CN112926190A - Multi-path weakening method and device based on VMD algorithm - Google Patents

Multi-path weakening method and device based on VMD algorithm Download PDF

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CN112926190A
CN112926190A CN202110116828.3A CN202110116828A CN112926190A CN 112926190 A CN112926190 A CN 112926190A CN 202110116828 A CN202110116828 A CN 202110116828A CN 112926190 A CN112926190 A CN 112926190A
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高成发
张瑞成
赵庆
朋子涵
尚睿
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Southeast University
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Abstract

The invention discloses a multi-path weakening method based on a VMD algorithm. Aiming at the defect that the traditional MHM (multipath hemisphere diagram model) algorithm cannot well deal with the influence of observed value noise on the accuracy of a multipath correction model, the method provides an improved multipath weakening method (called as an MHM _ V method) based on VMD (variational modal decomposition) and the MHM algorithm by utilizing the spatial repeatability of multipath delay in a fixed environment. Firstly, carrier noise in single difference residual errors is eliminated by utilizing a VMD algorithm, and multipath delay is extracted, so that a multipath correction database for the previous day or multiple days is established. And then correcting the current pseudorange and the original carrier wave observation value according to the altitude angle and azimuth angle nearest principle so as to weaken the influence of multipath on ambiguity fixation and positioning accuracy. And finally, applying the model to bridge deformation monitoring.

Description

Multi-path weakening method and device based on VMD algorithm
Technical Field
The invention relates to the technical field of multipath weakening of a Global Navigation Satellite System (GNSS) applied to a static environment, in particular to a multipath weakening method and a multipath weakening device based on a VMD algorithm.
Background
Global Navigation Satellite Systems (GNSS) are currently in wide use in a number of high-precision positioning applications, including traditional mapping, deformation monitoring, and the like. For multipath delay, it is difficult to parameterize and cannot be eliminated or attenuated by means of difference, so it becomes the most important error source in GNSS high-precision applications.
As known from previous studies, multipath delays are related only to the relative positions of the satellites and the reflectors, and are repetitive in both time and space due to the repetitive satellite orbits. For static or quasi-static (bridge, etc.) environments, there are currently multipath mitigation algorithms such as sidereal day filtering (SF) and lookup table (or called multipath hemisphere map, MHM), where the MHM algorithm does not consider different constellation orbit repetition periods and is not affected by satellite orbit maneuvering, so that it is more suitable for real-time data processing. For the observation noise contained in the multipath correction model, the MHM algorithm calculates the mean value correction in each grid according to the post-processing multipath delay of multiple days to weaken the influence of the noise. However, analysis of the currently-used MHM algorithm shows that the multipath of the same satellite still has a relatively obvious variation trend even in a grid of 1 ° × 1 °, so that the method for weakening the noise influence by averaging the multipath in the grid is not strict enough. Therefore, the invention provides that the extracted multipath delay is denoised by using a Variational Modal Decomposition (VMD) algorithm so as to improve the precision of the multipath correction model. The improved multipath weakening model can greatly weaken the residual error of the GNSS observation value, and further improve the precision, the convergence speed and the reliability of deformation monitoring.
At present, the application of the GNSS technology in deformation monitoring is more and more common, wherein multipath modeling and weakening have a significant meaning for improving the accuracy and reliability of GNSS monitoring. Therefore, the research of the improved multipath weakening method has important practical significance.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defect that the traditional MHM algorithm cannot well deal with the influence of noise on the accuracy of the multipath model, the MHM _ V model based on the VMD and the MHM algorithm is provided by utilizing the spatial repeatability of multipath delay in a fixed environment so as to improve the accuracy of multipath modeling and further improve the reliability, success rate and accuracy of GNSS resolving.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that: a multi-path weakening method based on a VMD algorithm comprises the following steps:
(1) calculating single-difference residual errors of carrier waves and pseudo-range observation values of all satellites by using a single-difference observation model according to historical GNSS observation data;
(2) separating out multipath delay from the single-difference residual error of the observed value by utilizing a VMD algorithm, and establishing a multipath correction database according to the altitude and the azimuth of the satellite;
(3) and according to the principle that the altitude angle and the azimuth angle are nearest, and according to the spatial repeatability of multipath, performing multipath correction on the current observed value in real time.
Further, in step (1), a single-difference observation model is used to calculate single-difference residuals of carrier waves and pseudo-range observations of all satellites, where the single-difference observation model is expressed as:
Figure BDA0002921031210000021
Figure BDA0002921031210000022
in the formula, Δ represents a single difference operator,
Figure BDA00029210312100000214
denotes a double difference operator, the indices k and l denote the mobile station and reference station numbers, respectively, the indices s and r denote the observation satellite and reference satellite numbers, respectively, and the index j denotes the observation satellite and reference satellite numbers, respectivelyFrequency number, λjIs the wavelength with frequency number j; c represents the speed of light;
Figure BDA0002921031210000023
respectively representing the difference of pseudo-range observed values from a satellite s to a mobile station k and a reference station l and the difference of carrier observed values on a j frequency point;
Figure BDA0002921031210000024
represents the difference between the distances of the satellite s from the mobile station k and the reference station l; delta dtj，kl，PAnd Δ dtj，kl，φRespectively representing the difference between the receiver pseudo range clock differences of a mobile station k and a reference station l on a j frequency point and the difference between carrier clock differences;
Figure BDA0002921031210000025
a difference value representing the difference between the ambiguities of the satellite s to the rover k and the reference station l and the difference between the ambiguities of the reference satellite r to the rover k and the reference station l;
Figure BDA0002921031210000026
and
Figure BDA0002921031210000027
respectively representing the difference of pseudo-distance multipath from a satellite s to a mobile station k and a reference station l and the difference of carrier multipath on a j frequency point;
Figure BDA0002921031210000028
and
Figure BDA0002921031210000029
the differences of pseudo-range noise and carrier noise from the satellite s to the mobile station k and the reference station l at the j frequency point are respectively shown.
Furthermore, known single-difference station satellite range and double-difference carrier ambiguity are substituted into formulas (1) and (2), and then a single-difference satellite clock difference is obtained by using a least square principle, so that carrier and pseudo-range single-difference residual errors of each satellite can be obtained, wherein the carrier and pseudo-range single-difference residual errors comprise multipath delay and observed value noise:
Figure BDA00029210312100000210
Figure BDA00029210312100000211
in the formula:
Figure BDA00029210312100000212
and
Figure BDA00029210312100000213
the differences of pseudo-range residuals from the satellite s to the mobile station k and the reference station l and the differences of carrier residuals are respectively shown at the j frequency points.
Furthermore, the VMD algorithm is used for separating the multipath delay from the single difference residual error, and compared with the traditional multipath weakening algorithm, the influence of observation value noise on the multipath model precision can be reduced.
Further, the multipath correction database established in the step (2) according to the satellite altitude and the satellite azimuth is specifically: data tables in a database are established according to the interval that the altitude angle and the azimuth angle of the satellite are respectively 10 degrees, and are named in the format of 'altitude angle _ azimuth angle' (for example, the data table 10_20 is used for storing multipath correction information of the satellite with the altitude angle of 10-20 degrees and the azimuth angle of 20-30 degrees), and fields in the data tables comprise satellite PRN numbers, GPS time, observation value residuals, pseudo-range multipath and carrier multipath extracted by a VMD algorithm, and the like. The data table of all elevation angles and azimuth angles constitutes the multipath correction database described in step (2).
Further, the specifically describing of performing multipath correction on the observation values in the step (3) is that, according to the PRN number, the altitude angle, and the azimuth information of a certain satellite at the current time, a corresponding multipath correction value is searched from the database, the corresponding multipath correction value is subtracted from the pseudo range and the carrier observation value of the satellite, and the above steps are repeated for all the satellite observation values, so that the multipath correction at the current time is completed.
Figure BDA0002921031210000031
Figure BDA0002921031210000032
In the formula (I), the compound is shown in the specification,
Figure BDA0002921031210000033
and
Figure BDA0002921031210000034
the pseudo range and the carrier observed value after multipath correction from the satellite s to the receiver k on the frequency point j are represented;
Figure BDA0002921031210000035
and
Figure BDA0002921031210000036
representing the pseudo range and the carrier observed value before correction;
Figure BDA0002921031210000037
and
Figure BDA0002921031210000038
indicating the pseudoranges and carrier multipath delay corrections found from the database.
Further, the closest principle of the height angle and the azimuth angle in the step (3) is specifically as follows: and the sum of the altitude angle and the azimuth angle of the satellite to be corrected and the absolute value of the difference value of the altitude angle and the azimuth angle in the multipath correction model is minimum, and corresponding multipath correction values are matched in the multipath correction database according to the principle.
The present invention also proposes an improved multipath mitigation device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the computer program, when loaded into the processor, implements any of the improved multipath mitigation methods.
The invention also proposes a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements any of the improved multipath mitigation methods.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
aiming at the defect that the traditional MHM algorithm cannot perfectly deal with the influence of noise on multipath, the invention provides the MHM _ V model based on the VMD algorithm by utilizing the spatial repeatability of multipath delay in a fixed environment. The method fully utilizes the advantage that the VMD algorithm can well avoid the modal aliasing problem and the endpoint effect, is applied to eliminating the carrier noise in the single-difference residual error, and improves the precision of the multipath correction model. By combining the advantages of few parameters, simple modeling and real-time calculation of the MHM algorithm, the influence of multipath delay on the GNSS observation value is greatly reduced, and the ambiguity calculation success rate, reliability and positioning accuracy of the GNSS in deformation monitoring are improved.
Drawings
FIG. 1 is a flow diagram of an improved multipath mitigation method;
fig. 2 shows carrier single-difference residual and VMD extraction results;
FIG. 3 shows the residual error reduction result of each satellite carrier after multipath mitigation;
FIG. 4 shows the effect of the number of days of multipath modeling data on the multipath mitigation effect;
FIG. 5 is a comparison result of the ambiguity fixed Ratio values before and after multipath mitigation;
FIG. 6 shows ambiguity floating solution bias comparison results before and after multipath mitigation.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, an improved multipath weakening method disclosed in the embodiment of the present invention first calculates single-difference residuals of carrier waves and pseudo-range observation values of all satellites by using a single-difference observation model with respect to historical observation data; secondly, separating out multipath delay from the single-difference residual error of the observed value by using a VMD algorithm, establishing a multipath correction model, and storing the multipath correction model into a database; and finally, performing multi-path correction on the current observed value according to the principle that the altitude angle and the azimuth angle are nearest and the spatial repeatability of the multi-path. The method comprises the following specific steps:
step 1) calculating single-difference residuals of carrier waves and pseudo-range observation values of all satellites by using a single-difference observation model:
and solving the satellite distance and the carrier ambiguity of the station through post resolving, and substituting the satellite distance and the carrier ambiguity into a single difference observation model to calculate the single difference residual errors of the carrier and pseudo-range observation values of all satellites. The single-difference observation model is represented as:
Figure BDA0002921031210000041
Figure BDA0002921031210000042
in the formula: a represents a single difference operator and is,
Figure BDA0002921031210000043
denotes a double difference operator, k and l denote station numbers, s and r denote satellite numbers, j denote frequency numbers, P and phi denote pseudoranges and carrier observations, P denotes a station range, c denotes a speed of light, dt denotes a clock difference, lambda denotes a wavelength, N denotes a carrier ambiguity, e denotes an observation noise, M denotes a carrier ambiguity, andP、Mφrepresenting pseudoranges and multipath delays of the carrier. The single-difference residual error obtained by calculation contains multipath delay and observed value noise.
Step 2) separating the multipath delay from the single-difference residual error of the observed value by utilizing a VMD algorithm, establishing a multipath correction model, and storing the multipath correction model into a database, wherein the method specifically comprises the following steps:
a) and separating the multipath delay from the observed value residual error by utilizing a VMD algorithm so as to realize the purpose of denoising the observed value residual error.
b) And storing information such as satellite PRN numbers, GPS time, satellite altitude angles, satellite azimuth angles, observed value residuals, multipath delays extracted by a VMD algorithm and the like into a database or a text file, and establishing a multipath correction model.
