A system for improving single-point positioning accuracy using water vapor tomography inversion

Abstract

The present invention relates to the field of meteorological forecasting technology, and discloses a system for improving the accuracy of single-point positioning by using water vapor tomography inversion, including: a data acquisition and preprocessing module: used to acquire GNSS observation data, meteorological station observation data, numerical weather forecast data and terrain data, a mathematical and physical modeling module: defining the dynamic evolution relationship of water vapor density distribution, forming an optimization target for water vapor distribution inversion, an efficient optimization solution module: used to solve the optimization target and obtain a three-dimensional water vapor density distribution, a wet delay correction module: based on the solved three-dimensional water vapor density distribution, calculating the wet delay correction value of each GNSS signal path, and a single-point positioning calculation module: used to perform error correction on GNSS pseudorange observation data according to the wet delay correction value. Through multi-source data fusion, physical modeling and efficient solution, the wet delay correction accuracy and calculation efficiency are effectively improved, and the GNSS single-point positioning accuracy is significantly improved.

Description

Technical Field

[0001] The invention relates to the technical field of meteorological forecasting, and in particular to a system that utilizes water vapor tomography inversion to improve single-point positioning accuracy. Background Art

[0002] GNSS (Global Navigation Satellite System) has been widely used in the fields of navigation, mapping, traffic monitoring and meteorological research. As a core technology, single-point positioning relies on GNSS pseudo-range observations and known satellite orbit parameters to determine the user's position by calculating the geometric distance between the receiver and the satellite. However, since GNSS signals are affected by multiple errors in the troposphere, ionosphere and multipath effects during propagation, the pseudo-range observations contain significant error terms, especially the tropospheric wet delay, which becomes an important factor limiting the improvement of positioning accuracy.

[0003] In the prior art, the correction of tropospheric wet delay mainly relies on empirical models, such as the Saastamoinen model and the Hopfield model, which usually make static estimates of wet delay based on average meteorological conditions. However, since the change of wet delay has significant spatial and temporal dynamics, the correction accuracy of such models often performs poorly under complex meteorological conditions, especially in areas with drastic humidity changes (such as heavy rainfall areas or tropical climate areas). The static assumptions of the model are inadequate, making it difficult to fully eliminate the wet delay error. In addition, these models fail to be dynamically updated in combination with actual observation data, and their results are difficult to reflect the true distribution of local water vapor, which seriously affects the GNSS positioning accuracy.

[0004] In recent years, with the accumulation of GNSS path wet delay observation data and meteorological station data, as well as the gradual application of numerical weather forecast data, some studies have begun to try to correct wet delay through data-driven methods. For example, the wet delay is calculated by simple interpolation or integration methods using numerical weather forecast data combined with GNSS path wet delay observations. However, some methods still have certain shortcomings. On the one hand, these improved methods lack the ability to physically model water vapor distribution, and fail to systematically describe wet delay based on the physical laws of water vapor convection, diffusion, and local evaporation. Due to the poor physical consistency of the model, unreasonable deviations are easily introduced. On the other hand, these methods have low computational efficiency in wet delay inversion in high-resolution or large-scale areas, especially in real-time positioning scenarios, and it is difficult to meet the demand for rapid response. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a system that uses water vapor tomography inversion to improve the single-point positioning accuracy, which solves the problems in the prior art of insufficient accuracy of tropospheric wet delay error correction, limited physical modeling capabilities, low real-time computing efficiency and poor system flexibility.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: A system for improving single-point positioning accuracy by using water vapor tomography inversion, comprising: Data acquisition and preprocessing module: used to collect GNSS observation data, meteorological station observation data, numerical weather forecast data and terrain data, and perform denoising, interpolation and gridding preprocessing on the above data to generate initial water vapor density distribution; Mathematical and physical modeling module: used to establish a partial differential equation model, define the dynamic evolution relationship of water vapor density distribution, and form the optimization target of water vapor distribution inversion through GNSS path wet delay constraints and boundary conditions; An efficient optimization solution module: used to solve the optimization target and obtain a three-dimensional water vapor density distribution that meets the physical constraints; a wet delay correction module: used to calculate the wet delay correction value of each GNSS signal path based on the solved three-dimensional water vapor density distribution; Single-point positioning calculation module: used to perform error correction on GNSS pseudo-range observation data according to the wet delay correction value and output high-precision positioning results.

[0007] Preferably, the data acquisition and preprocessing module includes: The data fusion unit is used to integrate the GNSS path wet delay observations, the atmospheric parameter data provided by the meteorological station, and the wind field speed distribution in the numerical weather forecast to generate a three-dimensional initial water vapor density distribution; The grid division unit is used to divide the target area into three-dimensional grids according to the spatial dimension, and the grid size is dynamically adjusted according to the terrain data.

