CN111751853B - GNSS dual-frequency carrier phase integer ambiguity resolution method - Google Patents
GNSS dual-frequency carrier phase integer ambiguity resolution method Download PDFInfo
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- 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
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- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
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Abstract
The application provides a GNSS dual-frequency carrier phase integer ambiguity resolution method, and belongs to the technical field of satellite high-precision positioning. According to the method, after preprocessing a double-frequency carrier phase observation value, a better carrier observation value is screened out to construct a double-difference geometric-free ionosphere-free observation value and a wide lane carrier combined observation value, on the premise of estimating the wide lane ambiguity floating point solution precision and the single-epoch wide lane ambiguity passing rate, the LAMBDA method is utilized to search and fix the wide lane whole-cycle ambiguity, the LAMBDA method is utilized to estimate the ambiguity floating point solution of the ionosphere-free combined observation value, the LAMBDA method is utilized to search and fix the narrow lane whole-cycle ambiguity, and finally the positioning equation set is utilized to carry out the back-generation solution, so that the satellite high-precision positioning and attitude calculation are realized. According to the application, the problem of low fixed rate of the wide lane ambiguity is solved by using the LAMBDA searching algorithm while the accuracy of the wide lane ambiguity floating point solution is considered, and meanwhile, the narrow lane ambiguity floating point solution is well estimated, so that the whole fixed rate of the base line is improved.
Description
Technical Field
The application belongs to the technical field of satellite high-precision positioning, and particularly relates to a GNSS dual-frequency carrier phase integer ambiguity resolution method.
Background
Currently, four global satellite navigation systems (Global Navigation Satellite System, GNSS) include the GPS in the united states, GLONASS in russia, BDS in china, and Galileo system in the european union. The global satellite navigation system performs real-time relative positioning, namely RTK (Real Time Kinematic), by eliminating or weakening common errors such as satellite orbit errors, atmospheric propagation delay errors, satellite and receiver clock errors by making a difference between receivers and satellites, and realizes centimeter-level or even millimeter-level positioning by using high-precision carrier phase observables. The method has the characteristics of high precision, high reliability, 24-hour uninterruption and the like, and has wide application in civil and military fields. For example, RTKs may find application in traditional mapping fields, unmanned navigation, and the like.
The key to achieving high accuracy positioning is to correctly resolve carrier phase integer ambiguity, while the difficulty of correctly resolving ambiguity is to resolve integer estimates of ambiguity floating point solutions. Under the condition of a short base line with the base line length smaller than 15km, ionospheric delay errors, tropospheric delay errors, satellite clock errors and receiver errors can be greatly eliminated or weakened by constructing a carrier phase double-difference observation equation between the receiver and the satellite, and the whole-cycle ambiguity is generally easier to fix, so that a high-precision positioning result is obtained. However, under the condition that the base line length is larger than 15km, partial atmospheric delay errors and multipath errors can be absorbed into an ambiguity floating solution due to the weakening of the spatial correlation, so that the whole-cycle ambiguity is difficult to fix accurately, and the accuracy and reliability of RTK positioning are reduced. Common ambiguity estimation methods are: rounding, integer Least square, FARA (Fast Ambiguity Resolution Approach), LAMBDA (Least-squares Ambiguity Decorrelation Adjustment). Among them, the LAMBDA method is recognized as an ambiguity resolution method which is the most widely used and has the best effect. However, the LAMBDA algorithm has a certain requirement on the ambiguity floating solution accuracy, and if the ambiguity floating solution accuracy to be solved is poor, the searched integer solution will generally have a deviation from one week to at most one week. When the traditional method is used for resolving the medium and long base lines, the whole-lane integer ambiguity and the narrow-lane integer ambiguity are resolved by directly utilizing a rounding-floating solution method, and the method is relatively long in initialization time and limited in fixing success rate because of the fact that multi-epoch smooth resolving is needed and the resolving reliability is relatively poor.
Disclosure of Invention
Aiming at the defects in the prior art, the application provides a novel integer ambiguity resolution method, which fully utilizes the advantages of LAMBDA algorithm and utilizes the characteristic that the integer ambiguity of a wide lane can be quickly and reliably fixed, when resolving the ambiguity of the wide lane, the floating point resolution accuracy is evaluated, and the LAMBDA method is used for searching and fixing the integer ambiguity of the wide lane, when resolving the ambiguity of a narrow lane, the fixed solution of the wide lane with higher reliability and the floating point solution of the ionosphere-free ambiguity estimated by Kalman filtering are utilized, and the LAMBDA method is used for searching and fixing the integer ambiguity of the narrow lane. The method shortens the initialization time, improves the fixation rate of the base line, and realizes the rapid convergence of the whole-cycle ambiguity and the high-precision positioning of the satellite.
In order to achieve the above purpose, the present application adopts the following specific technical scheme.
A GNSS dual-frequency carrier phase integer ambiguity resolution method comprises the following steps:
step one, modeling a model without geometry and ionosphere;
the first step specifically comprises the following steps:
step 1.1, constructing ionosphere-free double-frequency carrier combined observed quantity and ionosphere-free pseudo-range combined observed quantity through GNSS double-frequency carrier phase observed quantity and double-frequency pseudo-range observed quantity after quality check and cycle slip detection processing;
step 1.2, constructing a double-difference observation equation of a geometric ionosphere-free model by utilizing ionosphere-free carrier combination observed quantity and ionosphere-free pseudo-range combination observed quantity;
step two, searching and fixing the widelane ambiguity;
the second step specifically comprises the following steps:
2.1, constructing MW combined observables by using double-frequency carrier phase observables and double-frequency pseudo-range observables, wherein the observables are wide-lane ambiguity floating solutions;
2.2, carrying out precision estimation on the wide-lane ambiguity floating solution, and judging whether the passing rate of the epoch wide-lane ambiguity is more than 80%;
step 2.3, inputting a preferable wide lane ambiguity floating solution and a covariance matrix thereof, and searching and fixing the whole-cycle ambiguity of the wide lane by using an LAMBDA method;
step three, ionospheric-free ambiguity Kalman filtering estimation;
the third step specifically comprises the following steps:
step 3.1, constructing a Kalman filtering equation without ionospheric ambiguity;
step 3.2, estimating ionospheric-free ambiguity by using a Kalman filter;
step four, narrow lane ambiguity searching and fixing;
the fourth step specifically comprises:
step 4.1, solving an ionosphere-free ambiguity floating solution and a wide lane integer ambiguity fixed solution by utilizing filtering, and reversely solving a narrow lane ambiguity floating solution;
step 4.2, evaluating the narrow lane ambiguity floating solution precision and the narrow lane combined observed measurement precision, screening a better narrow lane ambiguity floating solution, and fixing the narrow lane integer ambiguity by using an LAMBDA method;
and 4.3, resolving the single-frequency point whole-cycle ambiguity and the fixed ionosphere-free ambiguity, and performing the recurrent solving of the filtering equation.
Further, in the first step, the pseudo-range ionosphere-free combined observed quantity and the carrier phase ionosphere-free combined observed quantity are respectively expressed as:
in the formula ,PIF 、Φ IF Respectively pseudo-range ionosphere-free combined observed quantity and carrier ionosphere-free combined observed quantity, f 1 、f 2 Respectively the frequencies of two frequency points of the GNSS system, lambda 1 、λ 2 For its corresponding wavelength, P 1 、P 2 For the original pseudo-range observations of two frequency points of the GNSS system,the method comprises the steps of obtaining the original carrier observed quantity of two frequency points of a GNSS system;
ionosphere-free combined observed ambiguity floating solution BC is defined as:
further, in the second step, the double-difference pseudo-range and the double-difference carrier observation equation are respectively expressed as follows:
first, a MW combination is constructed, and the double-difference wide-lane ambiguity of the satellite pair is solved as
In the above-mentioned method, the step of,lambda is respectively in metersUnit double-difference carrier combined observed quantity, double-difference pseudo-range combined observed quantity and wide lane combined wavelength, [ # ]] ROUND Is a rounding operator;
taking the standard deviation sigma of pseudo-range measurement P =0.3m, the variance of the combined pseudorange measurements is
The single difference noise variance is expressed as
Where el is the satellite altitude.
The measurement noise variance of the widelane ambiguity can be expressed as
Wherein, the superscript i, j is respectively expressed as indexes of a reference star and a target star, and m is a smooth epoch number;
ambiguity resolution pass ratio is expressed as
in the formula ,Psucc To pass rate, n fix 、n all Respectively representing the number of the ambiguities passing a certain condition and the total number of the ambiguities participating in resolving;
and secondly, searching and resolving the widelane ambiguity.
Preferably, the method for searching and resolving the widelane ambiguity comprises the following steps:
and circularly resolving all wide lane ambiguity floating solutions of the current epoch, setting the whole ambiguity error of the wide lane floating solutions to be smaller than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be smaller than 0.2, wherein the proportion of the double-difference wide lane ambiguity of the current epoch meeting the two conditions is larger than 80%, and storing the corresponding wide lane ambiguity floating solutions after meeting the conditions, otherwise, the current epoch is not resolved, returning the algorithm to the step one, and resolving the next epoch again.
Further, in the third step, the state estimation of the positioning equation is performed by adopting the extended kalman filter, and the specific flow is as follows:
measurement update (one)
In the above-mentioned method, the step of, and Pk Respectively represent epoch t k Time state estimation vector and covariance matrix thereof, (+), and (-) respectively represent the identifications before and after the filter update, H (x), H (x) and R k The measurement model vector, the design matrix and the covariance matrix of the measurement error are represented, respectively.
(II) time update
In the above-mentioned method, the step of, and />The covariance matrices of the Kalman filter transfer matrix and the system noise are represented, respectively.
State vector:
x＝(r r T ,v r T ,B 1 T ,B 2 T ) T
measurement vector:
y＝(Φ IF , T P IF T ) T
in the formula ,
measuring a model vector:
h(x)＝(h Φ,IF T ,h P,IF T ) T
designing a matrix:
measuring a noise covariance matrix:
in the above-mentioned method, the step of,
is a single difference measurement matrix;
is a line-of-sight direction vector;
measuring a noise covariance matrix for ionosphere-free carrier combination observables;
measuring a noise covariance matrix for ionosphere-free pseudo-range combined observables;
the standard deviation of the observed measurement error of the carrier without the ionosphere is calculated;
the standard deviation of the measurement error is the ionosphere-free pseudo-range observed quantity.
Further, in step four, ionospheric-free ambiguity is further represented as
In the above-mentioned method, the step of,is a narrow lane wavelength.
Obtaining the single-frequency point ambiguity floating solution of the narrow lane by the relation between the wide lane ambiguity and the ionosphere-free ambiguity
Carrying out narrow-lane ambiguity resolution by the wide-lane ambiguity fixed resolution in the second step and the ionosphere-free ambiguity floating resolution in the third step; setting a single-frequency point ambiguity floating point solution rounding error smaller than 0.35 week in the narrow-lane ambiguity floating point solution estimation part, storing the narrow-lane ambiguity floating point solution meeting the conditions, and then carrying out double-difference single-frequency point ambiguity integer solution solving by using an LAMBDA method according to the calculated narrow-lane ambiguity covariance matrix, if the narrow-lane ambiguity solution fails, failing the current epoch ambiguity solution, and returning to the step one to carry out next epoch solution again.
After the narrow-lane ambiguity fixed solution is obtained, the single-frequency point fixed solution is reversely obtained, further the back-band solution of the filtering positioning equation is carried out, and finally the satellite high-precision positioning is carried out.
Compared with the limitations of the prior art, the application has the following beneficial effects
According to the application, a more rigorous LAMBDA method is used for replacing the existing method for resolving the middle and long base lines by directly taking the whole wide lane ambiguity floating point solution, and the double-difference wide lane integer ambiguity of more satellite pairs is fixed to the maximum extent while the wide lane ambiguity floating point solution precision is considered, so that the correct fixation of the double-difference wide lane integer ambiguity is realized.
According to the application, not only is the narrow-lane ambiguity floating solution reasonably evaluated, but also the precision of the ionosphere-free ambiguity floating solution is limited, and on the basis of considering the passing rate of the wide-lane ambiguity solution, a more strict LAMBDA method is utilized to replace the existing method for directly solving the ambiguity of the narrow-lane ambiguity floating solution, so that the reliable solution of the double-difference narrow-lane ambiguity is realized, and the purposes of shortening the initialization time and improving the baseline fixing rate are achieved.
Drawings
FIG. 1 is a flow chart of a dual-frequency carrier phase integer ambiguity algorithm of the present application;
FIG. 2 is a flowchart of the widelane ambiguity resolution of the present application;
FIG. 3 is a flow chart of the wide lane ambiguity floating solution accuracy estimation of the present application;
FIG. 4 is a flowchart of a narrow-lane ambiguity resolution in accordance with the present application;
FIG. 5 is a graph of BDS 8km baseline solution of the present application;
FIG. 6 is a graph of the GPS 66km baseline solution of the present application;
FIG. 7 is a graph of the BDS 66km baseline solution of the present application.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
The application relates to an improved double-frequency RTK integer ambiguity resolution method, which comprises the steps of GNSS geometric free ionosphere model construction, wide-lane ambiguity search fixation, ionosphere free ambiguity Kalman filtering estimation and narrow-lane ambiguity search fixation.
The overall flow chart of the present application is shown in fig. 1. Firstly screening out better carrier waves and pseudo-range observables after quality check and cycle slip detection processing of GNSS original observables, constructing double-difference geometry-free ionosphere-free combined observables and wide-lane carrier wave combined observables and narrow-lane pseudo-range combined observables, solving wide-lane ambiguity floating solutions and estimating the accuracy of the wide-lane ambiguity floating solutions, searching and fixing wide-lane integer ambiguity by using an LAMBDA method, simultaneously estimating ambiguity floating solutions of ionosphere-free combined observables by using a Kalman filter, then searching and fixing the narrow-lane integer ambiguity by using a LAMBDA method by using a narrow-lane ambiguity searching and fixing module, and finally carrying out recurrent solving of an equation set to realize satellite high-accuracy positioning.
The application is suitable for reliably fixing the double-difference integer ambiguity of the short baseline and the medium-long baseline.
Step one: model modeling without geometry and ionosphere (IF combination)
And constructing a geometric ionosphere-free model by using GNSS double-frequency carrier waves and double-frequency pseudo-range original observables after quality check and cycle slip detection processing.
The pseudo-range ionosphere-free combined observables and carrier phase ionosphere-free combined observables can be expressed as respectively
in the formula ,PIF 、Φ IF Respectively pseudo-range ionosphere-free combined observed quantity and carrier ionosphere-free combined observed quantity, f 1 、f 2 Respectively the frequencies of two frequency points of the GNSS system, lambda 1 、λ 2 For its corresponding wavelength, P 1 、P 2 For the original pseudo-range observations of two frequency points of the GNSS system,the method is used for observing the original carrier of two frequency points of the GNSS system.
Ionosphere-free combined observed ambiguity floating solution BC (in m) is defined as
Step two: wide lane ambiguity search fixing
The widelane ambiguity resolution is shown in FIG. 2.
The double-difference pseudo-range and double-difference carrier observation equation can be expressed as follows:
first, a MW combination is constructed, then the double-difference wide-lane ambiguity resolution of the satellite pair is
In the above-mentioned method, the step of,lambda is the combined observed quantity of double-difference carrier waves in meter units, the combined observed quantity of double-difference pseudo-range and the combined wavelength of wide lane, [ + ]] ROUND To round operators.
Because of the high accuracy of the carrier phase measurements, only the measurement of the combined pseudorange measurements is considered hereThe quantity error, here taking the standard deviation sigma of the pseudo-range measurements P =0.3m. From the error propagation law, the variance of the combined pseudo-range measurement is
The single difference noise variance can be expressed as
Where el is the satellite altitude.
The measurement noise variance of the widelane ambiguity can be expressed as
In the formula, the superscript i, j is respectively expressed as indexes of a reference star and a target star, and m is a smooth epoch number.
Ambiguity resolution pass ratio is expressed as
in the formula ,Psucc To pass rate, n fix 、n all The number of ambiguities passing a certain condition and the total number of the participation in resolving ambiguities are represented respectively.
Secondly, searching and resolving the widelane ambiguity:
and circularly resolving all wide lane ambiguity floating solutions of the current epoch, setting the whole ambiguity error of the wide lane floating solutions to be smaller than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be smaller than 0.2, wherein the proportion of the double-difference wide lane ambiguity of the current epoch meeting the two conditions is larger than 80%, and storing the corresponding wide lane ambiguity floating solutions after meeting the conditions, otherwise, the current epoch is not resolved, returning the algorithm to the step one, and resolving the next epoch again. The flow is shown in fig. 3.
With the wide lane ambiguity floating solution and the ambiguity covariance matrix corresponding to the wide lane ambiguity floating solution, the whole-cycle ambiguity of the wide lane can be searched and fixed by using an LAMBDA method.
Step three: ionospheric-free ambiguity Kalman filter estimation
And carrying out state estimation of a positioning equation by adopting extended Kalman filtering, wherein the specific flow is as follows.
(III) measurement update
In the above-mentioned method, the step of, and Pk Respectively represent epoch t k Time state estimation vector and covariance matrix thereof, (+), and (-) respectively represent the identifications before and after the filter update, H (x), H (x) and R k The measurement model vector, the design matrix and the covariance matrix of the measurement error are represented, respectively.
(IV) time update
In the above-mentioned method, the step of, and />Respectively represent Kalman filtering transfer matrix and systemCovariance matrix of system noise.
State vector:
x＝(r r T ,v r T ,B 1 T ,B 2 T ) T
measurement vector:
y＝(Φ IF , T P IF T ) T
in the formula ,
measuring a model vector:
h(x)＝(h Φ,IF T ,h P,IF T ) T
designing a matrix:
measuring a noise covariance matrix:
in the above-mentioned method, the step of,
is a single difference measurement matrix;
is a line-of-sight direction vector;
combined observed quantity measurement noise for ionosphere-free carrierAn acoustic covariance matrix;
measuring a noise covariance matrix for ionosphere-free pseudo-range combined observables;
the standard deviation of the observed measurement error of the carrier without the ionosphere is calculated;
the standard deviation of the measurement error is the ionosphere-free pseudo-range observed quantity.
And D, obtaining a floating solution without ionosphere ambiguity through the third step, and storing and carrying out the fourth step.
Step four: narrow lane ambiguity search fixing
The narrow-lane ambiguity resolution flow is shown in FIG. 4.
Ionospheric-free ambiguity can be further expressed as
In the above-mentioned method, the step of,is a narrow lane wavelength.
Obtaining the single-frequency point ambiguity floating solution of the narrow lane by the relation between the wide lane ambiguity and the ionosphere-free ambiguity
And (3) carrying out narrow-lane ambiguity resolution by the wide-lane ambiguity fixed solution in the second step and the ionosphere-free ambiguity floating solution in the third step. Setting a single-frequency point ambiguity floating point solution rounding error smaller than 0.35 week in the narrow-lane ambiguity floating point solution estimation part, storing the narrow-lane ambiguity floating point solution meeting the conditions, and then carrying out double-difference single-frequency point ambiguity integer solution solving by using an LAMBDA method according to the calculated narrow-lane ambiguity covariance matrix, if the narrow-lane ambiguity solution fails, failing the current epoch ambiguity solution, and returning to the step one to carry out next epoch solution again.
After the narrow-lane ambiguity fixed solution is obtained, the single-frequency point fixed solution is reversely obtained, further the back-band solution of the filtering positioning equation is carried out, and finally the satellite high-precision positioning is carried out.
Experimental results
Experiment one: the data are derived from static BDS double-frequency baseline data of a certain area in Shanghai city, the baseline length is 8.2km, the sampling frequency is 1Hz, the total data is 3167 epochs, the height cut-off angle during data processing is set to be 10 degrees, and the ratio threshold is set to be 2.0.
TABLE 1 8km baseline solution result positioning bias
As shown in table 1, the baseline fixing rate was 99.1%, and the positioning errors RMS of the baseline fixing solution in the direction of the local coordinate system ENU were 0.46cm, 1.27cm, and 3.25cm, respectively.
The BDS 8km baseline solution is shown in FIG. 5. In fig. 5, the dashed line represents the baseline floating solution, and the solid line represents the baseline fixed solution. As can be seen from FIG. 5, the ambiguity can be quickly converged and the fixing rate is high when the BDS (B1, B3) 8km baseline is resolved by the algorithm of the application.
Experiment II:
experimental data: the data are derived from static GPS/BDS dual-system dual-frequency baseline data of a certain area in Beijing city, the baseline length is 66.3km, the sampling frequency is 1Hz, the data duration is 14400 calendar elements in 4 hours, the height cut-off angle during data processing is set to be 10 degrees, and the ratio threshold is set to be 2.0.
TABLE 2 66km baseline solution result positioning bias
As can be seen from table 2, when the 66km baselines of the dual-frequency GPS (L1, L2) and BDS (B1, B3) were calculated by the new algorithm, the fixed rates were 91.7% and 93.1%, respectively; the positioning errors RMS of the GPS baseline fixing solution in the direction of the local coordinate system ENU are 2.50cm, 1.36cm and 4.62cm respectively, and the positioning errors RMS of the BDS baseline fixing solution in the direction of the local coordinate system ENU are 3.07cm, 2.40cm and 4.58cm respectively.
The GPS 66km baseline solution is shown in FIG. 6, and the BDS 66km baseline solution is shown in FIG. 7. In fig. 6 and 7, the dashed line indicates the baseline floating solution result, and the solid line indicates the baseline fixed solution result. As can be seen from fig. 6 and 7, after a long-time smooth solution, the positioning error gradually converges, which indicates that the ambiguity resolution is correct, and reliable resolution of long-distance baselines is realized, which indicates that the resolving method of the application is practical and effective.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The present application is not limited to any specific form of combination of hardware and software. In summary, the above embodiments are only preferred embodiments of the present application, and are not intended to limit the scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (4)
1. A GNSS dual-frequency carrier phase integer ambiguity resolution method is characterized by comprising the following steps:
step one, modeling a model without geometry and ionosphere;
the first step specifically comprises the following steps:
step 1.1, constructing ionosphere-free double-frequency carrier combined observed quantity and ionosphere-free pseudo-range combined observed quantity through GNSS double-frequency carrier phase observed quantity and double-frequency pseudo-range observed quantity after quality check and cycle slip detection processing;
step 1.2, constructing a double-difference observation equation of a geometric ionosphere-free model by utilizing ionosphere-free carrier combination observed quantity and ionosphere-free pseudo-range combination observed quantity;
step two, searching and fixing the widelane ambiguity;
the second step specifically comprises the following steps:
2.1, constructing MW combined observables by using double-frequency carrier phase observables and double-frequency pseudo-range observables, wherein the observables are wide-lane ambiguity floating solutions;
2.2, carrying out precision estimation on the wide-lane ambiguity floating solution, and judging whether the passing rate of the epoch wide-lane ambiguity is more than 80 percent or not;
step 2.3, inputting a screened wide lane ambiguity floating solution and a covariance matrix thereof, and searching and fixing the whole-cycle ambiguity of the wide lane by using an LAMBDA method;
first, a MW combination is constructed, and the double-difference widelane ambiguity floating solution of the satellite pair is:
in the above-mentioned method, the step of,、/>、/>double-difference carrier combined observed quantity, double-difference pseudo-range combined observed quantity and wide lane combined wavelength which are respectively expressed in meter>Is a rounding operator;
taking the standard deviation of pseudo-range measurementThe variance of the combined pseudorange measurements is
wherein ,、/>the frequencies of two frequency points of the GNSS system are respectively;
the single difference noise variance is expressed as:
in the formula ,is the satellite altitude;
the measurement noise variance of the widelane ambiguity can be expressed as:
in the superscriptIndex denoted as reference star and target star, respectively, < >>Is a smoothed epoch number;
the ambiguity resolution pass rate is expressed as:
in the formula ,for passing rate->、/>Respectively representing the number of the ambiguities passing a certain condition and the total number of the ambiguities participating in resolving;
secondly, searching and resolving the widelane ambiguity;
the searching and resolving method for the widelane ambiguity comprises the following steps:
circularly resolving all wide lane ambiguity floating solutions of the current epoch, setting the whole ambiguity errors of the wide lane floating solutions to be smaller than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be smaller than 0.2, wherein the proportion of the double-difference wide lane ambiguity of the current epoch to be larger than 80%, storing the corresponding wide lane ambiguity floating solutions after the above conditions are met, otherwise, not resolving the current epoch, returning the algorithm to the step one, and resolving the next epoch again;
step three, ionospheric-free ambiguity Kalman filtering estimation;
the third step specifically comprises the following steps:
step 3.1, constructing a Kalman filtering equation without ionospheric ambiguity;
step 3.2, estimating ionospheric-free ambiguity by using a Kalman filter;
step four, narrow lane ambiguity searching and fixing;
the fourth step specifically comprises:
step 4.1, solving an ionosphere-free ambiguity floating solution and a wide lane integer ambiguity fixed solution by utilizing filtering, and reversely solving a narrow lane ambiguity floating solution;
step 4.2, evaluating the narrow lane ambiguity floating solution precision and the narrow lane combined observed measurement precision, screening a better narrow lane ambiguity floating solution, and fixing the narrow lane integer ambiguity by using an LAMBDA method;
and 4.3, resolving the single-frequency point whole-cycle ambiguity and the fixed ionosphere-free ambiguity, and performing the recurrent solving of the filtering equation.
2. The method of claim 1, wherein,
in the first step, pseudo-range ionosphere-free combined observables and carrier phase ionosphere-free combined observables are respectively expressed as:
in the formula ,、/>pseudo-range ionosphere-free combined observables and carrier ionosphere-free combined observables, respectively +.>、/>Frequencies of two frequency points of GNSS system respectively, < >>、/>For its corresponding wavelength, +.>、/>For the original pseudo-range observations of two frequency points of the GNSS system, < +.>、/>The method comprises the steps of obtaining the original carrier observed quantity of two frequency points of a GNSS system;
ionosphere-free combined observed ambiguity floating solution BC is defined as:
。
3. the GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 1, wherein in step three, the state estimation of the positioning equation is performed using extended kalman filtering.
4. The GNSS dual-frequency carrier phase integer ambiguity resolution method of claim 2, wherein:
in step four, the ionospheric-free ambiguity is further expressed as:
in the above-mentioned method, the step of,is a narrow lane wavelength;
obtaining the single-frequency point ambiguity floating solution of the narrow lane by the relation between the wide lane ambiguity and the ionosphere-free ambiguity
Carrying out narrow-lane ambiguity resolution by the wide-lane ambiguity fixed resolution in the second step and the ionosphere-free ambiguity floating resolution in the third step; setting a single-frequency point ambiguity floating point solution rounding error smaller than 0.35 week in the narrow-lane ambiguity floating point solution estimation part, storing the narrow-lane ambiguity floating point solution meeting the conditions, then carrying out double-difference single-frequency point ambiguity integer solution by using an LAMBDA method according to the calculated narrow-lane ambiguity covariance matrix, if the narrow-lane ambiguity solution fails, failing the current epoch ambiguity solution, and returning to the step one to carry out next epoch solution again;
after the narrow-lane ambiguity fixed solution is obtained, the single-frequency point fixed solution is reversely obtained, further the back-band solution of the filtering positioning equation is carried out, and finally the satellite high-precision positioning is carried out.
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