A method and apparatus for estimating tropospheric tilt delay for GNSS monitoring

Abstract

This specification discloses a method and apparatus for estimating tropospheric tilt delay for GNSS monitoring, relating to the field of GNSS satellite navigation and positioning technology, and addressing the problem of low accuracy in existing methods. The method includes: determining the visible satellite observation values ​​of multiple GNSS monitoring stations within a preset area at the current time, and a preset visible spatial hemisphere, to determine the visible spatial hemisphere grid to which each visible satellite observation value belongs, and incorporating this grid as a parameter to be estimated for tropospheric tilt delay into the GNSS array observation equation to obtain the current GNSS array observation equation; solving the parameter to be estimated in the current GNSS array observation equation based on a Kalman filter estimator to obtain the current tropospheric tilt delay value for each visible spatial hemisphere grid; and using the current tropospheric tilt delay value of each visible spatial hemisphere grid as input for the next time step to obtain the estimated tropospheric tilt delay value for each visible spatial hemisphere grid at the next time step.

Description

Technical Field

[0001] This specification relates to the field of GNSS satellite navigation and positioning technology, and in particular to a method and apparatus for estimating tropospheric tilt delay for GNSS monitoring. Background Technology

[0002] The troposphere causes propagation delays for space observation technologies that primarily use electromagnetic waves for detection, such as Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), satellite laser ranging, and Synthetic Aperture Radar Interferometry (SAR). This delay is highly time-varying, influenced by meteorological conditions such as temperature, pressure, and water vapor content, and varies with geographical location and propagation path. Furthermore, it cannot be eliminated using multi-frequency combined observations, making it one of the main bottlenecks restricting the accuracy of space geodesy technologies.

[0003] Currently, traditional tropospheric delay modeling methods in GNSS tropospheric modeling mainly rely on the estimation of zenith delay, combined with empirical mapping functions to project the zenith delay onto the line-of-sight directions of each satellite. However, the isotropic assumption in this approach leads to systematic biases in the slant path delay estimation. Furthermore, traditional mapping functions such as GMF and VMF perform well in high elevation angle regions, but their accuracy drops significantly at low elevation angles. Moreover, for GNSS monitoring station arrays within a small area, the distance between stations is typically within a few kilometers, and there are subtle but significant differences in tropospheric delay between stations. However, existing large-scale tropospheric models, due to their limited spatial resolution, cannot capture these small-scale spatial variation characteristics. While atmospheric tomography can theoretically reconstruct three-dimensional atmospheric conditions, it has strict requirements on the geometric distribution of GNSS monitoring stations within a small area and has high computational complexity, making it difficult to meet the needs of real-time processing. In the era of multi-system GNSS, with the increase in the number of available satellites, existing methods for utilizing these multi-azimuth observation data lack effective azimuth partitioning modeling methods, making it difficult 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 tropospheric delays among stations within a small region is not fully considered, resulting in limited accuracy and stability of parameter estimation. Furthermore, existing methods often employ simple cutoff strategies when processing low-elevation-angle observation data, which not only loses valuable observational information but may also lead to systematic biases in parameter estimation. Summary of the Invention

[0004] To address the aforementioned technical problems, one or more embodiments of this specification provide a method for estimating tropospheric tilt delay for GNSS monitoring.

[0005] One or more embodiments of this specification employ the following technical solutions:

[0006] This specification provides one or more embodiments of a method for estimating tropospheric tilt delay for GNSS monitoring, the method comprising:

[0007] 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.

[0008] 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.

[0009] 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.

[0010] 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.

[0011] Optionally, 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, specifically including:

[0012] 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.

[0013] 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;

[0014] 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.

[0015] Optionally, in one or more embodiments of this specification, the mapping function of each satellite signal path relative to the center of the preset area and each GNSS monitoring station is determined based on the satellite signal paths corresponding to each of the visible satellites, specifically including:

[0016] Determine whether there is a geometric interaction between the visible space hemispherical grid to which each visible satellite observation belongs and the satellite signal path corresponding to each visible satellite;

[0017] 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;

[0018] If there is no geometric interaction, then the mapping function is determined as follows: ;

[0019] 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: .

