Troposphere inclination delay estimation method and troposphere inclination delay estimation device for GNSS (Global Navigation Satellite System) monitoring

Abstract

The embodiment of the invention discloses a troposphere tilt delay estimation method and device for GNSS (Global Navigation Satellite System) monitoring, relates to the technical field of GNSS satellite navigation and positioning, and is used for solving the problem of low accuracy in the prior art. The method comprises the following steps: according to visible satellite observation values of multiple GNSS monitoring stations in a preset area at the current moment and a preset visible airspace hemisphere, determining a visible airspace hemisphere grid to which each visible satellite observation value belongs, and adding the visible airspace hemisphere grid as a troposphere tilt delay to-be-estimated parameter into a GNSS array observation equation to obtain a current GNSS array observation equation; calculating a to-be-estimated parameter of the current GNSS array observation equation based on a Kalman filtering estimator so as to obtain a current troposphere inclination delay value of each visible airspace hemisphere grid; and taking the current troposphere tilt delay value of each visible airspace hemisphere grid as the input of the next moment, and obtaining the troposphere tilt delay estimation value of each visible airspace hemisphere grid at the next moment.

Description

TECHNICAL FIELD

[0001] The present specification relates to the field of GNSS satellite navigation and positioning technology, and in particular to a method and device for estimating the tropospheric slant delay for GNSS monitoring. BACKGROUND

[0002] The troposphere causes a propagation delay for space observation technologies that mainly use electromagnetic waves as the main detection means, such as the global navigation satellite system (GNSS), very long baseline interferometry, satellite laser ranging, synthetic aperture radar interferometry, and the like. This delay is affected by meteorological conditions such as air temperature, air pressure, water vapor content, and the like, is highly time-varying, varies with geographical location and propagation path, and cannot be eliminated by using multi-frequency combination observations, and has become one of the main bottlenecks restricting the accuracy of space geodetic techniques.

[0003] The current traditional tropospheric delay modeling method in the field of GNSS tropospheric modeling mainly relies on the estimation of the zenith direction delay, and projects the zenith delay to the line-of-sight direction of each satellite in combination with an empirical mapping function, but the isotropic assumption in this way will cause a systematic deviation in the estimation of the slant path delay. In addition, traditional mapping functions such as GMF, VMF, and the like perform well in the high elevation angle region, but the accuracy significantly decreases in the low elevation angle case. And for a GNSS monitoring station array in a small area, the distance between stations is usually within a few kilometers, and there are small but important differences in the tropospheric delay between each station. However, due to the limited spatial resolution of existing large-scale tropospheric models, these small-scale spatial variation characteristics cannot be captured. While atmospheric tomography can theoretically reconstruct the three-dimensional atmospheric conditions, it has strict requirements for the geometric distribution of GNSS monitoring stations in a small area, and has high computational complexity, making it difficult to meet the real-time processing requirements. In the era of multi-system GNSS, with the increase in the number of available satellites, the existing methods lack effective azimuthal partition modeling methods to fully utilize the independent information provided by satellites at different azimuth angles. Second, when jointly processing multi-station observation data, the spatial correlation of the tropospheric delay of each station in a small area is not fully considered, which limits the accuracy and stability of parameter estimation. In addition, the existing methods often adopt a simple cutoff strategy when processing low-elevation angle observation data, which not only loses valuable observation information, but also can cause systematic bias in parameter estimation. SUMMARY

[0004] To solve the above technical problems, one or more embodiments of the present specification provide a method for estimating the tropospheric slant delay for GNSS monitoring.

[0005] One or more embodiments of the present specification adopt the following technical solutions: One or more embodiments of the present specification provide a method for estimating tropospheric slant delay for GNSS monitoring, the method comprising: determining, according to visible satellite observation values of preset regions of GNSS monitoring stations at a current time and a preset visible airspace hemisphere, a visible airspace hemisphere grid to which each of the visible satellite observation values belongs in the preset visible airspace hemisphere; adding, as tropospheric slant delay parameters to be estimated, the visible airspace hemisphere grid to which each of the visible satellite observation values belongs to a GNSS array observation equation to obtain a current GNSS array observation equation; solving, based on a Kalman filter estimator, the parameters to be estimated of the current GNSS array observation equation to obtain current tropospheric slant delay values of each of the visible airspace hemisphere grids; wherein a state transition matrix of the Kalman filter estimator is determined based on historical visible satellite observation values of each of the visible airspace hemisphere grids at a previous time and the visible satellite observation values; inputting, as input at a next time, the current tropospheric slant delay values of each of the visible airspace hemisphere grids to determine, based on the Kalman filter estimator, tropospheric slant delay estimated values of each of the visible airspace hemisphere grids at the next time.

