CN114814907A - Beidou double-frequency cycle slip detection and restoration method based on arc segment division - Google Patents
Beidou double-frequency cycle slip detection and restoration method based on arc segment division Download PDFInfo
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Abstract
The invention relates to a Beidou double-frequency cycle slip detection and restoration method based on arc segment division, which comprises the following steps: obtaining a carrier phase and a pseudo range of Beidou double-frequency, and resolving MW combined observation values and GF combined observation values of each satellite according to an epoch period; and carrying out arc segment division on the observation arc segment, carrying out cycle slip detection and repairing. The invention verifies the feasibility and effect of the method by using experiments, can provide reliable Beidou dual-frequency observation data for Beidou precise data processing, and can lay a foundation for cycle slip detection and repair of subsequent Beidou dual-frequency observation values and precise single-point positioning model research and provide a theoretical basis. The cycle slip detection method effectively improves cycle slip detection efficiency by dividing the observation arc section, divides the whole observation arc section by taking the RMS value as a target, reduces the epoch number of cycle slip detection, and has certain superiority.
Description
Technical Field
The invention relates to the technical field of satellite positioning, in particular to a Beidou double-frequency cycle slip detection and restoration method based on arc segment division.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
With the development of a Global Navigation Satellite System (GNSS) and the successful overall networking of a BDS-3 constellation, users have higher and higher requirements for high-precision and high-real-time positioning, in precision positioning, carrier phase positioning is higher relative to pseudo-range positioning (meter level) because the precision (centimeter level) of the carrier phase positioning is higher, and because the problems of building shielding, ionosphere change and receiver hardware delay in actual positioning cause the cycle counter of a receiver to jump, thereby causing cycle jump and seriously affecting the positioning precision.
Currently, the commonly used cycle slip processing methods include a high-order difference method, a doppler integration method, a MW combination method (Melbourne-wubiena combination), a geometric-Free GF combination method, and a TurboEdit method. The high-order difference method is a relatively simple cycle slip detection method, wherein the high-order difference is obtained when more than three-order difference is obtained between epochs, the clock slip, satellite clock slip, ionosphere and troposphere errors and the like of a receiver can be weakened by obtaining the high-order difference, however, the cycle slip and the accumulation of residual errors are caused along with the increase of the difference order, the method can detect the larger cycle slip, but the cycle slip smaller than 5 cycles is difficult to detect; the detection cycle slip precision of the Doppler integration method depends on the precision of the Doppler observed value, and the use of the method has certain limitation because the precision of the Doppler observed values obtained by different receivers is different; the cycle slip detection by the MW combination method is obtained by subtracting the narrow lane combination of the pseudo-range observation value from the wide lane combination of the phase observation value of the same epoch, so that the real-time performance is high, but the equivalent cycle slip combination cannot be detected by the method; the GF method detects cycle slip by ionospheric residual error, but has a problem of multivalue, and is difficult to detect for a specific cycle slip. The methods are all to traverse each epoch of the whole arc section, the time for traversing is long, and the detection efficiency of cycle slip is not high.
Disclosure of Invention
In order to solve the problems, the invention provides a Beidou double-frequency cycle slip detection and restoration method based on arc segment division, so that cycle slip detection efficiency can be effectively improved through the method, and reliable BDS multi-frequency observation data are provided for next-step precise single-point positioning. The invention improves the cycle slip detection efficiency, verifies the feasibility and effect of the method by using experiments, and provides reliable BDS multi-frequency observation data for the next precise single-point positioning.
Interpretation of terms:
1. RMS, Root Mean Square;
2. and marking the gross error by setting the value of the epoch to 1 when the RMS of the arc section is greater than 0.5 and the STD value which is greater than 3 times is taken as a standard.