[0020] Optionally, in one or more embodiments of this specification, the current GNSS array observation equation is:

[0021] ;

[0022] 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, .

[0023] Optionally, in one or more embodiments of this specification, before solving the parameters to be estimated in the current GNSS array observation equations based on a Kalman filter estimator to obtain the current tropospheric tilt delay values ​​for each of the visible spatial domain hemispherical grids, the method further includes:

[0024] 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;

[0025] If so, then the diagonal elements of the state transition matrix of the Kalman filter estimator are determined to be 1;

[0026] 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.

[0027] Optionally, in one or more embodiments of this specification, the parameters to be estimated in the current GNSS array observation equation are solved based on a Kalman filter estimator to obtain the current tropospheric tilt delay values ​​for each of the visible spatial domain hemispherical grids, specifically including:

[0028] 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;

[0029] 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.

[0030] Optionally, in one or more embodiments of this specification, the current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids is used as the input for the next moment, so as to determine the estimated tropospheric tilt delay value of each of the visible spatial domain hemispherical grids for the next moment based on the Kalman filter estimator, specifically including:

[0031] The current state vector is determined based on the current tropospheric tilt delay value of the visible spatial hemispherical grid.

[0032] 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.

[0033] Optionally, in one or more embodiments of this specification, based on the visible satellite observations of 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 belongs is determined is specifically included:

[0034] 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;

[0035] Based on the directional components, determine the elevation angle and azimuth angle of each visible satellite;

[0036] 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.

[0037] 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.

[0038] Optionally, in one or more embodiments of this specification, determining the elevation angle and azimuth angle of each visible satellite based on the direction components specifically includes:

[0039] The elevation and azimuth angles of each visible satellite are obtained by processing the direction components based on the arctangent function.

[0040] ;

[0041] ;

[0042] 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 the azimuth angle 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.

[0043] This specification provides one or more embodiments of a tropospheric tilt delay estimation device for GNSS monitoring, the device comprising:

[0044] 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.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] The above-described at least one technical solution adopted in the embodiments of this specification can achieve the following beneficial effects:

[0049] This technical solution directly estimates the tropospheric tilt delay, avoiding the over-reliance on uniform atmospheric distribution that is a drawback of traditional methods. By determining the visible hemispherical grid to which each visible satellite observation belongs within a pre-defined visible hemisphere, subsequent estimations of the tropospheric tilt delay in various directions are achieved, avoiding the problems associated with existing isotropic assumptions. This also ensures the effective use of all satellite observations, avoiding the information loss caused by low-elevation-angle observation data cutoff strategies. The solution to the current GNSS array observation equations fully utilizes the spatial correlation of data, improving the accuracy of tropospheric tilt delay estimation. Furthermore, this approach improves the ability of small-area GNSS monitoring stations to calculate tropospheric delay through data processing rather than hardware upgrades, avoiding the problem of traditional models being unable to distinguish small-scale tropospheric delay variation characteristics. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0051] Figure 1 This specification provides a schematic flowchart of a tropospheric tilt delay estimation method for GNSS monitoring, as illustrated in the embodiments of this specification.

[0052] Figure 2 A logic diagram for jointly estimating multi-azimuth tropospheric tilt delay using an array of GNSS monitoring stations, as provided in this specification.

[0053] Figure 3 This is a schematic diagram of a tropospheric tilt delay estimation device for GNSS monitoring, provided as an embodiment of this specification. Detailed Implementation

[0054] This specification provides a method and apparatus for estimating tropospheric tilt delay for GNSS monitoring.

[0055] 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.

[0056] 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:

[0057] 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.

[0058] 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.

