CN110907960B - Cycle slip detection method and device based on K-Means dynamic clustering analysis - Google Patents

Cycle slip detection method and device based on K-Means dynamic clustering analysis Download PDF

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CN110907960B
CN110907960B CN201811085727.9A CN201811085727A CN110907960B CN 110907960 B CN110907960 B CN 110907960B CN 201811085727 A CN201811085727 A CN 201811085727A CN 110907960 B CN110907960 B CN 110907960B
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陈亮
蒋智
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Qianxun Spatial Intelligence Inc
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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
    • G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/27—Acquisition or tracking or demodulation of signals transmitted by the system creating, predicting or correcting ephemeris or almanac data within the receiver
    • 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
    • G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment

Abstract

The invention provides a cycle slip detection method and a cycle slip detection device based on K-Means dynamic clustering analysis, wherein the cycle slip detection method comprises the following steps: forming an inter-epoch difference observation equation by the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection volume; checking the chi-square checking quantity, if the chi-square checking quantity passes, all the observed values of the current epoch do not have cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity; and circularly executing the steps until the chi-square passes the inspection. The invention can effectively solve the problem that the threshold value is difficult to determine in cycle slip detection.

Description

Cycle slip detection method and device based on K-Means dynamic clustering analysis
Technical Field
The invention relates to the technical field of cycle slip detection, in particular to a cycle slip detection method and device based on K-Means dynamic clustering analysis.
Background
In the existing single-station single-frequency cycle slip detection and restoration method based on inter-epoch difference, a reference station of a previous epoch is assumed, a current epoch is a rover, observed values of cycle slip are identified according to residual errors after testing of the obtained observed values by combining an RTK positioning principle with robust least square estimation, and when at least 4 cycles of cycle slip does not occur, the cycle slip detection success rate is high.
And performing QR decomposition on the coefficient matrix, wherein the observed quantity with gross errors has strong correlation with the residual error after the experiment, namely the correlation distance is minimum, and the observed value with gross errors can be identified through common cluster analysis.
Cycle slip detection is a difficult problem that must be solved in GNSS (Global Navigation Satellite System) high-precision positioning technology. To acquire high-precision position information, a high-precision carrier phase observation value is required to be used, cycle slip inevitably exists in the carrier phase observation value, particularly, the cycle slip is frequent in complex environments such as urban canyons, and the finding of an effective cycle slip detection method is the key for realizing high-precision positioning. In the current cycle slip detection method, a cycle slip detection quantity is constructed, and a certain function model is selected to process the cycle slip detection quantity, so that a proper threshold value is selected to judge whether cycle slip occurs or not, wherein the threshold value can be constant or time-varying. For a static station with a wide observation environment, a better effect can be achieved, however, urban environments are complex and various, shielding is serious, pseudo-range and multi-path are frequent, and the effect of cycle slip detection by observation values similar to MW combination can be influenced. For the complex environment, the threshold value of cycle slip detection is often difficult to determine, and if the selected threshold value is too small, the 'normal observation value' is easily misjudged as the observation value with cycle slip; if the selected threshold is too large, the cycle slip may be missed for 1-2 weeks. Both of the above situations occur, which affect the performance of the positioning.
Disclosure of Invention
The invention provides a cycle slip detection method and device based on K-Means dynamic clustering analysis, which improve the GNSS positioning performance in a complex environment and solve the technical problems.
The technical scheme adopted by the invention is as follows:
a cycle slip detection method based on K-Means dynamic clustering analysis comprises the following steps:
forming an inter-epoch difference observation equation by the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection volume;
carrying out chi-square test on chi-square test quantity, if chi-square test is passed, all observed values of the current epoch have no cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
and circularly executing the steps until the chi-square passes the test.
Further, the current epoch data and the previous epoch data constitute an inter-epoch difference observation equation according to the following formula:
Figure BDA0001802763640000021
Figure BDA0001802763640000022
Figure BDA0001802763640000023
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
Figure BDA0001802763640000024
