CN111751853A - GNSS double-frequency carrier phase integer ambiguity resolution method - Google Patents
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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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
Abstract
The invention provides a GNSS double-frequency carrier phase integer ambiguity resolution method, and belongs to the technical field of satellite high-precision positioning. According to the method, after a dual-frequency carrier phase observation value is preprocessed, a better carrier observation value is screened out to form a double-difference geometric ionosphere-free observation value and a wide lane carrier combination observation value, on the premise of estimating the resolution precision of a wide lane ambiguity floating solution and the single-epoch wide lane ambiguity passing rate, a fixed wide lane integer ambiguity is searched by using an LAMBDA method, the ambiguity floating solution of the ionosphere-free combination observation value is estimated by using a Kalman filter, the narrow lane integer ambiguity is searched and fixed by using the LAMBDA method, and finally a positioning equation set is subjected to back-substitution solution to realize high-precision positioning and attitude resolution of the satellite. According to the method, the problem of low ambiguity fixed rate of the wide lane is solved by using the LAMBDA search algorithm while the ambiguity floating solution precision of the wide lane is considered, and meanwhile, the ambiguity floating solution of the narrow lane is well estimated, so that the overall fixed rate of a base line is improved.
Description
Technical Field
The invention belongs to the technical field of satellite high-precision positioning, and particularly relates to a GNSS double-frequency carrier phase integer ambiguity resolution method.
Background
Currently, the four major Global Navigation Satellite System (GNSS) systems include GPS in the united states, GLONASS in russia, BDS in china, and Galileo in the european union. The global satellite navigation system real-Time relative positioning is called RTK (real Time kinematic) for short, and common errors such as satellite orbit errors, atmospheric propagation delay errors, satellite and receiver clock errors are eliminated or weakened by making difference between receivers and satellites, and centimeter-level and even millimeter-level positioning is realized by utilizing high-precision carrier phase observed quantity. The method has the characteristics of high precision, high reliability, 24-hour continuity and the like, and is widely applied to the civil and military fields. For example, RTK may be applied in the field of traditional surveying, unmanned navigation, etc.
The key to realize high-precision positioning is to correctly solve the carrier phase integer ambiguity, and the difficulty in correctly solving the ambiguity is the integer estimation of an ambiguity floating solution. Under the condition of a short baseline with the baseline length less than 15km, an ionosphere delay error, a troposphere delay error, a satellite clock error and a receiver error can be greatly eliminated or weakened by establishing a carrier phase double-difference observation equation between the receiver and a satellite, the whole-cycle ambiguity is generally easy to fix, and a high-precision positioning result is obtained. However, in the case that the base line length is greater than 15km, due to the weakened spatial correlation, part of the atmospheric delay error and the multipath error are absorbed into the ambiguity floating solution, so that the whole-cycle ambiguity is difficult to fix accurately, and the precision and the reliability of the RTK positioning are reduced. Common ambiguity estimation methods are: rounding, integer Least squares, FARA (fast AmbigutyResolution approach), LAMBDA (Least-square Ambiguty Decorrelation Adjustment). Among them, the LAMBDA method is known as an ambiguity resolution method having the best effect and the most widely used. However, the LAMBDA algorithm has a certain requirement on the precision of the ambiguity floating solution, and if the precision of the ambiguity floating solution to be solved is poor, the searched integer solution generally has a deviation of one week or more. When a middle-long baseline is calculated, a method of taking a whole floating point solution is directly used for solving wide lane whole-cycle ambiguity and narrow lane whole-cycle ambiguity, and therefore the method needs multi-epoch smooth calculation and is poor in reliability of calculation, so that the initialization time is long, and the fixed success rate is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a novel integer ambiguity resolution method, which fully utilizes the advantages of an LAMBDA algorithm and simultaneously utilizes the characteristic that the wide-lane integer ambiguity can be quickly and reliably fixed, evaluates the floating solution precision of the wide-lane ambiguity when resolving the wide-lane ambiguity, searches the fixed wide-lane integer ambiguity by using an LAMBDA method, and searches the fixed-lane narrow integer ambiguity by using a highly reliable wide-lane ambiguity fixed solution and an ionosphere-free ambiguity floating solution estimated by Kalman filtering when resolving the narrow-lane ambiguity. The method shortens the initialization time, improves the fixation rate of the base line, and realizes the fast convergence of the integer ambiguity and the high-precision positioning of the satellite.
