CN115755115A - PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology - Google Patents
PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology Download PDFInfo
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Abstract
The invention discloses a GNSS troposphere chromatography technology-based PPP (Point-to-Point protocol) improvement method, which relates to the technical field of GNSS precise single-point positioning and aims at solving the problems that troposphere delay contained in an observation equation in the existing PPP technology is difficult to be precisely estimated as an unknown parameter, the number of the unknown parameters in the observation equation is large, and the positioning precision and the convergence speed of the PPP technology are not accurate enough, and the following scheme is proposed and comprises the following steps: s1: estimating the troposphere delay STD of the inclined path based on PPP technology; s2: performing refractive index inversion in the grid of the chromatographic zone; s3: performing STD inversion on the troposphere by utilizing an inclined path of a GNSS troposphere chromatography technology; s4: the GNSS troposphere chromatography technology improves the PPP positioning method. The invention introduces the GNSS troposphere chromatography technology, inverts the STD value on the satellite signal path, and corrects the inverted STD value into the observation equation of the PPP technology, so as to reduce unknown parameters in the observation equation and further improve the positioning accuracy and the convergence speed of the PPP technology.
Description
Technical Field
The invention relates to the technical field of GNSS precision single-point positioning, in particular to a PPP improvement method based on a GNSS troposphere chromatography technology.
Background
The most core and basic functions and services of the global positioning and navigation system are time service and positioning, wherein positioning can be divided into relative positioning and absolute positioning. The relative Positioning technology is typically a real-time carrier phase difference Positioning technology, and the absolute Positioning technology is typically a Precision Point Positioning (PPP) technology. The PPP technology is to utilize the real-time or after precise orbit and clock error products of the satellite to accurately correct each error in the observation equation, and adopt a proper parameter estimation strategy at the same time, under the condition of only needing one GNSS receiver, the precise absolute positioning in the global scope can be realized. However, GNSS signals are also subject to various types of error interference, and when the signals pass through neutral atmospheric layers below 50km, refraction is caused by the neutral atmospheric interference, and the refraction effect is called tropospheric delay. Depending on the satellite altitude, tropospheric delay can have an error effect on the positioning result of several meters or even tens of meters. Thus, tropospheric delay is one of the most dominant error sources in PPP positioning.
In conventional PPP positioning, the diagonal path Tropospheric Delay (STD) can be expressed as the product of Zenith Tropospheric Delay (ZTD) and Mapping Function (MF), plus the product of the atmospheric horizontal gradient correction term and its Mapping function. ZTD can be divided into Zenith Hydro Delay (ZHD) and Zenith Wet Delay (ZWD). In processing, because ZHD is stable and easy to model, it is often corrected using empirical models, such as Saastamoinen model, hopfiled model, etc.; the ZWD uncertainty is strong, and an accurate model is difficult to establish for correction, so the size of the ZWD uncertainty is determined by using a parameter estimation method; the gradient correction term is the horizontal gradient mapping function multiplied by the components of the horizontal gradient correction north and east directions. However, the empirical model and the unknown parameter estimation often have certain deviation, and in order to reduce the estimation error, the invention provides a method for improving the PPP positioning accuracy and the convergence speed by utilizing the GNSS chromatography technology.
The ground-based GNSS troposphere chromatography technology is a method for reconstructing a three-dimensional troposphere delay structure of a region by utilizing information on a large number of satellite signal rays. Firstly, dispersing a research area into a plurality of grids, and assuming that the refractive index of a satellite signal in each grid is a constant within a certain time and is uniformly distributed; the observation value on each signal path contains troposphere delay information on the path, therefore, the refractive index of each ray in different grids is multiplied by the intercept of the satellite signal in the grid, and the total delay of the inclined paths on the path is further obtained through integration, all inclined path observation equations formed by a plurality of observation stations for a plurality of satellites form a GNSS troposphere chromatographic observation equation, and then a GNSS troposphere chromatographic model is obtained through combining the established chromatographic constraint equation, and then the GNSS troposphere chromatographic model is solved through an iterative algorithm or a non-iterative algorithm, so that the refractive index information of each grid is obtained.
