CN110554419B - Ambiguity reduction correlation evaluation method - Google Patents
Ambiguity reduction correlation evaluation method Download PDFInfo
- Publication number
- CN110554419B CN110554419B CN201910859519.8A CN201910859519A CN110554419B CN 110554419 B CN110554419 B CN 110554419B CN 201910859519 A CN201910859519 A CN 201910859519A CN 110554419 B CN110554419 B CN 110554419B
- Authority
- CN
- China
- Prior art keywords
- ambiguity
- variance
- matrix
- conditional
- decorrelation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000011156 evaluation Methods 0.000 title claims abstract description 9
- 239000011159 matrix material Substances 0.000 claims abstract description 57
- 238000000034 method Methods 0.000 claims abstract description 30
- 230000009466 transformation Effects 0.000 claims abstract description 25
- 230000007547 defect Effects 0.000 claims abstract description 16
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 8
- 230000015556 catabolic process Effects 0.000 claims abstract description 5
- 238000006731 degradation reaction Methods 0.000 claims abstract description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000008030 elimination Effects 0.000 claims description 3
- 238000003379 elimination reaction Methods 0.000 claims description 3
- 238000010845 search algorithm Methods 0.000 claims description 3
- 238000004458 analytical method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 230000006835 compression Effects 0.000 description 2
- 238000007906 compression Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000003491 array Methods 0.000 description 1
- 230000001174 ascending effect Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 150000007524 organic acids Chemical class 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
Images
Classifications
-
- 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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
-
- 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
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- 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
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Signal Processing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention discloses a method for evaluating ambiguity degradation correlation, which comprises the following steps: acquiring observation data of a global navigation satellite system, constructing an observation equation through carrier waves and pseudo-range observation values, and obtaining a ambiguity variance matrix by adopting least square estimationTo pairPerforming Cholesky decomposition to obtain a unit lower triangular matrix L and a diagonal variance matrix D respectively, and calculating the conditional variance defect degree gamma 0 (ii) a Integer transformation is respectively carried out on L and D by adopting integer Gaussian transformation and conditional variance exchange to realizeIs calculated, and the conditional variance defect degree after the decorrelation is calculatedJudgment ofAnd if the ambiguity is not found, the decorrelation is successful, the ambiguity of the whole cycle can be quickly searched, otherwise, the ambiguity cannot be effectively estimated due to the decorrelation failure, and a proper decorrelation algorithm needs to be selected again. Compared with the existing ambiguity decorrelation evaluation method, the method can scientifically and reasonably evaluate the decorrelation performance of different algorithms, provides reference for effective selection of the decorrelation algorithms, and has good practical value.
Description
Technical Field
The invention relates to the technical field of satellite navigation positioning, in particular to a ambiguity reduction correlation evaluation method.
Background
The fast and accurate resolving of the integer ambiguity is the key to the high-precision positioning of the carrier phase. Among many ambiguity resolution methods, the ambiguity resolution success rate based on integer least squares estimation is the highest. Estimating ambiguity using integer least squares essentially searches a set of integer ambiguity candidate solutions satisfying the quadratic minimum of ambiguity residual within an integer space, so the computational efficiency depends on the size of the integer search space, and the size of the search space is determined by the ambiguity variance matrix characteristic. Because the original ambiguity variance matrix is a random and irregular matrix, a larger search space is faced when the ambiguity is directly searched, and the ambiguity of the whole cycle is difficult to quickly and effectively estimate. Therefore, in order to accelerate the search process of the ambiguity, a correlation reduction algorithm is usually adopted to perform integer transformation on the ambiguity variance matrix so as to reduce the size of the search space and improve the search efficiency of the ambiguity.