In order to achieve the above object, the present invention adopts the following specific technical solutions.
A GNSS dual-frequency carrier phase integer ambiguity resolution method comprises the following steps:
modeling a non-geometric non-ionosphere model;
the first step specifically comprises:
step 1.1, constructing ionosphere-free dual-frequency carrier combination observed quantity and ionosphere-free pseudo range combination observed quantity through GNSS dual-frequency carrier phase observed quantity and dual-frequency pseudo range observed quantity which are subjected to quality check and cycle slip detection processing;
step 1.2, constructing a double-difference observation equation of a geometric non-ionosphere model by using the non-ionosphere carrier combination observed quantity and the non-ionosphere pseudo-range combination observed quantity;
step two, searching and fixing the ambiguity of the wide lane;
the second step specifically comprises:
step 2.1, constructing MW combined observed quantity by using dual-frequency carrier phase observed quantity and dual-frequency pseudo-range observed quantity, wherein the observed quantity is a wide lane ambiguity floating solution;
step 2.2, performing precision estimation on the wide lane ambiguity floating solution, and meanwhile, judging whether the epoch wide lane ambiguity passing rate is greater than 80%;
step 2.3, inputting an optimal wide lane ambiguity floating solution and a covariance matrix thereof, and searching and fixing the wide lane integer ambiguity by using an LAMBDA (label mapping and data acquisition) method;
step three, non-ionosphere ambiguity Kalman filtering estimation;
the third step specifically comprises:
step 3.1, constructing a Kalman filtering equation without ionosphere ambiguity;
step 3.2, estimating the ionospheric-free ambiguity by using a Kalman filter;
step four, narrow lane ambiguity searching and fixing;
the fourth step specifically comprises:
step 4.1, utilizing the non-ionosphere ambiguity floating solution and wide lane integer ambiguity fixed solution solved by filtering to reversely solve the narrow lane ambiguity floating solution;
step 4.2, evaluating the precision of the narrow lane ambiguity floating solution and the measurement precision of the narrow lane combined observation quantity, screening a better narrow lane ambiguity floating solution, and fixing the whole-cycle ambiguity of the narrow lane by using an LAMBDA method;
and 4.3, resolving the single-frequency point integer ambiguity and the fixed ionosphere-free ambiguity, and carrying out back substitution solution on the filter equation.
Further, in the first step, the pseudorange ionospheric-free combined observed quantity and the carrier-phase ionospheric-free combined observed quantity are respectively expressed as:
in the formula ,PIF、ΦIFRespectively are pseudo-range ionosphere-free combined observed quantity, carrier ionosphere-free combined observed quantity, f1、 f2Frequency, lambda, of two frequency points of the GNSS system, respectively1、λ2Is it corresponding toWavelength, P1、P2For raw pseudorange observations at two frequency points of the GNSS system,
original carrier observed quantity of two frequency points of a GNSS system;
the ionospheric-free combined observer ambiguity float solution BC is defined as:
further, in the second step, the double-difference pseudorange and the double-difference carrier observation equation are respectively expressed as follows:
first, a MW combination is constructed, the double-difference wide-lane ambiguity float solution of the satellite pair is
In the above formula, the first and second carbon atoms are,
lambda is the double-difference carrier wave combined observed quantity, double-difference pseudo range combined observed quantity and wide lane combined wavelength]ROUNDIs the operator of rounding;
taking pseudo-range measurement standard deviation sigmaP0.3m, the variance of the combined pseudorange measurements is
The variance of the single difference noise is expressed as
Wherein el is the satellite altitude.