[0006] Optionally, in one or more embodiments of the present specification, adding, as tropospheric slant delay parameters to be estimated, the visible airspace hemisphere grid to which each of the visible satellite observation values belongs to a GNSS array observation equation to obtain a current GNSS array observation equation specifically comprises: adding, as tropospheric slant delay parameters to be estimated, the visible airspace hemisphere grid to which each of the visible satellite observation values belongs to construct a tropospheric slant delay parameter vector corresponding to the tropospheric slant delay parameters to be estimated; determining, according to each satellite signal path corresponding to each of the visible satellites, a mapping function vector of each satellite signal path relative to a center of the preset region and each GNSS monitoring station; adding the mapping function vector and the tropospheric slant delay parameter vector to the GNSS array observation equation to obtain a current GNSS array observation equation.

[0007] Optionally, in one or more embodiments of the present specification, determining, according to each satellite signal path corresponding to each of the visible satellites, a mapping function of each satellite signal path relative to a center of the preset region and each GNSS monitoring station specifically comprises: determining whether there is geometric interaction between the visible airspace hemisphere grid to which each of the visible satellite observation values belongs and each satellite signal path corresponding to each of the visible satellites; if there is geometric interaction, determining the mapping function as: wherein, a number of the visible space hemisphere grid to which each satellite observation belongs, , a number of the visible space hemisphere grids; a visible satellite, , a number of visible satellites; a number of GNSS monitoring stations in the preset area, ; a rough distance of the visible satellite to the receiver; a rough distance of the visible satellite to the center of the area; ; if there is no geometric interaction, the mapping function is determined as: ; the mapping functions corresponding to each visible space hemisphere grid are summarized to obtain the mapping function of each satellite signal path relative to the center of the preset area and a number of GNSS monitoring stations is: .

[0008] Optionally, in one or more embodiments of the present specification, the current GNSS array observation equation is: ; wherein, the ionosphere-free combined pseudorange observation value of a number of GNSS monitoring stations; the ionosphere-free combined phase observation value of a number of GNSS monitoring stations; the satellite-to-receiver direction cosine of a number of GNSS monitoring stations; the coordinate increment of a number of GNSS monitoring stations; the speed of light in vacuum; the receiver clock error of a number of GNSS monitoring stations; the slant tropospheric delay of the direction from the center of the area to the center of the visible space hemisphere grid, a number of the visible space hemisphere grids; the carrier phase integer ambiguity parameter of a number of GNSS monitoring stations; the mapping function of each satellite signal path relative to the center of the preset area and a number of GNSS monitoring stations, .

[0009] Optionally, in one or more embodiments of the present specification, before the current tropospheric slant delay values of each of the visible airspace hemispherical grids are obtained by solving the to-be-estimated parameters of the current GNSS array observation equation based on the Kalman filter estimator, the method further comprises: determining whether there are historical visible satellite observation values at the previous time and current visible satellite observation values for each of the visible airspace hemispherical grids; if yes, determining that the diagonal elements of the state transition matrix of the Kalman filter estimator are 1; if it is determined that there are no historical visible satellite observation values at the previous time for each of the visible airspace hemispherical grids, it is determined that the diagonal elements of the state transition matrix of the Kalman filter estimator are 0.

[0010] Optionally, in one or more embodiments of the present specification, the current tropospheric slant delay values of each of the visible airspace hemispherical grids are obtained by solving the to-be-estimated parameters of the current GNSS array observation equation based on the Kalman filter estimator, specifically comprising: obtaining the to-be-estimated parameters of the current GNSS array observation equation to construct the current time state vector of the Kalman filter estimator based on the to-be-estimated parameters; inputting the previous time state vector into the state transition matrix of the Kalman filter estimator to predict the current time state vector, correcting the predicted current time state vector according to the observation values contained in the current time state vector, and obtaining the current tropospheric slant delay values of each of the visible airspace hemispherical grids.

[0011] Optionally, in one or more embodiments of the present specification, the current tropospheric slant delay values of each of the visible airspace hemispherical grids are inputted as the next time to determine the tropospheric slant delay estimation values of each of the visible airspace hemispherical grids at the next time based on the Kalman filter estimator, specifically comprising: determining the current time state vector according to the current tropospheric slant delay values of the visible airspace hemispherical grids; inputting the current time state vector into the state transition matrix of the Kalman filter estimator to predict the next time state vector, and obtaining the tropospheric slant delay estimation values of each of the visible airspace hemispherical grids at the next time according to the next time state vector.