And 3) carrying out multipath correction on the subsequent observed value according to the nearest principle of the altitude angle and the azimuth angle and the spatial repeatability of multipath.
a) The altitude and azimuth recency principle can be described specifically as:
the sum of absolute values of differences between the altitude angle and the azimuth angle of the multipath correction model and the altitude angle and the azimuth angle of the satellite to be corrected is minimum; for a multipath correction model established by multiple days, the final multipath correction value determining method comprises the steps of obtaining the correction values of each day through the principle that the altitude angle and the azimuth angle are nearest, and calculating the average value of the correction values of the multiple days.
b) And obtaining a multipath correction value by using the principle that the altitude angle and the azimuth angle are nearest, and correcting the observed values of all satellites in the current epoch.
Based on the same inventive concept, the embodiment of the present invention discloses an improved multipath mitigation method and apparatus, which may be a device applied in the field of deformation monitoring and the like, and includes a memory, a processor, and a computer program stored in the memory and running on the processor, where the computer program is loaded into the processor to implement the improved multipath mitigation method.
Fig. 2 is a spectrogram of carrier single-difference residuals and VMD extraction results, which sequentially include carrier residuals, multipath delays, and carrier observed value noise from top to bottom, with the left side showing time-series results of the values, and the right side showing the values. It can be seen that the separated noise and the altitude angle have an obvious negative correlation relationship, that is, the observation noise is obviously increased along with the reduction of the altitude angle, and the characteristic of the carrier noise is met, which shows that the multi-path delay can be effectively extracted by using the VMD algorithm.
Fig. 3 shows the reduction result of the residual errors of the satellite carriers after multipath weakening, and it can be seen that the weakening effect of the MHM _ V algorithm provided by the present invention on the multipath is significantly better than that of the MHM algorithm; the satellite residual RMS values are smaller after multipath is attenuated by the MHM _ V algorithm, and are reduced by about 38% and 41% compared with the carrier residual RMS of the satellites L1 and L2 without multipath improvement, and are reduced by about 26% and 31% by the MHM algorithm.
Fig. 4 shows the effect of the number of days of the multipath modeling data on the multipath fading effect, and it can be seen that the fading effect of MHM _ V on the multipath is about 10% higher than that of MHM, and the residual improvement rate of the carrier L2 is better than that of the carrier L1; for the MHM _ V method, the multipath mitigation effect increases with the number of days of multipath modeling data, continues to increase from 1 to 5 days, and then stabilizes at a level of 40%.
Fig. 5 shows the comparison result of the ambiguity fixing Ratio values before and after multipath weakening, with Ratio equal to 3 as a threshold value, as a determination condition for whether ambiguity fixing is successful, the fixed success rate under the condition of un-weakened multipath is counted to be 88.0%, and the ambiguity fixing success rate reaches 99.4% after the multipath is eliminated by using the MHM _ V algorithm provided by the method;
fig. 6 shows the comparison result of ambiguity floating solution skews before and after multipath fading, after the multipath fading is performed by using the MHM _ V method, the time (convergence time) required for all ambiguity floating solution skews to be less than 0.5 cycles is shorter, and the converged floating solution skews are smaller than the time required for no multipath correction.

Claims (8)

1. A multi-path weakening method based on a VMD algorithm is characterized by comprising the following steps:
(1) calculating single-difference residual errors of carrier waves and pseudo-range observation values of all satellites by using a single-difference observation model according to historical GNSS observation data;
(2) separating out multipath delay from the single-difference residual error of the observed value by utilizing a VMD algorithm, and establishing a multipath correction database according to the altitude and the azimuth of the satellite;
(3) and according to the principle that the altitude angle and the azimuth angle are nearest, and according to the spatial repeatability of multipath, performing multipath correction on the current observed value in real time.
