CN115963516A - Multi-path error joint modeling correction method for multi-system GNSS signals - Google Patents
Multi-path error joint modeling correction method for multi-system GNSS signals Download PDFInfo
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Abstract
The invention relates to a multi-system GNSS signal multi-path error joint modeling correction method. In the modeling, firstly, pseudo-range and residual errors of carrier phase observed values are extracted through multi-system GNSS precise single-point positioning; then, multi-path model construction of multi-system GNSS overlapping frequency bands is carried out on the same sky image, and correlation analysis is carried out on multi-system GNSS residuals in the same grid; and finally, storing the obtained model value into a multi-path correction table. When the multi-path error is corrected, a specific GNSS system in a multi-path space-sky plot does not need to be distinguished, corresponding multi-path model values in a data set are searched only according to the altitude angle and the azimuth angle of a target satellite in the space-sky plot, and the multi-path error is directly corrected in real time in the GNSS original observed value. According to the method, the correction effect similar to that of full-orbit periodic modeling is obtained by using a shorter modeling period by adopting multi-system GNSS data combined modeling, the calculation efficiency is greatly improved, and the nonlinear change characteristics of multiple paths in a grid point are considered.
Description
Technical Field
The invention belongs to the technical field of satellite positioning navigation, and particularly relates to a multi-system GNSS signal multi-path error joint modeling correction method.
Background
In 31/7/2020, a Beidou three-dimensional global navigation satellite system (BDS-3) in China is completely built, real-time, convenient and high-precision service is provided for global users, and the broadcast new-generation open service signals B1C and B2a can be compatible and interoperated with overlapped frequency band signals of a GPS and a Galileo system, so that the system is suitable for multi-system GNSS Precision Point Positioning (PPP). The multipath error caused by the actual complex environment is one of bottleneck errors for limiting the multi-system GNSS PPP to obtain the cm-mm positioning accuracy. The method cannot be eliminated through difference, is difficult to provide a universal analytic form for parameter solution, becomes a difficult point which cannot be effectively eliminated in the international high-precision satellite positioning, and is also a hotspot and frontier problem of related scientific research.
Because the orbit repetition periods of all GNSS systems are different, the multipath time domain repeatability correction method needs to calculate the repetition period of each satellite, find the model data corresponding to the repetition periods of the satellites and correct the observation epoch, and the implementation complexity is high. At present, a multipath spatial domain repeatability correction method has the advantages of simple algorithm, easiness in implementation and capability of correcting multipath errors in real time, and a multipath semi-celestial sphere map (T-MHM) based on trend surface analysis can be corrected only by knowing the positions (altitude angle and azimuth angle) of satellites on a sky map without extrapolation, so that the method is not only suitable for static observation, but also suitable for dynamic observation of multipath effects mainly from carriers, such as airplanes and ships. The space repeatability method is adopted to carry out multi-path modeling and correction on the GNSS satellite with different orbit repetition periods more conveniently. However, the above method based on spatial repetition is only suitable for a single GNSS system. The GPS is found to obtain the best correction result by utilizing the observation data modeling of 5-7 repetition periods. Accordingly, the orbital repetition period of Galileo is 10 sidereal days, about two months of observation data are required to obtain the best multi-path correction effect, and most real-time GNSS monitoring applications can only collect observation data within a very limited time span.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-path error joint modeling correction method of a multi-system GNSS signal, which is used for multi-path correction of a GPS, BDS-3 and Galileo compatible interoperation frequency signal in a typical scene. According to the method, multi-system GNSS data combined modeling is adopted, the spatial coverage rate of a multi-path sky map sampling point can be improved, the non-linear change characteristics of multi-paths in grid points can be more accurately expressed, the sky map modeling full coverage is completed by utilizing a shorter modeling period, and the computing efficiency is greatly improved. The invention has more obvious advantages in emergency application and wider application scenes.
The technical scheme provided by the invention is a multi-system GNSS signal multi-path error joint modeling correction method, which comprises the following steps:
step 3.1, determining the optimal modeling days of the GPS, BDS-3 and Galileo three systems;
step 3.2, dividing sky grids, and performing trend surface fitting on multipath residual error values inside the grid points;
3.3, judging whether multiple collinearity exists or not by using constrained least square fitting aiming at the single track grid points;
step 3.4, carrying out statistical test on the result of the trend surface analysis;
and 5, correcting the multi-system GNSS single-point precision positioning multipath error in real time.
