CN109541663A - The correcting method of appearance Multipath Errors is surveyed in a kind of GNSS positioning - Google Patents
The correcting method of appearance Multipath Errors is surveyed in a kind of GNSS positioning Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
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- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/53—Determining attitude
- G01S19/54—Determining attitude using carrier phase measurements; using long or short baseline interferometry
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Abstract
The correcting method for surveying appearance Multipath Errors is positioned the invention discloses a kind of GNSS, this method comprises: short base line extraction and multipath calculate；Multipath hemisphere model foundation based on trend surface analysis；Multipath real time correction.Usage trend surface analysis method is fitted the multipath spatial distribution characteristic in sky grid, improves the multipath modeling method based on space repeatability to the modeling ability of high frequency multiplex diameter, improves positioning and survey appearance precision；The requirement to sky mesh scale is reduced, computational efficiency is improved.This method is suitable for the static and constant dynamic scene of multi-path environment simultaneously.
Description
Technical Field
The invention relates to the field of satellite positioning and navigation, in particular to a correction method for GNSS positioning and attitude determination multipath errors.
Background
The modeling method based on multipath space-time repeatability can realize real-time processing of multipath effects in GNSS positioning. The multipath modeling method based on spatial repeatability, such as a spherical harmonic model and a multipath semi-celestial sphere map (MHM) method, is not only suitable for a static positioning mode, but also suitable for positioning a dynamic carrier with unchanged multipath environment, such as a ship, an airplane and the like, and therefore has remarkable advantages. There are significant limitations to these several approaches. The accuracy of the spherical harmonic model depends on the fitting order, and the accuracy and the calculation efficiency of the model are difficult to be considered. Although the calculation efficiency of the MHM method is greatly improved compared with that of a spherical harmonic function model, the average residual error in the grid is used as a correction value, and the difference of multipath values in the grid is ignored, so that the high-frequency multipath modeling is poor and the precision can be ensured by fine grid segmentation.
Disclosure of Invention
The invention aims to provide a correction method for multi-path errors of GNSS positioning and attitude measurement. The method utilizes a trend surface method to fit the multipath spatial distribution characteristics in the sky plot grid, improves the modeling capability of high-frequency multipath, and simultaneously reduces the requirement on the grid scale to a certain extent so as to improve the calculation efficiency.
The specific technical scheme for realizing the purpose of the invention is as follows:
a correction method for multi-path errors of GNSS positioning and attitude measurement comprises the following steps:
step 1: short baseline solution and multi-path computation
(1) Establishing a common clock single difference model
Based on the common clock multi-antenna receiver, the short base line is solved, the single difference between stations can eliminate the atmospheric delay, the satellite clock difference and the receiver clock difference, and a common clock single difference model is obtained:
in the formula, delta represents a single difference operator; λ is the carrier wavelength; phi is ai、ri、NiAnd phii mthRespectively a carrier phase observation value, a geometric distance between a satellite and an antenna, an ambiguity parameter and a multipath effect; phi is aUPDIs a UPD (uncalibrated phasedelay) parameter;
(2) resolving short baselines
Adopting Kalman filtering to resolve a single difference model; for k epochs, the matrix form of the observation equation is:
Zk＝HkXk+εk(2)
X＝[dBxdBydBzVBxVByVBz-ΔN1… -ΔNmΔφUPD]T(3)
wherein Z iskSubtracting the initial geometric distance, the initial ambiguity and the initial UPD value from the single-difference observation value; xkIs a state vector; [ dB ]xdBydBz]TRepresenting baseline vector increments；[VBxVByVBz]TRepresenting a baseline velocity vector increment; delta NiIncrement the ambiguity parameter of the ith satellite; hkTo design the matrix,/x,ly,lzDirection cosine of the satellite-receiver connection; (X)i,Yi,Zi) Is a satellite coordinate; (X)0,Y0,Z0) Approximate coordinates for the receiver; rho0Approximating the distance between the coordinates for a satellite to a receiverεkTo observe noise; superscript T represents the transpose of the matrix;
from k epoch to k +1 epoch, the prediction equation of the state vector and its covariance matrix are:
Xk+1,k＝AkXk(6)