In order to achieve the purpose, the invention adopts the following technical scheme:
a Beidou double-frequency cycle slip detection and restoration method based on arc segment division comprises the following steps:
obtaining a carrier phase and a pseudo-range observation value of Beidou double-frequency, and resolving a MW combined observation value and a GF combined observation value of each satellite;
and carrying out arc segment division on the observation arc segment, carrying out cycle slip detection and repairing.
Further preferably, the arc segment division is performed on the observation arc segment, cycle slip detection is performed, and the repair is performed, including:
step 1: dividing the observation arc section into two sub-arc sections with equal length, obtaining RMS, wherein the sub-arc section with larger RMS contains the largest cycle slip and is called a first sub-arc section, and the other arc section does not contain the cycle slip or contains the smaller cycle slip and is called a second sub-arc section;
step 2: traversing all epochs in the first sub-arc section from one end close to the second sub-arc section, and if the difference between the MW combined observed value of a certain epoch and the mean value of the MW combined observed values of the second sub-arc section is greater than the MW combined cycle slip judgment threshold value of 3.5, determining that cycle slip occurs at the epoch to carry out cycle slip repair; otherwise, continuously traversing;
and step 3: taking an epoch in which the cycle slip occurs as a demarcation point, dividing the observation arc section into two new sub-arc sections, if the RMS of the new sub-arc sections is greater than the threshold value of 0.5, marking the gross error in the new sub-arc sections by taking the STD value which is greater than 3 times as the standard, and entering the step 5; otherwise, if the RMS of the new sub-arc segment is not greater than the threshold value of 0.5, the new sub-arc segment is not subjected to gross error, and the step 4 is entered;
and 4, step 4: if the difference of the mean values of the MW combined observed values of the first sub-arc segment and the second sub-arc segment exceeds 3.5, calculating the cycle slip of the first sub-arc segment, and repairing the first sub-arc segment;
if only one sub-arc section in the first sub-arc section and the second sub-arc section exceeds 3.5, resolving the cycle slip of the sub-arc section, repairing the cycle slip of the observation arc section, connecting two new sub-arc sections, removing the set gross error mark, recalculating the RMS of the whole continuous observation arc section, and detecting the next cycle slip until no new cycle slip exists;
and 5: and (4) performing gross error elimination on the whole observation arc section by using errors larger than 3 and 4 times as a criterion, and performing cycle slip repair.
Further preferably, the calculating the MW combination observation value of each satellite includes:
obtaining a MW combined observation using equations (1) and (2):
in the formula (1), L mw Represents a MW combined observed quantity, f 1 、f 3 Representing the carrier frequency of the signal; l is 1 、L 3 Expressed as carrier phase observations, P 1 、P 3 Representing pseudorange observations; for the Beidou satellite system, the two frequencies are respectively f 1 、f 3 The frequency points of (A) correspond to the signals B1I, B3I and P 1 、P 3 Pseudo-range observation values respectively corresponding to the B1I signal and the B3I signal;
N mw represents the MW combined ambiguity, calculated from equation (2):
in the formula (2), λ mw The combined wavelength for the MW combined observations is calculated from equation (3):
in the formula (3), c is the speed of light;
the MW combined observed value comprises a MW combined observed quantity L mw And MW Combined ambiguity N mw 。
Further preferably, the calculating of the GF combination observation for each satellite includes:
the carrier observed value without geometric combination is solved by using the formula (4):
L GF ＝L 1 -L 3 +P 1 -P 3 (4)
in the formula (4), L GF Is a carrier observation without geometric combination;
obtaining a GF combined observed value Q by polynomial fitting obtained by the formula (5) GF (i)：
In the formula (5), the fitting order is
n is the total epoch number; l is GF (i) Carrier observations, Q, for the geometry-free combination of the ith epoch GF (i) Fitting a GF combined observations, L, to a polynomial for the ith epoch GF (i-1) Carrier observations, Q, for geometry-free combinations of the i-1 th epoch GF (i-1) fitting of polynomial to GF combined observations, L, for the i-1 th epoch GF (i +1) is a carrier observation, Q, of the i +1 th epoch without geometric combination GF (i +1) fitting a polynomial to the GF combined observations for the (i +1) th epoch.