However, tropospheric delay contained in an observation equation in the current PPP technology is difficult to estimate accurately as an unknown parameter, there are many unknown parameters in the observation equation, and the positioning accuracy and convergence speed of the PPP technology are not accurate enough.
Disclosure of Invention
The invention aims to solve the defects that troposphere delay contained in an observation equation in the existing PPP technology is difficult to accurately estimate as an unknown parameter, the number of unknown parameters in the observation equation is large, and the convergence speed of the PPP technology is low, and provides a method for improving the precision single-point positioning precision and accelerating the convergence speed of the GNSS troposphere chromatography technology.
In order to achieve the purpose, the invention adopts the following technical scheme:
the PPP improvement method based on the GNSS troposphere chromatography technology comprises the following steps:
s1: estimating the troposphere delay STD of the inclined path based on the PPP technology:
when the STD is estimated by using the PPP technology, the errors of each item of the observation equation need to be comprehensively considered, the obtained STD is ensured to have more reliable initial precision, and the STD calculation specific process is as follows:
s1.1: PPP observation equation establishment:
the GNSS signals are interfered by various errors in the propagation from satellites to a receiver, the errors affect the positioning accuracy to different degrees, and because the accuracy of a GNSS pseudo-range observation value is in a meter level, a carrier phase observation equation with higher correction accuracy is selected, and under the condition of fully considering the various errors, the carrier phase observation equation in the GNSSPPP technology is specifically expressed as follows:
in the formula (I), the compound is shown in the specification,
representing the carrier phase observations, i being the satellite signal frequency, r and s representing the receiver and satellite system respectively,
representing the geometric distance of the star to the earth, t r,i In order for the receiver to be out of clock,
which represents the clock error of the satellite or satellites,
in order to be an ionospheric delay,
for tropospheric delay, B r,i And
then the phase hardware delay, lambda, at the receiver end and the satellite end, respectively i Is the wavelength of the frequency of the signal,
the degree of ambiguity of the whole-cycle is represented,
a residual term that is a carrier phase;
s1.2: zenith tropospheric delay ZTD estimation:
in the traditional PPP resolving, the coordinate of a reference station is used as a constant to be processed, under the condition that the accurate coordinate of the reference station is known, the prior ZHD is calculated through Saastamoinen and other experience models which can jointly measure the air pressure on the ground surface, the known coordinate and the calculated prior ZHD are brought into an observation equation to be used as calculation data, then the observation equation is linearized, an observation equation matrix is further constructed by combining multi-station and multi-satellite observation signals, and the overall least square or Kalman filtering method is utilized to carry out resolving, so that the estimated zenith convection layer total delay ZTD and the gradient term can be obtained;
s1.3: the total delay STD of the inclined path is calculated:
the diagonal path tropospheric delay can be expressed as the product of the zenith direction tropospheric delay and the mapping function plus the product of the atmospheric horizontal gradient correction term and its mapping function;
the zenith troposphere total delay ZTD mainly comprises a zenith dry delay ZHD and a zenith wet delay ZWD, the ZHD is accurately calculated through the terrestrial meteorological parameters, and then the ZHD is subtracted from the ZTD estimated by PPP to obtain the zenith wet delay ZWD which is expressed as follows:
ZWD＝ZTD-ZHD(2)
thus, the diagonal path tropospheric delay STD can be expressed as follows:
in the formula, MF h Representing diagonal path stem mapping function, MF, corresponding to ZHD w Representing inclined path wet mapping function, MF, corresponding to ZWD g Representing a horizontal gradient mapping function, G n And G e Respectively representing the north and east components of the horizontal gradient correction,
for azimuth angles, e, of stations to satellites t Represents the tropospheric delay residual;
s2: refractive index inversion in the grid of the chromatographic zone:
the method is characterized in that the inclined path troposphere delay STD estimated by the PPP technology is used for constructing a GNSS troposphere chromatographic model, and comprises the following specific steps:
s2.1: constructing a chromatographic model observation equation:
by dividing the tomographic region into a plurality of discrete grids in the three-dimensional direction and integrating the refractive index on the satellite signal ray passing through each grid, an integral equation of the STD with the refractive index can be constructed:
STD＝10 -6 ·∫ s Nds (4)
where N is the index of refraction of the atmosphere, including the dry and wet indices of refraction, and s represents the path length of the signal propagating from the satellite to the receiver.
