CN110851773A - GNSS real-time clock error evaluation algorithm - Google Patents

GNSS real-time clock error evaluation algorithm Download PDF

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CN110851773A
CN110851773A CN201911038327.7A CN201911038327A CN110851773A CN 110851773 A CN110851773 A CN 110851773A CN 201911038327 A CN201911038327 A CN 201911038327A CN 110851773 A CN110851773 A CN 110851773A
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陈国�
赵齐乐
陈卓敏
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Zhonghai Beidou Shenzhen Navigation Technology Co Ltd
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Abstract

The invention relates to an evaluation algorithm of GNSS real-time clock error, supposing that the GNSS real-time orbit and clock error and reference orbit and clock error products can be obtained, and the resolved GNSS real-time clock error and reference products contain common satellite clock error data, calculating a clock error consistency correction item by using the real-time orbit and reference orbit products, detecting and marking abnormal data of the GNSS real-time clock error by using a median gross error detection method, realizing jump detection and segment marking on a single difference sequence of the GNSS clock error by using a total variation regularization method, and calculating jump size; by adopting a median gross error detection method, abnormal data in the real-time clock error can be quickly and effectively identified and removed, and the damage of the abnormal data to the real-time clock error evaluation result is prevented; aiming at the problem of frequent jump of clock difference caused by specific real-time clock difference data strategies (such as data interruption, switching of a reference clock and the like), the jump detection of the real-time clock difference is creatively realized by using a total variation regularization method.

Description

GNSS real-time clock error evaluation algorithm
Technical Field
The invention relates to an evaluation algorithm of GNSS real-time clock error, in particular to an evaluation algorithm under the conditions that the real-time orbit and the clock error have strong coupling and the real-time clock error has frequent jumping.
Background
In the non-difference positioning mode, the orbit and the clock difference of the satellite are often substituted into an observation model as known quantities for modeling, so that high-precision orbit and clock difference products are preconditions for obtaining a high-precision positioning result. Different from a GNSS satellite orbit, the GNSS satellite atomic clock can be well constrained through a kinetic equation, and not only do the GNSS satellite atomic clock have the phenomena of frequency deviation, frequency drift and the like in the operation, but also are influenced by random errors formed by various noises; in order to promote the application in real time, the IGS has provided an ultra-fast orbit and a predicted clock error, the orbit prediction accuracy of which is better than 5 cm, but the predicted clock error accuracy is 3 ns, which is far from meeting the application requirement of real-time precise positioning, so the real-time determination of the GNSS precise satellite clock error is a research focus in recent years, the GNSS observation quantity is the relative time delay between satellites, all satellite and receiver clock error parameters cannot be determined simultaneously in the GNSS data processing, in order to prevent the singular problem of the law equation, a certain stable reference clock is generally selected as a reference, the correction number of other clocks relative to the reference clock is calculated, or a zero-mean constraint condition is added to the specified satellite/receiver clock error parameter, and the calculated clock error parameter is the correction number relative to the gravity center reference clock.
With the rise of multi-navigation satellite systems, multi-GNSS satellite clock error products provided by different mechanisms are still influenced by unmodeled antenna phase center correction, sunlight compression molding, inter-frequency deviation and the like, and even the clock error products of different mechanisms can be different due to sub-system step processing and multi-system combined processing.
The satellite real-time orbit and clock error are the most important reference information for real-time precision positioning of a user, and the prediction reliability of the real-time positioning precision is directly influenced by the precision evaluation of the real-time orbit and clock error; however, the current real-time clock error assessment algorithm has two problems: firstly, the existing algorithms for evaluating the clock error are evaluated based on a post-double-error mode, the double-error method eliminates the reference difference between different clock error products, but ignores the problem of frequent jumping of the real-time clock error, and leads to the fact that the corresponding evaluation result is too pessimistic; secondly, the existing clock error assessment algorithm is carried out independently, and strong coupling between the satellite orbit and the clock error is not considered, so that the clock error assessment result simultaneously contains errors of the satellite orbit and the clock error assessment, and the clock error performance is not objectively reflected, therefore, the problem of frequent jump of the real-time clock error is solved in the real-time clock error assessment, the real-time orbit and the clock error are decoupled, an objective and reliable real-time clock error precision assessment result is obtained, and the method has important reference significance for further improving the real-time clock error performance.
