CN107450085B - Micro cycle slip detection method based on ITD fuzzy entropy - Google Patents

Micro cycle slip detection method based on ITD fuzzy entropy Download PDF

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CN107450085B
CN107450085B CN201710469137.5A CN201710469137A CN107450085B CN 107450085 B CN107450085 B CN 107450085B CN 201710469137 A CN201710469137 A CN 201710469137A CN 107450085 B CN107450085 B CN 107450085B
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邹金慧
张雨琦
韩昭嵘
吴建德
王晓东
范玉刚
黄国勇
冯早
叶波
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Kunming University of Science and 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
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    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
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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
    • G01S19/29—Acquisition or tracking or demodulation of signals transmitted by the system carrier including Doppler, related

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Abstract

The invention relates to a micro cycle slip detection method based on ITD fuzzy entropy, and belongs to the technical field of satellite positioning. The method comprises the steps of firstly selecting original Beidou carrier phase observation data, constructing a cycle slip checking quantity time sequence on the original Beidou carrier phase observation data by utilizing a pseudo-range phase method, carrying out ITD self-adaptive decomposition on the cycle slip checking quantity time sequence to obtain PR components with different frequencies, calculating correlation coefficients of each PR component and the original time sequence by using a correlation coefficient method, further selecting the first 7 meaningful PR components, carrying out fuzzy entropy calculation on the PR components, and finally determining whether the micro cycle slip occurs or not according to the relative ratio of a fuzzy entropy value calculated when the cycle slip does not occur and a fuzzy entropy value calculated when the cycle slip occurs. The invention can be used for accurately detecting whether cycle slip occurs in the Beidou carrier phase signal, and improves the sensitivity of cycle slip detection.

Description

Micro cycle slip detection method based on ITD fuzzy entropy
Technical Field
The invention relates to a micro cycle slip detection method based on ITD fuzzy entropy, and belongs to the technical field of satellite positioning.
Background
In the process of receiving satellite signals, the satellite signals are temporarily interrupted due to some reasons, such as obstruction, receiver failure, low signal-to-noise ratio and the like, the radio signals interfere to cause lock losing, and the counter cannot count continuously, so that when the signals are tracked again, the whole-cycle counting is incorrect, but the phase observed value of less than one whole cycle is still correct, and the phenomenon is called cycle slip. The existence of cycle slip seriously affects the carrier wave observation value, and cycle slip of 10 weeks or more in the carrier wave observation data is easy to be found, while cycle slip less than 10 weeks, especially tiny cycle slip of 1-5 weeks, is difficult to be found. Therefore, a method for accurately detecting minute cycle slip is urgently needed.
There are various methods for cycle slip detection. The commonly used research methods for detecting cycle slip at present include a high-order difference method, an ionosphere parameter difference method, a Kalman filtering method, a polynomial fitting method and the like. The high-order difference method is suitable for detecting larger cycle slip, the ionosphere parameter difference method is beneficial to detecting small cycle slip, and the detection effect is greatly influenced if the ionosphere changes too much or the multipath effect is serious. In the kalman filtering method, a mode for performing segmented filtering on data in a filtering process needs to repeatedly determine a filtering initial value, so that the filtering process is complicated and the calculation amount is increased. Therefore, it is necessary to provide a technical means to solve the above problems.
Disclosure of Invention
The invention provides a micro cycle slip detection method based on an ITD fuzzy entropy, which is used for improving the sensitivity of cycle slip detection.
The technical scheme of the invention is as follows: a tiny cycle slip detection method based on ITD fuzzy entropy includes the steps of firstly selecting original Beidou carrier phase observation data, constructing cycle slip detection quantity time sequences on the original Beidou carrier phase observation data by utilizing a pseudo-range phase method, conducting ITD self-adaptive decomposition on the cycle slip detection quantity time sequences to obtain PR components of different frequencies, calculating correlation coefficients of each PR component and the original time sequences through a correlation coefficient method, further selecting the first 7 meaningful PR components, conducting fuzzy entropy calculation on the PR components, and finally determining whether tiny cycle slip occurs according to the relative ratio of fuzzy entropy calculated when cycle slip does not occur and fuzzy entropy calculated when cycle slip occurs.