Discretizing the above equation, the total tropospheric delay on the GNSS signal slope path, STD, represents the sum of the product of the intercept of the satellite signal through each mesh and the index of refraction of the atmosphere within that mesh:
STD＝∑ ijk (a ijk ·x ijk ) (5)
in the formula, x ijk Denotes the refractive index to be estimated, a, within the (i, j, k) grid ijk Represents the ray intercept within the (i, j, k) grid and STD represents the estimate of the total tropospheric delay on the GNSS satellite signal diagonal path estimated by the PPP technique.
The STD of all the signal rays emerging from the top in the investigation region is expressed by equation (5), which constitutes the following tomographic equation:
y＝A·x (6)
where y is the column vector formed by the STD on the signal rays passing out of the top of the investigation region, a is the coefficient matrix of the observation equation, and x is the column vector formed by the unknown refractive index parameters.
S2.2: constructing a chromatographic constraint equation:
due to uneven distribution of GNSS satellites above a chromatographic region and insufficient number of stations, many grids in the chromatographic region do not have rays to pass through, so that a coefficient matrix of an observation equation is ill-conditioned, and an ill-defined problem can occur when the chromatographic equation is solved. In addition, the prior information of the chromatographic model can be established according to the radio sounding data, the numerical prediction reanalysis data and the like in the chromatographic region;
s2.3: construction of a GNSS troposphere chromatography model:
according to the constructed GNSS chromatographic observation equation, the horizontal constraint equation, the vertical constraint equation and the prior constraint equation, establishing a GNSS troposphere chromatographic model:
in the formula, H, V and I respectively refer to coefficient matrixes of horizontal, vertical and prior constraint equations, and C represents prior constraint information or a refractive index value in a chromatography region obtained through statistics of sounding data and other methods.
S2.4: GNSS tropospheric tomographic model solution:
the method solves the GNSS troposphere chromatographic model (7) by a Singular Value Decomposition (SVD) method, and solves the chromatographic model coefficient matrix
The decomposition is as follows:
B＝UΛV T (8)
wherein B ∈ R m×n ，U∈R m×m ，V∈R n×n ，
∑＝diag(σ 1 ,σ 2 ,…,σ r )，σ 1 ≥σ 2 ≥…≥σ r ，σ i (i =1,2, \ 8230;, r) is the matrix A T The square root of the eigenvalues of A, r is the rank of matrix B (r ≦ min (m, n)), U is represented by matrix AA T Is an orthogonal matrix composed of the eigenvectors of, V is a matrix A T And the feature vectors of A form an orthogonal matrix.If the generalized inverse of matrix B is defined as:
B -1 ＝VΛ -1 U Τ (9)
then, the solution of the system of linear equations Bx = L, i.e. the refractive index within the tomographic region, can be expressed as:
x＝B -1 L＝VΛ -1 U Τ L(10)
s3: performing inclined path troposphere delay STD inversion by utilizing GNSS troposphere chromatography technology:
the total tropospheric delay STD on the GNSS signal inclined path may be represented as the sum of the product of the refractive index of the ray passing through the tomographic grid and the intercept of the signal in the grid, so that based on the refractive index in each grid of the tomographic area obtained by the GNSS tropospheric tomography technique, the STD of the satellite signal in the grid may be calculated according to the intercept of the satellite signal in each grid, and finally the STD on the satellite signal path is obtained by an accumulation method, which has the following specific formula:
in the formula, x ijk Denotes the refractive index, a, in the (i, j, k) grid obtained by the inversion of the tomography technique ijk Represents the intercept of the ray within the (i, j, k) grid,
representing the total delay recovery value of the troposphere of the inclined path inverted by utilizing a GNSS troposphere chromatography technology;
by the method, the total troposphere delay STD on the GNSS signal inclined path at different altitude angles and azimuth angles in the chromatographic zone can be calculated;
s4: the GNSS troposphere chromatography technology improves PPP positioning method:
adding STD on a satellite signal propagation path inverted by a GNSS troposphere tomography technology into a PPP observation equation, and improving the traditional PPP observation equation, the formula (1) can be expressed as follows:
in the formula (I), the compound is shown in the specification,
the total tropospheric delay of the oblique path from the satellite s to the receiver r obtained by inversion using GNSS tomography is shown.