And in the step 1, combining an observation file, a precise ephemeris, a precise clock error, an antenna phase center deviation correction number and a tide correction of the GNSS observation station, constructing a multi-system GNSS non-differential non-combination PPP observation equation, and solving a residual sequence of a pseudo range and a carrier phase observation value.
The observation equation of the original pseudo range P and the carrier phase L is as follows:
wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; the subscript r denotes the receiver; i is the observed value frequency band number;
is the geometric distance between the satellite and the survey station; />
Is the corresponding carrier wavelength; c represents the speed of light; ISB denotes intersystem bias; dt r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively; />
Integer ambiguity as carrier phase; />
The pseudo-range and the multipath error of the carrier phase are respectively; />
Respectively pseudo-range and random noise of carrier phase; when the receiver antenna rotates, a ground-based carrier phase wrap-around, Δ Φ, appears in the carrier phase observation equation GPWU Term and receiver clock term dt r Coupling, combining them into a "clock" parameter in the carrier phase observation equation
The intersystem bias ISB is expressed as:
in the formula, the superscript M denotes GNSS systems other than GPS, (dD) M -dD G ) A bias representing the delay of the GNSS hardware,
representing the time difference of different GNSS systems.
Pseudorange residual η and carrier phase residual
Comprises the following steps:
wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; the subscript r denotes the receiver; i is an observed value frequency band number; p is pseudo range; l is a carrier phase;
is the geometric distance between the satellite and the survey station; />
Is the corresponding carrier wavelength; c represents the speed of light; ISB denotes intersystem bias; dt r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively; />
Is the integer ambiguity of the carrier phase.
Furthermore, the continuous N is calculated in the step 2 0 Non-differential non-combined PPP static positioning solution of GPS, BDS-3 and Galileo three systems of observation stations every day for longitude, latitude and altitude, N 0 And taking the average value of the PPP position solution of the day as a position true value of the current survey station, substituting the position true value into a PPP position fixed solution mode of resolving software, resolving a pseudo range and a carrier phase residual error, extracting an azimuth angle and an altitude angle of the satellite by using a satellite precise ephemeris file, and respectively storing the pseudo range, the carrier phase residual error, the azimuth angle and the altitude angle into corresponding data sets.
In step 3.2, the sky map is divided into 1 degree × 1 degree, the multipath error is projected to the corresponding sky map according to the altitude and azimuth of the satellite, and in order to fit the spatial variation of the multipath residual inside the grid points, the residual is expressed as:
in the formula, mp 1 For PPP observed residual, az i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
for multipath estimation, γ 1 Are the residuals that do not fit within the grid.
Fitting the equation using a polynomial function:
in the formula, az i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
as multipath estimate, c 0 -c 9 The coefficients are respectively the fitting coefficients of the trend surface obtained by least square estimation, and the equations (7), (8) and (9) are respectively linear, quadratic and cubic fitting equations.
In step 3.3, whether the trajectory of the space diagram is linearly distributed is determined by multiple collinearity, and whether multiple collinearity exists is determined by using constrained least square fitting for a single trajectory lattice:
in the formula, N is an observation variable matrix; m = [ mp = 1 mp 2 ... mp n ] T ，mp i Is PPP observation residual error; c = [ C = 1 c 2 ... c p ] T ，c 1 c 2 … c p Representing the fitting coefficient; az i 、el i Respectively, the altitude angle and the azimuth angle of the satellite; k and l are fitting coefficients.
If az i ＝k·el i If the goodness of fit of + l is greater than lambda, the grid is judged to have multiple collinearity, otherwise, the grid does not exist.
If multiple collinearity exists, substituting the fitting equation (10) into the observation variable matrix to obtain a constraint variable matrix N':
obtaining a trend surface fitting coefficient by using a least square method:
and finally, calculating to obtain a multipath estimation value:
in the formula, N is an observation variable matrix,
fitting coefficients to a trend surface>
For multipath estimates, k and l are fitting coefficients,M＝[mp 1 mp 2 ... mp n ] T ，mp l is the PPP observed residual.