the update formula of the state vector and its covariance matrix are:
Xk+1＝Xk+1,k+Kk+1(Zk+1-Ak+1Xk+1,k) (8)
Ck+1＝Ck+1,k-Kk+1Ak+1Ck+1,k(9)
wherein A iskBeing a state transition matrix, QkError covariance matrix, P, being the state transition equationk+1To observe the variance matrix of the noise, Kk+1Is a gain matrix, RkTo observe the variance matrix of the noise, Ck+1,kAnd Ck+1Respectively, a prediction variance matrix and an updated varianceArraying;
floating point solution N of ambiguity parameters obtainable using Kalman filteringiFurther, the floating ambiguity is fixed as follows: selecting a reference satellite i, and determining the floating ambiguity N of the satelliteiCombining the UPD parameter and the UPD parameter into a new UPD parameter; the new UPD parameter is actually the sum of the UPD and the floating ambiguity of the reference satellite, and the floating ambiguities of the other non-reference satellites become the difference between the original floating ambiguity and the floating ambiguity of the reference satellite; as shown in the following formula:
wherein,new UPD parameters are obtained for the combination; n is a radical ofiTo refer to the floating ambiguity for satellite i,i-1, i + i, …, where n is the new floating ambiguity of satellite k after the UPD parameter is combined with the reference satellite floating ambiguity; ambiguity fixing is performed by three steps: firstly, ignoring integer characteristics of ambiguity, and resolving a baseline vector and an ambiguity floating solution by adopting a parameter estimation method; then, ambiguity fixing is carried out by satellite according to integer characteristics by using ambiguity floating solution and covariance matrix thereof; re-resolving the integer ambiguity by replacing the original observation equation to obtain a baseline vector solution with fixed ambiguity;
(3) computing multipath based on obtained solutions
The posterior residual of the Kalman filtering solution is the multipath of the satellite:
step 2: multipath semi-celestial sphere model establishment based on trend surface analysis
(1) Assigning multipath data to sky grid
Calculating an altitude azimuth for the satellite for which the multipath data has been obtained; firstly, calculating an observation vector [ delta e delta n delta u ] from a user to a satellite under a station center coordinate system]T：
Wherein, [ Δ x Δ y Δ z [ ]]TThe observation vector from the user to the satellite under the earth-centered earth-fixed rectangular coordinate system; λ and φ are longitude and latitude, respectively; secondly, calculating an observation vector [ delta x 'delta y' delta z 'from the user to the satellite in a carrier coordinate system']T：
The psi, the theta and the gamma are respectively a carrier course angle, a pitch angle and a roll angle; the satellite elevation angle ele and azimuth azi are:
dividing the sky into different grids according to the altitude angle and the azimuth angle, and distributing satellite multi-path data corresponding to the altitude angle and the azimuth angle into the grids;
(2) constructing multi-path trend surface model of each sky grid
Firstly, establishing a primary trend surface model and a secondary trend surface model for multiple paths of a sky grid:
primary trend surface:
secondary trend surface:
in the formula, xi,yiRepresenting azimuth and elevation angles, a, corresponding to the ith multipath value in the sky grid0,a1,...anRepresents the fitting coefficient of the trend surface,fitting values of the trend surface model;
next, fitting of moderate R was performed2Testing and significance F testing; wherein the fitting degree coefficient R2Using regression sum of squares SSRSum of squared deviations SSTIs expressed by the specific gravity of (A); r2The value is between 0 and 1, and the higher the value is, the higher the fitting degree of the model is; the calculation formula is as follows:
wherein z isiIs thatIs the remaining sum of squares
If R is2If the value is larger than the preset threshold value, judging that the model passes the test;
if the two models pass the inspection and then are optimized by using an F inspection, the F inspection is used for inspecting whether the trend surface equation is obvious or not, and the calculation formula is as follows:
in the formula, p represents the degree of freedom of regression sum of squares, consisting ofF obeys F distribution with the degree of freedom of (p, n-p-1), and under the condition of a given confidence level, by looking up an F distribution table, a critical value F is obtained, so that the fitted trend surface equation is tested to be more obvious under the confidence level α;
if the residual mean values do not pass through the trend surface model, directly replacing the trend surface model with the residual mean values in the grids;
and step 3: multipath real-time correction
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, selecting a multi-path trend surface model corresponding to a space-sky-map grid for multi-path estimation, and correcting the satellite observation data.