Represents the carrier phase observed value, with week as unit;
Figure BDA0001802763640000025
representing a defense distance; t is a unit ofi sRepresenting tropospheric delay;
Figure BDA0001802763640000026
indicating ionospheric delay; t is tiAnd ts，iRespectively a receiver clock error and a satellite clock error; biAnd bs，iCarrier phase hardware delays at the receiver end and the satellite end respectively;
Figure BDA0001802763640000027
for blurring the whole weekDegree; epsiloniMeasurement noise that is a carrier phase observation; Δ represents the single difference operator between epochs;
Figure BDA0001802763640000028
is the cycle slip value in weeks.
Further, the differential observation equation is linearized and written in matrix form:
Figure BDA0001802763640000029
wherein H is a coefficient matrix; δ x is a parameter to be estimated, including a relative position parameter and a receiver clock drift parameter; l is the pre-test residual error; v is the post-test residual.
Further, carrying out QR decomposition on the H coefficient matrix to obtain:
H＝QR。
wherein Q is an orthogonal matrix; r is an upper triangular matrix with positive diagonal elements.
Further, the chi-square test quantity is equal to TLTTL, chi square assay compliance2(n-m) distribution, wherein m is the number of parameters to be estimated, n is the number of observed values, and T is taken as a matrix QT(QTThe transpose of the Q matrix), TL ═ T × L.
Further, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method specifically comprises the following steps: constructing a data object; data objects are divided into two classes: the observed value of the cycle slip which does not occur and the observed value of the cycle slip which occurs; an observed value for occurrence of cycle slip is identified.
Further, the data object is constructed by the following formula:
Figure BDA0001802763640000031
where w is n-m, w represents the number of redundant observations, and each column in the formula represents a data object, i.e., d1、d2Each is expressed asThe similarity measure of the same data object is Euclidean distance, and d is selectedn+1And dn+1The most distant Euclidean vector is the initial clustering center and the vector dn+1The same category is the observed value of the occurrence of cycle slip.
The invention also provides a cycle slip detection device based on K-Means dynamic clustering analysis, which comprises:
the chi-square inspection volume construction unit is used for forming an inter-epoch difference observation equation based on the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix and constructing chi-square inspection volume;
the chi-square testing unit is used for carrying out chi-square testing on chi-square testing quantity, if the chi-square testing quantity passes, all the observed values of the current epoch do not have cycle slip, and then the observed value of the next epoch is processed; and if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity.
The invention also provides a memory, in which a computer program is stored, the computer program performing the steps of:
Forming an inter-epoch differential observation equation by the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection variables;
carrying out chi-square test on chi-square test quantity, if chi-square test is passed, all the observed values of the current epoch do not have cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
and circularly and repeatedly executing the steps until the chi-square passes the test.
The invention has the following beneficial effects: the observed value of the cycle slip is identified by applying K-Means dynamic clustering analysis and chi-square test in mathematical statistics, and the problem that the threshold value is difficult to determine in cycle slip detection can be effectively solved.
Drawings
FIG. 1 is a cycle slip detection flow chart according to the present invention.
Detailed Description
The invention solves the technical problem that the threshold value is difficult to determine in cycle slip detection by applying chi-square test and K-Means dynamic clustering analysis. The invention is further illustrated below with reference to the figures and examples.
The first embodiment is as follows:
the invention provides a cycle slip detection method based on K-Means dynamic clustering analysis, a flow chart is shown in figure 1, and the cycle slip detection method comprises the following steps:
Step 1, a difference observation equation between epochs can be formed by current epoch data and previous epoch data according to a formula (2), QR decomposition (orthogonal triangle decomposition, Q is an orthogonal matrix, and R is an upper triangle matrix with positive diagonal elements) is carried out on an obtained coefficient array, and then a chi-square inspection quantity Test is constructed according to a formula (5).
Figure BDA0001802763640000041
Wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
Figure BDA0001802763640000042
represents a carrier phase observation in units of weeks;
Figure BDA0001802763640000043
representing a defense distance; t isi sRepresenting tropospheric delay;
Figure BDA0001802763640000044
indicating ionospheric delay; t is tiAnd ts，iRespectively a receiver clock error and a satellite clock error; biAnd bs，iCarrier phase hardware delays at the receiver end and the satellite end respectively;
Figure BDA0001802763640000045
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation.
The differential observation equation between epoch i +1 and epoch i can be obtained according to equation (1):
Figure BDA0001802763640000046