Furthermore, in step 3.4, in order to avoid over-fitting and under-fitting situations, statistical tests, including a validity test and a significance test, are performed on the results of the trend surface analysis.
The adequacy test equation is:
R 2 ＝SS R /SS T (16)
in the formula, SS R To return the sum of squares, SS T As sum of squares of total deviations, R 2 To determine the coefficients, z is the number of residuals in a certain grid point, mp 1 For the PPP observation residual to be,
is a multipath estimate>
Is the residual mean.
The significance test equation is:
SS D ＝SS T -SS R (17)
in the formula, SS D As the remaining sum of squares of the dispersion, SS R To return the sum of squares, SS T Is the sum of squares of the total deviations, z is the total number of residuals in the grid, p and q are the order of the trend surface, K is the order of the trend surface, and F are the order of the trend surface K→K+1 F distributions obeying degrees of freedom (p-1, z-p) and (q-p, z-p) are represented, respectively.
If the statistical test is passed, storing the fitting coefficient; otherwise, averaging the pseudo range and the carrier phase residual error inside the sky grid point, and forming a multi-path model value correction table by the fitting coefficient, the range and the carrier phase residual error mean value.
In step 4, correlation analysis is performed on multipath errors of different GNSS systems in the sky grid, and whether GNSS joint modeling correction can be performed is detected; for the carrier phase observation, the carrier phase range error ψ caused by multipath is calculated as follows:
where α is the reflection coefficient of the reflector, γ is the phase delay of the reflected signal resulting from the extra path, H is the antenna height, λ is the satellite signal wavelength, and ε is the angle of incidence of the reflected signal.
Analyzing the correlation of residual sequences among the frequency bands of different systems by using a Pearson correlation coefficient rho, wherein the calculation formula is as follows:
wherein x (t) and y (t) are residual sequences, and cov and var respectively represent covariance and variance vectors.
When the absolute value of rho is in N 1 -N 2 In between, no or very weak correlation is indicated; in N 2 -N 3 In between, indicating a weak correlation; at N 3 -N 4 In between, indicating moderate correlation; in N 4 -N 5 In between, indicating a strong correlation; in N 5 -N 6 In between, high correlation is indicated.
The established multi-system GNSS multi-path model needs to perform correlation analysis on different GNSS systems in the grid, namely correlation coefficients of residual sequences of different GNSS systems in the same grid need to be calculated, if the correlation coefficients are strong correlation or highly correlated, the grid point performs multi-system GNSS multi-path error combined modeling, and if the correlation coefficients are not strong correlation or highly correlated, the current grid is excluded and modeling correction is not performed.
And in the step 5, the GNSS observation data are collected in real time, the altitude angle and the azimuth angle of the satellite in the carrier coordinate system are calculated, the multipath correction table is inquired to obtain a fitting coefficient, the multipath trend surface model corresponding to the sky image grid is selected for multipath estimation, the multipath correction value is calculated, and the satellite observation data are corrected.
Compared with the prior art, the invention has the following advantages:
1) Only a multi-path sky map containing multi-system GNSS mutual compatibility interoperation frequency band data is needed to be established, and when multi-path correction is carried out, specific satellites do not need to be determined, and only multi-path correction values corresponding to positions of current satellites in the sky map are searched.
2) The multi-system GNSS data combined modeling can improve the space coverage rate of the multi-path space map sampling points, and obtains a correction effect similar to the full-orbit period modeling by using a shorter modeling period, so that the calculation efficiency is greatly improved.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 shows PPP positioning error sequences before and after multipath error correction in the embodiment of the invention, the left of the diagram is a trend surface analysis multipath semispherical method, and the right of the diagram is the method provided by the invention.
Fig. 3 is a carrier phase residual sequence chart before and after correcting multipath errors according to an embodiment of the present invention.
Detailed Description
The invention provides a multi-system GNSS signal multi-path error joint modeling correction method, and the technical scheme of the invention is further explained by combining the accompanying drawings and an embodiment.