The decorrelation is generally considered to improve the search efficiency by reducing the correlation of the ambiguity variance matrix to the maximum extent to achieve the compression of the search ellipsoid. The idea that theory and algorithm comparison verification are respectively adopted by Borno et al (2014) and Lu Li fruit et al (2015) to obtain that the idea that the maximum degree of compression of the ellipsoid can be improved by reducing the correlation between ambiguity variance components is one-sided, and the performance of the correlation reduction algorithm cannot be accurately measured by indexes such as correlation coefficient reduction, condition number and orthogonal defect degree (Teunessen, 1994 Liu et al, 1999 and Feng,2013; xiehai Karma et al, 2014; vanlong et al, 2014). Therefore, an index is required to be provided for scientifically and reasonably evaluating the decorrelation performance of different algorithms.
Disclosure of Invention
The embodiment of the invention provides a method for evaluating ambiguity degradation correlation, which is used for solving the problems in the background technology.
The embodiment of the invention provides a method for evaluating ambiguity degradation correlation, which comprises the following steps:
acquiring observation data of a global navigation satellite system, constructing an observation equation through carrier waves and pseudo-range observation values, and determining a ambiguity variance matrix according to an observation equation by adopting a least square estimation method
To ambiguity variance matrixCholesky decomposition is performed to obtain an ambiguity variance matrix>Calculating the conditional variance defect degree of the original ambiguity by using the triangle matrix L and the diagonal variance matrix D under the unit of the original ambiguity;
performing integer transformation on the lower unit triangular matrix L by adopting integer Gaussian transformation, performing integer transformation on the diagonal variance matrix D by adopting conditional variance transformation, and calculating the ambiguity conditional variance defect degree after the integer transformation;
judging whether the conditional variance defect degree of the reduced correlation ambiguity is less than or equal to the conditional variance defect degree of the original ambiguity, if so, adopting a search algorithm to carry out search on the ambiguity variance matrixSearching is carried out; otherwise, the decorrelation algorithm is reselected.
wherein,P B =B(B T P yy B) -1 B T P yy (ii) a A is a coefficient matrix of the ambiguity; b is a coefficient matrix of the baseline component; i is n Is an n-dimensional identity matrix; p yy Is a weighted array of observations.
Further, the conditional variance defect degree is expressed as follows:
wherein d is i To representThe conditional variance of (a); i | · | is a determinant of a matrix; n is the dimension of the ambiguity.
Further, the unit lower triangular matrix L is subjected to integer transformation by adopting integer Gaussian transformation; specifically, the method comprises the following steps:
the integer Gaussian transformation is to perform Gaussian elimination on a unit lower triangular matrix L, and the lower triangular matrix elements need to be updated:
wherein, [ ·] int Is a rounding operation on an element.
Further, the diagonal variance matrix D is subjected to integer transformation by adopting conditional variance exchange; the method specifically comprises the following steps:
the conditional variance exchange is to sort the adjacent conditional variances in the diagonal variance matrix D when the conditional variances are satisfiedFor the adjacent conditional variance (d) i-1 ,d i ) Performing an exchange, wherein the calculation formula after the exchange is as follows:
compared with the prior art, the embodiment of the invention provides a method for evaluating the ambiguity reduction correlation, which has the following beneficial effects:
the invention adopts least square estimation to obtain an ambiguity variance matrixTo (X)>Performing Cholesky decomposition to obtain a unit lower triangular matrix L and a diagonal variance matrix D respectively, and calculating the conditional variance defect degree gamma 0 (ii) a Integer transformation for L and D using integer Gaussian transformation and conditional variance exchange to achieve->And calculates the conditional variance measure after the down-correlation>Judgment>And if the ambiguity is not found, the decorrelation is successful, the ambiguity of the whole cycle can be quickly searched, otherwise, the ambiguity cannot be effectively estimated due to the fact that the decorrelation fails, and a proper decorrelation algorithm needs to be selected again. Compared with the existing ambiguity decorrelation evaluation method, the method can scientifically and reasonably evaluate the decorrelation performance of different algorithms, provides reference for effective selection of the decorrelation algorithms, and has good practical value.