wherein the content of the first and second substances,
Figure BDA0001802763640000047
Δ represents the single difference operator between epochs;
Figure BDA0001802763640000048
is the cycle slip value in weeks. And equation (2) ignores the amount that can be considered constant in a short time.
Linearize equation (2) and write in matrix form:
Figure BDA0001802763640000049
wherein H is a coefficient matrix (design matrix); and deltax is a parameter to be estimated, including a relative position parameter and a receiver clock drift parameter, L is a residual before the experiment, and v is a residual after the experiment. The cycle slip parameter is omitted from equation (3) assuming that no cycle slip occurs for all observations.
Performing QR decomposition on the H matrix in equation (3) to obtain:
H＝QR (4)
wherein Q is an orthogonal matrix; r is an upper triangular matrix with positive diagonal elements.
Assuming that the number of the parameters to be estimated is m, the number of the observed values is n, QTIs the transpose of the Q matrix. Get matrix QTThe lower half (denoted T) of (n-m) × n is multiplied by the upper matrix to obtain:
TL＝T*L (5)
let Test be TLTTL de: test compliance chi2(n-m) distribution, and chi-square Test is performed on Test. If passing the testIf the result is verified, the observation data of the epoch is considered to have no cycle slip; if the test is not passed, the cycle slip of the epoch data is shown, and the cycle slip observed value is identified by the K-Means dynamic clustering analysis method in the step 2.
And 2, if the chi-square passes the checking, all the observed values of the epoch have no cycle slip, and then the observed data of the next epoch is processed. And if the chi-square test is not passed, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, and removing the observed value.
K-Means cluster analysis classifies a plurality of data objects, and the data objects can be classified into K classes. While for cycle slip detection the data can be categorized into two categories: one is an observed value in which cycle slip does not occur; the other is the observed value of cycle slip. Let w be n-m, w denote the number of redundant observations, and now construct the data object as follows:
Figure BDA0001802763640000051
Each column in equation (6) represents a data object, i.e., d1、d2Etc. respectively representing different data objects, and the similarity measure is Euclidean distance. Now set the value of k to 2, and divide equation (6) into two categories. Selection of dn+1And dn+1The vector with the farthest Euclidean distance is the initial clustering center. Classifying the data object by adopting a K-Means dynamic clustering analysis method and vector dn+1The same category is the observed value of the occurrence of cycle slip.
And 3, circularly and repeatedly executing the step 1 and the step 2 until the chi-square passes the inspection.
Often, only one observed value of cycle slip can be identified for one K-Means cluster analysis, the observed value of cycle slip is often the largest, and in order to solve the problem that multiple observed values simultaneously generate cycle slip, iteration processing needs to be performed on the step 1 and the step 2, that is: and eliminating cycle slip observed values identified by each K-Means dynamic analysis, and then carrying out chi-square test, and repeating the steps until the chi-square test is passed.
The second embodiment:
the invention also provides a cycle slip detection device based on K-Means dynamic clustering analysis, which comprises:
the chi-square inspection volume construction unit is used for forming an inter-epoch differential observation equation based on the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix and constructing chi-square inspection volume;
The chi-square testing unit is used for carrying out chi-square testing on chi-square testing quantity, if the chi-square testing quantity passes, all the observed values of the current epoch do not have cycle slip, and then the observed value of the next epoch is processed; and if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity.
Further, the differential observation equation is as follows:
Figure BDA0001802763640000061
Figure BDA0001802763640000062
Figure BDA0001802763640000063
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
Figure BDA0001802763640000064
represents a carrier phase observation in units of weeks;
Figure BDA0001802763640000065
representing a defense distance; t isi sRepresenting tropospheric delay;
Figure BDA0001802763640000066
indicating ionospheric delay; t is tiAnd ts，iRespectively a receiver clock error and a satellite clock error; biAnd bs，iCarrier phase hardware delays at the receiver end and the satellite end respectively;
Figure BDA0001802763640000067
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation; Δ represents the single difference operator between epochs;
Figure BDA0001802763640000068
is the cycle slip value in weeks.
Example three:
the invention also provides a memory, in which a computer program is stored, the computer program performing the steps of:
forming an inter-epoch difference observation equation by the current epoch data and the previous epoch data, carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection volume;
Checking the chi-square checking quantity, if the chi-square checking quantity passes, all the observed values of the current epoch do not have cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
and circularly executing the steps until the chi-square passes the test.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (6)