[0008] Preferably, the mathematical and physical modeling module constructs a water vapor distribution control model based on a partial differential equation through the initial water vapor density distribution, GNSS path observation data and meteorological boundary conditions provided by the data acquisition and preprocessing module, wherein the partial differential equation is expressed as: Among them, ρ w is the water vapor density, u is the wind field velocity vector, D is the water vapor diffusion coefficient, and S is the water vapor source term.

[0009] Preferably, the convection characteristics of the partial differential equation model are based on the wind field velocity distribution, the diffusion characteristics are defined by the diffusion coefficient of water vapor molecules, the source term characteristics include the water vapor changes caused by surface evaporation and precipitation, and the diffusion coefficient of the water vapor molecules and the source term characteristics are specifically defined as follows: The wind field velocity vector is established through the three-dimensional wind field information in the numerical weather forecast data; The diffusion coefficient of water vapor molecules is used to describe the local diffusion effect in water vapor distribution, and its value is determined according to the diffusion characteristics of water vapor molecules; the source term characteristics are used to describe the increase or decrease of local water vapor.

[0010] Preferably, the mathematical and physical modeling module adopts the following boundary conditions: The surface boundary conditions and water vapor density are provided by atmospheric parameters observed by meteorological stations; Tropopause boundary condition, water vapor density is set to zero.

[0011] Preferably, the efficient optimization solution module uses the Riemann manifold optimization method to perform gradient descent iterative solution on the optimization target established by the mathematical and physical modeling module, and realizes multi-grid acceleration based on dynamic resolution adjustment of the grid during the optimization process.

[0012] Preferably, the wet delay correction module calculates the wet delay correction value on the path based on the gridding result of the three-dimensional water vapor density distribution and the geometric relationship of the GNSS path.

[0013] Preferably, the single-point positioning calculation module corrects the pseudorange in real time based on the wet delay correction value, and outputs user location information with centimeter-level accuracy through a positioning algorithm.

[0014] Preferably, the gradient descent optimization step is based on a metric definition in a Riemann manifold, and the optimization path is the shortest distance between the physical constraint and the observation constraint.

[0015] The present invention also provides a method for improving single-point positioning accuracy by using water vapor tomography inversion, comprising the following steps: The data acquisition and preprocessing module acquires data and performs data cleaning, interpolation and three-dimensional gridding to generate the initial water vapor density distribution; The mathematical and physical modeling module is used to define the dynamic evolution relationship of water vapor density distribution and form the optimization target of water vapor distribution inversion; the optimization target is solved through the efficient optimization solution module to obtain the optimized three-dimensional water vapor density distribution; The wet delay correction module is used to calculate the wet delay correction value based on the three-dimensional water vapor density distribution and the geometric relationship of the GNSS path; The wet delay correction value is input into the single point positioning calculation module to correct the GNSS pseudorange observation value, and the high-precision positioning result is calculated and output.

[0016] The present invention provides a system for improving single-point positioning accuracy by using water vapor tomography inversion. It has the following beneficial effects: 1. The present invention uses water vapor tomography inversion to accurately calculate the impact of tropospheric wet delay on GNSS signal propagation, and corrects pseudo-range data based on the optimized three-dimensional water vapor density distribution, significantly reducing the impact of wet delay error on positioning accuracy. Compared with the traditional empirical model, the present invention can achieve centimeter-level single-point positioning accuracy, meeting the needs of high-precision navigation and positioning.

[0017] 2. The multi-source data fusion technology of the present invention includes GNSS observation data, meteorological observation data and numerical weather forecast data, and dynamically inverts the three-dimensional water vapor density distribution through mathematical and physical modeling and optimization solution. Unlike the traditional method that relies on a fixed empirical model, the present invention can dynamically adjust the modeling and solution strategy for complex meteorological conditions, thereby improving the reliability and stability of the positioning results.

[0018] 3. The present invention adopts modular design, and the data acquisition and preprocessing module, mathematical and physical modeling module, efficient optimization solution module, wet delay correction module, and single-point positioning calculation module are independent of each other and efficiently cooperate. The modular architecture is not only convenient for the expansion and upgrading of system functions, but also can be flexibly integrated into the existing GNSS positioning system, greatly reducing the complexity of system development and application.