As shown in fig. 1, the process of the embodiment of the present invention includes the following steps:
And combining an observation file, a precise ephemeris, a precise clock error, an antenna phase center deviation correction number and tide correction of the GNSS observation station to construct a multi-system GNSS non-differential non-combination PPP observation equation and solve a residual sequence of a pseudo range and a carrier phase observation value.
The observation equation of the original pseudo range P and the carrier phase L is as follows:
wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; the subscript r denotes the receiver; i is an observed value frequency band number;
is the geometric distance between the satellite and the survey station; />
Is the corresponding carrier wavelength; c represents the speed of light; ISB denotes intersystem bias; dt r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively; />
Integer ambiguity as carrier phase; />
The pseudo-range and the multipath error of the carrier phase are respectively; />
Respectively pseudo-range and random noise of carrier phase; as the receiver antenna rotates, a ground-based carrier phase wrap-around, Δ Φ, appears in the carrier phase observation equation GPWU Term and receiver clock term dt r Coupled to combine them into a "clock" parameter->
The intersystem bias ISB is expressed as:
in the formula, the superscript M denotes GNSS systems other than GPS, (dD) M -dD G ) A bias representing the delay of the GNSS hardware,
representing the time difference of different GNSS systems.
As can be seen from equation (3), ISB is related to not only the hardware delay difference of GNSS system, but also the time difference introduced by different clock error references of different systems.
Pseudorange residual η and carrier phase residual
Comprises the following steps:
wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; the subscript r denotes the receiver; i is an observed value frequency band number; p is pseudo range; l is the carrier phase;
is the geometric distance between the satellite and the survey station; />
Is the corresponding carrier wavelength; c represents the speed of light; ISB denotes intersystem bias; dt r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively; />
Is the integer ambiguity of the carrier phase.
And step 2, determining the true value of the position of the observation station.
Calculating non-differential non-combination PPP static positioning solutions (longitude, latitude and altitude) of three systems (GPS, BDS-3 and Galileo) of an observation station every day for 10 days, taking an average value of the PPP position solutions for 10 days as a position true value of a current observation station, substituting the position true value into a PPP position fixed solution mode of resolving software, resolving a pseudo range and a carrier phase residual error, extracting an azimuth angle and an altitude angle of a satellite by using a satellite precise ephemeris file, and respectively storing the pseudo range, the carrier phase residual error, the azimuth angle and the altitude angle into corresponding data sets.
And 3, performing multi-system GNSS multi-path error combined modeling.
And 3.1, determining the optimal modeling days of the GPS, BDS-3 and Galileo three systems.
The orbit repetition period of the GPS satellite is about 1 sidereal day, the highest orbit repetition period of the BDS-3 satellite is about 7 sidereal days, and the orbit repetition period of the Galileo satellite is about 10 sidereal days. Due to the fact that orbit running tracks of the GPS, the BDS-3 and the Galileo are different, the orbit coverage rate of the multi-path sky plot can be improved through combined modeling. Through a large number of experimental analyses, the optimal modeling time of three multi-system combination GPS/BDS-3, GPS/Galileo and GPS/BDS-3/Galileo is respectively 3 days, 3 days and 4 days.
And 3.2, dividing sky grids, and performing trend surface fitting on multipath residual error values inside the grid points.
And dividing the sky map by 1 degree multiplied by 1 degree, and projecting the multipath error to the corresponding sky map according to the altitude angle and the azimuth angle of the satellite.
To fit the spatial variation of the multipath residuals within a grid point, the residuals are expressed as:
in the formula, mp i For PPP observation residual, za i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
is a multi-path estimate, y i Are the residuals that do not fit within the grid.
Fitting the equation using a polynomial function:
in the formula, az i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
is a multipath estimate, c 0 -c 9 The fitting coefficients of the trend surfaces obtained by least square estimation are respectively, and the equations (7), (8) and (9) are respectively linear, quadratic and cubic fitting equations.
And 3.3, judging whether multiple collinearity exists by using constraint least square fitting aiming at the single track lattice points.
Considering that the GPS satellite orbit repetition period is 1 day, even if modeling is performed using data of a plurality of days, there are cases where many grid points cover only 1 satellite at a certain time. Even if multi-day and multi-system GNSS data joint modeling is used, the situation that the distribution of satellites in a plurality of grid points is sparse still exists, particularly for a GPS L5 wave band with poor orbit coverage rate. Because the track of a single satellite in a grid point is similar to a straight line, and the parameters are highly correlated in value, the method needs to perform multiple collinearity judgment to judge whether the track of the space diagram is in linear distribution.