The measured noise variance of the widelane ambiguity can be expressed as
In the formula, superscripts i and j are respectively expressed as indexes of a reference star and a target star, and m is a smooth epoch number;
the ambiguity resolution pass rate is expressed as
in the formula ,PsuccIs the passage rate, nfix、nallRespectively representing the number of ambiguities passing through a certain condition and the total number of the ambiguities participating in resolving;
secondly, searching and resolving the widelane ambiguity.
Preferably, the method for searching and resolving the widelane ambiguity includes:
circularly resolving all the wide lane ambiguity floating solutions of the current epoch, setting the ambiguity rounding error of the wide lane ambiguity floating solution to be less than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be less than 0.2, setting the proportion of the double-difference wide lane ambiguity of the current epoch meeting the two conditions to be more than 80%, storing the corresponding wide lane ambiguity floating solution after the two conditions are met, otherwise, the current epoch is not resolved, returning the algorithm to the first step, and re-resolving the next epoch.
Further, in step three, the state estimation of the positioning equation is performed by using extended kalman filtering, and the specific flow is as follows:
measurement update
In the above formula, the first and second carbon atoms are,
and PkRespectively representing epochs tkState estimation vector and covariance matrix at moment, (+), (-) represent mark before and after filter updating, h (x), H (x) and RkRepresenting the measurement model vector, the design matrix and the covariance matrix of the measurement errors, respectively.
(II) time update
In the above formula, the first and second carbon atoms are,
and
respectively representing a Kalman filtering transfer matrix and a covariance matrix of system noise.
State vector:
x＝(rr T,vr T,B1 T,B2 T)T
vector measurement:
y＝(ΦIF T,PIF T)T
in the formula ,
measuring a model vector:
h(x)＝(hΦ,IF T,hP,IF T)T
designing a matrix:
measuring a noise covariance matrix:
in the above formula, the first and second carbon atoms are,
Further, in step four, the ionospheric-free blur is further expressed as
In the above formula, the first and second carbon atoms are,
is a narrow lane wavelength.
Obtaining narrow lane single-frequency point ambiguity floating solution from the relationship between the wide lane ambiguity and the non-ionosphere ambiguity
Resolving the narrow lane ambiguity by using the wide lane ambiguity fixed solution in the second step and the non-ionosphere ambiguity floating solution in the third step; in the narrow lane ambiguity floating solution estimation part, a single frequency point ambiguity floating solution rounding error is set to be less than 0.35 week in resolving, after the qualified narrow lane ambiguity floating solution is stored, a double difference single frequency point ambiguity integer solution is solved by using an LAMBDA method according to a calculated narrow lane ambiguity covariance matrix, if the narrow lane ambiguity solution fails, the current epoch ambiguity solution fails, and the next epoch solution is carried out again in the returning step I.
And after solving the narrow lane ambiguity fixed solution, reversely solving the single-frequency point fixed solution, further carrying out the loop solution of the filtering positioning equation, and finally carrying out the high-precision positioning of the satellite.
The present invention achieves the following advantageous effects with respect to the limitations of the prior art
According to the method, a more rigorous LAMBDA method is used for replacing a current resolving method for directly taking the integer wide lane ambiguity floating solution when a medium-long baseline is resolved, the double-difference wide lane integer ambiguity of more satellite pairs is fixed to the maximum extent while the precision of the wide lane ambiguity floating solution is considered, and the correct fixation of the double-difference wide lane integer ambiguity is realized.
The method reasonably evaluates the narrow lane ambiguity floating solution, limits the precision of the non-ionosphere ambiguity floating solution, replaces the prior resolving method of directly taking integer narrow lane ambiguity floating solution ambiguity by a more rigorous LAMBDA method on the basis of considering the resolution pass rate of the wide lane ambiguity, realizes the reliable solution of the double-difference narrow lane ambiguity, and achieves the purposes of shortening the initialization time and improving the baseline fixation rate.