[0019] 4. The present invention introduces a multi-grid optimization strategy and a gradient descent method to efficiently solve the optimization objective function, significantly reducing the computational cost of solving complex mathematical and physical models. Especially in large-scale regional and high-resolution water vapor inversion scenarios, the computational efficiency of the present invention is several times higher than that of traditional methods, and can meet the application requirements of real-time positioning and high-frequency data updates. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a system framework diagram of a system for improving single-point positioning accuracy by using water vapor tomography inversion according to the present invention; Figure 2 The present invention is a flowchart of the steps of a method for improving single-point positioning accuracy by using water vapor tomography inversion. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] Please see attached Figure 1 The embodiment of the present invention provides a system for improving single-point positioning accuracy by using water vapor tomography inversion, comprising: Data acquisition and preprocessing module: used to collect GNSS observation data, meteorological station observation data, numerical weather forecast data and terrain data, and perform denoising, interpolation and gridding preprocessing on the above data to generate initial water vapor density distribution; Mathematical and physical modeling module: used to establish a partial differential equation model, define the dynamic evolution relationship of water vapor density distribution, and form the optimization target of water vapor distribution inversion through GNSS path wet delay constraints and boundary conditions; An efficient optimization solution module: used to solve the optimization target and obtain a three-dimensional water vapor density distribution that meets the physical constraints; a wet delay correction module: used to calculate the wet delay correction value of each GNSS signal path based on the solved three-dimensional water vapor density distribution; Single-point positioning calculation module: used to perform error correction on GNSS pseudo-range observation data according to the wet delay correction value and output high-precision positioning results.

[0023] In this example, the data acquisition and preprocessing module is the basic module of the entire system. Its main function is to collect and preprocess GNSS observation data, meteorological station observation data, numerical weather forecast data and terrain data, and generate the initial three-dimensional water vapor density distribution and related boundary conditions suitable for water vapor tomography inversion through interpolation, denoising and gridding. The output results of this module are directly used as the input of the mathematical and physical modeling module to ensure the accuracy and reliability of the tropospheric water vapor distribution model.

[0024] In general, to ensure the temporal and spatial consistency of multi-source data, this module needs to perform unified interpolation processing on different data sources and grid the data according to the resolution requirements of the modeling area. As an option, this module can also smooth sparse or noisy data through data fusion algorithms. The specific implementation method is: Generally, GNSS observation data is obtained through GNSS receivers, mainly including pseudo-range observation data P cbs and wet delay observation data ZWD obs Specifically, the wet delay ZWD obs It is obtained by deducting the dry delay ZHD from the pseudorange delay, and its calculation formula is: ZTD=ZHD+ZWD Among them, ZTD is the total delay, ZHD is the dry delay, and ZWD is the wet delay.

[0025] In one possible implementation, the dry delay ZHD is usually calculated by the Saastamoinen model: ZHD=0.0022768·p Where p is the surface pressure.

[0026] By deducting ZHD from the total pseudorange observation delay ZTD, the wet delay ZWD can be obtained. obs To improve data accuracy, as an option, a sliding window averaging method can be used to denoise the wet delay observations.

[0027] Specifically, the geometric information of the GNSS path, such as the start point, end point and direction of the path, can be derived from the known satellite orbit data and the receiver position. This path geometry information will be used in the wet delay integration model.

[0028] Meteorological station observation data are mainly used to provide surface boundary conditions of the modeling area, including temperature T obs , air pressure p obs , water vapor pressure e obs These data are usually provided in the form of discrete sites. In order to meet modeling requirements, these data need to be interpolated and expanded to the surface grid points of the entire modeling area.

[0029] As an implementation method, the bilinear interpolation method can be used to expand the data of discrete meteorological stations to the surface boundary points of the three-dimensional grid. Specifically, the water vapor pressure e obs It can be calculated from the relative humidity RH and temperature T provided by the weather station, and the relationship is: e=e s RH Among them, e s is the saturated water vapor pressure, and RH is the relative humidity. The saturated water vapor pressure can be calculated by the following formula: Where T is the temperature, the water vapor pressure e obs Used for subsequent calculation of surface water vapor density.

[0030] Surface water vapor density ρ w (x,y,0,t) is calculated by the following formula: Among them, R v =461.5J / (kg·K) is the gas constant of water vapor.

[0031] In some embodiments, the numerical weather forecast data includes a three-dimensional wind field velocity vector u(X, Y, Z, t) and an initial water vapor distribution These data are usually provided at fixed time intervals (e.g. 3 hours) and fixed spatial resolution (e.g. 0.25 degrees).

[0032] The wind field velocity vector u(X,Y,Z,t) can be decomposed into velocity components in three directions: u(X,Y,Z,t)=(u(X,y,Z,t),v(X,y,Z,t),w(X,y,Z,t)) Among them, u, v, and w are the velocity components of the wind field in the X, Y, and Z directions. In order to meet the needs of grid modeling, three-dimensional linear interpolation can be performed on the wind field data to expand it to the grid nodes in the modeling area.

[0033] Initial water vapor density distribution It can be calculated using the water vapor pressure and temperature data provided by numerical weather forecasts. The calculation formula is: Where e is the water vapor pressure and T is the temperature.

[0034] In the modeling area, terrain height data is provided by a digital elevation model, with a resolution of 30 meters or higher. In general, the modeling area needs to be divided into three-dimensional grids, and the spacing of grid nodes can be dynamically adjusted according to the complexity of the terrain. For example, more dense grid points are set in areas with large terrain changes, and sparse grid points are set in areas with flat terrain.