[0059] Specifically, in one or more embodiments of this specification, based on the visible satellite observations of multiple GNSS monitoring stations in a preset area at the current time and a preset visible spatial hemisphere, the visible spatial domain hemisphere grid to which each visible satellite observation belongs is determined. This process specifically includes the following steps:

[0060] For GNSS monitoring station arrays within a small area, the distance between stations is typically within a few kilometers, and there are subtle but significant differences in tropospheric delay between stations. Existing large-scale tropospheric models, due to their limited spatial resolution, cannot capture these small-scale spatial variation characteristics. Therefore, to address the needs of small-area GNSS monitoring, this embodiment uses the center of a pre-defined area as the reference station to determine a hemisphere with the area center as the reference as the pre-defined visible spatial domain hemisphere. Based on the approximate coordinates of the reference station and each satellite, the direction components of the local coordinate system are determined. These direction components include an east direction component, a north direction component, and a celestial direction component. Then, based on the direction components, the elevation angle and azimuth angle of each visible satellite are determined. The pre-defined visible spatial domain hemisphere is then uniformly divided according to the pre-defined azimuth and elevation angles, resulting in multiple visible spatial domain hemisphere grids. 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.

[0061] This process uses azimuth and elevation angles as coordinate axes to divide a predefined visible airspace hemisphere into multiple regular regions, known as visible airspace hemispherical grids. Each visible satellite is assigned to a corresponding visible airspace hemispherical grid based on its azimuth and elevation angles relative to the center of the predefined region. This ensures that regardless of which GNSS monitoring station receives a visible satellite within the predefined region, as long as it corresponds to the same visible airspace hemispherical grid, it indicates that the same atmospheric region has been sampled. Therefore, this process transforms the traditional numerical estimation of tropospheric tilt delay based on a single zenith delay parameter into a numerical estimation of tropospheric tilt delay corresponding to the directions of several visible airspace hemispherical grids, thus resolving the systematic bias problem caused by the existing isotropic assumption.

[0062] Specifically, in one or more embodiments of this specification, determining the elevation angle and azimuth angle of each visible satellite based on the direction component includes:

[0063] The direction components are processed based on the arctangent function to obtain the elevation angle and azimuth angle of each visible satellite; wherein, the elevation angle and azimuth angle of the visible satellite are:

[0064] ;

[0065] (1)

[0066] 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 the azimuth angle 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:

[0067] (2)

[0068] in, For rotation matrix:

[0069] (3)

[0070] in, and These are geodetic longitude and geodetic latitude:

[0071] ;

[0072] (4)

[0073] 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.

[0074] 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.

[0075] 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:

[0076] 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:

[0077] (5)

[0078] 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:

[0079] (6)

[0080] 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:

[0081] ;

[0082] ;

[0083] (7)

[0084] 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 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, .

[0085] This process constructs a tropospheric tilt delay parameter vector with the same dimension as the number of hemispherical grids in the visible spatial domain. This transforms the parameters from belonging to each receiver to belonging to each spatial direction. In other words, the parameters are transformed from being attributed to the receiver as the unit of reference to the spatial direction as the unit of reference. Compared with the traditional method of estimating zenith delay for each station, this changes the modeling object and avoids the problems of existing methods that cannot represent atmospheric changes in different directions within a small area and ignore the correlation between inter-station data.

[0086] Furthermore, in one or more embodiments of this specification, the mapping function of each satellite signal path relative to the center of a preset area and each GNSS monitoring station is determined based on the satellite signal paths corresponding to each visible satellite. This specifically includes the following process:

[0087] Traditional tropospheric delay modeling methods primarily rely on estimating the zenith direction delay and projecting it onto the line-of-sight directions of each satellite using an empirical mapping function. However, for GNSS monitoring station arrays within a small area, the distances from each station to the satellites vary, resulting in subtle differences in path length and the atmospheric column traversed even when the direction is the same. Therefore, to address the problems of existing empirical mapping projections, this application's embodiments determine whether there is a geometric interaction between the visible spatial domain hemispherical grid to which each visible satellite observation belongs and the corresponding satellite signal path. If the visible spatial domain hemispherical grid numbered k has a geometric interaction with the satellite signal path, then the mapping function is determined as follows:

[0088] (8)

[0089] in, For mapping functions, 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 The approximate distance.

[0090] If there is no geometric interaction between the visible spatial hemispherical grid numbered k and the satellite signal path, then the mapping function is determined as follows:

[0091] (9)

[0092] Typically, observations between a satellite and a monitoring station interact with only one hemispherical grid. Then, by summing the mapping functions corresponding to each visible spatial hemispherical grid, the mapping functions for each satellite signal path relative to the center of the preset area and each GNSS monitoring station are obtained as follows:

[0093] (10)

[0094] Where m is the number of GNSS monitoring stations in the pre-defined area.