Drawings
FIG. 1 is a flow chart of a dual-frequency carrier-phase integer ambiguity algorithm of the present invention;
FIG. 2 is a flowchart of the widelane ambiguity resolution of the present invention;
FIG. 3 is a flowchart of the widelane ambiguity floating solution precision estimation of the present invention;
FIG. 4 is a narrow lane ambiguity resolution flow diagram of the present invention;
FIG. 5 is a graph of the BDS 8km baseline resolution of the present invention;
FIG. 6 is a GPS 66km baseline solution result diagram of the present invention;
fig. 7 is a diagram of the 66km baseline solution results for the BDS of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The invention relates to an improved dual-frequency RTK integer ambiguity resolution method, and the algorithm comprises the steps of GNSS geometry-free ionosphere-free model construction, wide lane ambiguity search fixing, ionosphere-free ambiguity Kalman filtering estimation and narrow lane ambiguity search fixing.
The overall flow chart of the present invention is shown in fig. 1. Firstly, after the GNSS original observed quantity is subjected to quality checking and cycle slip detection, the superior carrier waves and pseudo-range observed quantity are screened out to form a double-difference geometry-free ionosphere-free combined observed quantity, a wide-lane carrier combined observed quantity and a narrow-lane pseudo-range combined observed quantity, a wide-lane ambiguity floating solution is obtained and the precision of the wide-lane ambiguity floating solution is estimated, the fixed wide-lane integer ambiguity is searched by using an LAMBDA method, meanwhile, the ambiguity floating solution of the ionosphere-free combined observed quantity is estimated by using a Kalman filter, then, the narrow-lane ambiguity is searched by using a narrow-lane ambiguity searching and fixing module, the narrow-lane integer ambiguity is searched and fixed by using an LAMBDA method, and finally, the back-substitution solution of an equation set is carried out to realize the high-precision positioning of the satellite.
The method is suitable for reliably fixing double-difference integer ambiguity of the short baseline and the medium-long baseline.
The method comprises the following steps: geometry-free ionospheric-free (IF-combinatorial) model modeling
A geometry-free and ionosphere-free model is constructed by GNSS double-frequency carrier waves and double-frequency pseudo-range original observed quantities after quality check and cycle slip detection processing.
The pseudo-range ionosphere-free combined observed quantity and the carrier phase ionosphere-free combined observed quantity can be respectively expressed as
in the formula ,PIF、ΦIFRespectively are pseudo-range ionosphere-free combined observed quantity, carrier ionosphere-free combined observed quantity, f1、 f2Frequency, lambda, of two frequency points of the GNSS system, respectively1、λ2For its corresponding wavelength, P1、P2For raw pseudorange observations at two frequency points of the GNSS system,
and obtaining the original carrier observed quantity of two frequency points of the GNSS system.
The ionospheric-free combined observer ambiguity float solution BC (in m) is defined as
Step two: wide lane ambiguity search fixing
The widelane ambiguity resolution process is shown in figure 2.
The double-difference pseudorange and the double-difference carrier observation equation can be respectively expressed as follows:
first, construct MW combinations, then the double-differenced widelane ambiguity float solution of the satellite pair is
In the above formula, the first and second carbon atoms are,
lambda is the double-difference carrier wave combined observed quantity, double-difference pseudo range combined observed quantity and wide lane combined wavelength]ROUNDThe rounding operator.
Because the carrier phase measurement precision is higher, only the measurement error of the pseudo-range combined measurement value is considered, and the pseudo-range measurement standard deviation sigma is takenP0.3 m. The variance of the combined pseudorange measurements, known from the law of error propagation, is
The single difference noise variance can be expressed as
Wherein el is the satellite altitude.
The measured noise variance of the widelane ambiguity can be expressed as
In the formula, the superscripts i, j are respectively expressed as indexes of the reference star and the target star, and m is a smooth epoch number.
The ambiguity resolution pass rate is expressed as
in the formula ,PsuccIs the passage rate, nfix、nallRespectively representing the number of ambiguities passing through a condition and the total number of involved resolving ambiguities.