[0035] As an implementation method, a uniform grid division method can be used to divide the modeling area into three-dimensional grids with a grid size of (Δx, Δy, Δz). After the grid division is completed, the GNSS path, meteorological station observation data, and numerical weather forecast data need to be mapped to the grid nodes.

[0036] In this embodiment, after all data collection and processing are completed, the data collection and preprocessing module generates the following data output: Three-dimensional initial water vapor density distribution GNSS path wet delay observation value ZWD obs ; Wind field velocity distribution u(X,Y,Z,t); Surface water vapor density ρ w (x,y,0,t).

[0037] The above output data will be passed to the mathematical and physical modeling module in a unified grid format to establish the control equation model and boundary conditions of tropospheric water vapor distribution.

[0038] The data acquisition and preprocessing module in the present invention solves the problem of inconsistency of multi-source data through multi-source data fusion, interpolation, denoising and gridding processing, and provides high-quality input data for the mathematical and physical modeling module.

[0039] In this example, the mathematical and physical modeling module is the core functional module of the system of the present invention, which is responsible for constructing a mathematical and physical model describing the dynamic distribution of tropospheric water vapor based on the multi-source data output by the data acquisition and preprocessing module, including the initial water vapor density distribution, wind field speed, GNSS path wet delay observations, and boundary conditions. This module defines the dynamic evolution law of water vapor density based on partial differential equations, and by introducing GNSS path wet delay constraints and boundary conditions, it transforms the model into an optimization target with physical constraints and observation constraints, providing accurate input for the subsequent optimization solution module.

[0040] In general, this module needs to establish a complete tropospheric water vapor distribution equation based on the physical characteristics of convection, diffusion and source terms, and introduce observation data and boundary conditions to strengthen the model. In one possible implementation, the stability of the model is improved by adding regularization terms, and dynamic constraints are used to adjust to complex meteorological conditions. The specific implementation method is: In general, the dynamic changes of tropospheric water vapor are affected by the combined effects of convection, diffusion and source terms. In this embodiment, the water vapor density ρ is described by the following partial differential control equation: w The spatiotemporal evolution of (x,y,Z,t): in, is the rate of change of water vapor density with time t, is the convection term of water vapor with wind field velocity u(X,Y,Z,t): u(x,y,z,t)=(u(x,y,z,t),v(x,y,z,t),w(x,y,z,t)) Among them, u, v, and w are the components of the wind field velocity in the x, y, and z directions respectively. The wind field velocity must meet the non-divergence condition: is the diffusion term of water vapor molecules, D is the diffusion coefficient, and the diffusion coefficient decays exponentially with the height z. Its expression is: Where D0 = 2 × 10 -5 m 2 / s is the initial surface diffusion coefficient, z is the height, H = 12,000m is the height of the troposphere top; S is the water vapor source term, which is defined as S=S evap (x,y,t)-S precip (x,y,t) in: S evap (x, y, t) is the water vapor increase caused by surface evaporation, calculated based on the observation data of the meteorological station; S precip (x, y, t) is the water vapor reduction caused by precipitation, estimated from numerical weather forecast data.

[0041] The above equations comprehensively describe the dynamic evolution characteristics of tropospheric water vapor density, covering the impact of convection, diffusion and local water vapor changes on distribution.

[0042] The GNSS path wet delay is related to the integral of the water vapor density on the signal path, and its calculation formula is: Among them, ZWD i is the wet delay of the i-th GNSS path; k w is the wet delay coefficient, L i is the path trajectory, dI represents the differential length of the path, ρ w (x,y,z) is the water vapor density along the path.

[0043] As an option, the geometric information of each path is provided by the data acquisition and preprocessing module, including the path start point, end point and direction data. obs Will be used to impose observational constraints on the inversion model.

[0044] In order to ensure that the mathematical model matches the actual physical environment, the following two types of boundary conditions are defined in this embodiment: surface boundary conditions, the surface water vapor density is calculated by the water vapor pressure e(x, y, 0, t) and temperature T(x, y, 0, t) provided by the meteorological station, and the formula is: The boundary condition of the tropopause, where the water vapor density is assumed to be zero, is defined as: ρ w (x,y,H,t)=0 In one possible implementation, boundary conditions can be dynamically adjusted to adapt to the spatiotemporal changes in meteorological data, thereby improving the accuracy of modeling.

[0045] In order to transform the partial differential equation, path wet delay constraint and boundary conditions into a unified optimization problem, the following optimization objective function is constructed in this embodiment: in, is the constraint of the control equation, which indicates the degree of deviation between the inversion solution and the physical law. is the regularization constraint, The initial water vapor density distribution provided to the data acquisition and preprocessing module is used to enhance the stability of the solution. α is the regularization weight parameter used to balance the influence of the control equation constraints and the prior constraints. Ω is the three-dimensional spatial range of the modeling area.