2. The VMD algorithm-based multipath mitigation method of claim 1, wherein in step (1), the carrier and pseudorange observations single-difference residuals of all satellites are computed using a single-difference observation model, which is expressed as:
Figure FDA0002921031200000011
Figure FDA0002921031200000012
in the formula, Δ represents a single difference operator,
Figure FDA0002921031200000013
denotes a double difference operator, the indices k and l denote the mobile station and reference station numbers, respectively, the indices s and r denote the observation satellite and reference satellite numbers, respectively, the index j denotes the frequency number, λjThe wavelength of the observed value of the carrier wave of the j frequency point; c represents the speed of light;
Figure FDA0002921031200000014
respectively representing the difference of pseudo-range observed values from a satellite s to a mobile station k and a reference station l and the difference of carrier observed values on a j frequency point;
Figure FDA0002921031200000015
represents the difference between the distances of the satellite s from the mobile station k and the reference station l; delta dtj，kl，PAnd Δ dtj，kl，φRespectively representing the difference between the receiver pseudo range clock differences of a mobile station k and a reference station l on a j frequency point and the difference between carrier clock differences;
Figure FDA0002921031200000016
a difference value representing the difference between the ambiguities of the satellite s to the rover k and the reference station l and the difference between the ambiguities of the reference satellite r to the rover k and the reference station l;
Figure FDA0002921031200000017
and
Figure FDA0002921031200000018
respectively representing the difference of pseudo-distance multipath from a satellite s to a mobile station k and a reference station l and the difference of carrier multipath on a j frequency point;
Figure FDA0002921031200000019
and
Figure FDA00029210312000000110
the differences of pseudo-range noise and carrier noise from the satellite s to the mobile station k and the reference station l at the j frequency point are respectively shown.
3. The multi-path weakening method based on the VMD algorithm as claimed in claim 2, wherein the known single-difference station satellite range and double-difference carrier ambiguity are substituted into equations (1) and (2), and then the single-difference satellite clock difference is obtained by using the least square principle, so as to obtain the carrier and pseudo-range single-difference residual error of each satellite, wherein the single-difference residual error comprises the multi-path delay and the observed value noise:
Figure FDA00029210312000000111
Figure FDA00029210312000000112
in the formula:
Figure FDA00029210312000000113
and
Figure FDA00029210312000000114
the differences of pseudo-range residuals from the satellite s to the mobile station k and the reference station l and the differences of carrier residuals are respectively shown at the j frequency points.
4. The VMD based multipath weakening method as claimed in claim 1, wherein the multipath correction database established according to the satellite altitude and the satellite azimuth in the step (2) is: and (3) establishing data tables in a database according to the 10-degree intervals of the altitude angle and the azimuth angle of the satellite, naming the data tables in an altitude angle-azimuth format, wherein fields in the data tables comprise satellite PRN numbers, GPS time, observation value residual errors, pseudo-range multipath and carrier multipath information extracted by a VMD algorithm, and the data tables of all the altitude angles and the azimuth angles form the multipath correction database in the step (2).
5. The VMD-based multipath mitigation method of claim 1, wherein the multipath correction of the observation in step (3) is specifically described as finding the corresponding multipath correction value from the database according to the PRN number, altitude angle and azimuth angle information of a certain satellite at the current time, subtracting the corresponding multipath correction value from the pseudorange and carrier observation of the satellite, and repeating the above steps for all the satellite observations to complete the multipath correction at the current time:
Figure FDA0002921031200000021
Figure FDA0002921031200000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002921031200000023
and
Figure FDA0002921031200000024
the pseudo range and the carrier observed value after multipath correction from the satellite s to the receiver k on the frequency point j are shown,
Figure FDA0002921031200000025
and
Figure FDA0002921031200000026
representing the pseudoranges and carrier observations before correction,
Figure FDA0002921031200000027
and
Figure FDA0002921031200000028
indicating the pseudoranges and carrier multipath delay corrections found from the database.
6. The multi-path weakening method based on the VMD algorithm as claimed in claim 1, wherein the altitude and azimuth nearest principle in step (3) is specifically: and the sum of the altitude angle and the azimuth angle of the satellite to be corrected and the absolute value of the difference value of the altitude angle and the azimuth angle in the multipath correction model is minimum, and corresponding multipath correction values are matched in the multipath correction database according to the principle.
7. An improved multipath mitigation device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the computer program, when loaded into the processor, implements the improved multipath mitigation method of any one of claims 1 to 6.
8. A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the improved multipath mitigation method of any one of claims 1-6.
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