the time-varying ZWD of the present application incorporates a time attribute, and t is omitted from the following equations for simplicity of description.
And 120, analyzing the spatial variation characteristic of the regional troposphere delay according to the time-varying ZWD value calculated by simulation.
The area may refer to a latitude zone, for example. And (3) counting ZWD variation function values of each latitude zone in each month, determining a corresponding theoretical model according to variation trend, and further determining related parameters of the theoretical model, such as variation, block gold value, partial base station value and the like, wherein the calculation flow is shown in figure 2.
The variance function is a statistic describing the spatial correlation of ZWD, and may be defined as, for example, the variance between the ZWD values at two spatial points in space.
The variation trend of the ZWD is obtained through a large amount of empirical data analysis, the variation trend theoretical model is determined through fitting according to the variation trend, and the variation value between two points can be calculated by directly adopting the model in the follow-up practical application.
As an example, the method for calculating the variance function value of the regional tropospheric delay may be
Where h is called separation distance, N h Is within a distance (x i +h,x i ) The method defines h as a proper interval, and obtains the median in each interval range as the variation value of the interval. The basic formula of the variation function is formula (2), c 0 All of c and a are parameters describing variation characteristics, and h represents the relative distance.
γ(h)＝c 0 +c·F(a,h) (2)
The determination of the theoretical model of the variation function will be determined from the long-term variation law of the calculated variation value. The theoretical model of the variation trend includes, for example, a model with a base, a model without a base, a model with a cavity effect, and the like. For example, fig. 3 shows an example of a variation function that monotonically increases over the range of distances over which the variation is set. It should be noted that, the variation function does not monotonically increase after h is greater than a certain distance, but fluctuates at a certain period, and thus can be represented as a cavity model.
It should be noted that, according to the set time resolution, the ZWD value of any period is spatially fitted to obtain a variation function (including a variation function model and a parameter) of the period, so that different variation function models or parameters can be obtained for different periods, and a time-efficient regional tropospheric delay variation function set is generated, where each 1 variation function in the set is applicable to at least a portion of the period.
And 130, interpolating to calculate the ZWD of the regular lattice points according to the ZWD value and the variation function value of the GNSS observation station.
It should be noted that the observation station is an actual existing observation station from land-state network, such as Beidou foundation enhancement, etc., as represented by triangle symbols in fig. 4, x i Is indicative of the location of the observation station. Lattice points, defined by the points of intersection of the regular lattice (dot-shaped symbols), x in FIG. 4 0 Is indicative of where the grid point is located.
The ZWD value of the GNSS observation station is a ZWD value obtained by calculating based on site observation information, and can be connected to be an observation value.
By interpolating the data search, the GNSS observatory stations used for interpolation are selected within a certain range, and the search range can be determined according to the actual observatory station distribution (r=10 km, r=5 km, …).
The regional troposphere delay variation function set with timeliness is used for constructing a regular troposphere grid model, as shown in fig. 4, the delay correction value of the grid point is obtained by delay interpolation calculated by a GNSS observation station in an effective region, and an interpolation formula (3)
ZWD(x 0 ) Representing lattice point x 0 The ZWD at the location(s),ZWD(x i ) Representing an observation station x i ZWD at. Lambda (lambda) i The weight of the observation station i in the network is represented, and n represents the number of observation stations used for interpolation.
The minimum error variance of unbiased estimation and estimation value is used as the constraint condition of Kriging interpolation. The unbiased means that the mean value of the obtained estimated value is the same as the true value of the parameter to be estimated. The variance S can be deduced by minimum estimated variance, a Lagrangian multiplier mu is introduced when the estimated variance is minimum, first-order partial derivatives are calculated for each weight coefficient lambda, a Kriging linear equation system for calculating the weight is obtained, and the weight factor lambda can be obtained by solving the equation system i And a lagrangian multiplier factor mu.
Wherein lambda is i Interpolation according to Kriging can be calculated from equation (4).
Wherein n represents the number of stations, gamma ij Representing the variation value between site i and site j, gamma 0j Representing variation between lattice point and jth site, lambda i Representing the weight of station i in the network; μ represents the constraintWhere i, j=1 to n. The variance value γ between the sites is calculated from the model determined in step 120, and thus can be obtained by solving the equation (λ 1 、λ 2 、…、λ n μ), μ. The lattice points and observation points are collectively referred to herein as sites.
