CN110554419B - Ambiguity reduction correlation evaluation method - Google Patents

Ambiguity reduction correlation evaluation method Download PDF

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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
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ambiguity
variance
matrix
conditional
decorrelation
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卢立果
刘万科
马立烨
吴汤婷
鲁铁定
王胜平
王建强
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East China Institute of Technology
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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
    • 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

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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 estimation
Figure DDA0002199284930000011
To pair
Figure DDA0002199284930000012
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 is respectively carried out on L and D by adopting integer Gaussian transformation and conditional variance exchange to realize
Figure DDA0002199284930000013
Is calculated, and the conditional variance defect degree after the decorrelation is calculated
Figure DDA0002199284930000014
Judgment of
Figure DDA0002199284930000015
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 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

Ambiguity reduction correlation evaluation method
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
Figure BDA0002199284910000021
To ambiguity variance matrix
Figure BDA0002199284910000022
Cholesky decomposition is performed to obtain an ambiguity variance matrix>
Figure BDA0002199284910000023
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 matrix
Figure BDA0002199284910000024
Searching is carried out; otherwise, the decorrelation algorithm is reselected.
Further, the ambiguity variance matrix
Figure BDA0002199284910000025
The expression is as follows:
Figure BDA0002199284910000026
/>
wherein the content of the first and second substances,
Figure BDA0002199284910000027
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:
Figure BDA0002199284910000028
wherein d is i To represent
Figure BDA0002199284910000029
The 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:
Figure BDA0002199284910000031
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 satisfied
Figure BDA0002199284910000032
For the adjacent conditional variance (d) i-1 ,d i ) Performing an exchange, wherein the calculation formula after the exchange is as follows:
Figure BDA0002199284910000033
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 matrix
Figure BDA0002199284910000034
To (X)>
Figure BDA0002199284910000035
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->
Figure BDA0002199284910000036
And calculates the conditional variance measure after the down-correlation>
Figure BDA0002199284910000037
Judgment>
Figure BDA0002199284910000038
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
Figure BDA0002199284910000041
Specifically, an ambiguity variance matrix is obtained by adopting least square estimation
Figure BDA0002199284910000042
The calculation process is as follows:
assuming that the general expression of the linearized double-difference observation equation is: equation Section (Next)
Figure BDA0002199284910000043
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:
Figure BDA0002199284910000044
wherein v is a correction number;
Figure BDA0002199284910000045
and &>
Figure BDA0002199284910000046
The float solution for the ambiguity and baseline components are represented separately.
The above equation can be further written as:
Figure BDA0002199284910000047
written in the form of the normal equation:
Figure BDA0002199284910000048
in order to ensure that the water-soluble organic acid,
Figure BDA0002199284910000051
precision of the parameter to be estimated:
Figure BDA0002199284910000052
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002199284910000053
therefore, the precision of the floating ambiguity can be obtained
Figure BDA0002199284910000054
Figure BDA0002199284910000055
Wherein the content of the first and second substances,
Figure BDA0002199284910000056
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 pair
Figure BDA0002199284910000057
Cholesky 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:
Figure BDA0002199284910000058
in the formula, d i Represent
Figure BDA0002199284910000059
The 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:
Figure BDA00021992849100000510
in the formula (I), the compound is shown in the specification,
Figure BDA00021992849100000511
lower bound of γ:
Figure BDA00021992849100000512
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 realize
Figure BDA0002199284910000061
And calculates the ambiguity conditional variance deficiency after the down-correlation>
Figure BDA0002199284910000062
Specifically, integer transformation is carried out on L and D by adopting integer Gaussian transformation and conditional variance exchange to realize
Figure BDA0002199284910000063
The 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:
Figure BDA0002199284910000064
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 with
Figure BDA0002199284910000065
For the adjacent conditional variance (d) i-1 ,d i ) And (4) performing exchange, wherein the calculation formula after exchange is as follows:
Figure BDA0002199284910000066
and 4, step 4: judgment of
Figure BDA0002199284910000067
If 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
Figure BDA0002199284910000068
Figure BDA0002199284910000071
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
Figure FDA0003894104780000011
To ambiguity variance matrix
Figure FDA0003894104780000012
Cholesky decomposition is carried out to obtain an ambiguity variance matrix
Figure FDA0003894104780000013
Calculating 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 matrix
Figure FDA0003894104780000014
Searching is carried out; otherwise, reselecting a correlation reduction algorithm;
the ambiguity variance matrix
Figure FDA0003894104780000015
The expression is as follows:
Figure FDA0003894104780000016
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003894104780000017
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:
Figure FDA0003894104780000018
wherein d is i To represent
Figure FDA0003894104780000019
The conditional variance of (a); i | · | is a determinant of a matrix; n is the dimension of the ambiguity.
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:
Figure FDA00038941047800000110
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 satisfied
Figure FDA0003894104780000021
For the adjacent conditional variance (d) i-1 ,d i ) And (4) performing exchange, wherein the calculation formula after the exchange is as follows:
Figure FDA0003894104780000022
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