Whether multiple collinearity exists is judged by using constrained least squares fitting for single-track grid points:
in the formula, N is an observation variable matrix; m = [ mp = 1 mp 2 ... mp n ] T ，mp l Is PPP observation residual error; c = [ C ] 1 c 2 ... c p ] T ，c 1 c 2 ... c p Representing the fitting coefficient; az i 、el i Respectively, the altitude angle and the azimuth angle of the satellite; k and l are fitting coefficients.
If az i ＝k·el i And if the goodness of fit of + l is greater than 0.9, judging that the grid has multiple collinearity, otherwise, judging that the grid does not exist.
If multiple collinearity exists, substituting the fitting equation (10) into the observation variable matrix to obtain a constraint variable matrix N':
obtaining a trend surface fitting coefficient by using a least square method:
and finally, calculating to obtain a multipath estimation value:
in the formula, N is an observation variable matrix,
fitting coefficients to a trend surface>
For multipath estimates, k and l are fitting coefficients, M = [ mp = 1 mp 2 ... mp n ] T ，mp i The residual is observed for PPP. />
And 3.4, carrying out statistical test on the result of the trend surface analysis.
To avoid overfitting and under-fitting situations, statistical tests, including a moderation test and a significance test, were performed on the results of the trend surface analysis.
The adequacy test equation is:
R 2 ＝SS R /SS T (16)
in the formula, SS R To return the sum of squares, SS T As sum of squares of total deviations, R 2 To determine the coefficients, z is the number of residuals in a certain grid point, mp i For the PPP observation residual to be,
for multipath estimates, <' > based on>
Is the residual mean.
The significance test equation is:
SS D ＝SS T -SS R (17)
in the formula, SS D As the remaining sum of squares of the dispersion, SS R To return the sum of squares, SS T Is the sum of squares of the total deviations, z is the total number of residuals in the grid, p and q are the order of the trend surface, K is the order of the trend surface, and F are the order of the trend surface K→K+1 F distributions obeying degrees of freedom (p-1, z-p) and (q-p, z-p) are represented, respectively.
If the statistical test is passed, storing the fitting coefficient; otherwise, averaging the pseudo range and the carrier phase residual error inside the sky grid point, and forming a multi-path model value correction table by the fitting coefficient, the range and the carrier phase residual error mean value.
And 4, performing correlation analysis on multi-system GNSS multi-path residual error values in the same sky grid.
And performing correlation analysis on multipath errors of different GNSS systems in the grid, and detecting whether GNSS combined modeling correction can be performed or not.
For the carrier phase observation, the carrier phase range error ψ due to multipath is calculated as follows:
where α is the reflection coefficient of the reflector, γ is the phase delay of the reflected signal resulting from the extra path, H is the antenna height, λ is the satellite signal wavelength, and ε is the angle of incidence of the reflected signal. Theoretically, the multipath values of satellites with the same frequency at the same position are the same, namely L1-B1C-E1/L5-B2a-E5a.
Analyzing the correlation of residual sequences among frequency bands of different systems by using a Pearson correlation coefficient rho, wherein the calculation formula is as follows:
wherein x (t) and y (t) are residual sequences, cov and var respectively represent covariance and variance vectors.
When the absolute value of rho is between 0.8 and 1.0, high correlation is represented; between 0.6 and 0.8, indicating a strong correlation; between 0.4 and 0.6, indicating moderate correlation; between 0.2 and 0.4, indicating a weak correlation; between 0.0 and 0.2, no or very weak correlation is indicated.
The established multi-system GNSS multi-path model needs to perform correlation analysis on different GNSS systems in the grid, namely correlation coefficients of residual sequences of different GNSS systems in the same grid need to be calculated, if the correlation coefficients are strong correlation or highly correlated, the grid point can perform multi-system GNSS multi-path error combined modeling, and if the correlation coefficients are not strong correlation or highly correlated, the current grid is excluded and modeling correction is not performed.
And 5, correcting the multi-system GNSS single-point precise positioning multi-path error in real time.