The method for detecting the small cycle slip based on the ITD fuzzy entropy comprises the following specific steps:
step1, selecting original Beidou carrier phase observation data, and utilizing a pseudo-range phase method to obtain a pseudo-range observation value R(t+△t)Subtracting the carrier phase observed value phi(t+△t)And then the difference is calculated between epochs to obtain a cycle slip checking quantity time sequence D (t);
Figure BDA0001324949510000021
in the formula, t is the time for obtaining a pseudo-range observation value and a carrier phase observation value, n is cycle slip with the size of n generated at epoch t + delta t, and lambda is the carrier wavelength of a certain frequency band of the Beidou;
step2, obtaining a cycle slip detection quantity time sequence D (t) from 0 to t, and setting the time sequence D (t) to include M extreme points XkCorresponding to the time of occurrence of tauk(k ═ 1,2, …, M), τ is extracted by the following formulakTo tauk+1Baseline signal over time period l (t):
Figure BDA0001324949510000022
Figure BDA0001324949510000023
in the formula, LK+1Is taukTo tauk+1A baseline extraction operator in a time period, α is a constant coefficient, and α is generally taken as 0.5;
step3 at τkTo tauk+1Defining rotation component extraction operator H in time periodt+1＝D(t)-Lt+1For reasonable rotation component (PR), operator L is extracted by using base lineK+1And rotation component extraction operator Ht+1Decomposing the time series D (t) into:
Figure BDA0001324949510000024
in the formula, HLkD (t) is the (k + 1) th rational rotation component, LpD (t) is a monotonous trend or a residual term, and the steps 2 and 3 are repeated until the decomposition is stopped when the baseline signal is a monotonous function or a constant function;
step4, artificially adding cycle slip in 200 epochs and 500 epochs of a cycle slip checking quantity time sequence D (t), and respectively carrying out intrinsic time scale decomposition on the time sequence with the cycle slip added and the time sequence without the cycle slip added, namely obtaining PR components by ITD self-adaptive decomposition;
step5, calculating the correlation coefficient of each PR component and the time series D (t) of the original cycle slip checking quantity by using a correlation coefficient method, wherein the correlation coefficients of the PR component and the time series D (t) of the original cycle slip checking quantity are shown as the following formulas:
Figure BDA0001324949510000031
wherein r is a correlation coefficient, x is a PR component, y is an original cycle slip checking quantity time series D (t), Cov (x, y) is a covariance between the PR component and the original cycle slip checking quantity time series D (t),
Figure BDA0001324949510000032
is the variance of the PR component and,
Figure BDA0001324949510000033
variance of the original cycle slip test volume time series D (t);
step6, respectively selecting the first 7 meaningful PR components in the ITD decomposed PR components added with 200 epoch cycle slip and 500 epoch cycle slip for carrying out fuzzy entropy analysis, as shown in the following formula:
FuzzyEn(m，n，r，N)＝lnφm(n,r)-lnφm+1(n,r) (6)
where the phase space dimension m is 2, the boundary width r is 0.2SD, SD is the standard deviation of the original data, and the number of time-series points N is 10m～30mThe similarity margin gradient n is 2;
and finally, determining whether the minute cycle slip occurs by comparing the fuzzy entropy calculated when the cycle slip does not occur with the fuzzy entropy calculated when the cycle slip occurs.
The principle of the invention is as follows: when no cycle slip occurs, the cycle slip detection quantity is represented as a random error characteristic on a time sequence; if cycle slip occurs, the random error characteristic is destroyed, and the time sequence has mutation, and the larger the cycle slip value is, the more obvious the mutation is. For the minute cycle slip of 1-5 weeks, the human eye is not easy to directly observe the mutation, the intrinsic time-scale decomposition (ITD) can adaptively decompose a complex signal into the sum of intrinsic scale components with physical significance of a plurality of instantaneous frequencies, mutation information in the intrinsic scale components is extracted, and then each component after ITD decomposition is subjected to fuzzy entropy analysis and comparison to convert the components into specific values, so that the cycle slip information is clearer, and the detection of the minute cycle slip is completed.