Drawings
Fig. 1 is a flowchart of an ambiguity reduction correlation evaluation method according to an embodiment of the present invention;
FIG. 2a is a diagram illustrating conditional variance defectivity of four methods when the ambiguity is 22-dimensional according to an embodiment of the present invention;
FIG. 2b is a diagram illustrating the conditional variance defectivity of the four methods when the ambiguity is 28-dimensional according to the embodiment of the present invention;
FIG. 2c is a diagram illustrating the conditional variance defectivity of four methods for 32-dimensional ambiguity provided by an embodiment of the present invention;
FIG. 2d shows the conditional variance defectivity of the four methods when the ambiguity is 39-dimensional according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention provides a method for evaluating ambiguity reduction correlation, where the method includes:
the invention provides a method for evaluating ambiguity degradation correlation, which specifically comprises the following steps as shown in figure 1:
step 1: reading a GNSS observation file, constructing an observation equation by utilizing carrier waves and pseudo-range observation values, and obtaining a ambiguity variance matrix by adopting least square estimation
Specifically, an ambiguity variance matrix is obtained by adopting least square estimationThe calculation process is as follows:
assuming that the general expression of the linearized double-difference observation equation is: equation Section (Next)
Wherein E (-) and D (-) represent the expectation and variance symbols, respectively; y represents an observed value; a and b represent the ambiguity and baseline components, respectively; a and B are corresponding coefficient matrixes; Δ is the observation noise.
The above equation is written in the form of an error equation:
wherein v is a correction number;and &>The float solution for the ambiguity and baseline components are represented separately.
The above equation can be further written as:
written in the form of the normal equation:
in order to ensure that the water-soluble organic acid,
precision of the parameter to be estimated:
Wherein,P B =B(B T P yy B) -1 B T P yy (ii) a A is a coefficient matrix of the ambiguity; b is a coefficient matrix of the baseline component; I.C. A n Is an n-dimensional identity matrix; p yy Is a weighted array of observations.
Step 2: to pairCholesky decomposition is carried out to respectively obtain a unit lower triangular matrix L and a diagonal variance matrix D, and the conditional variance defect degree gamma of the original ambiguity is calculated 0 ;/>
Specifically, the conditional variance defectivity γ is adopted as an evaluation index of the ambiguity decorrelation performance. γ is defined as follows:
in the formula, d i RepresentThe conditional variance of (a); i | · | is a determinant of a matrix; n is the dimension of the ambiguity.
Wherein d is i Using Cholesky decomposition to obtain:
in the formula,
lower bound of γ:
from the above equation, it can be seen that as the gamma value is smaller and closer to the ambiguity dimension, the better the ambiguity condition variance ranking, the faster the ambiguity search process will be.
And 3, step 3: respectively adopting integer Gaussian transformation and conditional variance exchange to carry out integer transformation on L and D to realizeAnd calculates the ambiguity conditional variance deficiency after the down-correlation>
Specifically, integer transformation is carried out on L and D by adopting integer Gaussian transformation and conditional variance exchange to realizeThe process of the method is as follows:
the integer gaussian transformation is to perform gaussian elimination on L, and the lower triangular matrix elements need to be updated:
in the formula [ ·] int Representing a rounding operation on an element.
The conditional variance exchange is to order the adjacent conditional variances in D. When it is satisfied withFor the adjacent conditional variance (d) i-1 ,d i ) And (4) performing exchange, wherein the calculation formula after exchange is as follows:
and 4, step 4: judgment ofIf the ambiguity is not found, the correlation reduction is successful if the ambiguity is found, and a search algorithm can be adopted to search the ambiguity; otherwise, the decorrelation fails, and a proper decorrelation algorithm needs to be selected to perform decorrelation again.
Analysis of experiments
In order to verify whether the evaluation method of the embodiment can reasonably evaluate the decorrelation performance of different algorithms, four groups of ambiguity variance arrays with different dimensions are adopted for experimental analysis, the conditional variance defectiveness of four methods, namely an unadopted decorrelation algorithm (Origin), a natural ascending order sorting Algorithm (ASCE), an integer Gaussian transform algorithm (LIGT) based on lower triangular George's decomposition and a minimum column rotation sorting algorithm (SEQR) based on lower triangular George's decomposition, is respectively counted, and a conditional variance trend graph is adopted as a basis for judging whether the conditional variance defectiveness is reasonable. The results of the specific experimental analysis are shown in table 1, fig. 2a, fig. 2b, fig. 2c, fig. 2d.