[0012] Optionally, in one or more embodiments of the present specification, according to the visible satellite observation values of the multi-GNSS monitoring stations in the preset area at the current time and the preset visible airspace hemispheres, the visible airspace hemispherical grids to which each of the visible satellite observation values in the preset visible airspace hemispheres belongs are determined, specifically comprising: The center of the preset area is taken as a reference station, and a direction component of a local coordinate system is determined according to the reference station approximate coordinate and the approximate coordinates of the satellites; wherein the direction component comprises an east direction component, a north direction component and a zenith direction component. According to the direction component, the elevation angle and the azimuth angle of each visible satellite are determined. According to the preset azimuth angle and the preset elevation angle, the preset visible airspace hemisphere is uniformly divided to obtain a plurality of visible airspace hemisphere grids of the preset visible airspace hemisphere. The visible satellite observation values of the GNSS monitoring stations in the preset area at the current time are collected, and according to the elevation angle and the azimuth angle of each visible satellite and the azimuth angle interval and the elevation angle interval corresponding to each visible airspace hemisphere grid, the visible airspace hemisphere grid to which each visible satellite observation value belongs is determined.

[0013] Optionally, in one or more embodiments of the present specification, according to the direction component, the elevation angle and the azimuth angle of each visible satellite are determined, specifically comprising: The direction component is processed based on an inverse tangent function to obtain the elevation angle and the azimuth angle of each visible satellite: ; ; is the elevation angle of the visible satellite; is the azimuth angle of the visible satellite; is an inverse tangent function, is a four-quadrant inverse tangent function, and the range of the azimuth angle is when , then is increased by ; The east direction component, the north direction component and the zenith direction component of the local coordinate system determined based on the reference station approximate coordinate and the approximate coordinates of the satellites, respectively.

[0014] One or more embodiments of the present specification provide a device for estimating the tropospheric slant delay of GNSS monitoring, which comprises: A grid determination unit is configured to determine the visible airspace hemisphere grid to which each visible satellite observation value in the preset visible airspace hemisphere belongs according to the visible satellite observation values of the GNSS monitoring stations in the preset area at the current time and the preset visible airspace hemisphere; An equation acquisition unit is configured to add the visible airspace hemisphere grid to which each visible satellite observation value belongs as a tropospheric slant delay to-be-estimated parameter into a GNSS array observation equation to obtain a current GNSS array observation equation; The solving unit is configured to solve the to-be-estimated parameters of the current GNSS array observation equation based on a Kalman filter estimator to obtain current tropospheric slant delay values of each of the visible spatial hemispherical grids; wherein a state transition matrix of the Kalman filter estimator is determined based on historical visible satellite observation values of each of the visible spatial hemispherical grids at a previous time and the comparison results of the visible spatial hemispherical grids. The estimating unit is configured to take the current tropospheric slant delay values of each of the visible spatial hemispherical grids as inputs at a next time to determine tropospheric slant delay estimation values of each of the visible spatial hemispherical grids at the next time based on the Kalman filter estimator.

[0015] The above at least one technical solution adopted by the embodiments of the present specification can achieve the following beneficial effects: The technical solution directly estimates the tropospheric slant delay, avoiding the defect that the traditional method excessively relies on the uniform distribution of the atmosphere when calculating the tropospheric delay. By determining the visible spatial hemispherical grid to which each visible satellite observation value in the preset visible spatial hemispherical grid belongs, the estimation of the tropospheric slant delay in each direction is realized, avoiding the problem of the existing isotropic assumption. Also, all satellite observation values are effectively utilized, avoiding the problem of observation information loss caused by the low-elevation observation data cutoff strategy. The solving of the current GNSS array observation equation fully utilizes the spatial correlation of the data, improving the estimation accuracy of the tropospheric slant delay values. In addition, this method improves the ability of small-area GNSS monitoring stations to calculate the tropospheric delay through data processing rather than hardware upgrade, avoiding the problem that the traditional model cannot distinguish small-scale tropospheric delay variation characteristics. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present specification or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present specification, and those skilled in the art can also obtain other drawings according to these drawings without creating any inventive labor. In the drawings: Figure 1 A tropospheric slant delay estimation method flowchart for GNSS monitoring provided by the embodiments of the present specification; Figure 2 A logic diagram for jointly estimating multi-azimuth tropospheric slant delay by a GNSS monitoring station array provided by the embodiments of the present specification; Figure 3 A structure diagram of a tropospheric slant delay estimation device for GNSS monitoring provided by the embodiments of the present specification. DETAILED DESCRIPTION

[0017] This specification provides a method and apparatus for estimating tropospheric tilt delay for GNSS monitoring.

[0018] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0019] like Figure 1 As shown in the figure, this specification provides a flowchart illustrating a method for estimating tropospheric tilt delay for GNSS monitoring. Figure 1 As can be seen, in one or more embodiments of this specification, a method for estimating tropospheric tilt delay for GNSS monitoring specifically includes: S101: Based on the visible satellite observations of multiple GNSS monitoring stations in the current preset area and the preset visible spatial hemisphere, determine the visible spatial hemisphere grid to which each visible satellite observation belongs within the preset visible spatial hemisphere.