Further preferably, RMS is obtained by equation (6):
in the formula (6), X 1 …X n MW combined observations representing 1 st through nth epochs.
Further preferably, the STD value is obtained by the following formula (7):
in the formula (7), A i Is a random variable consisting of N observations, N being the number of observations,
further preferably, the cycle slip is calculated as follows:
l is obtained by solving equation set (8) 1 、L 3 Integer ambiguity of N 1 And N 3 ：
Wherein L is mw Represents a MW combined observation, L GF Observed values of GF combinations, lambda, for no geometrical combination 1 、λ 3 Are respectively f 1 、f 3 The wavelength of the frequency of the light beam,
is the combined ambiguity of the wide lane, N w ＝N 1 -N 3 Wide lane wavelength of (2);
k, J arc segment L is obtained by formula (9) 1 、L 3 Cycle slip value of
And
in the formula (9), the reaction mixture is,
is L 1 The mean value of the widelane ambiguities of the K, J th arc segment,
is L 3 Mean value of widelane ambiguities of the K, J th arc segment.
Further preferably, the repair process is as follows:
repair of L by the formula (10) 1 、L 3 Is subjected to cycle slip of
Wherein, L' 1 、L' 3 And the carrier phase observed value after cycle slip repair is obtained.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the Beidou double-frequency cycle slip detection and restoration method based on arc segment division, the feasibility and the effect of the method are verified through experiments, reliable Beidou double-frequency observation data can be provided for Beidou precise data processing, and meanwhile, a foundation can be laid for cycle slip detection and restoration and precise single-point positioning model research of follow-up Beidou double-frequency observation values and a theoretical basis can be provided.
2. According to the Beidou double-frequency cycle slip detection and restoration method based on arc segment division, the arc segment division is carried out on the observation arc segment, the cycle slip detection efficiency is effectively improved, the whole observation arc segment is divided by taking the RMS value as a target, the epoch number of cycle slip detection is reduced, and certain superiority is achieved.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and not to limit the application.
FIG. 1 is a schematic flow diagram of a Beidou double-frequency cycle slip detection and repair method based on arc segment division.
Fig. 2 is a percentage diagram of the improvement of the operating time of the PRN4, the PRN6 and the PRN22 in the arc segment division-based beidou dual-frequency cycle slip detection and repair method and the conventional method.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example 1
A Beidou double-frequency cycle slip detection and restoration method based on arc segment division comprises the following steps:
obtaining a carrier phase and a pseudo-range observation value of Beidou double-frequency, and resolving a MW combined observation value and a GF combined observation value of each satellite according to an epoch period;
resolving the MW combined observation value of each satellite, comprising:
obtaining a MW combined observation using equations (1) and (2):
in the formula (1), L mw Represents a MW combined observed quantity, f 1 、f 3 Representing the carrier frequency of the signal; l is 1 、L 3 Expressed as carrier phase observations, P 1 、P 3 Representing pseudorange observations; for the Beidou satellite system, the two frequencies are respectively f 1 、f 3 The frequency points of (A) correspond to the signals B1I, B3I and P 1 、P 3 Pseudo-range observation values respectively corresponding to the B1I signal and the B3I signal;
N mw represents the MW combined ambiguity, calculated from equation (2):
in the formula (2), λ mw The combined wavelength for the MW combined observations is calculated from equation (3):
in the formula (3), c is the speed of light;
the MW combined observed value comprises a MW combined observed quantity L mw And MW Combined ambiguity N mw 。
Resolving the GF combination observations for each satellite, comprising:
the carrier observed value without geometric combination is solved by using the formula (4):
L GF ＝L 1 -L 3 +P 1 -P 3 (4)
in the formula (4), L GF Is a carrier observation without geometric combination; the remaining parameters are in accordance with formula (1).