Therefore, the PPP observation equation after considering the improvement of GNSS chromatography can be expressed as follows:
in the formula (I), the compound is shown in the specification,
a carrier phase observation representing the removal of the STD term,
the carrier phase residual error after being corrected is unchanged in other items;
and finally, the above formula is further linearized, a function model and an error model of the PPP technology are established by combining the multi-station multi-satellite carrier phase observation values, the PPP function model is solved by using an overall least square or Kalman filtering method, a high-precision PPP positioning result is obtained, and the PPP convergence speed is accelerated.
In the PPP improvement method based on the GNSS troposphere chromatography technology, the GNSS troposphere chromatography technology is utilized to accurately estimate the inclined path troposphere delay STD required in the PPP observation equation, and the PPP technology is firstly utilized to estimate the STD on a plurality of satellite signal paths corresponding to different observation stations; then, constructing a GNSS troposphere chromatographic observation equation by using STD (structured beam diffraction) acquired by PPP (point-to-point protocol) technology, constructing a GNSS troposphere chromatographic model by combining a analytic constraint equation, and resolving the chromatographic model by an iterative or non-iterative method to obtain the refractive index in each grid of the chromatographic region; thirdly, calculating the STD on each satellite signal path according to the sum of the products of the refractive indexes of rays passing through grids in the chromatographic region and the corresponding intercept, wherein the tropospheric delay on the GNSS satellite signal inclined path can be expressed; finally, the estimated STD is reversely introduced into an observation equation of PPP, unknown parameters in the observation equation are reduced, and the purposes of improving the precision and the convergence speed are achieved;
the method is reasonable in design, introduces the GNSS troposphere chromatography technology aiming at the current situation that troposphere delay contained in an observation equation in the PPP technology is difficult to accurately estimate as an unknown parameter, inverts the STD value on a satellite signal path, corrects the inverted STD into the observation equation in the PPP technology so as to reduce the unknown parameter in the observation equation, makes up the defect of parameter estimation of the PPP technology by introducing the STD calculated by the GNSS troposphere chromatography technology, and further improves the positioning accuracy and convergence speed of the PPP technology.
Drawings
Fig. 1 is a flowchart illustrating steps of a PPP improvement method based on GNSS tropospheric tomography according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention.
Referring to fig. 1, this scheme provides an embodiment: the PPP improvement method based on the GNSS troposphere chromatography technology comprises the following steps:
s1: estimating the troposphere delay STD of the inclined path based on the PPP technology:
when the STD is estimated by using the PPP technology, the errors of each item of the observation equation need to be comprehensively considered, the obtained STD is ensured to have more reliable initial precision, and the STD calculation specific process is as follows:
s1.1: PPP observation equation establishment:
the GNSS signals are interfered by various errors in the propagation from satellites to a receiver, the errors affect the positioning accuracy to different degrees, and because the accuracy of a GNSS pseudo-range observation value is in a meter level, a carrier phase observation equation with higher correction accuracy is selected, and under the condition of fully considering the various errors, the carrier phase observation equation in the GNSSPPP technology is specifically expressed as follows:
in the formula (I), the compound is shown in the specification,
representing the carrier phase observations, i being the satellite signal frequency, r and s representing the receiver and satellite system respectively,
representing the geometric distance of the star to the earth, t r,i In order for the receiver to be out of clock,
which represents the clock error of the satellite or satellites,
in order to be an ionospheric delay,
for tropospheric delay, B r,i And
then the phase hardware delay, lambda, at the receiver end and the satellite end, respectively i Is the wavelength of the frequency of the signal,
the degree of ambiguity of the whole-cycle is represented,
a residual term that is a carrier phase;
s1.2: zenith tropospheric delay ZTD estimation:
in the traditional PPP resolving, the coordinate of a reference station is used as a constant to be processed, under the condition that the accurate coordinate of the reference station is known, the prior ZHD is calculated through Saastamoinen and other experience models which can jointly measure the air pressure on the ground surface, the known coordinate and the calculated prior ZHD are brought into an observation equation to be used as calculation data, then the observation equation is linearized, an observation equation matrix is further constructed by combining multi-station and multi-satellite observation signals, and the overall least square or Kalman filtering method is utilized to carry out resolving, so that the estimated zenith convection layer total delay ZTD and the gradient term can be obtained;
s1.3: the total delay STD of the inclined path is calculated:
the diagonal path tropospheric delay can be expressed as the product of the zenith direction tropospheric delay and the mapping function plus the product of the atmospheric horizontal gradient correction term and its mapping function;
the zenith troposphere total delay ZTD mainly comprises a zenith dry delay ZHD and a zenith wet delay ZWD, the ZHD is accurately calculated through surface meteorological parameters, and the zenith wet delay ZWD can be obtained by subtracting the ZHD from the ZTD estimated by PPP and is represented as follows:
ZWD＝ZTD-ZHD(2)
thus, the diagonal path tropospheric delay STD can be expressed as follows:
in the formula, MF h Representing diagonal path stem mapping function, MF, corresponding to ZHD w Representing inclined path wet mapping function, MF, corresponding to ZWD g Representing a horizontal gradient mapping function, G n And G e Respectively representing the north and east components of the horizontal gradient correction,
for azimuth angles, e, of stations to satellites t Representing tropospheric delay residuals;
s2: refractive index inversion in the grid of the chromatographic zone:
the method is characterized in that the inclined path troposphere delay STD estimated by the PPP technology is used for constructing a GNSS troposphere chromatographic model, and comprises the following specific steps:
s2.1: constructing a chromatographic model observation equation:
by dividing the tomographic area into a plurality of discrete grids in the three-dimensional direction and integrating the refractive index on the satellite signal ray passing through each grid, an integral equation of STD and refractive index can be constructed:
STD＝10 -6 ·∫ s Nds (4)
where N is the index of refraction of the atmosphere, including the dry and wet indices of refraction, and s represents the path length of the signal propagating from the satellite to the receiver.
Discretizing the above equation, the total tropospheric delay on the GNSS signal slope path, STD, then represents the sum of the intercept of the satellite signal through each mesh multiplied by the index of refraction of the atmosphere within that mesh:
STD＝∑ ijk (a ijk ·x ijk ) (5)
in the formula, x ijk Denotes the refractive index to be estimated, a, within the (i, j, k) grid ijk Represents the ray intercept within the (i, j, k) grid and STD represents the estimate of the total tropospheric delay on the GNSS satellite signal diagonal path estimated by the PPP technique.
The STD of all the signal rays emerging from the top in the investigation region is expressed by equation (5), which constitutes the following tomographic equation:
y＝A·x (6)
where y is the column vector formed by the STD on the signal rays passing out of the top of the investigation region, a is the coefficient matrix of the observation equation, and x is the column vector formed by the unknown refractive index parameters.
S2.2: constructing a chromatographic constraint equation:
due to uneven distribution of GNSS satellites above a chromatographic region and insufficient number of stations, many grids in the chromatographic region do not have rays to pass through, so that a coefficient matrix of an observation equation is ill-conditioned, and an ill-defined problem can occur when the chromatographic equation is solved. In addition, the prior information of the chromatographic model can be established according to radio sounding data, numerical prediction reanalysis data and the like in the chromatographic region;
s2.3: construction of a GNSS troposphere chromatography model:
according to the constructed GNSS chromatographic observation equation, the horizontal constraint equation, the vertical constraint equation and the prior constraint equation, establishing a GNSS troposphere chromatographic model:
in the formula, H, V and I respectively refer to coefficient matrixes of a horizontal constraint equation, a vertical constraint equation and a prior constraint equation, and C represents prior constraint information or a refractive index value in a chromatography region obtained through statistics of sounding data and other methods.