[0095] Since each visible spatial hemispherical grid actually corresponds to an atmospheric region in a specific direction, the above embodiments of this application ensure that the visible satellite observations are only applied to the parameters corresponding to the grids that actually pass through the satellite signal path by judging the geometric interaction. This ensures that each mapping function only reflects the atmospheric state in its own direction, thereby improving the accuracy of subsequent estimations.

[0096] S103: Solve the parameters to be estimated in the current GNSS array observation equation 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.

[0097] After obtaining the current GNSS array observation equations as described above, 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 hemispherical grid. It should be noted that the state transition matrix of this Kalman filter estimator is determined based on the historical visible satellite observations of each visible hemispherical grid at the previous moment and the visible satellite observations at the current moment.

[0098] Specifically, in one or more embodiments of this specification, the parameters to be estimated in the current GNSS array observation equation are solved based on a Kalman filter estimator to obtain the current tropospheric tilt delay values ​​for each visible spatial domain hemispherical grid. The specific process includes the following:

[0099] After obtaining the parameters to be estimated in the current GNSS array observation equations, such as Figure 2 The diagram shows the current state vector of the Kalman filter estimator constructed based on the parameters to be estimated. The previous state vector is then input into the state transition matrix of the Kalman filter estimator to predict the current state vector. Based on the observations contained in the current state vector, the predicted current state vector is corrected to obtain the current tropospheric tilt delay values ​​for each visible hemispherical grid.

[0100] Furthermore, in one or more embodiments of this specification, before solving for 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 visible spatial hemispherical grid, the method further includes the following process:

[0101] First, determine whether each visible hemispherical grid contains historical visible satellite observations from the previous moment, and whether there are visible satellite observations at the current moment. If so, set the diagonal elements of the state transition matrix of the Kalman filter estimator to 1. If it is determined that no historical visible satellite observations from the previous moment exist in each visible hemispherical grid, set the diagonal elements of the state transition matrix of the Kalman filter estimator to 0. Then, use the Kalman filter estimator to solve for the tropospheric tilt delay and other parameters to be estimated. The state transition equation of the Kalman filter estimator is:

[0102] (11)

[0103] in, For the present The tropospheric tilt atmospheric delay of the time estimate; For the previous The tropospheric tilt atmospheric delay in time estimation; Here is the state transition matrix:

[0104] (12)

[0105] in, for Diagonal matrix; if previously Time and Present Time number is If all grids contain satellite observations, then If previously The moment does not include the current moment. Time number is The satellite observations of the grid, then . The noise is process noise, assumed to be Gaussian white noise. ; Let be the process noise covariance matrix, and let be a diagonal matrix whose diagonal elements are all . .

[0106] S104: Use the current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids as the 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.

[0107] That is, after obtaining the current tropospheric tilt delay value of the visible spatial hemispherical grid through the above process, such as Figure 2 The diagram shows that the current tropospheric tilt delay values ​​of each visible spatial hemispherical grid are used as input for the next time step. Based on a Kalman filter estimator, the estimated tropospheric tilt delay values ​​for each visible spatial hemispherical grid at the next time step are determined. Specifically, this includes:

[0108] The current state vector is determined based on the current tropospheric tilt delay values ​​of the visible spatial hemispherical grid. This current state vector is then input into the state transition matrix of the Kalman filter estimator to predict the state vector for the next time step. Based on the next time step state vector, the estimated tropospheric tilt delay values ​​for each of the visible spatial hemispherical grids at the next time step are obtained. Because this method directly estimates the tropospheric tilt delay, it avoids the problem of traditional methods relying excessively on uniform atmospheric distribution when calculating tropospheric delay. Furthermore, it improves the ability of small-area GNSS monitoring stations to calculate tropospheric delay through data processing rather than hardware upgrades.