The invention has the beneficial effects that: the minor cycle slip detection method based on the ITD fuzzy entropy is suitable for a single-frequency receiver, can accurately detect whether minor cycle slip occurs in Beidou carrier phase signals, and improves the sensitivity of cycle slip detection.
Drawings
FIG. 1 is a flowchart of a method for detecting minute cycle slip based on ITD fuzzy entropy according to an embodiment of the present invention;
fig. 2 and fig. 3 are comparison diagrams before and after 200 epochs of the cycle slip checking quantity time sequence d (t) are added to the cycle slip, provided in the embodiment of the present invention;
fig. 4 and 5 are comparison diagrams before and after the addition of 500 epochs in the cycle slip checking quantity time sequence d (t) provided in the embodiment of the present invention;
FIG. 6 is a component diagram of the ITD decomposition of the cycle slip test quantity time series without cycle slip addition provided in the embodiment of the present invention;
FIG. 7 is a component diagram of an ITD decomposition of a cycle slip metric time series incorporating cycle slips at 200 epochs as provided in an embodiment of the present invention;
fig. 8 is a component diagram of ITD decomposition of a cycle slip metric time series incorporating cycle slips at 500 epochs as provided in an embodiment of the present invention.
Detailed Description
Example 1: as shown in fig. 1-8, a method for detecting a minute cycle slip based on ITD fuzzy entropy includes selecting original beidou carrier phase observation data, constructing a cycle slip checking quantity time sequence from the original beidou carrier phase observation data by using a pseudo-range phase method, performing ITD adaptive decomposition on the cycle slip checking quantity time sequence to obtain PR components with different frequencies, calculating correlation coefficients of each PR component and the original time sequence by using a correlation coefficient method, selecting the first 7 meaningful PR components, performing fuzzy entropy calculation on the PR components, and determining whether a minute cycle slip occurs according to a relative ratio of a fuzzy entropy calculated when a cycle slip does not occur and a fuzzy entropy calculated when a cycle slip occurs.
Further, the method for detecting the minute cycle slip based on the ITD fuzzy entropy comprises the following specific steps:
step1, selecting original Beidou carrier phase observation data, and utilizing a pseudo-range phase method to obtain a pseudo-range observation value R(t+△t)Subtracting the carrier phase observed value phi(t+△t)And then the difference is calculated between epochs to obtain a cycle slip checking quantity time sequence D (t);
Figure BDA0001324949510000041
in the formula, t is the time for obtaining a pseudo-range observation value and a carrier phase observation value, n is cycle slip with the size of n generated at epoch t + delta t, and lambda is the carrier wavelength of a certain frequency band of the Beidou;
step2, obtaining a cycle slip detection quantity time sequence D (t) from 0 to t, and setting the time sequence D (t) to include M extreme points XkCorresponding to the time of occurrence of tauk(k ═ 1,2, …, M), τ is extracted by the following formulakTo tauk+1Baseline signal over time period l (t):
Figure BDA0001324949510000051
Figure BDA0001324949510000052
in the formula, LK+1Is taukTo tauk+1A baseline extraction operator in a time period, α is a constant coefficient, and α is generally taken as 0.5;
step3 at τkTo tauk+1Defining rotation component extraction operator H in time periodt+1＝D(t)-Lt+1For rational rotation component (PR), operator is extracted using baselineLK+1And rotation component extraction operator Ht+1Decomposing the time series D (t) into:
Figure BDA0001324949510000053
in the formula, HLkD (t) is the (k + 1) th rational rotation component, LpD (t) is a monotonous trend or a residual term, and the steps 2 and 3 are repeated until the decomposition is stopped when the baseline signal is a monotonous function or a constant function;
step4, artificially adding cycle slip in 200 epochs and 500 epochs of a cycle slip checking quantity time sequence D (t), and respectively carrying out intrinsic time scale decomposition on the time sequence with the cycle slip added and the time sequence without the cycle slip added, namely obtaining PR components by ITD self-adaptive decomposition;