Secondly, searching and resolving the ambiguity of the wide lane:
circularly resolving all the wide lane ambiguity floating solutions of the current epoch, setting the ambiguity rounding error of the wide lane ambiguity floating solution to be less than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be less than 0.2, setting the proportion of the double-difference wide lane ambiguity of the current epoch meeting the two conditions to be more than 80%, storing the corresponding wide lane ambiguity floating solution after the two conditions are met, otherwise, the current epoch is not resolved, returning the algorithm to the first step, and re-resolving the next epoch. The flow is shown in fig. 3.
With the wide lane ambiguity floating solution and the corresponding ambiguity covariance matrix, the wide lane ambiguity can be searched and fixed by using the LAMBDA method.
Step three: ionosphere-free ambiguity Kalman filter estimation
And performing state estimation of the positioning equation by adopting extended Kalman filtering, wherein the specific flow is as follows.
(III) measurement update
In the above formula, the first and second carbon atoms are,
and PkRespectively-indicated calendarYuan tkState estimation vector and covariance matrix at moment, (+), (-) represent mark before and after filter updating, h (x), H (x) and RkRepresenting the measurement model vector, the design matrix and the covariance matrix of the measurement errors, respectively.
(IV) time updating
In the above formula, the first and second carbon atoms are,
and
respectively representing a Kalman filtering transfer matrix and a covariance matrix of system noise.
State vector:
x＝(rr T,vr T,B1 T,B2 T)T
vector measurement:
y＝(ΦIF T,PIF T)T
in the formula ,
measuring a model vector:
h(x)＝(hΦ,IF T,hP,IF T)T
designing a matrix:
measuring a noise covariance matrix:
in the above formula, the first and second carbon atoms are,
And obtaining a floating solution without ionosphere ambiguity through the third step, storing and performing the fourth step.
Step four: narrow lane ambiguity search fixing
The narrow lane ambiguity resolution flow is shown in figure 4.
The ionospheric-free haze can be further expressed as
In the above formula, the first and second carbon atoms are,
is a narrow lane wavelength.
Obtaining narrow lane single-frequency point ambiguity floating solution from the relationship between the wide lane ambiguity and the non-ionosphere ambiguity
And resolving the narrow lane ambiguity by using the wide lane ambiguity fixed solution in the second step and the non-ionosphere ambiguity floating solution in the third step. In the narrow lane ambiguity floating solution estimation part, a single frequency point ambiguity floating solution rounding error is set to be less than 0.35 week in resolving, after the qualified narrow lane ambiguity floating solution is stored, a double difference single frequency point ambiguity integer solution is solved by using an LAMBDA method according to a calculated narrow lane ambiguity covariance matrix, if the narrow lane ambiguity solution fails, the current epoch ambiguity solution fails, and the next epoch solution is carried out again in the returning step I.
And after solving the narrow lane ambiguity fixed solution, reversely solving the single-frequency point fixed solution, further carrying out the loop solution of the filtering positioning equation, and finally carrying out the high-precision positioning of the satellite.
Results of the experiment
Experiment one: the data is derived from static BDS dual-frequency baseline data of a certain region in Shanghai city, the length of the baseline is 8.2km, the sampling frequency is 1Hz, the data has 3167 epochs, the height cut-off angle is set to be 10 degrees during data processing, and the ratio threshold is set to be 2.0.
TABLE 18 km baseline resolution positioning error
As can be seen from Table 1, the baseline fixation ratio is 99.1%, and the positioning errors RMS of the baseline fixation solution in the direction of the local coordinate system ENU are 0.46cm, 1.27cm, and 3.25cm, respectively.
The BDS 8km baseline solution results are 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 converged quickly when the algorithm of the present invention is used to solve the BDS (B1, B3)8km baseline, and the fixed rate is very high.
Experiment two:
experimental data: the data are derived from static GPS/BDS dual-system dual-frequency baseline data of a certain region in Beijing, the length of the baseline is 66.3km, the sampling frequency is 1Hz, the data duration is 4 hours and has 14400 epochs, the altitude cut-off angle is set to be 10 degrees during data processing, and the ratio threshold is set to be 2.0.