[0046] Alternatively, a regularization term can be added to the gradient constraints to smooth out local variations in the solution and reduce numerical oscillations.

[0047] The mathematical and physical modeling module of the present invention completely describes the dynamic distribution characteristics of tropospheric water vapor density by constructing a partial differential equation model and introducing path wet delay constraints and boundary conditions, and transforms the problem into a solvable form by optimizing the objective function.

[0048] In this example, the efficient optimization solution module is the core computing unit in the system of the present invention. Its main task is to quickly solve the optimization objective function generated by the mathematical and physical modeling module to obtain the optimal three-dimensional water vapor density distribution that meets the physical constraints and observation constraints. This module converts the continuous optimization problem into a computable discrete form through numerical discretization, and combines gradient calculation and optimization algorithm design to achieve efficient iterative solution of the optimization target. In addition, in order to improve the solution efficiency, a multi-grid acceleration strategy is further adopted, and the computational complexity is significantly reduced through multi-level optimization with gradually refined resolution.

[0049] In general, solving the optimization objective function is a high-dimensional nonlinear problem, and the amount of computation required to solve it directly is large. In one possible implementation, the gradient descent method is combined with the Riemann manifold optimization framework to effectively shorten the optimization path and improve the stability of the solution. At the same time, through the multi-grid method, the global optimal solution is quickly approached on the coarse grid, and local refinement is performed on the fine grid to ensure the accuracy and efficiency of the solution. The specific implementation method is as follows: In this embodiment, the optimization objective function is firstly numerically discretized so as to perform numerical calculation in a discrete space.

[0050] The spatial discretization uses the finite difference method to divide the modeling area Ω into a uniform three-dimensional grid with a grid node spacing of (Δx, Δy, Δz). On the discrete grid, the water vapor density ρ w The derivative and second-order derivative of are discretized by the central difference method. For example, the discretized form of the spatial derivative is: The discrete form of the second-order derivative is: The time discretization uses the explicit Euler method to convert the changes in continuous time into a step-by-step update form. The time derivative included in the optimization objective function is discretized into: in, is the water vapor density at the current time step n, and Δt is the time step.

[0051] Through the above discretization method, the continuous form of the optimization objective function is converted into a discrete equation, which is suitable for computer numerical solution.

[0052] In this embodiment, the solution of the optimization objective function relies on gradient calculation to determine the improvement direction of the current solution. The optimization objective function is: The gradient calculation is divided into two parts: Solve the gradient of the control equation, the formula is: Specifically expanded as follows: The gradient includes the derivatives of the convection term, diffusion term, and source term.

[0053] The gradient of the regularization term is solved as follows: Expands to: The final gradient is the sum of two parts: The calculation results of the above gradients are used to update the subsequent optimization algorithm.

[0054] In this embodiment, the optimization algorithm uses a gradient descent method combined with a Riemann manifold optimization framework to ensure that the solution process converges quickly under physical constraints.

[0055] The update formula of the optimization process is: Among them, η is the learning rate, which determines the step size of gradient update. is the Riemann gradient, which is used to ensure the rationality of the optimization process within the constraint space. It is defined as: g is the Riemann metric tensor, which reflects the geometric characteristics of water vapor density in spatial distribution.

[0056] In one possible implementation, the learning rate η can be optimized by dynamically adjusting the strategy so that it is larger in the initial stage to accelerate convergence, and gradually reduced when approaching the optimal solution to improve the accuracy of the solution.

[0057] In order to improve the computational efficiency of the optimization solution, a multi-grid method is used in this embodiment to achieve rapid convergence by gradually refining the resolution.

[0058] First, the optimization process is initialized on a coarser resolution grid to quickly approach the global optimal solution. For example, the initial grid node spacing is (Δx, Δy, Δz) = (500m, 500m, 200m) The coarse grid solution is then mapped to a higher resolution grid, for example, (Δx, Δy, Δz) = (100m, 100m, 50m), and local optimization is performed on the fine grid to further improve the accuracy of the solution.

[0059] The step-by-step optimization strategy of the multigrid method can significantly reduce the overall calculation time while ensuring the accuracy of the solution.

[0060] The efficient optimization solution module of the present invention realizes efficient solution of the optimization objective function through numerical discretization, gradient calculation, optimization algorithm design and multi-grid acceleration method.

[0061] In this example, the wet delay correction module is one of the key functional modules of the system of the present invention. It is mainly used to accurately calculate the wet delay value of each path based on the three-dimensional water vapor density distribution output by the efficient optimization solution module and the geometric information of the GNSS signal path, and generate wet delay correction data for the subsequent single-point positioning calculation module to perform pseudorange error correction.