The method comprises the steps of collecting GNSS observation data in real time, calculating the altitude angle and the azimuth angle of a satellite in a carrier coordinate system, inquiring a multi-path correction table to obtain a fitting coefficient, selecting a multi-path trend surface model corresponding to a space-sky-map grid to carry out multi-path estimation, calculating a multi-path correction value, and correcting the satellite observation data. It is noted that the established multipath correction model is independent of the satellite system and the satellite PRN, and depends only on the position of the satellite in the sky map.
Fig. 2 shows a PPP positioning error sequence obtained by correcting a multipath error by using two methods, and as can be seen from fig. 2, the PPP positioning solution is more stable after the multipath error is corrected by using the method of the present invention, so that the enhancement effect of the PPP positioning performance by the method of the present invention is better than that of T-MHM. Fig. 3 shows residual sequences of a single satellite, such as GPS (G25), BDS-3 (C27 MEO, C39 IGSO) and Galileo (E13), extracted before and after multipath error correction by the method of the present invention, as shown in fig. 3, the residual sequences of the GNSS systems tend to be white noise sequences after multipath correction by the method of the present invention.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (10)
1. A multi-system GNSS signal multi-path error joint modeling correction method is characterized by comprising the following steps:
step 1, constructing a multisystem GNSS non-differential non-combination PPP observation equation, and solving a single-day PPP position estimation solution;
step 2, determining a true value of the position of the observation station;
step 3, multi-system GNSS multi-path error joint modeling;
step 3.1, determining the optimal modeling days of the GPS, BDS-3 and Galileo three systems;
step 3.2, dividing sky grids, and performing trend surface fitting on multipath residual error values inside the grid points;
3.3, judging whether multiple collinearity exists or not by using constrained least square fitting aiming at the single track grid points;
step 3.4, carrying out statistical test on the result of the trend surface analysis;
step 4, performing correlation analysis on multi-system GNSS multi-path residual error values in the same grid;
and 5, correcting the multi-system GNSS single-point precise positioning multi-path error in real time.
2. The method as claimed in claim 1, wherein the method for correcting the multi-system GNSS signals by joint modeling of multipath errors comprises: combining an observation file, a precise ephemeris, a precise clock error, an antenna phase center deviation correction number and a tide correction of a GNSS observation station, constructing a multi-system GNSS non-differential non-combination PPP observation equation, and solving a residual sequence of a pseudo range and a carrier phase observation value;
the observation equation of the original pseudo range P and the carrier phase L is as follows:
wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; subscript r denotes the receiver; i is an observed value frequency band number;
is the geometric distance between the satellite and the survey station; />
For a corresponding carrierA wavelength of the wave; c represents the speed of light; ISB denotes intersystem bias; dt is r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively; />
Integer ambiguity as carrier phase; />
The pseudo-range and the multipath error of the carrier phase are respectively; />
Respectively pseudo range and random noise of carrier phase; as the receiver antenna rotates, a ground-based carrier phase wrap-around, Δ Φ, appears in the carrier phase observation equation GPWU Term and receiver clock term dt r Coupling, combining them into a "clock" parameter in the carrier phase observation equation
3. The method as claimed in claim 2, wherein the method for correcting multi-path error joint modeling of multi-system GNSS signals comprises: the inter-system bias ISB in step 1 is expressed as:
in the formula, the superscript M represents GNSS systems other than GPS (dD) M -dD G ) A bias representing the delay of the GNSS hardware,
representing time differences of different GNSS systems;
pseudorange residual η and carrier phase residual
Comprises the following steps: />
Wherein G represents GPS; c represents BDS-3; e represents Galileo; superscript s denotes satellite; subscript r denotes the receiver; i is an observed value frequency band number; p is pseudo range; l is the carrier phase;
is the geometric distance between the satellite and the survey station; />
Is the corresponding carrier wavelength; c represents the speed of light; ISB denotes intersystem bias; dt is r 、dt s Receiver and satellite clock offsets, respectively; />
Is the ionospheric delay error; />
Is tropospheric delay error; UCD r，i 、/>
Uncorrected pseudorange hardware delays for the receiver and the satellite, respectively;
is the integer ambiguity of the carrier phase.