S2.4: resolving the GNSS troposphere chromatographic model:
the method solves the GNSS troposphere chromatographic model (7) by a Singular Value Decomposition (SVD) method, and solves the chromatographic model coefficient matrix
The decomposition is as follows:
B＝UΛV T (8)
in the formula, B is belonged to R m×n ，U∈R m×m ，V∈R n×n ，
∑＝diag(σ 1 ,σ 2 ,…,σ r )，σ 1 ≥σ 2 ≥…≥σ r ，σ i (i =1,2, \ 8230;, r) is the matrix A T The square root of the eigenvalues of A, r the rank of matrix B (r ≦ min (m, n)), U is represented by matrix AA T Is an orthogonal matrix composed of the eigenvectors of, V is a matrix A T And the feature vectors of A form an orthogonal matrix. If the generalized inverse of matrix B is defined as:
B -1 ＝VΛ -1 U Τ (9)
then, the solution of the system of linear equations Bx = L, i.e. the refractive index within the tomographic region, can be expressed as:
x＝B -1 L＝VΛ -1 U Τ L(10)
s3: performing inclined path troposphere delay STD inversion by utilizing GNSS troposphere chromatography technology:
the total tropospheric delay STD on the GNSS signal inclined path may be represented as the sum of the product of the refractive index of the ray passing through the tomographic grid and the intercept of the signal in the grid, so that based on the refractive index in each grid of the tomographic area obtained by the GNSS tropospheric tomography technique, the STD of the satellite signal in the grid may be calculated according to the intercept of the satellite signal in each grid, and finally the STD on the satellite signal path is obtained by an accumulation method, which has the following specific formula:
in the formula, x ijk Denotes the refractive index, a, in the (i, j, k) grid obtained by the inversion of the tomography technique ijk Represents the intercept of the ray in the (i, j, k) grid,
the total delay recovery value of the inclined path troposphere is expressed by utilizing the GNSS troposphere chromatography inversion;
by the method, the total troposphere delay STD on the GNSS signal inclined path at different altitude angles and azimuth angles in the chromatographic region can be calculated;
s4: the GNSS troposphere chromatography technology improves PPP positioning method:
adding the STD on the satellite signal propagation path inverted by the troposphere tomography of GNSS into the PPP observation equation, and improving the conventional PPP observation equation, formula (1) can be expressed as follows:
in the formula (I), the compound is shown in the specification,
representation inversion using GNSS chromatographyThe diagonal path to the receiver r from the arriving satellite s is the tropospheric total delay.
Therefore, the PPP observation equation after considering the improvement of GNSS tomography can be expressed as follows:
in the formula (I), the compound is shown in the specification,
a carrier phase observation representing the removal of the STD term,
the carrier phase residual error after being corrected is unchanged in other items;
and finally, the above formula is further linearized, a function model and an error model of the PPP technology are established by combining the multi-station multi-satellite carrier phase observation values, the PPP function model is solved by using an overall least square or Kalman filtering method, a high-precision PPP positioning result is obtained, and the PPP convergence speed is accelerated.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (1)
1. The PPP improvement method based on the GNSS troposphere chromatography technology is characterized by comprising the following steps:
s1: estimating the troposphere delay STD of the inclined path based on the PPP technology:
when the STD is estimated by using the PPP technology, the errors of each item of the observation equation need to be comprehensively considered, the obtained STD is ensured to have more reliable initial precision, and the STD calculation specific process is as follows:
s1.1: PPP observation equation establishment:
the GNSS signals are interfered by various errors in the propagation from a satellite to a receiver, the errors affect the positioning accuracy to different degrees, and as the accuracy of the GNSS pseudo-range observation value is meter-level, a carrier phase observation equation with higher correction accuracy is selected, and under the condition of fully considering the various errors, the carrier phase observation equation in the GNSSPPP technology is specifically expressed as follows:
in the formula (I), the compound is shown in the specification,
representing carrier phase observations, i being the satellite signal frequency, r and s representing the receiver and satellite system respectively,
representing the geometric distance of the star to the earth, t r,i In order to be the clock difference of the receiver,
which represents the clock error of the satellite or satellites,
in order to provide an ionospheric delay,
delay of troposphere, B r,i And
the phase hardware delay, λ, is then the receiver side and the satellite side, respectively i Is the wavelength of the frequency of the signal,
the number of the integer ambiguities is expressed,
a residual term that is a carrier phase;
s1.2: zenith tropospheric delay ZTD estimation:
in the traditional PPP resolving, the coordinate of a reference station is used as a constant to be processed, under the condition that the accurate coordinate of the reference station is known, the prior ZHD is calculated through Saastamoinen and other experience models which can jointly measure the air pressure on the ground surface, the known coordinate and the calculated prior ZHD are brought into an observation equation to be used as calculation data, then the observation equation is linearized, an observation equation matrix is further constructed by combining multi-station and multi-satellite observation signals, and the overall least square or Kalman filtering method is utilized to carry out resolving, so that the estimated zenith convection layer total delay ZTD and the gradient term can be obtained;
s1.3: the total delay STD of the inclined path is calculated:
the diagonal path tropospheric delay can be expressed as the product of the zenith direction tropospheric delay and the mapping function plus the product of the atmospheric horizontal gradient correction term and its mapping function;
the zenith troposphere total delay ZTD mainly comprises a zenith dry delay ZHD and a zenith wet delay ZWD, the ZHD is accurately calculated through surface meteorological parameters, and the zenith wet delay ZWD can be obtained by subtracting the ZHD from the ZTD estimated by PPP and is represented as follows:
ZWD＝ZTD-ZHD(2)
thus, the diagonal path tropospheric delay STD can be expressed as follows:
in the formula, MF h Representing diagonal path stem mapping function, MF, corresponding to ZHD w Representing inclined path wet mapping function, MF, corresponding to ZWD g Representing a horizontal gradient mapping function, G n And G e Respectively representing the north component and the east component of the horizontal gradient correction,
for measuring station-to-satellite azimuth angle, e t Represents the tropospheric delay residual;
s2: refractive index inversion in the tomographic region grid:
the method is characterized in that the inclined path troposphere delay STD estimated by the PPP technology is used for constructing a GNSS troposphere chromatographic model, and comprises the following specific steps:
s2.1: constructing a chromatographic model observation equation:
by dividing the tomographic region into a plurality of discrete grids in the three-dimensional direction and integrating the refractive index on the satellite signal ray passing through each grid, an integral equation of the STD with the refractive index can be constructed:
STD＝10 -6 ·∫ s Nds(4)
where N is the index of refraction of the atmosphere, including the dry and wet indices of refraction, and s represents the path length of the signal propagating from the satellite to the receiver.
Discretizing the above equation, the total tropospheric delay on the GNSS signal slope path, STD, represents the sum of the product of the intercept of the satellite signal through each mesh and the index of refraction of the atmosphere within that mesh:
STD＝∑ ijk (a ijk ·x ijk ) (5)
in the formula, x ijk Denotes the index of refraction to be estimated, a, within the (i, j, k) grid ijk Represents the ray intercept within the (i, j, k) grid and STD represents the estimate of the total tropospheric delay on the GNSS satellite signal diagonal path estimated by the PPP technique.
If the STD of all the signal rays emerging from the top in the investigation region is expressed by equation (5), the following tomographic equation is formed:
y＝A·x(6)
where y is the column vector consisting of the STD on the signal rays passing out from the top of the investigation region, a is the coefficient matrix of the observation equation, and x is the column vector consisting of unknown refractive index parameters.