[0020] Traditional tropospheric delay modeling methods primarily rely on estimating the zenith delay and projecting it onto the line-of-sight directions of each satellite using empirical mapping functions. This approach is based on the assumption of atmospheric isotropy, meaning that the tropospheric delay is symmetrically distributed along the zenith. However, actual atmospheric conditions often exhibit significant spatial anisotropy, especially in low-elevation regions and complex terrain conditions. This isotropy assumption can lead to systematic biases in the slant path delay estimation. Therefore, to avoid the problems of existing isotropy assumptions, this embodiment first assigns the observations of each visible satellite to a corresponding visible spatial hemisphere grid, facilitating subsequent estimation of tropospheric tilt delay values ​​for each visible spatial hemisphere grid, i.e., each direction. To determine the visible spatial hemisphere grid to which each visible satellite observation belongs, such as... Figure 2 The system acquires the visible satellite observations of multiple GNSS monitoring stations within a preset area at the current time, along with a preset visible spatial hemisphere. Based on the visible satellite observations of multiple GNSS monitoring stations within a preset area at the current time, and the preset visible spatial hemisphere, it determines the visible spatial hemisphere grid to which each visible satellite observation belongs within the preset visible spatial hemisphere.

[0021] Specifically, in one or more embodiments of the present specification, according to the visible satellite observation values of the multiple GNSS monitoring stations in the preset region at the current time, and the preset visible airspace hemisphere, the visible airspace hemisphere grid to which each visible satellite observation value belongs in the preset visible airspace hemisphere is determined, and the process specifically includes the following steps: For a GNSS monitoring station array in a small area range, the distance between stations is usually within a few kilometers, and there is a small but important difference in the tropospheric delay between each station. Due to the limited spatial resolution of existing large-scale tropospheric models, these small-scale spatial variation characteristics cannot be captured. Therefore, in order to meet the needs of small-area GNSS monitoring, in the embodiments of the present application, the center of the preset region is taken as the reference station to determine the hemisphere with the center of the region as the reference as the preset visible airspace hemisphere, and the direction components of the local coordinate system are determined according to the approximate coordinates of the reference station and the approximate coordinates of each satellite. The direction components include: east direction component, north direction component and sky direction component. Then, according to the direction components, the elevation angle and the azimuth angle of each visible satellite are determined. The preset azimuth angle and the preset elevation angle are used to uniformly divide the preset visible airspace hemisphere to obtain multiple visible airspace hemisphere grids of the preset visible airspace hemisphere. The visible satellite observation values of the multiple GNSS monitoring stations in the preset region at the current time are collected, and the visible airspace hemisphere grid to which each visible satellite observation value belongs is determined according to the elevation angle and the azimuth angle of each visible satellite and the azimuth angle interval and the elevation angle interval corresponding to each visible airspace hemisphere grid.

[0022] In this process, the preset visible airspace hemisphere is divided into multiple regular regions, that is, visible airspace hemisphere grids, by using the azimuth angle and the elevation angle as coordinate axes. For each visible satellite, it is allocated to the corresponding visible airspace hemisphere grid according to its azimuth angle and elevation angle relative to the center of the preset region, so that the visible satellites in the preset region are sampled from the same atmospheric region as long as they correspond to the same visible airspace hemisphere grid, regardless of which GNSS monitoring station receives them. Therefore, this process realizes the conversion of the traditional tropospheric slant delay value estimation based on one zenith delay parameter to the tropospheric slant delay value estimation corresponding to the direction of several visible airspace hemisphere grids, solving the systematic deviation problem caused by the existing isotropic assumption.

[0023] Specifically, in one or more embodiments of the present specification, according to the direction components, the elevation angle and the azimuth angle of each visible satellite are determined, and the process specifically includes: The direction components are processed based on the inverse tangent function to obtain the elevation angle and the azimuth angle of each visible satellite; wherein the elevation angle of the visible satellite and the azimuth angle of the visible satellite are: ; (1) wherein, It is the elevation angle of the visible satellite; It is the azimuth angle of the visible satellite; It is the arctangent function. It is the arctangent function in the four quadrants, and the range of azimuth angles is... ,when At that time, then Increase ; These are the eastward, northward, and celestial components of the local coordinate system, determined based on the approximate coordinates of the reference station and each satellite: (2) in, For rotation matrix: (3) in, and These are geodetic longitude and geodetic latitude: ; (4) S102: The visible space hemispherical grid to which each visible satellite observation belongs is added as a parameter to be estimated for tropospheric tilt delay to the GNSS array observation equation to obtain the current GNSS array observation equation.