TABLE 1 conditional variance Defect statistical results for different decorrelation methods
The experimental results of table 1, fig. 2a, fig. 2b, fig. 2c and fig. 2d show that the conditional variance defectivity can accurately measure the decorrelation performance of different methods.
The above disclosure is only a few specific embodiments of the present invention, and those skilled in the art can make various modifications and variations of the present invention without departing from the spirit and scope of the present invention, and it is intended that the present invention also include the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.
Claims (3)
1. A method for evaluating ambiguity degradation correlation, comprising:
acquiring observation data of a global navigation satellite system, constructing an observation equation through carrier waves and pseudo-range observation values, and determining a ambiguity variance matrix according to the observation equation by adopting a least square estimation method
To ambiguity variance matrixCholesky decomposition is carried out to obtain an ambiguity variance matrixCalculating the conditional variance defect degree of the original ambiguity by using the unit lower triangular matrix L and the diagonal variance matrix D;
performing integer transformation on the unit lower triangular matrix L by adopting integer Gaussian transformation, performing integer transformation on the diagonal variance matrix D by adopting conditional variance transformation, and calculating the ambiguity conditional variance defect degree after the integer transformation;
judging whether the conditional variance defect degree of the reduced correlation ambiguity is less than or equal to the conditional variance defect degree of the original ambiguity, if so, adopting a search algorithm to carry out search on the ambiguity variance matrixSearching is carried out; otherwise, reselecting a correlation reduction algorithm;
wherein,P B =B(B T P yy B) -1 B T P yy (ii) a A is a coefficient matrix of the ambiguity; b is a coefficient matrix of the baseline component; i is n Is an n-dimensional identity matrix; p yy A weight matrix of the observed values;
the conditional variance defect degree is expressed as follows:
2. The ambiguity decorrelation evaluation method according to claim 1, wherein the unit lower triangular matrix L is integer transformed using an integer gaussian transform; the method specifically comprises the following steps:
the integer Gaussian transformation is to perform Gaussian elimination on a unit lower triangular matrix L, and the elements of the lower triangular matrix need to be updated:
wherein [ ·] int Is a rounding operation on an element.
3. The ambiguity decorrelation method according to claim 2, wherein the diagonal variance matrix D is integer transformed using conditional variance exchange; the method specifically comprises the following steps:
the conditional variance exchange is to sort the adjacent conditional variances in the diagonal variance matrix D when the conditional variances are satisfiedFor the adjacent conditional variance (d) i-1 ,d i ) And (4) performing exchange, wherein the calculation formula after the exchange is as follows:
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201910859519.8A CN110554419B (en) | 2019-09-11 | 2019-09-11 | Ambiguity reduction correlation evaluation method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201910859519.8A CN110554419B (en) | 2019-09-11 | 2019-09-11 | Ambiguity reduction correlation evaluation method |
Publications (2)
Publication Number | Publication Date |
---|---|
CN110554419A CN110554419A (en) | 2019-12-10 |
CN110554419B true CN110554419B (en) | 2023-03-24 |
Family
ID=68740002
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201910859519.8A Active CN110554419B (en) | 2019-09-11 | 2019-09-11 | Ambiguity reduction correlation evaluation method |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN110554419B (en) |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111650615B (en) * | 2020-01-14 | 2023-05-09 | 东华理工大学 | Ambiguity lattice reduction quality evaluation method |
CN114584202B (en) * | 2022-04-28 | 2022-07-05 | 环球数科集团有限公司 | Beidou satellite short message remote communication data acquisition system |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN101833080A (en) * | 2009-03-12 | 2010-09-15 | 周迅 | Method for measuring attitude of carrier by using additional constraint condition of GPS system |