[0109] like Figure 3 As shown in the figure, this specification provides a schematic diagram of a tropospheric tilt delay estimation device for GNSS monitoring. Figure 3 As can be seen, one or more embodiments of this specification provide a tropospheric tilt delay estimation device for GNSS monitoring, the device comprising:

[0110] The grid determination unit 301 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 preset area at the current time and the preset visible space hemisphere.

[0111] The equation acquisition unit 302 is used to add the visible space domain hemispherical grid to which each visible satellite observation value belongs as the tropospheric tilt delay to be estimated parameter into the GNSS array observation equation to obtain the current GNSS array observation equation.

[0112] The calculation unit 303 is used to solve the parameters to be estimated in the current GNSS array observation equation based on the Kalman filter estimator 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.

[0113] The estimation unit 304 is used to take the current tropospheric tilt delay value of each of the visible spatial domain hemispherical grids as the 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.

[0114] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of apparatus, devices, and non-volatile computer storage media are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0115] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0116] The above description is merely one or more embodiments of this specification and is not intended to limit this specification. Various modifications and variations can be made to the one or more embodiments of this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of one or more embodiments of this specification should be included within the scope of the claims of this specification.

Claims

1. A method for tropospheric tilt delay estimation for GNSS monitoring, characterized in that, The method comprises: According to the preset region, the visible satellite observation value of the multi-GNSS monitoring station at the current time, and the preset visible space hemisphere, the visible satellite observation value in each visible space hemisphere grid in the preset visible space hemisphere is determined; Each visible satellite observation value belongs to a visible space hemisphere grid, which is added to the GNSS array observation equation as a tropospheric delay estimated parameter to obtain a current GNSS array observation equation; Based on the Kalman filter estimator, the estimated parameters of the current GNSS array observation equation are solved to obtain the current tropospheric delay value of each visible space hemisphere grid; wherein the state transition matrix of the Kalman filter estimator is determined based on the historical visible satellite observation value of each visible space hemisphere grid at the last time and the visible satellite observation value; The current tropospheric delay value of each visible space hemisphere grid is input as the next time to determine the tropospheric delay estimation value of each visible space hemisphere grid at the next time based on the Kalman filter estimator.

2. The method for estimating the tropospheric slant delay for GNSS monitoring according to claim 1, characterized in that, Each visible satellite observation value belongs to a visible space hemisphere grid, which is added to the GNSS array observation equation as a tropospheric delay estimated parameter to obtain a current GNSS array observation equation, which specifically comprises: Each visible satellite observation value belongs to a visible space hemisphere grid, which is added to the GNSS array observation equation as a tropospheric delay estimated parameter to obtain a current GNSS array observation equation, which specifically comprises: According to the satellite signal path corresponding to each visible satellite, the mapping function vector of each satellite signal path relative to the center of the preset region and each GNSS monitoring station is determined; The mapping function vector and the tropospheric delay estimated parameter vector are added to the GNSS array observation equation to obtain the current GNSS array observation equation.

3. A method for estimating tropospheric slant delay for GNSS monitoring according to claim 2, characterized in that, According to the satellite signal path corresponding to each visible satellite, the mapping function vector of each satellite signal path relative to the center of the preset region and each GNSS monitoring station is determined; If there is geometric interaction, the mapping function is determined as: where, is the number of the visible space hemispherical grid to which each satellite observation belongs, , is the number of visible space hemispherical grids; is the visible satellite, , is the number of visible satellites; is the number of GNSS monitoring stations in the preset area, ; is the approximate distance from the visible satellite to the receiver; is the approximate distance from the visible satellite to the center of the area ; If there is no geometric interaction, then the mapping function is determined as: ; Summing up the mapping functions corresponding to each visible airspace hemispherical grid, the mapping functions of each satellite signal path relative to the center of the preset area and the mapping function of a GNSS monitoring station is: .

4. A method for estimating tropospheric slant 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 the tropospheric slant delay for GNSS monitoring according to claim 1, wherein, Before the Kalman filter estimator is used to solve the estimated parameters of the current GNSS array observation equation to obtain the current tropospheric delay value of each visible space hemisphere grid, the method further comprises: Determine whether each visible space hemisphere grid has a last time historical visible satellite observation value and a current time visible satellite observation value; If yes, the diagonal elements of the state transition matrix of the Kalman filter estimator are 1; If it is determined that each visible space hemisphere grid does not have a last time historical visible satellite observation value, the diagonal elements of the state transition matrix of the Kalman filter estimator are 0.