[0024] like Figure 2 As shown, after determining the visible space hemispherical grid to which each visible satellite observation belongs based on step S101, this application addresses the problem that existing joint processing of multi-station observation data fails to fully consider the spatial correlation of tropospheric delay among stations within a small area, resulting in limited accuracy and stability of parameter estimation. In this embodiment, the visible space hemispherical grid to which each visible satellite observation belongs is added as a parameter to be estimated for tropospheric tilt delay to the GNSS array observation equation, thus obtaining the current GNSS array observation equation. It is understood that the current GNSS array observation equation assumes that the tropospheric delay within a region is direction-dependent, but has little relation to the specific station in that direction. Therefore, based on the visible satellite observations from all monitoring stations for the same visible space hemispherical grid, the tropospheric tilt delay parameter corresponding to the same grid is estimated, achieving full consideration of the spatial correlation of tropospheric delay among stations within a small area. Furthermore, each visible satellite observation includes low-elevation angle data, avoiding the simple cutoff strategy often used in traditional methods when processing low-elevation angle observation data. This not only loses valuable observation information but may also lead to systematic biases in parameter estimation.

[0025] Specifically, in one or more embodiments of this specification, the visible spatial domain hemispherical grid to which each visible satellite observation belongs is added as a parameter to be estimated for tropospheric tilt delay to the GNSS array observation equation to obtain the current GNSS array observation equation. The specific process includes the following: The visible spatial domain hemispherical grid to which each visible satellite observation belongs is used as the parameter to be estimated for tropospheric tilt delay, thereby constructing the corresponding tropospheric tilt delay parameter vector. The tropospheric tilt delay parameter vector is as follows: (5) This refers to the hemispherical grid number of the visible space domain to which each visible satellite observation belongs. It should be noted that the dimension of the vector representing the tropospheric tilt delay estimation parameter is the same as the number of visible space domain hemispherical grids determined in step S101 above. Based on the satellite signal paths corresponding to each visible satellite, the center of each satellite signal path relative to the preset area and the mapping function vector of each GNSS monitoring station are determined. The mapping function vector and the vector representing the tropospheric tilt delay estimation parameter are added to the GNSS array observation equation to obtain the current GNSS array observation equation. The current GNSS array observation equation is: (6) in, for Ionospheric pseudorange observations from one GNSS monitoring station; for Ionospheric combined phase observations from one GNSS monitoring station; for The satellite-to-receiver direction cosine of each GNSS monitoring station: ; ; (7) in, for Approximate coordinates of the monitoring stations; for The coordinate difference between the approximate coordinates of each monitoring station and the coordinates of visible satellites; for Approximate distance between each monitoring station and a visible satellite. for Coordinate increments of each GNSS monitoring station; The speed of light in a vacuum; for The receiver clock bias of each GNSS monitoring station; among which... for ionosphere-free combined pseudorange observation value of the GNSS monitoring station; is ionosphere-free combined phase observation value of the GNSS monitoring station; is satellite-to-receiver direction cosine of the GNSS monitoring station; is coordinate increment of the GNSS monitoring station; is the speed of light in vacuum; is receiver clock error of the GNSS monitoring station; is the slant tropospheric delay from the center of the region to the center of the visible airspace hemisphere grid, is the number of visible airspace hemisphere grids; is carrier phase integer ambiguity parameter of the GNSS monitoring station; is the satellite signal path corresponding to each visible satellite and is the mapping function of the GNSS monitoring station, .

[0026] In this process, by constructing a tropospheric slant delay estimated parameter vector with the same dimension as the number of visible airspace hemisphere grids, the estimated parameters belonging to each receiver are changed to belong to each airspace direction, that is, the estimated parameters are changed from belonging to the receiver as the unit of attribution to belonging to the airspace direction as the unit of attribution. Compared with the traditional method of estimating zenith delay for each station, the modeling object is changed, and the problems of being unable to represent the atmospheric changes in different directions in a small region and ignoring the correlation between stations are avoided.

[0027] Further, in one or more embodiments of the present specification, the mapping function of each GNSS monitoring station and the satellite signal path corresponding to each visible satellite relative to the center of the preset region are determined according to the satellite signal path corresponding to each visible satellite, and specifically include the following process: The traditional tropospheric delay modeling method mainly relies on the estimation of zenith direction delay, and projects the zenith delay to the line-of-sight direction of each satellite combined with the empirical mapping function. However, for a GNSS monitoring station array in a small region, the distances from each station to the satellite are different, which leads to slight differences in path length and atmospheric column through even if the directions are the same. Therefore, in order to solve the problem of existing empirical mapping projection, the present embodiment determines whether the visible airspace hemisphere grid to which the observation value of each visible satellite belongs and the satellite signal path corresponding to each visible satellite exist geometric interaction. If the visible airspace hemisphere grid numbered k and the satellite signal path exist geometric interaction, then the mapping function is determined as: , (8) wherein, is a mapping function, is a number of a visible space hemisphere grid to which each visible satellite observation belongs, , is a number of visible space hemisphere grids; is a visible satellite, , is a number of visible satellites; is a number of GNSS monitoring stations in the preset area, ; is an approximate distance from the visible satellite to the receiver; is an approximate distance from the visible satellite to the center of the area.