[0062] In general, wet delay is the signal propagation delay caused by the water vapor distribution in the troposphere, and its magnitude directly depends on the water vapor density distribution on the path and the spatial geometric characteristics of the path. In one possible implementation, the wet delay correction module calculates the wet delay value through the path integration method, combines the three-dimensional water vapor density distribution with the geometric information on the path, and ensures the calculation accuracy through strategies such as piecewise integration. In addition, the module also provides an optimized calculation strategy for complex path scenarios (such as long path lengths or complex regional terrain). The specific implementation method is as follows: In this embodiment, the wet delay correction module includes two parts: path wet delay calculation and correction result output. Generally, the wet delay value ZWD i It represents the propagation time delay caused by water vapor density when the signal propagates in the troposphere, which can be calculated by integrating the water vapor density on the path. The specific formula is: Among them, ZWD i is the wet delay of the i-th path, indicating the total delay of the signal on this path, k w is the wet delay coefficient, L i The geometric trajectory of the i-th GNSS signal path is described by the starting point, end point and space curve of the path. dI is the differential length on the path, which is defined as: Specifically, the water vapor density ρ wThe values ​​of (x, y, z) are determined by the three-dimensional water vapor density distribution provided by the efficient optimization solution module, while the geometric information of the path is provided by the data acquisition and preprocessing module.

[0063] In order to improve the computational efficiency and accuracy, the path integral adopts a discretization strategy. i It is divided into N segments, and the wet delay value of each segment is approximately the average value of water vapor density multiplied by the path length. Its discrete form is: Among them, ρ w (x j ,y j ,z j ) is the water vapor density at the midpoint of the segment, ΔI j is the path length of the jth segment.

[0064] As an option, the integration accuracy can be further optimized, for example, by using the trapezoidal integration method or the Simpson integration method. Taking the trapezoidal integration method as an example, the calculation formula for the wet delay value is: In one possible implementation, in order to handle the complex geometric characteristics of the path, the segment length ΔI of the path j It can be adjusted dynamically. For example, in areas with large height changes, shorter segments are used to improve calculation accuracy.

[0065] The output of the wet delay correction module is the wet delay correction value ZWD of each path. i , and stored and output in matrix form. The rows of the matrix represent different GNSS paths, the columns represent different time steps, and each element in the matrix represents the wet delay correction value of the i-th path at time t.

[0066] Specifically, the output of the correction results includes the following steps: For all GNSS paths, the wet delay value is calculated using the path geometry information and the three-dimensional water vapor density distribution; The wet delay values ​​of all paths are stored in time series to form a wet delay correction matrix; The wet delay correction matrix is ​​passed to the single point positioning calculation module for error correction of pseudorange observation data.

[0067] In some embodiments, in order to further improve the efficiency and adaptability of the wet delay correction module, the following technical improvements may be introduced: The path length and geometric complexity are analyzed to dynamically adjust the segment length of the path. For example, if the path length is short or the water vapor density changes slowly in the area, a longer segment can be used; if the path crosses complex terrain or the water vapor density changes dramatically, a shorter segment can be used.

[0068] When the number of path segments is small, a high-order numerical integration method (such as Simpson integration method) is used to improve the calculation accuracy.

[0069] For areas with densely distributed paths, the wet delay contribution value of the area is pre-calculated and stored. When calculating the wet delay of the path, the table is directly looked up and summed, thereby improving the calculation efficiency.

[0070] The wet delay correction module of the present invention realizes accurate correction of the wet delay value of the GNSS path by calculating the path integral of the optimized water vapor density distribution. The module adopts path discretization, dynamic segmentation strategy and high-order integration method to ensure high accuracy and efficiency of wet delay calculation in complex scenes.

[0071] In this example, the single point positioning calculation module is the terminal module in the system of the present invention, and its function is to calculate the wet delay correction value ZWD output by the wet delay correction module and the GNSS pseudo-range observation data P obs , by correcting the pseudorange error and establishing a nonlinear positioning equation group, the precise three-dimensional position of the user receiver and the receiver clock error are finally calculated. This module is closely connected with the wet delay correction module and the data acquisition and preprocessing module. By using the corrected pseudorange data, the influence of tropospheric wet delay on positioning accuracy is effectively reduced.