The Kriging estimation error variance can be used as accuracy information of lattice points,representing the variance of the grid point estimation values obtained by the method.
Gamma in formula (5) represents x0 and x i Variation between two points.
The weight matrix of the interpolation data is the 1 st matrix at the left end of the formula (4), and the (lambda 1, lambda) is calculated by the formula (4) 2 、…、λ n ) And the contribution of the tropospheric delay calculated by the GNSS observation station in the fitting area to the tropospheric delay of the grid points is represented.
Step 140, function model of grid point ZWD time-varying product for optimizing PPPAnd random model->Enhancing PPP resolution.
In the functional model of the present invention,the pseudorange observations and the carrier phase observations are represented, and Δt is the ZWD tropospheric delay correction value calculated by step 130.
In the optimization model, the process of the optimization model,for describing the accuracy of the pseudorange observations and the carrier phase observations, the ratio of accuracy between them is typically 1:100,/>The variance obtained for equation (5) is used to describe the model accuracy.
Fig. 4 is a schematic diagram of a convection Cheng Gewang model. In the tropospheric grid model, the circles of the regular grid intersections represent grid points of a certain resolution, the circles and dashed lines represent fitting areas of the tropospheric grid model (Tropospheric Grid Point, RTGP, TGP), the triangular symbols represent actual stations, and the triangular symbols (shown in gray) within the dashed line represent stations where the fitting areas are used to interpolate grid points.
Fig. 5 illustrates a tropospheric modeling apparatus embodiment of the present application. The embodiment of the application also provides a troposphere modeling device, which is used for realizing the method of any embodiment of the application, and comprises the following steps:
the acquisition module is used for setting virtual stations according to the set spatial resolution and calculating the ZWD of each virtual station according to the weather analysis data;
the fitting module is used for analyzing the spatial variation characteristics of the troposphere delay of the region according to the time-varying ZWD value calculated by simulation and fitting a variation function;
the determining module is used for interpolating and calculating the ZWD of the regular lattice points according to the ZWD value and the variation function value of the GNSS observation station;
and the resolving module is used for PPP resolving by using the rule lattice point ZWD.
Specifically, for a further specific processing procedure for implementing the relevant function, the modules are described in the above method embodiments, which are not repeated here.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Accordingly, the present application also proposes a computer readable storage medium, on which a computer program is stored, which program, when being executed by a processor, implements a method as described in any of the embodiments of the present application.
Further, the application also proposes an electronic device comprising a memory, a processor and a computer program stored on the memory and executable by the processor, said processor implementing a method according to any of the embodiments of the application when executing said computer program.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Fig. 6 is a schematic structural diagram of an electronic device according to an embodiment of the present application. The electronic device 600 shown is merely an example and should not be construed to limit the functionality and scope of use of embodiments of the present application. It comprises the following steps: one or more processors 620; a storage device 610, configured to store one or more programs that, when executed by the one or more processors 620, cause the one or more processors 620 to implement a tropospheric modeling method provided by embodiments of the present application, the method comprising:
setting virtual stations according to the set spatial resolution, and calculating ZWD of each virtual station according to weather analysis data;
according to the space variation characteristic of the troposphere delay of the time-varying ZWD value analysis area calculated by simulation, fitting a variation function;
according to the ZWD value and the variation function value of the GNSS observation station, interpolating to calculate the ZWD of the regular lattice points;
PPP solution is performed using regular lattice points ZWD.
In one typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory. The memory may include volatile memory in a computer-readable medium, random Access Memory (RAM) and/or nonvolatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of computer-readable media.
The electronic device 600 further comprises input means 630 and output means 640; the processor 620, the storage device 610, the input device 630, and the output device 640 in the electronic device may be connected by a bus or other means, which is shown as a connection via a bus 650.