4. The method as claimed in claim 1, wherein the method for correcting multi-path error joint modeling of multi-system GNSS signals comprises: calculating continuous N in step 2 0 The non-differential non-combined PPP static positioning solution of the GPS, BDS-3 and Galileo three systems of the observation stations every day solves the longitude, the latitude and the altitude, and is N 0 And taking the average value of the PPP position solution of the day as a position true value of the current survey station, substituting the position true value into a PPP position fixed solution mode of resolving software, resolving a pseudo range and a carrier phase residual error, extracting an azimuth angle and an altitude angle of the satellite by using a satellite precise ephemeris file, and respectively storing the pseudo range, the carrier phase residual error, the azimuth angle and the altitude angle into corresponding data sets.
5. The method as claimed in claim 1, wherein the method for correcting multi-path error joint modeling of multi-system GNSS signals comprises: in step 3.2, the sky map is divided by 1 degree × 1 degree, multipath errors are projected to the corresponding sky map according to the altitude and azimuth angles of the satellites, and in order to fit spatial variation of multipath residuals inside grid points, residuals are represented as:
in the formula, mp i For PPP observed residual, az i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
is the multi-path estimate value, y i Residual errors which are not fitted in the grids are obtained;
fitting the equation using a polynomial function:
in the formula, az i 、el i Respectively the altitude angle and the azimuth angle of the satellite,
is a multipath estimate, c 0 -c 9 The fitting coefficients of the trend surfaces obtained by least square estimation are respectively, and the equations (7), (8) and (9) are respectively linear, quadratic and cubic fitting equations.
6. The method as claimed in claim 5, wherein the method for correcting the multi-system GNSS signal by the joint modeling of multi-path errors comprises: and 3.3, judging whether the track of the space diagram is in linear distribution or not through multiple collinearity, and judging whether the multiple collinearity exists or not by using constrained least square fitting aiming at single track lattice points:
in the formula, N is an observation variable matrix; m = [ mp = 1 mp 2 ...mp n ] T ，mp i Is PPP observation residual error; c = [ C = 1 c 2 ...c p ] T ，c 1 c 2 ...c p Representing the fitting coefficient; az i 、el i Respectively, the altitude angle and the azimuth angle of the satellite; k and l are fitting coefficients;
if az i ＝k·el i If the goodness of fit of + l is greater than lambda, the grid is judged to have multipleCollinearity, otherwise, it is absent.
7. The method as claimed in claim 6, wherein the correction method comprises: if multiple collinearity exists in the step 3.3, substituting the fitting equation (10) into the observation variable matrix to obtain a constraint variable matrix N':
obtaining a trend surface fitting coefficient by using a least square method:
and finally, calculating to obtain a multipath estimation value:
wherein N is an observation variable matrix,
fitting coefficients to a trend surface>
For multipath estimates, k and l are fitting coefficients, M = [ mp = 1 mp 2 ...mp n ] T ，mp i The residual is observed for PPP.
8. The method as claimed in claim 7, wherein the method for correcting multi-path error joint modeling of multi-system GNSS signals comprises: in step 3.4, in order to avoid the situations of overfitting and under-fitting, statistical tests are carried out on the results of trend surface analysis, wherein the results comprise a moderation test and a significance test;
the adequacy test equation is:
in the formula, SS R To return the sum of squares, SS T As sum of squared deviations, R 2 To determine the coefficients, z is the number of residuals in a certain grid point, mp i For the PPP observation residual to be,
is a multipath estimate>
Is a residual mean value;
the significance test equation is:
SS D ＝SS T -SS R (17)
in the formula, SS D As the remaining sum of squares of the deviations, SS R To return the sum of squares, SS T Is the sum of squares of the total deviations, z is the total number of residuals in the grid, p and q are the order of the trend surface, K is the order of the trend surface, and F are the order of the trend surface K→K+1 Respectively representing F distributions obeying degrees of freedom (p-1, z-p) and (q-p, z-p);
if the statistical test is passed, storing the fitting coefficient; otherwise, averaging the pseudo range and the carrier phase residual error inside the sky grid point, and forming a multi-path model value correction table by the fitting coefficient, the range and the carrier phase residual error mean value.