1. A cycle slip detection method based on K-Means dynamic clustering analysis is characterized by comprising the following steps:
the current epoch data and the previous epoch data form an inter-epoch differential observation equation, the differential observation equation is linearized and written into a matrix form:
Figure FDA0003601502840000011
Wherein H is a coefficient matrix; δ x is a parameter to be estimated, including a relative position parameter and a receiver clock drift parameter; l is the pre-test residual error; v is the post-test residual; lambda [ alpha ]fRepresents a carrier wavelength;
Figure FDA0003601502840000012
representing a carrier phase observation;
Figure FDA0003601502840000014
representing a defense distance;
Figure FDA0003601502840000013
indicating ionospheric delay; t is ts,iIs the satellite clock error; f, i, s respectively represent frequency, epoch and satellite number; Δ represents the single difference operator between epochs;
carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection quantity; and carrying out QR decomposition on the H coefficient matrix to obtain: where Q is an orthogonal matrix and R is an upper triangular matrix with positive diagonal elements;
carrying out chi-square test on chi-square test quantity, if chi-square test is passed, all observed values of the current epoch have no cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
circularly executing the steps until the chi-square passes the inspection;
the chi-square test quantity is equal to TLTTL, chi square assay compliance2(n-m) distribution, wherein m is the number of parameters to be estimated, n is the number of observed values, and T is taken as a matrix Q TLower half of (n-m) × n, QTTL is the transpose of the Q matrix.
2. The cycle slip detection method based on K-Means dynamic cluster analysis of claim 1, wherein the current epoch data and the previous epoch data form an inter-epoch differential observation equation according to the following formula:
Figure FDA0003601502840000021
wherein the content of the first and second substances,
Figure FDA0003601502840000022
Figure FDA0003601502840000023
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
Figure FDA0003601502840000025
represents a carrier phase observation in units of weeks;
Figure FDA0003601502840000028
representing a defense distance;
Figure FDA0003601502840000027
representing tropospheric delay;
Figure FDA0003601502840000026
indicating ionospheric delay; t is tiAnd ts,iRespectively a receiver clock error and a satellite clock error; biAnd bs,iAre respectively connected toThe carrier phase hardware delay of the receiver end and the satellite end;
Figure FDA0003601502840000029
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation; Δ represents the single difference operator between epochs;
Figure FDA00036015028400000210
is the cycle slip value in weeks.
3. The cycle slip detection method based on K-Means dynamic cluster analysis as claimed in claim 1, wherein the step of identifying the observed value of the cycle slip by the K-Means dynamic cluster analysis specifically comprises the following steps:
constructing a data object;
data objects are divided into two classes: the observed value of the cycle slip which does not occur and the observed value of the cycle slip which occurs;
An observed value for occurrence of cycle slip is identified.
4. The cycle slip detection method based on K-Means dynamic clustering analysis as claimed in claim 1, wherein the data object is constructed by the following formula:
Figure FDA0003601502840000024
where w is n-m, w represents the number of redundant observations, and each column in the formula represents a data object, i.e., d1、d2The similarity measure is Euclidean distance, d is selectedn+1And dn+1The most distant Euclidean vector is the initial clustering center and the vector dn+1The same category is the observed value of the occurrence of cycle slip.
5. A cycle slip detection device based on K-Means dynamic clustering analysis is characterized by comprising:
the chi-square inspection volume construction unit is used for forming an inter-epoch difference observation equation based on the current epoch data and the previous epoch data, linearizing the difference observation equation and writing the difference observation equation into a matrix form:
Figure FDA0003601502840000031
wherein H is a coefficient matrix; δ x is a parameter to be estimated, including a relative position parameter and a receiver clock drift parameter; l is the pre-test residual error; v is the residual error after the test, λfRepresents a carrier wavelength;
Figure FDA0003601502840000032
representing a carrier phase observation;
Figure FDA0003601502840000034
representing a defense distance;
Figure FDA0003601502840000033
indicating ionospheric delay; t is ts,iIs the satellite clock error; f, i, s respectively represent frequency, epoch and satellite number; Δ represents the single difference operator between epochs; carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection quantity; carrying out QR decomposition on the H coefficient matrix to obtain: where Q is an orthogonal matrix and R is an upper triangular matrix with positive diagonal elements;
The chi-square checking unit is used for checking chi-square checking quantity, if the chi-square checking quantity passes, all the observed values of the current epoch do not have cycle slip, and then the observed value of the next epoch is processed; if the card party verification does not pass,
identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
the chi-square test quantity is equal to TLTTL, chi square test compliance χ2(n-m) distribution, wherein m is the number of parameters to be estimated, n is the number of observed values, and T is a matrix QTLower half of (n-m) × n, QTTL is the transpose of Q matrix.
6. A memory storing a computer program, the computer program performing the steps of:
the current epoch data and the previous epoch data form an inter-epoch differential observation equation, the differential observation equation is linearized and written into a matrix form:
Figure FDA0003601502840000041
wherein H is a coefficient matrix; δ x is a parameter to be estimated, including a relative position parameter and a receiver clock drift parameter; l is the pre-test residual error; v is the residual error after the test, λfRepresents a carrier wavelength;
Figure FDA0003601502840000042
representing a carrier phase observation;
Figure FDA0003601502840000044
representing a defense distance;
Figure FDA0003601502840000043
Representing ionospheric delay; t is ts,iIs the satellite clock error; f, i, s respectively represent frequency, epoch and satellite number; Δ represents the single difference operator between epochs; carrying out QR decomposition on the obtained coefficient matrix, and constructing chi-square inspection quantity; carrying out QR decomposition on the H coefficient matrix to obtain: where Q is an orthogonal matrix and R is an upper triangular matrix with positive diagonal elements;
carrying out chi-square test on chi-square test quantity, if chi-square test is passed, all the observed values of the current epoch do not have cycle slip, and then processing the observed value of the next epoch; if the chi-square test does not pass, identifying the observed value of the cycle slip by a K-Means dynamic clustering analysis method, removing the observed value and reconstructing chi-square test quantity;
circularly executing the steps until the chi-square is checked to pass;
the chi-square test quantity is equal to TLTTL, chi square assay compliance2(n-m) distribution, wherein m is the number of parameters to be estimated, n is the number of observed values, and T is taken as a matrix QTLower half of (n-m) × n, QTTL is the transpose of the Q matrix.
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