Because of P 1 -P 3 The obtained ionospheric delay difference is less accurate with respect to the carrier phase, so a further polynomial fit is generally performed on it, and the polynomial fit obtained by equation (5) yields the GF combination observation Q GF (i)：
In the formula (5), the fitting order is
n is the total epoch number; l is GF (i) Carrier observations, Q, for the geometry-free combination of the ith epoch GF (i) Fitting a GF combined observations, L, to a polynomial for the ith epoch GF (i-1) Carrier observations, Q, for geometry-free combinations of the i-1 th epoch GF (i-1) fitting of polynomial to GF combined observations, L, for the i-1 th epoch GF (i +1) is a carrier observation, Q, of the i +1 th epoch without geometric combination GF (i +1) fitting a polynomial to the GF combined observations for the (i +1) th epoch.
And carrying out arc segment division on the observation arc segment, carrying out cycle slip detection and repairing.
Example 2
According to embodiment 1, as shown in fig. 1, the Beidou dual-frequency cycle slip detection and repair method based on arc segment division is characterized in that:
for the Beidou system, the two frequencies are respectively frequency points and are respectively f 1 、f 3 The frequency points of the interference signal are respectively corresponding to B1I and B3I, a Australian Persian station (PETH) is obtained, and the observation time is selected to be 2018, the yearly integration date is 108, and the inter-epoch interval is 1s, and Beidou B1I and B3I carrier phase observation values and pseudo-range observation values are obtained; carry out the arc section to observing the arc section and divide, carry out cycle slip detection to restoreing, include:
step 1: dividing the observation arc section into two sub-arc sections with equal length, obtaining RMS, wherein the sub-arc section with larger RMS contains the largest cycle slip and is called a first sub-arc section (sub-arc section 1), and the other arc section does not contain the cycle slip or contains the smaller cycle slip and is called a second sub-arc section (sub-arc section 2); RMS is calculated by equation (6):
in the formula (6), X 1 …X n MW combined views representing 1 st through nth epochsAnd (6) measuring.
Step 2: traversing all epochs in the first sub-arc section from one end close to the second sub-arc section, and if the difference between the MW combined observed value of a certain epoch and the mean value of the MW combined observed values of the second sub-arc section is greater than the MW combined cycle slip judgment threshold value of 3.5, determining that cycle slip occurs at the epoch to carry out cycle slip repair; otherwise, continuously traversing;
and step 3: taking an epoch in which the cycle slip occurs as a demarcation point, dividing the observation arc section into two new sub-arc sections, if the RMS of the new sub-arc sections is greater than the threshold value of 0.5, marking the gross error in the new sub-arc sections by taking the STD value which is greater than 3 times as the standard, and entering the step 5; without gross marks, the RMS of the arc segment may be exceeded because of undetected cycle slip. Otherwise, if the RMS of the new sub-arc segment is not greater than the threshold value of 0.5, the new sub-arc segment is not subjected to gross error, and the step 4 is entered;
the STD value is obtained by the following formula (7):
in the formula (7), A i Is a random variable consisting of N observations, N being the number of observations,
and 4, step 4: if the difference of the mean values of the MW combined observed values of the first sub-arc segment and the second sub-arc segment exceeds 3.5, calculating the cycle slip of the first sub-arc segment, and repairing the first sub-arc segment;
if only one sub-arc section in the first sub-arc section and the second sub-arc section exceeds 3.5, resolving the cycle slip of the sub-arc section, repairing the cycle slip of the observation arc section, connecting two new sub-arc sections, removing the set gross error mark, recalculating the RMS of the whole continuous observation arc section, and detecting the next cycle slip until no new cycle slip exists;
and 5: and (4) performing gross error elimination on the whole observation arc section by using errors larger than 3 and 4 times as a criterion, and performing cycle slip repair.