[0072] In general, GNSS single-point positioning relies on pseudo-range observations from at least four satellites, combined with the known positions of the satellites and the unknown coordinates and clock errors of the receiver, and uses geometric relationships to establish a nonlinear set of equations for solution. In one possible implementation, the single-point positioning calculation module performs linearization and iterative solutions based on the corrected pseudo-ranges, and combines dynamic residual adjustment strategies to improve solution efficiency and result stability. Specific implementation methods: In this embodiment, the GNSS pseudorange observation value P is first obs Wet delay correction is performed to eliminate the main error caused by tropospheric wet delay. The expression of GNSS pseudorange observation value is: Among them, P obs is the pseudorange observation value, (x s ,y s ,z s ) is the three-dimensional position coordinate of the satellite, (x u ,y u , z u) is the unknown three-dimensional position coordinate of the receiver, is the variable to be solved, and c is the speed of light, which takes a value of 3×10 8 m / s, Δt is the receiver clock error, which is the variable to be solved, l is the ionospheric delay error, which can be eliminated by dual-frequency observation or corrected by the ionospheric model, T is the tropospheric dry delay error, which can be corrected by the empirical model, and ZWD is the tropospheric wet delay error, which is calculated and output by the wet delay correction module.

[0073] The wet delay correction value ZWD output by the wet delay correction module i , the corrected pseudorange observation value is: P 修正 =P obs -ZWD Among them, P 修正 is the corrected pseudorange observation value, which is used for subsequent positioning calculation.

[0074] As an option, on the basis of wet delay correction, the ionospheric error l and dry delay error T can be further combined to perform pseudorange joint correction to improve the accuracy of pseudorange data.

[0075] Based on the corrected pseudo-range data, the single-point positioning calculation module establishes the geometric relationship equation between the user position and the satellite position. The basic form of the positioning equation is: Among them, (x u ,y u , z u ) is the unknown three-dimensional position of the user receiver, and C·Δt is the correction of the receiver clock error.

[0076] To solve the user position, pseudo-range data from at least four satellites are needed to form the following nonlinear equations: Each equation in the above equation group corresponds to a satellite, and its input includes the known position coordinates of the satellite and the pseudorange correction value.

[0077] Since the above equations are nonlinear, an iterative optimization method is used to solve them in this embodiment, such as the Newton-Raphson method or the generalized least squares method.

[0078] Specifically, the steps for solving the positioning equation are as follows: Initialize the receiver position and clock error The initial value can be provided based on the most recent positioning result or approximate position; Based on the current estimate, calculate the pseudorange model value for each satellite: Compute the residual vector: b=P 修正 -P 模型 Among them, P 修正 is the observed pseudorange correction value, P 模型 To calculate the pseudorange model value; Compute the Jacobian matrix A, whose elements are the partial derivatives of the model values ​​with respect to the unknowns: Among them, X j =[x u ,y u ,z u ,Δt] is the variable to be solved.

[0079] Update the estimate via generalized least squares: ΔX=(A T A) -1 A T b X=X+ΔX Repeat the above steps until the residual vector b meets the convergence condition.

[0080] After the positioning solution is completed, the single-point positioning calculation module outputs the three-dimensional coordinates of the user receiver (x u ,y u ,z u ) and receiver clock error Δt. In addition, the user coordinates can be further converted into longitude, latitude and altitude in the geographic coordinate system. The conversion formula is: Among them, λ is the longitude, φ is the latitude, h is the altitude, and R is the radius of the reference ellipsoid.

[0081] The single-point positioning calculation module of the present invention realizes high-precision calculation of the user's position by correcting pseudo-range data with wet delay and solving the nonlinear positioning equation group. All formulas and technical details have been fully disclosed, including the pseudo-range correction formula, the establishment and solution method of the positioning equation group and the coordinate conversion formula.

[0082] Please refer to Figure 2 The embodiment of the present invention also provides a method for improving single-point positioning accuracy by using water vapor tomography inversion, comprising the following steps: The data acquisition and preprocessing module acquires data and performs data cleaning, interpolation and three-dimensional gridding to generate the initial water vapor density distribution; The mathematical and physical modeling module is used to define the dynamic evolution relationship of water vapor density distribution and form the optimization target of water vapor distribution inversion; the optimization target is solved through the efficient optimization solution module to obtain the optimized three-dimensional water vapor density distribution; The wet delay correction module is used to calculate the wet delay correction value based on the three-dimensional water vapor density distribution and the geometric relationship of the GNSS path; The wet delay correction value is input into the single point positioning calculation module to correct the GNSS pseudorange observation value, and the high-precision positioning result is calculated and output.

[0083] The method of this embodiment is executed based on the above-mentioned system embodiment, and its principles and technical effects are similar, so they will not be repeated here.

[0084] In summary, the present invention provides a system for improving the accuracy of single-point positioning by using water vapor tomography inversion, which works in collaboration with multiple modules, including a data acquisition and preprocessing module, a mathematical and physical modeling module, an efficient optimization solution module, a wet delay correction module, and a single-point positioning calculation module. The system first collects GNSS observation data, meteorological data, and numerical weather forecast data, and performs denoising, interpolation, and gridding preprocessing; then constructs a partial differential equation to describe the dynamic evolution characteristics of water vapor distribution, and combines the GNSS path wet delay constraints and boundary conditions to form an optimization objective function; through an efficient optimization solution method, the three-dimensional water vapor density distribution is inverted for wet delay correction; finally, the corrected pseudorange data is combined to solve the user position through a nonlinear positioning equation group. The present invention effectively eliminates the influence of tropospheric wet delay errors on GNSS positioning accuracy through precise modeling and optimization solutions, and achieves centimeter-level single-point positioning accuracy, which is suitable for high-precision positioning application scenarios such as navigation, surveying and mapping, and meteorological research.