6. The method for estimating the tropospheric slant delay for GNSS monitoring according to claim 1, wherein, Based on the Kalman filter estimator, the estimated parameters of the current GNSS array observation equation are solved to obtain the current tropospheric delay value of each visible space hemisphere grid, which specifically comprises: Obtain the estimated parameters of the current GNSS array observation equation to construct the current time state vector of the Kalman filter estimator based on the estimated parameters; The state transition matrix of the last time state vector is input into the Kalman filter estimator to predict the current time state vector, and the current time state vector is modified according to the observation value contained in the current time state vector, so as to obtain the current troposphere tilt delay value of each visible airspace hemisphere grid.

7. The method for estimating the tropospheric slant delay for GNSS monitoring according to claim 1, wherein, The current troposphere tilt delay value of each visible airspace hemisphere grid is taken as the input of the next time, and the troposphere tilt delay estimation value of each visible airspace hemisphere grid at the next time is determined based on the Kalman filter estimator, specifically comprising: determining the current time state vector according to the current troposphere tilt delay value of the visible airspace hemisphere grid; 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 the next time troposphere tilt delay estimation value of each visible airspace hemisphere grid is obtained according to the next time state vector.

8. The method for estimating the tropospheric slant delay for GNSS monitoring according to claim 1, characterized in that, According to the visible satellite observation value of the multi-GNSS monitoring station in the preset area at the current time, and the preset visible airspace hemisphere, the visible airspace hemisphere grid to which each visible satellite observation value in the preset visible airspace hemisphere belongs is determined, specifically comprising: Taking the center of the preset area as the reference station, the direction components of the local coordinate system are determined according to the reference station approximate coordinates and the satellite approximate coordinates; wherein the direction components include: east direction component, north direction component and sky direction component; According to the direction components, the elevation angle and 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; Collect the visible satellite observation value of the multi-GNSS monitoring station in the preset area at the current time, and determine the visible airspace hemisphere grid to which each visible satellite observation value belongs according to the elevation angle and azimuth angle of each visible satellite and the azimuth angle interval and elevation angle interval corresponding to each visible airspace hemisphere grid.

9. A method for estimating tropospheric tilt delay for GNSS monitoring according to claim 8, characterized in that, According to the direction components, the elevation angle and azimuth angle of each visible satellite are determined, specifically comprising: Based on the arctangent function, the direction components are processed to obtain the elevation angle and azimuth angle of each visible satellite: ； ； wherein is the elevation angle of the visible satellite; is the azimuth angle of the visible satellite; is the arctangent function, is the four-quadrant arctangent function, the azimuth angle ranging from when then is increased by ; are the east, north and zenith components of the local coordinate system, respectively determined based on the reference station's approximate coordinates and the approximate coordinates of each satellite.

10. A tropospheric slant delay estimation apparatus for GNSS monitoring, characterized in that, The device comprises: The grid determination unit is used 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 value of the multi-GNSS monitoring station in the preset area at the current time, and the preset visible airspace hemisphere; The equation acquisition unit is used to add the visible airspace hemisphere grid to which each visible satellite observation value belongs as the troposphere tilt delay to be estimated parameter into the GNSS array observation equation to obtain the current GNSS array observation equation; The solving unit is used to solve the to-be-estimated parameter of the current GNSS array observation equation based on the Kalman filter estimator to obtain the current troposphere tilt delay value of each visible airspace hemisphere grid; wherein the state transition matrix of the Kalman filter estimator is determined based on the comparison result of the last time historical visible satellite observation value of each visible airspace hemisphere grid and the visible airspace hemisphere grid. An estimation unit is configured to input the current tropospheric slant delay value of each of the visible airspace hemispherical grids as an input of the next time, and determine the tropospheric slant delay estimation value of each of the visible airspace hemispherical grids at the next time based on the Kalman filter estimator.

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