The storage device 610 is a computer readable storage medium, and may be used to store a software program, a computer executable program, and program instructions corresponding to a method for determining a cloud bottom height in the embodiments of the present application. The storage device 610 may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, at least one application program required for functions; the storage data area may store data created according to the use of the terminal, etc. In addition, the storage 610 may include high-speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid-state storage device. In some examples, the storage device 610 may further include memory remotely located with respect to the processor 620, which may be connected via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The input device 630 may be used to receive input numeric, character information, or voice information, and to generate key signal inputs related to user settings and function control of the electronic device. The output device 640 may include an electronic device such as a display screen, a speaker, etc.
The tropospheric model constructed by combining Kriging interpolation starts from the space-time characteristic change of tropospheric delay, and has the following steps: the model has the advantages of real-time high precision (the change of the ZTD can be obtained in real time based on the interpolation of the ZTD calculated in real time, the precision is high), sufficiency (the precision information obtained based on the Kriging interpolation can be used for refining the PPP stochastic model, the weight is reduced when the model precision is low, the weight is improved when the model precision is high), and the integrity (the model precision information can be used as a reference of the integrity threshold of the troposphere model, and the reliability of the system is improved).
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and changes may be made to the present application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. which are within the spirit and principles of the present application are intended to be included within the scope of the claims of the present application.
Claims (10)
1. A tropospheric modeling method comprising the steps of:
setting virtual stations according to the set spatial resolution, and calculating time-varying ZWD of each virtual station according to weather analysis data;
according to the space variation characteristic of the troposphere delay of the time-varying ZWD value analysis area calculated by simulation, fitting a variation function;
according to the ZWD value and the variation function value of the GNSS observation station, interpolating to calculate the ZWD of the regular lattice points;
PPP solution is performed using regular lattice points ZWD.
2. The tropospheric modeling method of claim 1, wherein,
the interpolation method uses Kriging interpolation.
3. The tropospheric modeling method of claim 1, wherein,
obtaining grid point ZWD values according to the weighted summation of the reference point ZWD values:
ZWD(x 0 ) Representing lattice point x 0 ZWD at the location, ZWD (x i ) Representing an observation station x i ZWD, lambda at i The weight of the observation station i in the network is represented, and n represents the number of observation stations used for interpolation.
4. The tropospheric modeling method of claim 1, wherein the interpolated weight values are interpolated using Kriging interpolation to satisfy:
wherein n represents the number of stations, gamma ij Representing the variation value between site i and site j, gamma 0j Represents the variation between the lattice point and the jth site, μ represents the constraintFactor lambda of (a) i The weight of a station i in the network is represented, where i, j=1 to n.
5. The tropospheric modeling method of claim 1, wherein,
the space resolution of the meteorological re-analysis data is 0.25 degrees multiplied by 0.25 degrees, the time resolution is hours, and the time-varying ZWD is obtained through calculation according to the set time resolution by a GNSS algorithm.
6. The tropospheric modeling method of claim 1, wherein,
taking the minimum variance of unbiased estimation and estimation value error as the constraint condition of interpolation.
7. The tropospheric modeling method of claim 1, wherein,
performing space fitting on the ZWD value of any period according to the set time resolution to obtain a variation function of the period;
and generating a time-efficient regional tropospheric delay variation function set, wherein every 1 variation function in the set is applicable to at least a part of the time period.
8. Tropospheric modeling apparatus for implementing the method of any one of claims 1 to 7, comprising:
the acquisition module is used for setting virtual stations according to the set spatial resolution and calculating the ZWD of each virtual station according to the weather analysis data;
the fitting module is used for analyzing the spatial variation characteristics of the troposphere delay of the region according to the time-varying ZWD value calculated by simulation and fitting a variation function;
the determining module is used for interpolating and calculating the ZWD of the regular lattice points according to the ZWD value and the variation function value of the GNSS observation station;
and the resolving module is used for PPP resolving by using the rule lattice point ZWD.
9. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the method according to any of claims 1-7.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any of claims 1-7 when executing the computer program.
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| CN117992706A (en) * | 2024-04-07 | 2024-05-07 | 武汉大学 | Point-to-plane conversion method and system for real-time troposphere zenith delay |
| CN117992706B (en) * | 2024-04-07 | 2024-06-11 | 武汉大学 | Point-to-plane conversion method and system for real-time troposphere zenith delay |
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