The method combines a trend surface analysis method with a traditional MHM method, has the advantages that a multipath modeling method based on spatial repeatability is continuously applied to dynamic positioning navigation application with static and multipath environment unchanged, and the trend surface method is used for fitting multipath spatial distribution characteristics in a sky map grid, so that the modeling capability of high-frequency multipath is improved, and the requirement on grid scale is reduced, so that the calculation efficiency is improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a comparison graph of power spectrum analysis of the multi-path semi-celestial model values in accordance with the present invention;
FIG. 3 is a graph showing a baseline solution comparison of two models at different grid resolutions.
Detailed Description
The invention is described in detail below with reference to the accompanying drawings and examples.
Examples
The method is suitable for multi-path error correction of the dynamic carrier with unchanged static and multi-path environments in GNSS positioning and navigation application. Compared with the existing multipath modeling method based on spatial repeatability, the method provided by the invention has the advantages that the modeling capability of high-frequency multipath is improved, and meanwhile, the requirement on grid scale is reduced, so that the calculation efficiency is improved.
In order to verify the invention, a static short baseline multipath correction experiment is implemented, and the specific implementation steps comprise:
step 1: short baseline solution and multi-path computation
(1) Establishing a common clock single difference model
Based on the common clock multi-antenna receiver, the short base line is solved, the single difference between stations can eliminate the atmospheric delay, the satellite clock difference and the receiver clock difference, and a common clock single difference model is obtained:
in the formula, delta represents a single difference operator; λ is the carrier wavelength; phi is ai、ri、NiAnd phii mthRespectively a carrier phase observation value, a geometric distance between a satellite and an antenna, an ambiguity parameter and a multipath effect; phi is aUPDIs a UPD (uncalibrated phasedelay) parameter.
(2) Resolving short baselines
And solving the single difference model by adopting Kalman filtering. For k epochs, the matrix form of the observation equation is:
Zk＝HkXk+εk(2)
X＝[dBxdBydBzVBxVByVBz-ΔN1… -ΔNmΔφUPD]T(3)
wherein Z iskSubtracting the initial geometric distance, the initial ambiguity and the initial UPD value from the single-difference observation value; xkIs a state vector; [ dB ]xdBydBz]TRepresenting a baseline vector increment; [ VBxVByVBz]TRepresenting a baseline velocity vector increment; delta NiIncrement the ambiguity parameter of the ith satellite; hkTo design the matrix,/x,ly,lzDirection cosine of the satellite-receiver connection; (X)i,Yi,Zi) Is a satellite coordinate; (X)0,Y0,Z0) Approximate coordinates for the receiver; rho0Approximating the distance between the coordinates for a satellite to a receiverεkTo observe the noise. The superscript T represents the transpose of the matrix.
From k epoch to k +1 epoch, the prediction equation of the state vector and its covariance matrix are:
Xk+1,k＝AkXk(6)
the update formula of the state vector and its covariance matrix are:
Xk+1＝Xk+1,k+Kk+1(Zk+1-Ak+1Xk+1,k) (8)
Ck+1＝Ck+1,k-Kk+1Ak+1Ck+1,k(9)
wherein A iskBeing a state transition matrix, QkError covariance matrix, P, being the state transition equationk+1To observe the variance matrix of the noise, Kk+1Is a gain matrix, RkTo observe the variance matrix of the noise, Ck+1,kAnd Ck+1Respectively a prediction variance matrix and an updated variance matrix.