The cycle slip is calculated as follows:
l is obtained by solving equation set (8) 1 、L 3 Integer ambiguity of N 1 And N 3 ：
Wherein L is mw Represents a MW combined observation, L GF Observed values of GF combinations, lambda, for no geometrical combination 1 、λ 3 Are respectively f 1 、f 3 The wavelength of the frequency of the light beam,
is the combined ambiguity of the wide lane, N w ＝N 1 -N 3 Wide lane wavelength of (2);
k, J arc segment L is obtained by formula (9) 1 、L 3 Cycle slip value of
And
in the formula (9), the reaction mixture is,
is L 1 The mean value of the widelane ambiguities of the K, J th arc segment,
is L 3 Mean value of widelane ambiguities of the K, J th arc segment.
The repair process is as follows:
repair of L by the formula (10) 1 、L 3 Is subjected to cycle slip of
Wherein, L' 1 、L' 3 And the carrier phase observed value after cycle slip repair is obtained.
Comparing the cycle slip detection efficiency by adopting a traditional method and the arc-segment-division-based Beidou dual-frequency cycle slip detection and repair method, wherein the method 1 is a traditional cycle slip analysis sequence detection method, and the method 2 is the arc-segment-division-based Beidou dual-frequency cycle slip detection and repair method. Fig. 2 is a percentage diagram of the improvement of the operating time of the PRN4, the PRN6 and the PRN22 in the arc segment division-based beidou dual-frequency cycle slip detection and repair method and the conventional method. The percentage increase for the six experiments is shown in the figure, compared to method 1, method 2 improves PRN4 by 88.22-87.34%, PRN6 by 67.88-69.71%, and PRN22 by 25.76-30.19%.
Claims (8)
1. A Beidou double-frequency cycle slip detection and restoration method based on arc segment division is characterized by comprising the following steps:
obtaining a carrier phase and a pseudo-range observation value of Beidou double-frequency, and resolving a MW combined observation value and a GF combined observation value of each satellite;
and carrying out arc segment division on the observation arc segment, carrying out cycle slip detection and repairing.
2. The Beidou double-frequency cycle slip detection and restoration method based on arc segment division according to claim 1, is characterized in that arc segment division is carried out on an observation arc segment, cycle slip detection is carried out, and restoration is carried out, and comprises the following steps:
step 1: dividing the observation arc section into two sub-arc sections with equal length, obtaining RMS, wherein the sub-arc section with larger RMS contains the largest cycle slip and is called a first sub-arc section, and the other arc section does not contain the cycle slip or contains the smaller cycle slip and is called a second sub-arc section;
step 2: traversing all epochs in the first sub-arc section from one end close to the second sub-arc section, and if the difference between the MW combined observed value of a certain epoch and the mean value of the MW combined observed values of the second sub-arc section is greater than the MW combined cycle slip judgment threshold value of 3.5, determining that cycle slip occurs at the epoch to carry out cycle slip repair; otherwise, continuously traversing;
and step 3: taking an epoch in which the cycle slip occurs as a demarcation point, dividing the observation arc section into two new sub-arc sections, if the RMS of the new sub-arc sections is greater than the threshold value of 0.5, marking the gross error in the new sub-arc sections by taking the STD value which is greater than 3 times as the standard, and entering the step 5; otherwise, if the RMS of the new sub-arc segment is not greater than the threshold value of 0.5, the new sub-arc segment is not subjected to gross error, and the step 4 is entered;
and 4, step 4: if the difference of the mean values of the MW combined observed values of the first sub-arc segment and the second sub-arc segment exceeds 3.5, calculating the cycle slip of the first sub-arc segment, and repairing the first sub-arc segment;
if only one sub-arc section in the first sub-arc section and the second sub-arc section exceeds 3.5, resolving the cycle slip of the sub-arc section, repairing the cycle slip of the observation arc section, connecting two new sub-arc sections, removing the set gross error mark, recalculating the RMS of the whole continuous observation arc section, and detecting the next cycle slip until no new cycle slip exists;
and 5: and (4) performing gross error elimination on the whole observation arc section by using errors larger than 3 and 4 times as a criterion, and performing cycle slip repair.