[0028] If the visible space hemisphere grid numbered k has no geometric interaction with the satellite signal path, the mapping function is determined as: (9) Generally, an observation between one satellite and one monitoring station only interacts with one hemisphere grid. Then, the mapping functions corresponding to each visible space hemisphere grid are summarized to obtain the mapping functions of each satellite signal path relative to the center of the preset area and each GNSS monitoring station as: (10) wherein m is a number of GNSS monitoring stations in the preset area.

[0029] Since each visible space hemisphere grid actually corresponds to an atmospheric area in a specific direction, the above embodiment of the present application ensures that the visible satellite observation is only applied to the parameters corresponding to the grid that actually passes through the satellite signal path by judging the geometric interaction, so as to ensure that each mapping function only reflects the atmospheric state in its own direction, and to improve the accuracy of subsequent estimation.

[0030] S103: solving the to-be-estimated parameters of the current GNSS array observation equation based on a Kalman filter estimator to obtain current values of the tropospheric slant delay of each visible space hemisphere grid; wherein a state transition matrix of the Kalman filter estimator is determined based on historical visible satellite observations of each visible space hemisphere grid at a previous moment and the visible satellite observations.

[0031] ​After the current GNSS array observation equation is obtained, the to-be-estimated parameters of the current GNSS array observation equation are solved based on a Kalman filter estimator to obtain current tropospheric slant delay values of each visible spatial hemispherical grid.

[0032] Specifically, in one or more embodiments of the present specification, the to-be-estimated parameters of the current GNSS array observation equation are solved based on a Kalman filter estimator to obtain current tropospheric slant delay values of each visible spatial hemispherical grid, and specifically include the following processes: After the to-be-estimated parameters of the current GNSS array observation equation are obtained, the current time state vector of the Kalman filter estimator is constructed based on the to-be-estimated parameters, as shown in formula (3). Figure 2 Then, the state transition matrix of the Kalman filter estimator is input with the last time state vector to predict the current time state vector. According to the observation values contained in the current time state vector, the predicted current time state vector is corrected to obtain the current tropospheric slant delay values of each visible spatial hemispherical grid.

[0033] Further, in one or more embodiments of the present specification, before the to-be-estimated parameters of the current GNSS array observation equation are solved based on the Kalman filter estimator to obtain the current tropospheric slant delay values of each visible spatial hemispherical grid, the method further includes the following processes: Firstly, it is determined whether there are historical visible satellite observation values at the last time and current visible satellite observation values for each visible spatial hemispherical grid. If yes, it is determined that the diagonal elements of the state transition matrix of the Kalman filter estimator are 1. If it is determined that there are no historical visible satellite observation values at the last time for each visible spatial hemispherical grid, it is determined that the diagonal elements of the state transition matrix of the Kalman filter estimator are 0. That is, the Kalman filter estimator is used to solve the tropospheric slant delay and other to-be-estimated parameters. The state transition equation of the Kalman filter estimator is as follows: (11) Wherein, is the current tropospheric slant delay; is the tropospheric slant delay estimated at the previous time; is the state transition matrix: (12) Wherein, is a diagonal matrix; if the previous time and the current time are the same, the diagonal matrix is 1; if the previous time and the current time are different, the diagonal matrix is 0. ​​ If the grid numbered contains satellite observations, then ; if the previous time does not contain the current satellite observations, then . . is the process noise, which is assumed to be Gaussian white noise ; is the process noise covariance matrix, which is a diagonal matrix with diagonal elements .

[0034] S104: input the current tropospheric slant delay values of each of the visible airspace hemisphere grids as the next time input, to determine the tropospheric slant delay estimated values of each of the visible airspace hemisphere grids at the next time based on the Kalman filter estimator.

[0035] That is, after obtaining the current tropospheric slant delay values of the visible airspace hemisphere grids in the above process, as shown in Figure 2 , the current tropospheric slant delay values of each of the visible airspace hemisphere grids are input as the next time input, to determine the tropospheric slant delay estimated values of each of the visible airspace hemisphere grids at the next time based on the Kalman filter estimator, specifically including: According to the current tropospheric slant delay values of the visible airspace hemisphere grids, the current time state vector is determined. Then the current time state vector is input into the state transition matrix of the Kalman filter estimator to predict the next time state vector, and according to the next time state vector, the tropospheric slant delay estimated values of each of the visible airspace hemisphere grids at the next time are obtained. Since this method directly estimates the tropospheric slant delay, it avoids the problem of excessive dependence on the uniform distribution of the atmosphere in the calculation of the tropospheric delay in the traditional method. And through data processing instead of hardware upgrading, the ability of small area GNSS monitoring station to calculate the tropospheric delay is improved.