step5, calculating the correlation coefficient of each PR component and the time series D (t) of the original cycle slip checking quantity by using a correlation coefficient method, wherein the correlation coefficients of the PR component and the time series D (t) of the original cycle slip checking quantity are shown as the following formulas:
Figure BDA0001324949510000054
wherein r is a correlation coefficient, x is a PR component, y is an original cycle slip checking quantity time series D (t), Cov (x, y) is a covariance between the PR component and the original cycle slip checking quantity time series D (t),
Figure BDA0001324949510000055
is the variance of the PR component and,
Figure BDA0001324949510000056
variance of the original cycle slip test volume time series D (t);
step6, respectively selecting the first 7 meaningful PR components in the ITD decomposed PR components added with 200 epoch cycle slip and 500 epoch cycle slip for carrying out fuzzy entropy analysis, as shown in the following formula:
FuzzyEn(m，n，r，N)＝lnφm(n,r)-lnφm+1(n,r) (6)
wherein the phase space dimension m is 2, the boundary width r is 0.2SD,SD is the standard deviation of the original data, and the number of time-series points N is 10m～30mThe similarity margin gradient n is 2;
and finally, determining whether the minute cycle slip occurs by comparing the fuzzy entropy calculated when the cycle slip does not occur with the fuzzy entropy calculated when the cycle slip occurs.
The principle of the invention is as follows: when no cycle slip occurs, the cycle slip detection quantity is represented as a random error characteristic on a time sequence; if cycle slip occurs, the random error characteristic is destroyed, and the time sequence has mutation, and the larger the cycle slip value is, the more obvious the mutation is. For the minute cycle slip of 1-5 weeks, the human eye is not easy to directly observe the mutation, the intrinsic time-scale decomposition (ITD) can adaptively decompose a complex signal into the sum of intrinsic scale components with physical significance of a plurality of instantaneous frequencies, mutation information in the intrinsic scale components is extracted, and then each component after ITD decomposition is subjected to fuzzy entropy analysis and comparison to convert the components into specific values, so that the cycle slip information is clearer, and the detection of the minute cycle slip is completed.
Example 2: as shown in fig. 1 to 8, the embodiment of the method for detecting a minute cycle slip based on ITD fuzzy entropy is the same as that in embodiment 1, data actually measured by a two-satellite five-frequency GNSS receiver of a certain company is used in the experiment, according to the characteristics of the big dipper data, a group of single-frequency carrier phase data of the big dipper B3 frequency band (wavelength 0.236m) is taken as an example, the sampling frequency of the data is 1Hz, the acquisition time is 1h, and 800 epochs in the middle of the observed data are extracted. The comparison graphs before and after the cycle slip is artificially added into 200 epochs of the time series D (t) of the cycle slip test quantity are shown in figures 2 and 3. And respectively carrying out intrinsic time-scale decomposition (ITD) on the time sequence of the original data and the time sequence added with the cycle slip to obtain PR components as shown in figures 6 and 7, solving correlation coefficients through a correlation coefficient formula of the PR components obtained after the two are decomposed as shown in table 1, wherein along with the increase of the PR number, the correlation coefficient between the time sequence added with the cycle slip and the PR component of the original sequence after the ITD decomposition is smaller and smaller, and based on the result, the PR component with the higher correlation coefficient of the first 7 can be selected as a meaningful component for continuous analysis. Fuzzy entropy analysis is respectively carried out on the PR component diagrams shown in the figures 6 and 7 to obtain a fuzzy entropy value table of a table 2, and the fuzzy entropy value in the cycle with cycle is compared with the fuzzy entropy value in the cycle without cycle, so that the fuzzy entropy value in the cycle with cycle is larger than the fuzzy entropy value in the cycle without cycle, and the 200 epochs can be detected to have the micro cycle slip.
TABLE 1 correlation coefficient comparison table for 200 epoch in week jump
PR component PR1 PR2 PR3 PR4 PR5 PR6 PR7
Without cycle slip 0.9232 0.5161 0.1804 0.0476 0.0177 0.0164 0.0134
Having cycle slip 0.9130 0.5298 0.2085 0.0937 0.0439 0.0420 0.0060
TABLE 2 fuzzy entropy comparison table when adding cycle skip to 200 epoch
PR component PR1 PR2 PR3 PR4 PR5 PR6 PR7
Having cycle slip 0.4742 0.4272 0.3457 0.3034 0.2123 0.1032 0.0012
Without cycle slip 0.3738 0.3365 0.2753 0.2469 0.1719 0.0813 0.0011
Example 3: the embodiment is the same as embodiment 1, wherein the specific experiment adopts data actually measured by a two-satellite five-frequency GNSS receiver of a certain company, according to the characteristics of the Beidou data, a group of single-frequency carrier phase data of a Beidou B3 frequency band (with a wavelength of 0.236m) is taken as an example for explanation, the sampling frequency of the data is 1Hz, the acquisition time is 1h, and 800 epochs in the middle of the observed data are extracted. The comparison graphs before and after the artificial addition of cycle slip at 500 epochs in the cycle slip test quantity time series D (t) are shown in FIGS. 4 and 5. And respectively carrying out intrinsic-time-scale decomposition (ITD) on the time sequence of the original data and the time sequence added with the cycle slip to obtain PR components as shown in figures 6 and 8, solving correlation coefficients through a correlation coefficient formula of the PR components obtained after the two are decomposed as shown in table 3, wherein along with the increase of the PR number, the correlation coefficient between the time sequence added with the cycle slip after ITD decomposition and the PR component of the original sequence after ITD decomposition is smaller and smaller, and based on the result, the PR component with the higher correlation number of the first 7 can be selected as a meaningful component for continuous analysis. Fuzzy entropy analysis is respectively carried out on the PR component diagrams shown in the figures 6 and 8 to obtain a fuzzy entropy value table shown in the table 4, and the fuzzy entropy value in the cycle with cycle is compared with the fuzzy entropy value in the cycle without cycle, so that the fuzzy entropy value in the cycle with cycle is larger than the fuzzy entropy value in the cycle without cycle, and the minute cycle with 500 epochs can be detected.
TABLE 3 correlation coefficient comparison table for 500 epoch adding cycle skip
PR component PR1 PR2 PR3 PR4 PR5 PR6 PR7
Without cycle slip 0.9232 0.5161 0.1804 0.0476 0.0177 0.0164 0.0134
Having cycle slip 0.9104 0.5176 0.1871 0.0765 0.0547 0.0451 0.0239
TABLE 4 fuzzy entropy comparison table when adding cycle skip to 500 epoch
PR component PR1 PR2 PR3 PR4 PR5 PR6 PR7
Having cycle slip 0.4944 0.4067 0.3257 0.2615 0.1922 0.1013 0.0011
Without cycle slip 0.3738 0.3365 0.2753 0.2469 0.1719 0.0843 0.0011
The fuzzy entropy values obtained by analyzing the first 7 PR components of the time sequence of the cycle slip checking quantity after ITD decomposition by adopting the fuzzy entropy method are shown in tables 2 and 4, the fuzzy entropy values under the two conditions of no cycle slip and cycle slip are the maximum fuzzy entropy of the first component PR1, and the fuzzy entropy values are gradually decreased from PR1, PR2, … and PR 7. In summary, it can be seen that the fuzzy entropy value when the cycle slip occurs is larger than the fuzzy entropy value when the cycle slip does not occur. And judging whether the micro cycle slip occurs or not according to the fuzzy entropy comparison.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (2)

1. A tiny cycle slip detection method based on ITD fuzzy entropy is characterized in that: firstly, selecting original Beidou carrier phase observation data, constructing a cycle slip checking quantity time sequence on the original Beidou carrier phase observation data by utilizing a pseudo-range phase method, carrying out ITD (inverse transformation of direct) adaptive decomposition on the cycle slip checking quantity time sequence to obtain PR (time-resolved) components with different frequencies, calculating correlation coefficients of each PR component and the original time sequence by using a correlation coefficient method, further selecting the first 7 meaningful PR components, carrying out fuzzy entropy calculation on the PR components, and finally determining whether micro cycle slip occurs or not according to the relative ratio of a fuzzy entropy value calculated when the cycle slip does not occur and a fuzzy entropy value calculated when the cycle slip occurs.
2. The ITD fuzzy entropy-based minute cycle slip detection method according to claim 1, characterized in that: the method for detecting the small cycle slip based on the ITD fuzzy entropy comprises the following specific steps:
step1, selecting original Beidou carrier phase observation data, and utilizing a pseudo-range phase method to obtain a pseudo-range observation value R(t+△t)Subtracting the carrier phase observed value phi(t+△t)And then the difference is calculated between epochs to obtain a cycle slip checking quantity time sequence D (t);
Figure FDA0002483360340000011
in the formula, t is the time for obtaining a pseudo-range observation value and a carrier phase observation value, n is cycle slip with the size of n generated at epoch t + delta t, and lambda is the carrier wavelength of a certain frequency band of the Beidou;
step2, obtaining a cycle slip detection quantity time sequence D (t) from 0 to t, and setting the time sequence D (t) to include M extreme points XkCorresponding to the time of occurrence of tauk(k ═ 1,2, …, M), τ is extracted by the following formulakTo tauk+1Baseline signal L over a period of timet：
Figure FDA0002483360340000012
Figure FDA0002483360340000013
In the formula, Lk+1Is taukTo tauk+1A baseline extraction operator in a time period, wherein α is a constant coefficient, and α is taken as 0.5;
step3 at τkTo tauk+1Defining rotation component extraction operator H in time periodt+1＝D(t)-Lt+1For reasonable rotation component (PR), operator L is extracted by using base linek+1And rotation component extraction operator Ht+1Decomposing the time series D (t) into:
Figure FDA0002483360340000014
in the formula, HLkD(t)Is the (k + 1) th rational rotation component, LpD (t) is a monotonous trend or a residual term, and the steps 2 and 3 are repeated until the decomposition is stopped when the baseline signal is a monotonous function or a constant function;
step4, artificially adding cycle slip in 200 epochs and 500 epochs of a cycle slip checking quantity time sequence D (t), and respectively carrying out intrinsic time scale decomposition on the time sequence with the cycle slip added and the time sequence without the cycle slip added, namely obtaining PR components by ITD self-adaptive decomposition;
step5, calculating the correlation coefficient of each PR component and the time series D (t) of the original cycle slip checking quantity by using a correlation coefficient method, wherein the correlation coefficients of the PR component and the time series D (t) of the original cycle slip checking quantity are shown as the following formulas:
Figure FDA0002483360340000021
wherein R is a correlation coefficient, x is a PR component, y is an original cycle slip checking quantity time sequence D (t), Cov (x, y) is a covariance between the PR component and the original cycle slip checking quantity time sequence D (t),
Figure FDA0002483360340000022
is the variance of the PR component and,
Figure FDA0002483360340000023
variance of the original cycle slip test volume time series D (t);
step6, respectively selecting the first 7 meaningful PR components in the ITD decomposed PR components added with 200 epoch cycle slip and 500 epoch cycle slip for carrying out fuzzy entropy analysis, as shown in the following formula:
FuzzyEn(m，n，r，N)＝lnφm(n,r)-lnφm+1(n,r) (6)
where the phase space dimension m is 2, the boundary width r is 0.2SD, SD is the standard deviation of the original data, and the number of time-series points N is 10m～30mThe similarity margin gradient n is 2;
and finally, determining whether the minute cycle slip occurs by comparing the fuzzy entropy calculated when the cycle slip does not occur with the fuzzy entropy calculated when the cycle slip occurs.
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