[0085] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A system for improving single-point positioning accuracy using water vapor tomography inversion, characterized in that: include: Data acquisition and preprocessing module: used to collect GNSS observation data, meteorological station observation data, numerical weather forecast data and terrain data, and perform denoising, interpolation and gridding preprocessing on the above data to generate initial water vapor density distribution; Mathematical and physical modeling module: used to establish a partial differential equation model, define the dynamic evolution relationship of water vapor density distribution, and form the optimization target of water vapor distribution inversion through GNSS path wet delay constraints and boundary conditions; An efficient optimization solution module: used to solve the optimization target and obtain a three-dimensional water vapor density distribution that meets the physical constraints; a wet delay correction module: used to calculate the wet delay correction value of each GNSS signal path based on the solved three-dimensional water vapor density distribution; Single-point positioning calculation module: used to perform error correction on GNSS pseudo-range observation data according to the wet delay correction value and output high-precision positioning results.

2. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The data acquisition and preprocessing module includes: The data fusion unit is used to integrate the GNSS path wet delay observations, the atmospheric parameter data provided by the meteorological station, and the wind field speed distribution in the numerical weather forecast to generate a three-dimensional initial water vapor density distribution; The grid division unit is used to divide the target area into three-dimensional grids according to the spatial dimension, and the grid size is dynamically adjusted according to the terrain data.

3. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The mathematical and physical modeling module constructs a water vapor distribution control model based on partial differential equations through the initial water vapor density distribution, GNSS path observation data and meteorological boundary conditions provided by the data acquisition and preprocessing module, where the partial differential equation is expressed as: Among them, ρ w is the water vapor density, u is the wind field velocity vector, D is the water vapor diffusion coefficient, and S is the water vapor source term.

4. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 3, characterized in that: The convection characteristics of the partial differential equation model are based on the wind field velocity distribution, the diffusion characteristics are defined by the diffusion coefficient of water vapor molecules, and the source term characteristics include the water vapor changes caused by surface evaporation and precipitation. The diffusion coefficient of water vapor molecules and the source term characteristics are specifically defined as follows: The wind field velocity vector is established through the three-dimensional wind field information in the numerical weather forecast data; The diffusion coefficient of water vapor molecules is used to describe the local diffusion effect in water vapor distribution, and its value is determined according to the diffusion characteristics of water vapor molecules; the source term characteristics are used to describe the increase or decrease of local water vapor.

5. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The mathematical and physical modeling module adopts the following boundary conditions: The surface boundary conditions and water vapor density are provided by atmospheric parameters observed by meteorological stations; Tropopause boundary condition, water vapor density is set to zero.

6. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The efficient optimization solution module uses the Riemann manifold optimization method to perform gradient descent iterative solution on the optimization target established by the mathematical and physical modeling module, and realizes multi-grid acceleration based on dynamic resolution adjustment of the grid during the optimization process.

7. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The wet delay correction module calculates the wet delay correction value on the path based on the gridding result of the three-dimensional water vapor density distribution and the geometric relationship of the GNSS path.

8. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 1, characterized in that: The single-point positioning calculation module corrects the pseudo-range in real time based on the wet delay correction value, and outputs user position information with centimeter-level accuracy through a positioning algorithm.

9. The system for improving single-point positioning accuracy by using water vapor tomography inversion according to claim 6, characterized in that: The gradient descent optimization step is based on a metric definition in a Riemann manifold, and the optimization path is the shortest distance between the physical constraints and the observation constraints.

10. A method for improving single-point positioning accuracy by using water vapor tomography inversion, applied to a system for improving single-point positioning accuracy by using water vapor tomography inversion as claimed in any one of claims 1 to 9, characterized in that: The following steps are involved: The data acquisition and preprocessing module acquires data and performs data cleaning, interpolation and three-dimensional gridding to generate the initial water vapor density distribution; The mathematical and physical modeling module is used to define the dynamic evolution relationship of water vapor density distribution and form the optimization target of water vapor distribution inversion; the optimization target is solved through the efficient optimization solution module to obtain the optimized three-dimensional water vapor density distribution; The wet delay correction module is used to calculate the wet delay correction value based on the three-dimensional water vapor density distribution and the geometric relationship of the GNSS path; The wet delay correction value is input into the single point positioning calculation module to correct the GNSS pseudorange observation value, and the high-precision positioning result is calculated and output.

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