Floating point solution N of ambiguity parameters obtainable using Kalman filteringiFurther, the floating ambiguity is fixed as follows: selecting a reference satellite i, and determining the floating ambiguity N of the satelliteiCombining the UPD parameter and the UPD parameter into a new UPD parameter; the new UPD parameter is actually the sum of the UPD and the floating ambiguity of the reference satellite, and the floating ambiguities of the other non-reference satellites become the difference between the original floating ambiguity and the floating ambiguity of the reference satellite; as shown in the following formula:
wherein,new UPD obtained for mergingA parameter; n is a radical ofiTo refer to the floating ambiguity for satellite i,i-1, i + i, n is a new floating ambiguity of the satellite k after the UPD parameter and the reference satellite floating ambiguity are combined; ambiguity fixing is performed by three steps: firstly, ignoring integer characteristics of ambiguity, and resolving a baseline vector and an ambiguity floating solution by adopting a parameter estimation method; then, ambiguity fixing is carried out by satellite according to integer characteristics by using ambiguity floating solution and covariance matrix thereof; and re-resolving the integer ambiguity by replacing the original observation equation to obtain a baseline vector solution with fixed ambiguity.
(3) Computing multipath based on obtained solutions
The posterior residual of the Kalman filtering solution is the multipath of the satellite:
step 2: multipath semi-celestial sphere model establishment based on trend surface analysis
(1) Assigning multipath data to sky grid
An attitude and azimuth angle is calculated for the satellite for which the multipath data has been acquired. Firstly, calculating an observation vector [ delta e delta n delta u ] from a user to a satellite under a station center coordinate system]T：
Wherein, [ Δ x Δ y Δ z [ ]]TThe observation vector from the user to the satellite under the earth-centered earth-fixed rectangular coordinate system; λ and φ are longitude and latitude, respectively; secondly, calculating an observation vector [ delta x 'delta y' delta z 'from the user to the satellite in a carrier coordinate system']T：
The psi, the theta and the gamma are respectively a carrier course angle, a pitch angle and a roll angle; the satellite elevation angle ele and azimuth azi are:
the sky is divided into different grids according to the elevation angle and the azimuth angle, and the dividing unit can take the degree as a unit (such as 1 degree by 1 degree, azimuth angle multiplied by the elevation angle); an equal area division method may be considered, that is, a grid division is performed in units of a certain area (the area of each grid point is kept uniform by keeping the interval of the elevation angle constant and the size of the azimuth angle interval different, for example, when the area of a grid point is M ° × N °, M grid points are divided between 0 ° and N ° for the elevation angle, and M × COS (N/360 × 2pi) grid points are divided between N ° and 2N ° for the elevation angle). The satellite multipath data for the corresponding attitude is then distributed into the grid.
(2) Constructing multi-path trend surface model of each sky grid
Firstly, establishing a primary trend surface model and a secondary trend surface model for multiple paths of a sky grid:
primary trend surface:
secondary trend surface:
in the formula, xi,yiRepresenting azimuth and elevation corresponding to ith multipath value in sky gridAngle of degree, a0,a1,...anRepresents the fitting coefficient of the trend surface,fitting values of the trend surface model;
next, fitting of moderate R was performed2Testing and significance F testing; wherein the fitting degree coefficient R2Using regression sum of squares SSRSum of squared deviations SSTIs expressed by the specific gravity of (A); r2The value is between 0 and 1, and the higher the value is, the higher the fitting degree of the model is; the calculation formula is
Wherein z isiIs thatIs the remaining sum of squares
If R is2And if the value is larger than a certain threshold value, judging that the model passes the test.
If the two models pass the inspection and then are optimized by using an F inspection, the F inspection is used for inspecting whether the trend surface equation is obvious or not, and the calculation formula is as follows:
in the formula, p represents the degree of freedom of regression sum of squares, consisting ofCalculating to obtain (n-p-1), wherein the degree of freedom of the residual square sum, r is the analysis times of the trend surface, and n is the total number of residual values in the lattice points; f clothesFrom the F distribution with degree of freedom (p, n-p-1), a cut-off value F was obtained by looking up the F distribution table at a given confidence level, thereby verifying which of the fitted trend surface equations was more significant at confidence level α.
If the residual mean values do not pass through the trend surface model, directly replacing the trend surface model with the residual mean values in the grids;
and step 3: multipath real-time correction
The method comprises the steps of collecting GNSS observation data in real time, calculating the azimuth angle of the altitude angle of a satellite in a carrier coordinate system, selecting a multi-path trend surface model corresponding to a space-sky-map grid for multi-path estimation, and correcting the satellite observation data.