9. The method as claimed in claim 1, wherein the method for correcting multi-path error joint modeling of multi-system GNSS signals comprises: performing correlation analysis on multipath errors of different GNSS systems in the sky grid in step 4, and detecting whether GNSS combined modeling correction can be performed or not; for the carrier phase observation, the carrier phase range error ψ caused by multipath is calculated as follows:
where α is the reflection coefficient of the reflector, γ is the phase delay of the reflected signal resulting from the extra path, H is the antenna height, λ is the satellite signal wavelength, and ε is the angle of incidence of the reflected signal;
analyzing the correlation of residual sequences among frequency bands of different systems by using a Pearson correlation coefficient rho, wherein the calculation formula is as follows:
wherein x (t) and y (t) are residual sequences, cov and var respectively represent covariance and variance vectors;
when the absolute value of rho is in N 1 -N 2 In between, no correlation or very weak correlation is indicated; in N 2 -N 3 In between, indicating a weak correlation; in N 3 -N 4 In between, indicating moderate correlation; in N 4 -N 5 In between, indicating a strong correlation; in N 5 -N 6 Represents highly correlated;
the established multi-system GNSS multi-path model needs to perform correlation analysis on different GNSS systems in the grid, namely correlation coefficients of residual sequences of different GNSS systems in the same grid need to be calculated, if the correlation coefficients are strong correlation or highly correlated, the grid point performs multi-system GNSS multi-path error combined modeling, and if the correlation coefficients are not strong correlation or highly correlated, the current grid is excluded and modeling correction is not performed.
10. The method as claimed in claim 1, wherein the method for correcting the multi-system GNSS signals by joint modeling of multipath errors comprises: and 5, acquiring GNSS observation data in real time, calculating the altitude angle and azimuth angle of the satellite in the carrier coordinate system, inquiring a multi-path correction table to obtain a fitting coefficient, selecting a multi-path trend surface model corresponding to the sky plot grid to perform multi-path estimation, calculating a multi-path correction value, and correcting the satellite observation data.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104122566A (en) * | 2014-07-01 | 2014-10-29 | 华东师范大学 | Multi-path error removing method of navigation satellite system and multi-path hemisphere model |
| CN112433240A (en) * | 2020-10-13 | 2021-03-02 | 武汉理工大学 | Phase multipath extraction and correction method based on non-differential non-combination PPP model |
-
2022
- 2022-12-09 CN CN202211577690.8A patent/CN115963516B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104122566A (en) * | 2014-07-01 | 2014-10-29 | 华东师范大学 | Multi-path error removing method of navigation satellite system and multi-path hemisphere model |
| CN112433240A (en) * | 2020-10-13 | 2021-03-02 | 武汉理工大学 | Phase multipath extraction and correction method based on non-differential non-combination PPP model |
Non-Patent Citations (7)
| Title |
|---|
| HU, C 等: "Improved Mitigation Method for the Multipath Delays of BDS-3 Code Observations with the Aid of a Sparse Modeling Algorithm", 《 JOURNAL OF SENSORS》 * |
| SHAOZU CAO等: "GVINS: Tightly Coupled GNSS–Visual–Inertial Fusion for Smooth and Consistent State Estimation", 《IEEE TRANSACTIONS ON ROBOTICS 》 * |
| XINGXING LI等: "Multi-GNSS Meteorology: Real-Time Retrieving of Atmospheric Water Vapor From BeiDou, Galileo, GLONASS, and GPS Observations", 《IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING》 * |
| 刘腾;袁运斌;张宝成;: "BDS/GLONASS非组合精密单点定位模型与算法", 地球物理学报, no. 04 * |
| 姜卫平等: "大地测量坐标框架建立的进展与思考", 《测绘学报》 * |
| 常军;党海龙;李昕;: "北斗卫星多路径***偏差改正的研究", 测绘地理信息, no. 01 * |
| 李昕;袁勇强;张柯柯;曾琪;张小红;李星星;: "联合GEO/IGSO/MEO的北斗PPP模糊度固定方法与试验分析", 测绘学报, no. 03 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117991303A (en) * | 2024-04-03 | 2024-05-07 | 武汉大学 | Multipath error correction method and device under condition of antenna environment change |
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