S2.2: constructing a chromatographic constraint equation:
due to uneven distribution of GNSS satellites above a chromatographic region and insufficient number of stations, a plurality of grids in the chromatographic region do not have rays to pass through, so that a coefficient matrix of an observation equation is ill-conditioned, and an ill-defined problem can occur when the chromatographic equation is solved. In addition, the prior information of the chromatographic model can be established according to radio sounding data, numerical prediction reanalysis data and the like in the chromatographic region;
s2.3: construction of a GNSS troposphere chromatography model:
according to the established GNSS chromatographic observation equation, the established horizontal constraint equation, the established vertical constraint equation and the established prior constraint equation, establishing a GNSS troposphere chromatographic model:
in the formula, H, V and I respectively refer to coefficient matrixes of horizontal, vertical and prior constraint equations, and C represents prior constraint information or a refractive index value in a chromatography region obtained through statistics of sounding data and other methods.
S2.4: GNSS tropospheric tomographic model solution:
the method solves the GNSS troposphere chromatographic model (7) by a Singular Value Decomposition (SVD) method, and solves the chromatographic model coefficient matrix
The decomposition is as follows:
B＝UΛV T (8)
in the formula, B is belonged to R m×n ，U∈R m×m ，V∈R n×n ，
∑＝diag(σ 1 ,σ 2 ,…,σ r )，σ 1 ≥σ 2 ≥…≥σ r ，σ i (i =1,2, \ 8230;, r) is the matrix A T The square root of the eigenvalues of A, r the rank of matrix B (r ≦ min (m, n)), U is represented by matrix AA T Is an orthogonal matrix composed of the eigenvectors of, V is a matrix A T And the feature vectors of A form an orthogonal matrix. If the generalized inverse of matrix B is defined as:
B -1 ＝VΛ -1 U Τ (9)
the solution of the system of linear equations Bx = L, i.e. the refractive index in the tomographic region, can be expressed as:
x＝B -1 L＝VΛ -1 U Τ L(10)
s3: performing inclined path troposphere delay STD inversion by utilizing GNSS troposphere chromatography technology:
the total tropospheric delay STD on the GNSS signal slant path may be expressed as the sum of the product of the refractive index of the ray through the tomographic grid and the signal intercept at the grid. Therefore, based on the refractive index in each grid of the tomographic region obtained by the GNSS troposphere tomography, the STD of the satellite signal in each grid can be calculated according to the intercept of the satellite signal in each grid, and finally the STD on the satellite signal path is obtained in an accumulation manner, with the following specific formula:
in the formula, x ijk Denotes the refractive index, a, in the (i, j, k) grid obtained by the inversion of the tomography technique ijk Represents the intercept of the ray in the (i, j, k) grid,
representing the total delay recovery value of the troposphere of the inclined path inverted by utilizing a GNSS troposphere chromatography technology;
by the method, the total troposphere delay STD on the GNSS signal inclined path at different altitude angles and azimuth angles in the chromatographic region can be calculated;
s4: the GNSS troposphere chromatography technology improves PPP positioning method:
adding STD on a satellite signal propagation path inverted by a GNSS troposphere tomography technology into a PPP observation equation, and improving the traditional PPP observation equation, the formula (1) can be expressed as follows:
in the formula (I), the compound is shown in the specification,
the total tropospheric delay of the oblique path from the satellite s to the receiver r obtained by inversion using GNSS tomography is shown.
Therefore, the PPP observation equation after considering the improvement of GNSS tomography can be expressed as follows:
in the formula (I), the compound is shown in the specification,
a carrier phase observation representing the removal of the STD term,
the carrier phase residual error after being corrected is unchanged in other items;
and finally, the above formula is further linearized, a function model and an error model of the PPP technology are established by combining the multi-station multi-satellite carrier phase observation values, the PPP function model is solved by using an overall least square or Kalman filtering method, a high-precision PPP positioning result is obtained, and the PPP convergence speed is accelerated.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116340710A (en) * | 2023-05-30 | 2023-06-27 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
| CN117970382A (en) * | 2024-03-29 | 2024-05-03 | 中国科学院国家空间科学中心 | GNSS simulation test method and system |
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| CN116340710A (en) * | 2023-05-30 | 2023-06-27 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
| CN116340710B (en) * | 2023-05-30 | 2023-09-12 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
| CN117970382A (en) * | 2024-03-29 | 2024-05-03 | 中国科学院国家空间科学中心 | GNSS simulation test method and system |
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