[0036] As shown in Figure 3 , the present specification embodiment provides a tropospheric slant delay estimation device for GNSS monitoring. As can be seen from Figure 3 , one or more embodiments of the present specification provide a tropospheric slant delay estimation device for GNSS monitoring, which comprises: A grid determination unit 301 is configured to determine, according to the visible satellite observation values of the multiple GNSS monitoring stations in a preset area at a current time and a preset visible airspace hemisphere, the visible airspace hemisphere grid to which each of the visible satellite observation values in the preset visible airspace hemisphere belongs. The equation obtaining unit 302 is configured to add the visible space hemispherical grid to which each visible satellite observation value belongs into the GNSS array observation equation as the tropospheric delay to-be-estimated parameter, and obtain a current GNSS array observation equation. The solving unit 303 is configured to solve the to-be-estimated parameter of the current GNSS array observation equation based on a Kalman filter estimator, to obtain a current tropospheric delay value of each visible space hemispherical grid; wherein a state transition matrix of the Kalman filter estimator is determined based on a historical visible satellite observation value of each visible space hemispherical grid at a previous moment and a comparison result of the visible space hemispherical grid. The estimating unit 304 is configured to take the current tropospheric delay value of each visible space hemispherical grid as an input at a next moment, to determine a tropospheric delay estimation value of each visible space hemispherical grid at the next moment based on the Kalman filter estimator.

[0037] Each of the embodiments in the specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the difference from other embodiments. In particular, for the device, equipment and non-volatile computer storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiment.

[0038] The above describes specific embodiments of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different than the order in the embodiments and still achieve the desired result. In addition, the processes depicted in the figures do not necessarily require the particular order shown or sequential order to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous or possible.

[0039] The above only describes one or more embodiments of the specification and does not limit the specification. One or more embodiments of the specification can have various changes and variations for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of one or more embodiments of the specification shall be included in the scope of the claims of the specification.

Claims

1. A method for estimating tropospheric tilt delay for GNSS monitoring, characterized in that, The method includes: Based on the visible satellite observations from multiple GNSS monitoring stations in the current preset area and the preset visible spatial hemisphere, determine the visible spatial hemisphere grid to which each visible satellite observation belongs within the preset visible spatial hemisphere. The visible spatial domain hemispherical grid to which each visible satellite observation belongs is added as a parameter to be estimated for tropospheric tilt delay to the GNSS array observation equation to obtain the current GNSS array observation equation. The parameters to be estimated in the current GNSS array observation equation are solved based on the Kalman filter estimator to obtain the current tropospheric tilt delay values ​​of each visible spatial domain hemispherical grid; wherein, the state transition matrix of the Kalman filter estimator is determined based on the historical visible satellite observation values ​​of each visible spatial domain hemispherical grid at the previous moment and the visible satellite observation values. The current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids is used as the input for the next time step, so as to determine the estimated tropospheric tilt delay value of each of the visible spatial domain hemispherical grids at the next time step based on the Kalman filter estimator.

2. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 1, characterized in that, The visible spatial domain hemispherical grid to which each visible satellite observation belongs is added as a parameter to be estimated for tropospheric tilt delay to the GNSS array observation equation, resulting in the current GNSS array observation equation, which specifically includes: The visible spatial domain hemispherical grid to which each visible satellite observation belongs is used as the tropospheric tilt delay parameter to be estimated, so as to construct the tropospheric tilt delay parameter vector corresponding to the tropospheric tilt delay parameter to be estimated. Based on the satellite signal paths corresponding to each of the visible satellites, determine the center of each satellite signal path relative to the preset area and the mapping function vector of each GNSS monitoring station; The mapping function vector and the tropospheric tilt delay parameter vector are added to the GNSS array observation equation to obtain the current GNSS array observation equation.

3. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 2, characterized in that, Based on the satellite signal paths corresponding to each of the visible satellites, determine the mapping function of each satellite signal path relative to the center of the preset area and each GNSS monitoring station, specifically including: If geometric interactions exist, then the mapping function is determined as follows: ,in, This refers to the hemispherical grid number of the visible space domain to which each visible satellite observation belongs. , This represents the number of grid cells in the visible spatial hemisphere. For visible satellites, , This represents the number of visible satellites. This represents the number of GNSS monitoring stations within the pre-defined area. ; This represents the approximate distance from the visible satellite to the receiver. Visible satellites To the regional center Approximate distance; If there is no geometric interaction, then the mapping function is determined as follows: ; By summarizing the mapping functions corresponding to each visible spatial hemispherical grid, the center of each satellite signal path relative to the preset area can be obtained. The mapping function for each GNSS monitoring station is: .

4. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 3, characterized in that, The current GNSS array observation equation is: ； in, for Ionospheric pseudorange observations from one GNSS monitoring station; for Ionospheric combined phase observations from one GNSS monitoring station; for The satellite-to-receiver direction cosine of a GNSS monitoring station; for Coordinate increments of each GNSS monitoring station; The speed of light in a vacuum; for Receiver clock bias of a GNSS monitoring station; The tilted tropospheric delay is defined as the direction from the regional center to the center of the visible hemispherical grid. This represents the number of grid cells in the visible spatial hemisphere. for Carrier phase integer ambiguity parameters of a GNSS monitoring station; The center of each satellite signal path relative to the preset area and Mapping function for GNSS monitoring stations, .

5. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 1, characterized in that, Before solving the parameters to be estimated in the current GNSS array observation equations based on the Kalman filter estimator to obtain the current tropospheric tilt delay values ​​for each of the visible spatial hemispherical grids, the method further includes: Determine whether each visible hemispherical grid has historical visible satellite observations from the previous moment, and whether it has visible satellite observations from the current moment; If so, then the diagonal elements of the state transition matrix of the Kalman filter estimator are determined to be 1; If it is determined that there are no historical visible satellite observations from the previous moment in each visible spatial hemispherical grid, then the diagonal elements of the state transition matrix of the Kalman filter estimator are determined to be 0.

6. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 1, characterized in that, The parameters to be estimated in the current GNSS array observation equations are solved using a Kalman filter estimator to obtain the current tropospheric tilt delay values ​​for each visible spatial hemispherical grid, specifically including: Obtain the parameters to be estimated in the current GNSS array observation equation, and construct the current time state vector of the Kalman filter estimator based on the parameters to be estimated; The state vector of the previous time step is input into the state transition matrix of the Kalman filter estimator to predict the state vector of the current time step. Based on the observation values ​​contained in the current time step state vector, the predicted current time step state vector is corrected to obtain the current tropospheric tilt delay value of each visible spatial hemispherical grid.

7. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 1, characterized in that, Using the current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids as input for the next time step, the estimated tropospheric tilt delay value of each of the visible spatial domain hemispherical grids for the next time step is determined based on the Kalman filter estimator. Specifically, this includes: The current state vector is determined based on the current tropospheric tilt delay value of the visible spatial hemispherical grid. The current state vector is input into the state transition matrix of the Kalman filter estimator to predict the state vector at the next moment. Based on the state vector at the next moment, the estimated tropospheric tilt delay values ​​of each visible spatial hemispherical grid at the next moment are obtained.

8. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 1, characterized in that, Based on the visible satellite observations from multiple GNSS monitoring stations within a preset area at the current time, and a preset visible spatial hemisphere, the visible spatial hemisphere grid to which each visible satellite observation within the preset visible spatial hemisphere belongs is determined, specifically including: Using the center of the preset area as a reference station, the directional components of the local coordinate system are determined based on the approximate coordinates of the reference station and the approximate coordinates of each satellite; wherein, the directional components include: east directional component, north directional component and sky directional component; Based on the directional components, determine the elevation angle and azimuth angle of each visible satellite; The preset visible spatial domain hemisphere is uniformly divided according to the preset azimuth angle and preset elevation angle to obtain multiple visible spatial domain hemisphere grids of the preset visible spatial domain hemisphere. Collect visible satellite observations from multiple GNSS monitoring stations within a pre-defined area at the current time, and determine the visible space hemisphere grid to which each visible satellite observation belongs based on the elevation and azimuth angles of each visible satellite and the corresponding azimuth and elevation angle intervals of each visible space hemisphere grid.

9. The method for estimating tropospheric tilt delay for GNSS monitoring according to claim 8, characterized in that, Based on the directional components, the elevation angle and azimuth angle of each visible satellite are determined, specifically including: The elevation and azimuth angles of each visible satellite are obtained by processing the direction components based on the arctangent function. ； ； in, It is the elevation angle of the visible satellite; It is the azimuth angle of the visible satellite; It is the arctangent function. It is the arctangent function in the four quadrants, and the range of azimuth angles is... ,when At that time, then Increase ; These are the eastward, northward, and celestial components of the local coordinate system, determined based on the approximate coordinates of the reference station and each satellite.

10. A tropospheric tilt delay estimation device for GNSS monitoring, characterized in that, The device includes: The grid determination unit is used to determine the visible space hemisphere grid to which each visible satellite observation value in the preset visible space hemisphere belongs, based on the visible satellite observation values ​​of multiple GNSS monitoring stations in the current preset area and the preset visible space hemisphere. The equation acquisition unit is used to add the visible spatial domain hemispherical grid to which each visible satellite observation value belongs as the tropospheric tilt delay parameter to be estimated into the GNSS array observation equation to obtain the current GNSS array observation equation. The calculation unit is used to solve the parameters to be estimated in the current GNSS array observation equation based on the Kalman filter estimator, so as to obtain the current tropospheric tilt delay value of each visible spatial domain hemispherical grid; wherein, the state transition matrix of the Kalman filter estimator is determined based on the comparison result between the historical visible satellite observation value of each visible spatial domain hemispherical grid at the previous moment and the visible spatial domain hemispherical grid. An estimation unit is used to take the current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids as input for the next moment, so as to determine the estimated value of the tropospheric tilt delay of each of the visible spatial domain hemispherical grids for the next moment based on the Kalman filter estimator.

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