CN110907960A - Cycle slip detection method and device based on K-Means dynamic clustering analysis - Google Patents
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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; 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 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
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 carrying out QR decomposition on the coefficient matrix, wherein the observed quantity with gross errors has strong correlation with the residual errors after the experiment, namely the correlation distance is the 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 these occurrences will 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 inspection.
Further, the current epoch data and the previous epoch data constitute an inter-epoch difference observation equation according to the following formula:
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
represents a carrier phase observation in units of weeks;
representing a defense distance; t isi sRepresenting tropospheric delay;
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;
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation; deltaRepresenting a single difference operator between epochs;
is the cycle slip value in weeks.
Further, the differential observation equation is linearized and written in matrix form:
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:
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+1Euclidean distance maximumThe far vector is the initial cluster center, and 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 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 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 (4) circularly and repeatedly executing the steps until the chi-square passes the inspection.
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).
Wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
represents a carrier phase observation in units of weeks;
representing a defense distance; t isi sRepresenting tropospheric delay;
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;
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):
wherein,
Δ represents the single difference operator between epochs;
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:
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 the test is passed, 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 represent the number of redundant observations, and now construct data objects as follows:
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 to say: 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.
Example two:
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.
Further, the differential observation equation is as follows:
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
represents a carrier phase observation in units of weeks;
representing a defense distance; t isi sRepresenting tropospheric delay;
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;
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation; Δ represents the single difference operator between epochs;
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;
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 executing the steps until the chi-square passes the inspection.
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 (9)
1. A cycle slip detection method based on K-Means dynamic clustering analysis is characterized by comprising 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 inspection.
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:
wherein,
wherein f, i, s respectively represent frequency, epoch and satellite number; lambda [ alpha ]fRepresents a carrier wavelength;
represents a carrier phase observation in units of weeks;
representing a defense distance; t isi sRepresenting tropospheric delay;
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;
is the integer ambiguity; epsiloniMeasurement noise that is a carrier phase observation; Δ represents the single difference operator between epochs;
is the cycle slip value in weeks.
3. The cycle slip detection method based on K-Means dynamic cluster analysis of claim 2, wherein the differential observation equation is linearized and written in the form of a matrix:
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.
4. The cycle slip detection method based on K-Means dynamic cluster analysis as claimed in claim 3, characterized in that, QR decomposition is performed 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.
5. The method of claim 4, wherein the chi-square test quantity is 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.
6. The cycle slip detection method based on K-Means dynamic cluster analysis as claimed in claim 5, 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.
7. The cycle slip detection method based on K-Means dynamic clustering analysis of claim 6, wherein the data object is constructed by the following formula:
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.
8. 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, 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.
9. A memory storing a computer program, 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;
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 executing the steps until the chi-square passes the inspection.
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