By comparing the method with the existing multipath modeling method (such as multipath semi-celestial sphere, MHM) based on spatial repeatability, the correction effect of the method on high-frequency multipath is better than that of the MHM. Fig. 2 shows the result of performing power spectrum analysis by extracting a model value of one satellite (taking G06 as an example) after using two methods of multipath models, and as shown in the figure, the power of the method of the present invention is higher than that of the MHM model in the whole frequency band, which indicates that the method of the present invention includes richer multipath variations compared with the MHM model, and not only can perform the low-frequency multipath correction better, but also improves the correction performance for the high-frequency multipath.
The sky is divided into grids of 1 degree by 1 degree, 2 degrees by 2 degrees, 5 degrees by 5 degrees and 9 degrees by 9 degrees respectively, the comparison result of the baseline solutions of the two methods is shown in figure 3, and the result shows that the baseline solution of the method is more stable along with the increase of the sky grid, which indicates that the method has lower requirements on the fineness degree of the sky grid, so the algorithm efficiency is higher.
Claims (1)
1. A correction method for multi-path errors of GNSS positioning and attitude measurement is characterized by comprising the following specific steps: step 1: short baseline solution and multi-path computation
(1) Establishing a common clock single difference model
Based on the common clock multi-antenna receiver, the short base line is solved, the single difference between stations can eliminate the atmospheric delay, the satellite clock difference and the receiver clock difference, and a common clock single difference model is obtained:
in the formula, delta represents a single difference operator; λ is the carrier wavelength; phi is ai、ri、NiAnd phii mthRespectively a carrier phase observation value, a geometric distance between a satellite and an antenna, an ambiguity parameter and a multipath effect; phi is aUPDIs a phase delay UPD parameter;
(2) resolving short baselines
Adopting Kalman filtering to resolve a single difference model; for k epochs, the matrix form of the observation equation is:
Zk＝HkXk+εk(2)
X＝[dBxdBydBzVBxVByVBz-ΔN1… -ΔNmΔφUPD]T(3)
wherein Z iskSubtracting the initial geometric distance, the initial ambiguity and the initial UPD value from the single-difference observation value; xkIs a state vector; [ dB ]xdBydBz]TRepresenting a baseline vector increment; [ VBxVByVBz]TRepresenting a baseline velocity vector increment; delta NiIncrement the ambiguity parameter of the ith satellite; hkTo design the matrix,/x,ly,lzDirection cosine of the satellite-receiver connection; (X)i,Yi,Zi) Is a satellite coordinate; (X)0,Y0,Z0) Approximate coordinates for the receiver; rho0Approximating the distance between the coordinates for a satellite to a receiverεkFor observing noise(ii) a Superscript T represents the transpose of the matrix;
from k epoch to k +1 epoch, the prediction equation of the state vector and its covariance matrix are:
Xk+1,k＝AkXk(6)
the update formula of the state vector and its covariance matrix are:
Xk+1＝Xk+1,k+Kk+1(Zk+1-Ak+1Xk+1,k) (8)
Ck+1＝Ck+1,k-Kk+1Ak+1Ck+1,k(9)
wherein A iskBeing a state transition matrix, QkError covariance matrix, P, being the state transition equationk+1To observe the variance matrix of the noise, Kk+1Is a gain matrix, RkTo observe the variance matrix of the noise, Ck+1,kAnd Ck+1Respectively a prediction variance matrix and an updated variance matrix;
floating point solution N of ambiguity parameters obtainable using Kalman filteringiFurther, the floating ambiguity is fixed as follows: selecting a reference satellite i, and determining the floating ambiguity N of the satelliteiCombining the UPD parameter and the UPD parameter into a new UPD parameter; the new UPD parameter is actually the sum of the UPD and the floating ambiguity of the reference satellite, and the floating ambiguities of the other non-reference satellites become the difference between the original floating ambiguity and the floating ambiguity of the reference satellite; as shown in the following formula:
wherein,new UPD parameters are obtained for the combination; n is a radical ofiTo refer to the floating ambiguity for satellite i,the new floating ambiguity of the satellite k after the UPD parameter and the reference satellite floating ambiguity are combined; ambiguity fixing is performed by three steps: firstly, ignoring integer characteristics of ambiguity, and resolving a baseline vector and an ambiguity floating solution by adopting a parameter estimation method; then, ambiguity fixing is carried out by satellite according to integer characteristics by using ambiguity floating solution and covariance matrix thereof; re-resolving the integer ambiguity by replacing the original observation equation to obtain a baseline vector solution with fixed ambiguity;
(3) computing multipath based on obtained solutions
The posterior residual of the Kalman filtering solution is the multipath of the satellite:
step 2: multipath semi-celestial sphere model establishment based on trend surface analysis
(1) Assigning multipath data to sky grid
Calculating an altitude azimuth for the satellite for which the multipath data has been obtained; firstly, calculating an observation vector [ delta e delta n delta u ] from a user to a satellite under a station center coordinate system]T：
Wherein, [ Δ x Δ y Δ z [ ]]TThe observation vector from the user to the satellite under the earth-centered earth-fixed rectangular coordinate system; λ and φ are longitude and latitude, respectively; secondly, calculating an observation vector [ delta x 'delta y' delta z 'from the user to the satellite in a carrier coordinate system']T：
The psi, the theta and the gamma are respectively a carrier course angle, a pitch angle and a roll angle; the satellite elevation angle ele and azimuth azi are:
dividing the sky into different grids according to the altitude angle and the azimuth angle, and distributing satellite multi-path data corresponding to the altitude angle and the azimuth angle into the grids;
(2) constructing multi-path trend surface model of each sky grid
Firstly, establishing a primary trend surface model and a secondary trend surface model for multiple paths of a sky grid:
primary trend surface:
secondary trend surface:
in the formula, xi,yiRepresenting azimuth and elevation angles, a, corresponding to the ith multipath value in the sky grid0,a1,...anRepresents the fitting coefficient of the trend surface,fitting values of the trend surface model;
next, fitting of moderate R was performed2Testing and significance F testing; wherein the fitting degree coefficient R2Using regression sum of squares SSRSum of squared deviations SSTIs expressed by the specific gravity of (A); r2The value is between 0 and 1, and the higher the value is, the higher the fitting degree of the model is; the calculation formula is as follows:
wherein z isiIs thatIs the remaining sum of squares
If R is2If the value is larger than the preset threshold value, judging that the model passes the test;
if the two models pass the inspection and then are optimized by using an F inspection, the F inspection is used for inspecting whether the trend surface equation is obvious or not, and the calculation formula is as follows:
in the formula, p represents the degree of freedom of regression sum of squares, consisting ofF obeys F distribution with the degree of freedom of (p, n-p-1), and under the condition of a given confidence level, by looking up an F distribution table, a critical value F is obtained, so that the fitted trend surface equation is tested to be more obvious under the confidence level α;
if the residual mean values do not pass through the trend surface model, directly replacing the trend surface model with the residual mean values in the grids;
and step 3: multipath real-time correction
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, selecting a multi-path trend surface model corresponding to a space-sky-map grid for multi-path estimation, and correcting the satellite observation data.
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| CN110068847A (en) * | 2019-04-01 | 2019-07-30 | 和芯星通科技(北京)有限公司 | A kind of method and apparatus that appearance is surveyed in the positioning of GNSS multi-aerial receiver |
| CN110456397A (en) * | 2019-07-29 | 2019-11-15 | 桂林电子科技大学 | A kind of multiple antennas ultra-short baseline positioning and monitoring method, device and storage medium |
| CN110687556A (en) * | 2019-11-04 | 2020-01-14 | 中国电子科技集团公司第五十四研究所 | Multi-path error modeling method suitable for LAAS |
| CN111505670A (en) * | 2020-05-06 | 2020-08-07 | 苏州象天春雨科技有限公司 | Multipath detection and suppression method and system using dual antennas |
| CN112612039A (en) * | 2020-12-23 | 2021-04-06 | 武汉大学 | GNSS indirect signal detection and elimination method and system for static survey station |
| CN114488228A (en) * | 2022-04-11 | 2022-05-13 | 南京北斗创新应用科技研究院有限公司 | GNSS multi-path error weakening method suitable for dynamic carrier platform |
| CN114488227A (en) * | 2022-01-26 | 2022-05-13 | 西南交通大学 | Multipath error correction method based on spatial correlation |
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