TABLE 266 km baseline resolution positioning bias
As can be seen from table 2, when the new algorithm is used to calculate the 66km baselines of the dual-frequency GPS (L1, L2) and the BDS (B1, B3), the fixed rates are 91.7% and 93.1%, respectively; positioning errors RMS of the GPS baseline fixed solution in the direction of the local coordinate system ENU are respectively 2.50cm, 1.36cm and 4.62cm, and positioning errors RMS of the BDS baseline fixed solution in the direction of the local coordinate system ENU are respectively 3.07cm, 2.40cm and 4.58 cm.
The GPS 66km baseline solution results are shown in fig. 6, and the BDS 66km baseline solution results are shown in fig. 7. In fig. 6 and 7, the dotted 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 long-time smooth solution, the positioning error gradually converges, indicating that the ambiguity solution is correct, and reliable solution of the long-distance baseline is achieved, indicating that the solution method of the present invention 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 an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The present application is not limited to any specific form of hardware or software combination. In summary, the above description is only a preferred embodiment of the present application, and is not intended to limit the scope of the present application. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (6)
1. A GNSS dual-frequency carrier phase integer ambiguity resolution method is characterized by comprising the following steps:
modeling a non-geometric non-ionosphere model;
the first step specifically comprises:
step 1.1, constructing ionosphere-free dual-frequency carrier combination observed quantity and ionosphere-free pseudo range combination observed quantity through GNSS dual-frequency carrier phase observed quantity and dual-frequency pseudo range observed quantity which are subjected to quality check and cycle slip detection processing;
step 1.2, constructing a double-difference observation equation of a geometric non-ionosphere model by using the non-ionosphere carrier combination observed quantity and the non-ionosphere pseudo-range combination observed quantity;
step two, searching and fixing the ambiguity of the wide lane;
the second step specifically comprises:
step 2.1, constructing MW combined observed quantity by using dual-frequency carrier phase observed quantity and dual-frequency pseudo-range observed quantity, wherein the observed quantity is a wide lane ambiguity floating solution;
step 2.2, performing precision estimation on the wide lane ambiguity floating solution, and meanwhile, judging whether the epoch wide lane ambiguity passing rate is greater than 80%;
step 2.3, inputting an optimal wide lane ambiguity floating solution and a covariance matrix thereof, and searching and fixing the wide lane integer ambiguity by using an LAMBDA (label mapping and data acquisition) method;
step three, non-ionosphere ambiguity Kalman filtering estimation;
the third step specifically comprises:
step 3.1, constructing a Kalman filtering equation without ionosphere ambiguity;
step 3.2, estimating the ionospheric-free ambiguity by using a Kalman filter;
step four, narrow lane ambiguity searching and fixing;
the fourth step specifically comprises:
step 4.1, utilizing the non-ionosphere ambiguity floating solution and wide lane integer ambiguity fixed solution solved by filtering to reversely solve the narrow lane ambiguity floating solution;
step 4.2, evaluating the precision of the narrow lane ambiguity floating solution and the measurement precision of the narrow lane combined observation quantity, screening a better narrow lane ambiguity floating solution, and fixing the whole-cycle ambiguity of the narrow lane by using an LAMBDA method;
and 4.3, resolving the single-frequency point integer ambiguity and the fixed ionosphere-free ambiguity, and carrying out back substitution solution on the filter equation.