3. The Beidou double-frequency cycle slip detection and restoration method based on arc segment division according to claim 1, wherein resolving MW combined observation values of each satellite comprises:
obtaining a MW combined observation using equations (1) and (2):
in the formula (1), L mw Represents a MW combined observed quantity, f 1 、f 3 Representing the carrier frequency of the signal; l is 1 、L 3 Expressed as carrier phase observations, P 1 、P 3 Representing pseudorange observations; for the Beidou satellite system, the two frequencies are respectively f 1 、f 3 The frequency points of (A) correspond to the signals B1I, B3I and P 1 、P 3 Pseudo-range observation values respectively corresponding to the B1I signal and the B3I signal;
N mw represents the MW combined ambiguity, calculated from equation (2):
in the formula (2), λ mw The combined wavelength for the MW combined observations is calculated from equation (3):
in the formula (3), c is the speed of light;
the MW combined observed value comprises a MW combined observed quantity L mw And MW Combined ambiguity N mw 。
4. The Beidou double-frequency cycle slip detection and restoration method based on arc segment division according to claim 1, wherein the step of solving GF combined observed values of each satellite comprises the following steps:
the carrier observed value without geometric combination is solved by using the formula (4):
L GF ＝L 1 -L 3 +P 1 -P 3 (4)
in the formula (4), L GF Is a carrier observation without geometric combination;
obtaining a GF combined observed value Q by polynomial fitting obtained by the formula (5) GF (i)：
In the formula (5), the fitting order is
n is the total epoch number; l is GF (i) Carrier observations, Q, for the geometry-free combination of the ith epoch GF (i) Fitting a GF combined observations, L, to a polynomial for the ith epoch GF (i-1) Carrier observations, Q, for geometry-free combinations of the i-1 th epoch GF (i-1) fitting of polynomial to GF combined observations, L, for the i-1 th epoch GF (i +1) is a carrier observation, Q, of the i +1 th epoch without geometric combination GF (i +1) fitting a polynomial to the GF combined observations for the (i +1) th epoch.
5. The Beidou double-frequency cycle slip detection and restoration method based on arc segment division according to claim 2 is characterized in that RMS is obtained by the following formula (6):
in the formula (6), X 1 …X n MW combined observations representing 1 st through nth epochs.
6. The Beidou dual-frequency cycle slip detection and restoration method based on arc segment division according to claim 2, is characterized in that the STD value is obtained according to the formula (7):
in the formula (7), A i Is a random variable consisting of N observations, N being the number of observations,
7. the Beidou dual-frequency cycle slip detection and restoration method based on arc segment division according to claim 2 is characterized in that the cycle slip calculation process is as follows:
l is obtained by solving equation set (8) 1 、L 3 Integer ambiguity of N 1 And N 3 ：
Wherein L is mw Represents a MW combined observation, L GF Observed values of GF combinations, lambda, for no geometrical combination 1 、λ 3 Are respectively f 1 、f 3 The wavelength of the frequency of the light beam,
is the combined ambiguity of the wide lane, N w ＝N 1 -N 3 Wide lane wavelength of (2);
k, J arc segment L is obtained by formula (9) 1 、L 3 Cycle slip value of
And
in the formula (9), the reaction mixture is,
is L 1 The mean value of the widelane ambiguities of the K, J th arc segment,
is L 3 Mean value of widelane ambiguities of the K, J th arc segment.
8. The Beidou double-frequency cycle slip detection and repair method based on arc segment division as claimed in claim 2, is characterized in that the repair process is as follows:
repair of L by the formula (10) 1 、L 3 Is subjected to cycle slip of
Wherein, L' 1 、L' 3 And the carrier phase observed value after cycle slip repair is obtained.
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