Disclosure of Invention
The invention is mainly provided aiming at the evaluation of GNSS real-time clock error, provides a detection method of real-time clock error jump, and simultaneously provides a method for separating orbit errors during the evaluation of the real-time clock error.
The technical problem of the invention is mainly solved by the following technical scheme: on the basis of comprehensively analyzing the error characteristics of the real-time clock error, aiming at the problems of abnormal numerical values, frequent jump and strong correlation with the track of the GNSS real-time clock error, the invention creatively provides a real-time clock error evaluation algorithm combining a median detection method of abnormal data, a clock error jump detection method based on total variation regularization TV-L1 and a track error deduction method in a real-time clock error product, and the GNSS real-time clock error evaluation result obtained by using the algorithm is more reliable compared with the traditional evaluation method.
GNSS real-time clock error estimation algorithm: supposing that GNSS real-time orbit and clock error and reference orbit and clock error products can be obtained, the resolved GNSS real-time clock error and reference product contain common satellite clock error data, calculating clock error consistency correction items by using the real-time orbit and reference orbit products, realizing abnormal data detection and marking of the GNSS real-time clock error by using a median gross error detection method, realizing jump detection and segment marking of a single-difference sequence of the GNSS clock error by using a total variation regularization method, and calculating jump size; the whole calculation steps are as follows:
step 1, selecting a real-time clock error product satellite system to be evaluated and a reference satellite forming double errors; calculating a consistency correction item of the real-time clock error by using the real-time orbit and the reference orbit product, correcting the consistency correction item to the satellite real-time clock error product, and finally obtaining each satellite real-time clock error sequence after consistency correction as the input of the next step;
step 2, forming a single difference sequence by using the real-time clock difference and the reference clock difference, performing de-linearization on the single difference sequence of the clock difference by using a minimum 1 norm condition solution, realizing abnormal value detection on the single difference residual sequence by using a median gross error detection method, and removing abnormal values in the sequence;
step 3, according to the single difference sequence of the clock difference, utilizing a total variation regularization method to carry out jump detection on the single difference sequence of each satellite, calculating the jump size among the sectional clock differences, and repairing;
and 4, calculating a double-difference sequence of the real-time clock difference according to the selected reference star, and counting the mean value and the standard deviation of each satellite clock difference double-difference sequence in the whole time period.
In the above-mentioned GNSS real-time clock error evaluation algorithm, it is assumed that the GNSS real-time orbit and clock error and the reference orbit and clock error products can be obtained, and the resolved GNSS real-time clock error and the reference product contain common satellite clock error data, so that the evaluation of the real-time clock error can be realized only in this way. In practice, this condition is very easy to satisfy, because there are many international organizations that provide GNSS precision orbit and clock error, and reference products can be obtained through various channels.
In fact, at present, a plurality of mechanisms provide GNSS precision product services at home and abroad, and the GNSS precision product services are very easy to obtain through a plurality of modes or a precision orbit clock difference product after the GNSS precision product is resolved by the mechanism.
The algorithm is described in detail below according to the algorithm steps: in step 1, assume that the real-time clock offset of a satellite isat solved by the agency ac is
Figure 513566DEST_PATH_IMAGE001
The total number of epochs is
Figure 774652DEST_PATH_IMAGE002
In chronological order:
Figure 473618DEST_PATH_IMAGE003
corresponding reference products are noted
Figure 393032DEST_PATH_IMAGE004
In general, clock difference is corrected by number
Figure 858956DEST_PATH_IMAGE001
Can be expressed as:
Figure 917041DEST_PATH_IMAGE005
。
wherein the content of the first and second substances,
Figure 24675DEST_PATH_IMAGE006
the reference clock adopted by the analysis center in the data processing is shown, and all satellite clock differences are relative to the reference clock;
Figure 731468DEST_PATH_IMAGE007
represents systematic deviations (including linear and non-linear components) associated with the analysis center and the satellite clock, such as deviations introduced by other relevant parameters and deviations due to inaccuracies of the error correction model;
Figure 76999DEST_PATH_IMAGE008
a certain portion of the clock's own characteristics, which can be generally represented by an initial time offset, a frequency offset and a frequency drift;
Figure 40407DEST_PATH_IMAGE009
representing random parts in the characteristics of the clock itself and other observed noise.
Calculating the projection of the satellite orbit difference in the direction of the geocentric sagittal diameter by using the reference orbit and the real-time orbit products, and taking the projection as a correction term of clock error consistency of each satellite, wherein a specific correction equation is as follows;
。
wherein the content of the first and second substances,
Figure 617592DEST_PATH_IMAGE011
and coordinate components of the real-time orbit and the precision reference orbit are respectively represented.
In step 2, reading real-time clock correction and reference clock correction products, calculating clock correction single-difference sequences of each satellite, calculating linear fitting coefficients of the single-difference sequences by adopting an L1 norm minimum constraint condition, and finally obtaining residual errors after linear fitting; identifying gross errors in the residual error sequence by adopting a median detection method, judging whether clock error numerical values of all epochs are outlier or not, if not, considering that the modified data are not abnormal, if so, marking as the gross errors and removing, and setting a real-time clock error single error sequence after consistency correction as a sequence
Figure 896258DEST_PATH_IMAGE012
The specific median detection method is as follows:
。
wherein the content of the first and second substances,
Figure 627640DEST_PATH_IMAGE015
as a function of the median of the data sequence,when is coming into contact withMedian when normally distributed
Figure 100002_DEST_PATH_IMAGE021
Equal to its standard deviation; determining data according toIs gross error:
Figure 100002_DEST_PATH_IMAGE025
。
wherein the integer is
Figure 100002_DEST_PATH_IMAGE027
Selecting according to the requirementWhen the data are normally distributed, it is equivalent to eliminate gross errors contained in the clock error data at a level of 99% confidence.
In step 3, forming single difference by using real-time satellite clock difference data after the gross error is removed
Figure 100002_DEST_PATH_IMAGE031
And establishing a total variation regularization model for the single difference sequence, wherein a specific model criterion can be expressed as:
Figure 100002_DEST_PATH_IMAGE033
。
wherein the content of the first and second substances,
Figure 100002_DEST_PATH_IMAGE035
the rate term representing the sequence of single differences,
Figure 100002_DEST_PATH_IMAGE037
an intercept term representing a sequence of single differences,
Figure 100002_DEST_PATH_IMAGE039
and
Figure 100002_DEST_PATH_IMAGE041
respectively, norm 1 and norm 2,
Figure 100002_DEST_PATH_IMAGE043
and
Figure DEST_PATH_IMAGE045
the regularization coefficients, which represent the rate term and intercept term, respectively, may take the default values 1200 and 80,
Figure DEST_PATH_IMAGE047
represents the i step differenceThe partial matrices, such as first and second order difference matrices, can be expressed as:
Figure DEST_PATH_IMAGE049
。
f checking the detected jump, repairing by using the jump passed by the check, connecting the clock error data of the next section to the data of the previous section, and specifically, the jump size of the previous section and the jump size of the next section
Figure DEST_PATH_IMAGE051
The calculation formula of (a) is as follows:
Figure DEST_PATH_IMAGE053
。
in step 4, repeating steps 2 and 3 until the gross error rejection and the jump size calculation of all satellites are completed, repairing the jump of all time periods, forming a double-error form for the real-time clock error data by using the clock error data of a reference satellite clock (default is a virtual central clock of all satellite clock errors), and calculating the standard deviation and the average value of a double-error sequence, namely the precision evaluation result of the real-time clock error.
Therefore, the invention has the following advantages: 1. the real-time orbit and clock error orbit products are adopted, the correlation between the real-time orbit and the clock error orbit products is fully utilized, and the orbit error part contained in the traditional clock error evaluation result can be deducted; 2. by adopting a median gross error detection method, abnormal data in the real-time clock error can be quickly and effectively identified and removed, and the damage of the abnormal data to the real-time clock error evaluation result is prevented; 3. aiming at the problem of frequent jump of clock difference caused by specific real-time clock difference data strategies (such as data interruption, switching of a reference clock and the like), the jump detection of the real-time clock difference is creatively realized by using a total variation regularization method.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a data processing flow of the present invention.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example 1: the GNSS real-time clock error evaluation algorithm comprises the following steps: in practice, GNSS precision products provided by the existing domestic and foreign institutions can be obtained in various ways, even after-event precision orbit clock error products which are internally resolved can be adopted; the algorithm is described in detail below according to the algorithm steps:
step 1, assuming that the real-time clock offset of a certain satellite isat calculated by an organization ac is
Figure 554484DEST_PATH_IMAGE001
The total number of epochs is
Figure DEST_PATH_IMAGE055
In chronological order:
Figure DEST_PATH_IMAGE057
corresponding reference products are notedIn general, clock difference is corrected by numberCan be expressed as:
Figure 775960DEST_PATH_IMAGE005
。
wherein the content of the first and second substances,
Figure 560376DEST_PATH_IMAGE006
the reference clock adopted by the analysis center in the data processing is shown, and all satellite clock differences are relative to the reference clock;
Figure 692280DEST_PATH_IMAGE007
represents systematic deviations (including linear and non-linear components) associated with the analysis center and the satellite clock, such as deviations introduced by other relevant parameters and deviations due to inaccuracies of the error correction model;
Figure 795103DEST_PATH_IMAGE008
a certain portion of the clock's own characteristics, which can be generally represented by an initial time offset, a frequency offset and a frequency drift;
Figure 421388DEST_PATH_IMAGE009
representing random parts in the characteristics of the clock itself and other observed noise.
Calculating the projection of the satellite orbit difference in the direction of the geocentric sagittal diameter by using the reference orbit and the real-time orbit products, and taking the projection as a correction term of clock error consistency of each satellite, wherein a specific correction equation is as follows;
Figure 981682DEST_PATH_IMAGE010
。
wherein the content of the first and second substances,
Figure 395739DEST_PATH_IMAGE011
and coordinate components of the real-time orbit and the precision reference orbit are respectively represented.
Step 2, calculating a clock error single difference sequence of each satellite according to the real-time clock error and a reference clock error product, calculating a linear item of the single difference sequence by utilizing the lowest L1 norm to finally obtain a residual error after linear fitting, identifying gross errors in the residual error sequence by adopting a median detection method, judging whether the clock error numerical values of each epoch are outliers, if so, marking the clock error numerical values as the gross errors and eliminating the gross errors, and setting the real-time clock error single difference sequence after consistency correction as the real-time clock error single difference sequence after consistency correction
Figure DEST_PATH_IMAGE060
The specific median detection method is as follows:
Figure DEST_PATH_IMAGE062
。
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE064
as a function of the median of the data sequence,
Figure DEST_PATH_IMAGE066
when is coming into contact with
Figure DEST_PATH_IMAGE068
Median when normally distributedEqual to its standard deviation, data is determined according to
Figure DEST_PATH_IMAGE072
Is gross error:
Figure DEST_PATH_IMAGE074
。
wherein the integer is
Figure DEST_PATH_IMAGE076
Selecting according to the requirement
Figure DEST_PATH_IMAGE078
When the data are normally distributed, it is equivalent to eliminate gross errors contained in the clock error data at a level of 99% confidence.
Step 3, forming single difference by using the real-time satellite clock difference data after the gross error is removedAnd establishing a total variation regularization model for the single difference sequence, wherein a specific model criterion can be expressed as:
Figure DEST_PATH_IMAGE082
。
wherein the content of the first and second substances,represents a single differenceThe rate term of the sequence is given by,
Figure DEST_PATH_IMAGE086
an intercept term representing a sequence of single differences,
Figure DEST_PATH_IMAGE088
andrespectively, norm 1 and norm 2,
Figure DEST_PATH_IMAGE092
and
Figure DEST_PATH_IMAGE094
the regularization coefficients, which represent the rate term and intercept term, respectively, may take the default values 1200 and 80,
Figure DEST_PATH_IMAGE096
an i-order difference matrix is represented, such as a first-order and a second-order difference matrix can be represented as:
Figure DEST_PATH_IMAGE098
。
f checking the detected jump, repairing by using the jump passed by the check, connecting the clock error data of the next section to the data of the previous section, and specifically, the jump size of the previous section and the jump size of the next section
Figure DEST_PATH_IMAGE100
The calculation formula of (a) is as follows:
Figure DEST_PATH_IMAGE102
。
and 4, repeating the step 2 and the step 3 until the gross error rejection and the jump size calculation of all satellites are completed, repairing the jump of all time periods, forming a double-error form for the real clock error data by using the clock error data of a reference satellite clock (which is a virtual central clock of all satellite clock errors as a default), and calculating the standard error and the average value of a double-error sequence, namely the precision evaluation result of the real clock error.
Embodiment 2, on the basis of embodiment 1, it is assumed that the GNSS real-time orbit and clock error and the reference orbit and clock error product can be acquired, and the resolved GNSS real-time clock error and the reference product contain common satellite clock error data, and only then the real-time clock error product can be effectively evaluated, and in practice, this condition is very easy to be satisfied, and in practice, the GNSS precision product provided by the existing domestic and foreign institutions or the precision orbit clock error product after the solution by the present institution is acquired in various ways.
The algorithm is described in detail below according to the algorithm steps:
in step 1, assume that the real-time clock offset of a satellite isat solved by the agency ac is
Figure 278202DEST_PATH_IMAGE001
The total number of epochs isIn chronological order:corresponding reference products are noted
Figure 409975DEST_PATH_IMAGE058
In general, clock difference is corrected by number
Figure 90355DEST_PATH_IMAGE001
Can be expressed as:
Figure DEST_PATH_IMAGE107
。
wherein the content of the first and second substances,
Figure 234502DEST_PATH_IMAGE006
the reference clock adopted by the analysis center in the data processing is shown, and all satellite clock differences are relative to the reference clock;represents systematic deviations (including linear and non-linear components) associated with the analysis center and the satellite clock, such as deviations introduced by other relevant parameters and deviations due to inaccuracies of the error correction model;a certain portion of the clock's own characteristics, which can be generally represented by an initial time offset, a frequency offset and a frequency drift;
Figure 549312DEST_PATH_IMAGE009
representing random parts in the characteristics of the clock itself and other observed noise.
In the step 2, the projection of the satellite orbit difference in the direction of the geocentric sagittal diameter is calculated by using the reference orbit and the real-time orbit products, and the projection is used as a correction term for the clock error consistency of each satellite, wherein a specific correction equation is as follows;
Figure 193920DEST_PATH_IMAGE010
。
wherein the content of the first and second substances,
Figure 197779DEST_PATH_IMAGE011
and coordinate components of the real-time orbit and the precision reference orbit are respectively represented.
In step 3, calculating a clock error single difference sequence of each satellite according to the real-time clock error and a reference clock error product, calculating a linear term of the single difference sequence by using the L1 norm to obtain a residual error after linear fitting; identifying gross errors in the residual error sequence by adopting a median detection method, judging whether the clock error numerical values of all epochs are outlier or not, marking the gross errors and removing the gross errors if the clock error numerical values of all epochs are outlier, and setting a real-time clock error single error sequence after consistency correction as a sequence
Figure DEST_PATH_IMAGE109
The specific median detection method is as follows:
Figure DEST_PATH_IMAGE111
。
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE113
as a function of the median of the data sequence,
Figure DEST_PATH_IMAGE115
when is coming into contact with
Figure DEST_PATH_IMAGE117
Median when normally distributed
Figure DEST_PATH_IMAGE119
Equal to its standard deviation, data is determined according to
Figure DEST_PATH_IMAGE121
Is gross error:
Figure DEST_PATH_IMAGE123
。
wherein the integer is
Figure DEST_PATH_IMAGE125
Selecting according to the requirement
Figure DEST_PATH_IMAGE127
When the data are normally distributed, it is equivalent to eliminate gross errors contained in the clock error data at a level of 99% confidence.
In step 4, forming single difference by using real-time satellite clock difference data after the gross error is removed
Figure DEST_PATH_IMAGE129
And establishing a total variation regularization model for the single difference sequence, wherein a specific model criterion can be expressed as:
Figure DEST_PATH_IMAGE131
。
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE133
the rate term representing the sequence of single differences,
Figure DEST_PATH_IMAGE135
an intercept term representing a sequence of single differences,
Figure DEST_PATH_IMAGE137
and
Figure DEST_PATH_IMAGE139
respectively, norm 1 and norm 2,
Figure DEST_PATH_IMAGE141
and
Figure DEST_PATH_IMAGE143
the regularization coefficients, which represent the rate term and intercept term, respectively, may take the default values 1200 and 80,
Figure DEST_PATH_IMAGE145
an i-order difference matrix is represented, such as a first-order and a second-order difference matrix can be represented as:
Figure DEST_PATH_IMAGE147
。
f checking the detected jump, repairing by using the jump passed by the check, connecting the clock error data of the next section to the data of the previous section, and specifically, the jump size of the previous section and the jump size of the next section
Figure DEST_PATH_IMAGE149
The calculation formula of (a) is as follows:
Figure DEST_PATH_IMAGE151
。
and 5, repeating all satellites until coarse difference elimination and jump size calculation of all satellites are completed, repairing jump of all time periods, forming a double difference form for real-time clock difference data by using clock difference data of a reference satellite clock (default is a virtual central clock of all satellite clock differences), and calculating a standard difference and an average value of a double difference sequence, namely a precision evaluation result of real-time clock differences.

Claims (2)

  1. The GNSS real-time clock error evaluation algorithm is characterized by comprising the following steps: GNSS real-time clock error products are comprehensively influenced by the performance of a satellite clock and a resolving strategy, and often show nonlinear characteristics; aiming at strong coupling of the orbit and the clock error, calculating a clock error consistency correction item by utilizing a real-time orbit product and a reference orbit product, detecting and marking abnormal data of the GNSS real-time clock error by utilizing a median gross error detection method, and aiming at the problem of frequently-occurring jump of the real-time clock error, realizing jump detection and segment marking of a single difference sequence of the GNSS clock error by utilizing a total variation regularization method, and calculating the jump size; the whole calculation steps are as follows:
    step 1, selecting a real-time clock error product satellite system to be evaluated and a reference satellite forming double errors; calculating a consistency correction item of the real-time clock error by using the real-time orbit and the reference orbit product, correcting the consistency correction item to the satellite real-time clock error product, and finally obtaining each satellite real-time clock error sequence after consistency correction as the input of the next step;
    step 2, forming a single difference sequence by using the real-time clock difference and the reference clock difference, resolving a linear fitting coefficient of the single difference sequence by using a minimum 1 norm condition, calculating a residual error of the single difference sequence after linearization, realizing abnormal value detection of the residual error sequence by using a median gross error detection method, and removing abnormal values in the sequence;
    step 3, according to the single difference sequence, utilizing a total variation regularization method to carry out jump detection on the single difference sequence of each satellite, calculating jump size among each segment clock difference, and repairing;
    and 4, calculating a double-difference sequence of the real-time clock difference according to the selected reference star, and counting the mean value and the standard deviation of each satellite clock difference double-difference sequence in the whole time period.
  2. 2. The GNSS real-time clock error evaluation algorithm of claim 1, wherein: in fact, at home and abroad, a plurality of mechanisms provide GNSS precision product services, and the GNSS precision product services are very easy to obtain through a plurality of modes or adopt the precision orbit clock difference products after the GNSS precision product services are resolved by the mechanism; the algorithm is described in detail below according to the algorithm steps:
    in step 1, assume that the real-time clock offset of a satellite isat solved by the agency ac is
    Figure 879034DEST_PATH_IMAGE001
    The total number of epochs is
    Figure 594049DEST_PATH_IMAGE002
    In chronological order:
    Figure 822905DEST_PATH_IMAGE003
    corresponding reference products are noted
    Figure 85739DEST_PATH_IMAGE004
    In general, clock difference is corrected by number
    Figure 945111DEST_PATH_IMAGE001
    Can be expressed as:
    Figure 881843DEST_PATH_IMAGE005
    ；
    wherein the content of the first and second substances,
    Figure 353538DEST_PATH_IMAGE006
    the reference clock adopted by the analysis center in the data processing is shown, and all satellite clock differences are relative to the reference clock;
    Figure DEST_PATH_IMAGE007
    represents systematic deviations (including linear and non-linear components) associated with the analysis center and the satellite clock, such as deviations introduced by other relevant parameters and deviations due to inaccuracies of the error correction model;
    Figure 551170DEST_PATH_IMAGE008
    a certain portion of the clock's own characteristics, which can be generally represented by an initial time offset, a frequency offset and a frequency drift;
    Figure 614066DEST_PATH_IMAGE009
    representing random parts in the characteristics of the clock itself and other observed noise; calculating the projection of the satellite orbit difference in the direction of the geocentric sagittal diameter by using the reference orbit and the real-time orbit products, and taking the projection as a correction term of clock error consistency of each satellite, wherein a specific correction equation is as follows;
    wherein the content of the first and second substances,
    Figure 812015DEST_PATH_IMAGE011
    respectively representing the coordinate components of the real-time orbit and the precision reference orbit;
    in step 2, reading real-time clock correction and reference clock correction products, calculating clock correction single-difference sequences of each satellite, calculating linear fitting coefficients of the single-difference sequences by adopting an L1 norm minimum constraint condition, and finally obtaining residual errors after linear fitting; identifying gross errors in the residual error sequence by adopting a median detection method, judging whether clock error numerical values of all epochs are outlier or not, if not, considering that the modified data are not abnormal, if so, marking as the gross errors and removing, and setting a real-time clock error single error sequence after consistency correction as a sequence
    Figure 772143DEST_PATH_IMAGE012
    The specific median detection method is as follows:
    Figure 973317DEST_PATH_IMAGE013
    ；
    wherein the content of the first and second substances,
    Figure 619062DEST_PATH_IMAGE014
    for taking the median position of the data sequenceAs a function of the number of the bits,
    Figure DEST_PATH_IMAGE015
    when is coming into contact with
    Figure 760456DEST_PATH_IMAGE016
    Median when normally distributed
    Figure DEST_PATH_IMAGE017
    Equal to its standard deviation; determining data according toIs gross error:
    Figure DEST_PATH_IMAGE019
    ；
    wherein the integer is
    Figure 71799DEST_PATH_IMAGE020
    Selecting according to the requirementWhen the data obeys normal distribution, the gross error contained in the clock error data is removed at the level of 99% of confidence;
    in step 3, forming single difference by using real-time satellite clock difference data after the gross error is removed
    Figure 267157DEST_PATH_IMAGE022
    And establishing a total variation regularization model for the single difference sequence, wherein a specific model criterion can be expressed as:
    Figure DEST_PATH_IMAGE023
    wherein the content of the first and second substances,
    Figure DEST_PATH_IMAGE025
    representing a sequence of single differencesThe rate term of (a) is,
    Figure DEST_PATH_IMAGE027
    an intercept term representing a sequence of single differences,
    Figure DEST_PATH_IMAGE029
    andrespectively, norm 1 and norm 2,
    Figure DEST_PATH_IMAGE033
    and
    Figure DEST_PATH_IMAGE035
    the regularization coefficients, which represent the rate term and intercept term, respectively, may take the default values 1200 and 80,an i-order difference matrix is represented, such as a first-order and a second-order difference matrix can be represented as:
    Figure DEST_PATH_IMAGE039
    f checking the detected jump, repairing by using the jump passed by the check, connecting the clock error data of the next section to the data of the previous section, and specifically, the jump size of the previous section and the jump size of the next section
    Figure DEST_PATH_IMAGE041
    The calculation formula of (a) is as follows:
    in step 4, repeating steps 2 and 3 until the gross error rejection and the jump size calculation of all satellites are completed, repairing the jump of all time periods, forming a double-error form for the real-time clock error data by using the clock error data of a reference satellite clock (default is a virtual central clock of all satellite clock errors), and calculating the standard deviation and the average value of a double-error sequence, namely the precision evaluation result of the real-time clock error.
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