2. The GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 1, wherein:
in the first step, the pseudo-range ionospheric-free combined observed quantity and the carrier phase ionospheric-free combined observed quantity are respectively expressed as:
in the formula ,PIF、ΦIFRespectively are pseudo-range ionosphere-free combined observed quantity, carrier ionosphere-free combined observed quantity, f1、f2Frequency, lambda, of two frequency points of the GNSS system, respectively1、λ2For its corresponding wavelength, P1、P2For raw pseudorange observations at two frequency points of the GNSS system,
original carrier observed quantity of two frequency points of a GNSS system;
the ionospheric-free combined observer ambiguity float solution BC is defined as:
3. the GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 1, wherein:
in the second step, the double-difference pseudorange and the double-difference carrier observation equation are respectively expressed as follows:
first, a MW combination is constructed, the double-difference wide-lane ambiguity float solution of the satellite pair is
In the above formula, Δ ▽ Φ, Δ ▽ P, λ are the double-difference carrier wave combination observed quantity in meters, the double-difference pseudo-range combination observed quantity and the wide lane combination wavelength [. lambda. ], respectively]ROUNDIs the operator of rounding;
taking pseudo-range measurement standard deviation sigmaP0.3m, the variance of the combined pseudorange measurements is
The variance of the single difference noise is expressed as
Wherein el is the satellite altitude.
The measured noise variance of the widelane ambiguity can be expressed as
In the formula, superscripts i and j are respectively expressed as indexes of a reference star and a target star, and m is a smooth epoch number;
the ambiguity resolution pass rate is expressed as
in the formula ,PsuccIs the passage rate, nfix、nallRespectively representing the number of ambiguities passing through a certain condition and the total number of the ambiguities participating in resolving;
secondly, searching and resolving the widelane ambiguity.
4. The GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 3, wherein:
the method for searching and resolving the widelane ambiguity comprises the following steps:
circularly resolving all the wide lane ambiguity floating solutions of the current epoch, setting the ambiguity rounding error of the wide lane ambiguity floating solution to be less than 0.2 week and the standard deviation of the wide lane ambiguity measurement noise to be less than 0.2, setting the proportion of the double-difference wide lane ambiguity of the current epoch meeting the two conditions to be more than 80%, storing the corresponding wide lane ambiguity floating solution after the two conditions are met, otherwise, the current epoch is not resolved, returning the algorithm to the first step, and re-resolving the next epoch.
5. The GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 1, wherein:
in the third step, the state estimation of the positioning equation is carried out by adopting the extended Kalman filtering, and the specific flow is as follows:
measurement update
In the above formula, the first and second carbon atoms are,
and PkRespectively representing epochs tkState estimation vector and covariance matrix at moment, (+), (-) represent mark before and after filter updating, h (x), H (x) and RkRepresenting the measurement model vector, the design matrix and the covariance matrix of the measurement errors, respectively.
(II) time update
In the above formula, the first and second carbon atoms are,
and
respectively representing a Kalman filtering transfer matrix and a covariance matrix of system noise.
State vector:
x＝(rr T,vr T,B1 T,B2 T)T
vector measurement:
y＝(ΦIF T,PIF T)T
in the formula ,
measuring a model vector:
h(x)＝(hΦ,IF T,hP,IF T)T
designing a matrix:
measuring a noise covariance matrix:
in the above formula, the first and second carbon atoms are,
6. The GNSS dual-frequency carrier-phase integer ambiguity resolution method of claim 1, wherein:
in step four, the ionospheric-free haze is further expressed as
In the above formula, the first and second carbon atoms are,
a narrow lane wavelength;
obtaining narrow lane single-frequency point ambiguity floating solution from the relationship between the wide lane ambiguity and the non-ionosphere ambiguity
Resolving the narrow lane ambiguity by using the wide lane ambiguity fixed solution in the second step and the non-ionosphere ambiguity floating solution in the third step; in the narrow lane ambiguity floating solution estimation part, a single frequency point ambiguity floating solution rounding error is set to be less than 0.35 week in resolving, after the qualified narrow lane ambiguity floating solution is stored, a double-difference single-frequency point ambiguity integer solution is solved by using an LAMBDA method according to a calculated narrow lane ambiguity covariance matrix, if the narrow lane ambiguity solution fails, the current epoch ambiguity solution fails, and the next epoch solution is carried out again in the returning step one;
and after solving the narrow lane ambiguity fixed solution, reversely solving the single-frequency point fixed solution, further carrying out the loop solution of the filtering positioning equation, and finally carrying out the high-precision positioning of the satellite.
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