CN105182378A (en) * | 2015-07-20 | 2015-12-23 | 武汉大学 | LLL (Lenstra-Lenstra-LovaszLattice) ambiguity decorrelation algorithm |
CN105549047A (en) * | 2015-12-07 | 2016-05-04 | 武汉大学 | Method for evaluating effect of decorrelation algorithm |
CN107957586A (en) * | 2017-11-21 | 2018-04-24 | 东华理工大学 | Correlation technique drops in a kind of fuzziness decomposed based on lower triangle Cholesky |
Family Cites Families (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US10393882B2 (en) * | 2016-03-18 | 2019-08-27 | Deere & Company | Estimation of inter-frequency bias for ambiguity resolution in global navigation satellite system receivers |
-
2019
- 2019-09-11 CN CN201910859519.8A patent/CN110554419B/en active Active
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN101833080A (en) * | 2009-03-12 | 2010-09-15 | 周迅 | Method for measuring attitude of carrier by using additional constraint condition of GPS system |
CN105182378A (en) * | 2015-07-20 | 2015-12-23 | 武汉大学 | LLL (Lenstra-Lenstra-LovaszLattice) ambiguity decorrelation algorithm |
CN105549047A (en) * | 2015-12-07 | 2016-05-04 | 武汉大学 | Method for evaluating effect of decorrelation algorithm |
CN107957586A (en) * | 2017-11-21 | 2018-04-24 | 东华理工大学 | Correlation technique drops in a kind of fuzziness decomposed based on lower triangle Cholesky |
Non-Patent Citations (2)
Title |
---|
GNSS模糊度降相关算法及其评价指标研究;刘志平等;《武汉大学学报(信息科学版)》;20110331;第36卷(第03期);全文 * |
On lattice reduction algorithms for solving weighted integer least squares problems: comparative study;Jazaeri S , Amiri-Simkooei A , Sharifi M A;《Gps Solutions》;20140131;第18卷(第01期);全文 * |
Also Published As
Publication number | Publication date |
---|---|
CN110554419A (en) | 2019-12-10 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
BARBER et al. | SAR sea ice discrimination using texture statistics- A multivariate approach | |
CN110554419B (en) | Ambiguity reduction correlation evaluation method | |
US20120259590A1 (en) | Method and apparatus for compressed sensing with joint sparsity | |
CN113050075B (en) | Underwater sound source matching field positioning method based on diffusion mapping | |
CN107133986B (en) | A kind of camera calibration method based on two-dimensional calibrations object | |
CN111160229B (en) | SSD network-based video target detection method and device | |
CN112633401B (en) | Hyperspectral remote sensing image classification method, device, equipment and storage medium | |
CN107341824B (en) | Comprehensive evaluation index generation method for image registration | |
CN102567970B (en) | Image restoring method and device | |
CN106067172A (en) | A kind of underwater topography image based on suitability analysis slightly mates and mates, with essence, the method combined | |
CN113064147A (en) | Novel matching field passive positioning method under low signal-to-noise ratio | |
CN114879231A (en) | GNSS signal compression capturing method and device, electronic equipment and storage medium | |
CN106443727A (en) | Whole-cycle ambiguity correctness checking method based on integrity monitoring | |
CN110517300B (en) | Elastic image registration algorithm based on local structure operator | |
CN109448037B (en) | Image quality evaluation method and device | |
Feng et al. | A Robust Method for Estimating the Fundamental Matrix. | |
CN116563096B (en) | Method and device for determining deformation field for image registration and electronic equipment | |
CN110109166B (en) | Method for rapidly obtaining high-reliability satellite positioning integer solution | |
CN117173425A (en) | Intelligent extraction method and system for roughness of rock structural surface | |
CN103903258B (en) | Method for detecting change of remote sensing image based on order statistic spectral clustering | |
CN113470085B (en) | Improved RANSAC-based image registration method | |
CN110907960B (en) | Cycle slip detection method and device based on K-Means dynamic clustering analysis | |
US20110093419A1 (en) | Pattern identifying method, device, and program | |
Lawrence | A new method for partial ambiguity resolution | |
Aouada et al. | Application of the bootstrap to source detection in nonuniform noise |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |