CN110208841B - Improved GNSS tight combination method facing non-overlapping frequencies - Google Patents

Improved GNSS tight combination method facing non-overlapping frequencies Download PDF

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CN110208841B
CN110208841B CN201910559647.0A CN201910559647A CN110208841B CN 110208841 B CN110208841 B CN 110208841B CN 201910559647 A CN201910559647 A CN 201910559647A CN 110208841 B CN110208841 B CN 110208841B
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贾春
李亮
陆仁锋
杨福鑫
赵琳
李慧
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—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

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Abstract

The invention discloses an improved GNSS tight combination method facing non-overlapping frequencies, belonging to the technical field of satellite precision navigation and positioning; the method comprises the steps of constructing a GNSS pseudo-range and carrier phase single-difference observation equation; establishing a DISB estimation model; constructing a CMC combined observed quantity and DISB correction model; then, performing traversal operation on the single-difference ambiguity search space, sequentially substituting the generated IFDB correction sequence into a DISB correction model, executing an LAMBDA ambiguity fixing algorithm, and counting the value of the ratio of the suboptimum ambiguity to the optimal value; then selecting a single-difference ambiguity value corresponding to the maximum value from the ratio sequence as an optimal solution; and finally, substituting the calculated optimal single-difference ambiguity into the DISB correction model to obtain the optimal ambiguity and a positioning solution value. The method solves the problem of accurately solving the single-difference ambiguity of the reference satellite, improves the ambiguity resolution success rate and the positioning performance, and finally effectively eliminates the influence of the IFDB on RTK ambiguity resolution.

Description

Improved GNSS tight combination method facing non-overlapping frequencies
Technical Field
The invention relates to the field of satellite precision navigation and positioning, in particular to an improved tight combination method of a GNSS facing to non-overlapping frequencies.
Background
Integer ambiguity resolution is a key technology for obtaining high precision and high reliability by a Real-time kinematic (RTK) carrier-phase differential positioning method. Under the environment of limited satellite collection such as cities and canyons, the integer ambiguity resolution and positioning performance of the traditional RTK method are adversely affected due to the insufficient number of available observables. With the modern construction of a Global Navigation Satellite System (GNSS), the technical advantages of multi-system combination are fully exploited, and a chance is provided for improving the whole-cycle ambiguity resolution success rate and the positioning accuracy of an RTK method in a satellite-receiving limited environment.
In the research of GNSS multi-system combination, a GNSS tight combination method is proposed based on the research that a receiver-side differential inter-system bias (dib) has a long-term stability characteristic. The method only selects 1 reference satellite to construct an inter-satellite difference model for all GNSS systems, removes DISB introduced in the model in a pre-calibration mode, increases the redundancy of the model compared with the traditional RTK method, and is helpful for improving the ambiguity resolution success rate and the positioning accuracy. At present, the GNSS tight combination method oriented to the overlapping frequency is widely used for improving the ambiguity resolution success rate and the positioning performance in the environment with satellite-receiving limitation. However, for non-overlapping frequencies, in addition to the need to remove the DISB, the problem of inter-frequency differential bias (IFDB) associated with frequency differences needs to be considered. IFDB depends on the product of the single-difference ambiguity and the frequency difference of the reference satellite. For a given tight combination of GNSS systems, such as BDS B1 in combination with Galileo E1, the frequency difference of the systems cannot be changed. Therefore, accurately solving the single-difference ambiguity of the reference satellite becomes one of effective methods for eliminating the IFDB effect. In the traditional method, the single-difference ambiguity of a reference satellite is solved by carrying-minus-code combination (CMC) combined observed quantity of a Carrier phase by near rounding, and the resolving ambiguity precision is limited by the pseudo-range observed quantity precision. When the pseudorange multipath error is large, a large single difference ambiguity bias will adversely affect IFDB cancellation. At present, the problem of how to accurately solve the single-difference ambiguity of the reference satellite is not effectively solved, so that the tight combination method of the GNSS oriented to non-overlapping frequencies cannot exert the advantages thereof, and the RTK ambiguity resolution and positioning performance is improved to the greatest extent.
Disclosure of Invention
The invention aims to provide an improved GNSS tight combination method facing non-overlapping frequencies, which mainly solves the problem of accurately solving the single-difference ambiguity of a reference satellite, so that IFDB can be effectively eliminated, and the ambiguity resolution success rate and the positioning performance are improved. The method improves the single-difference ambiguity strategy of solving the reference satellite by the traditional GNSS tight combination method facing non-overlapping frequencies, firstly determines a single-difference ambiguity search space by means of a CMC (global coefficient of control) nearest rounding method, then constructs a single-difference ambiguity search criterion to solve the optimal single-difference ambiguity, and finally effectively eliminates the influence of the IFDB on RTK ambiguity resolution. The specific implementation steps of the invention are as follows:
an improved tight combination method of GNSS facing to non-overlapped frequencies, the execution steps include:
the method comprises the following steps: constructing a GNSS pseudo-range and carrier phase single-difference observation equation, and performing linearization processing on the equation by using the approximate position of the station;
step two: in a system initialization stage, establishing a DISB estimation model, and determining a calibration value of the DISB by using data of specified initialization time;
step three: constructing a CMC combined observed quantity, determining a central ambiguity value of a single-difference ambiguity search space of a reference satellite by a near-rounding method, and determining a boundary of the search space according to a priori pseudo-range observation precision;
step four: constructing a DISB correction model by using the DISB calibration value determined in the step two;
step five: performing traversal operation on the single-difference ambiguity search space, generating an IFDB correction sequence, sequentially substituting the IFDB correction sequence into a DISB correction model, performing an LAMBDA ambiguity fixing algorithm, and counting the ratio value of the suboptimum ambiguity to the optimal value;
step six: selecting the single-difference ambiguity value corresponding to the maximum value as an optimal solution in the ratio sequence generated in the step five;
step seven: and substituting the optimal single-difference ambiguity resolved in the sixth step into the DISB correction model in the fourth step to obtain the optimal ambiguity and the positioning solution value.
The single-difference observation model in the first step is expressed as follows:
Figure GDA0003675176850000021
Figure GDA0003675176850000022
wherein s is different satellite numbers, B refers to BDS, E refers to Galileo; p and phi represent the single difference residual quantity of the observed quantity minus the calculated quantity of the pseudo range and the carrier phase; x represents a position increment vector, and the corresponding geometric matrix is u; t represents a receiver clock difference; d and delta respectively represent hardware delay errors of a pseudo range and a carrier phase; z is the ambiguity value; λ represents a wavelength; e and epsilon correspond to the pseudorange and carrier phase observed noise, respectively.
The DISB estimation model in the step two is as follows:
Figure GDA0003675176850000023
Figure GDA0003675176850000024
wherein
Figure GDA0003675176850000025
d BE DISB representing corresponding pseudoranges; delta. for the preparation of a coating BE DISB representing the corresponding carrier phase;
Figure GDA0003675176850000031
referred to herein as IFDB.
The central ambiguity value of the search space in the third step is as follows:
Figure GDA0003675176850000032
wherein [ ·] round "means the operation of rounding up is done nearby,
Figure GDA0003675176850000033
is the central ambiguity value;
Figure GDA0003675176850000034
search space for single-differenced ambiguities, denoted as
Figure GDA0003675176850000035
Wherein
Figure GDA0003675176850000036
Representing an integer set, and N is a spatial search boundary.
The DISB correction model in the fourth step is as follows:
Figure GDA0003675176850000037
Figure GDA0003675176850000038
wherein
Figure GDA0003675176850000039
Representing an estimate of IFDB.
And the ratio value of the suboptimum ambiguity to the optimal ambiguity in the step five is expressed as:
Figure GDA00036751768500000310
wherein "| · |" represents quadratic operation; z is a radical of min The ambiguity optimal solution is obtained; z is a radical of sec The ambiguity is a suboptimal solution;
Figure GDA00036751768500000311
expressed as degree of ambiguity
Figure GDA00036751768500000312
The covariance of (a).
The invention has the beneficial effects that:
the method solves the problem of accurately solving the single-difference ambiguity of the reference satellite, so that the IFDB can be effectively eliminated, and the ambiguity resolution success rate and the positioning performance are improved; the method improves the single-difference ambiguity strategy for solving the reference satellite by the traditional GNSS tight combination method facing non-overlapping frequencies, firstly determines a single-difference ambiguity search space by means of a CMC (global coefficient of control) nearest rounding method, then constructs a single-difference ambiguity search criterion to solve the optimal single-difference ambiguity, and finally effectively eliminates the influence of IFDB on RTK ambiguity resolution.
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FIG. 1 is a flowchart illustrating an improved tight combining GNSS method for non-overlapped frequencies according to the present invention.
Detailed Description
The invention aims to provide an improved tight combination method of GNSS facing to non-overlapping frequency, which mainly solves the problem that the traditional tight combination method of GNSS facing to non-overlapping frequency cannot accurately solve the single-difference ambiguity value of a reference satellite and is difficult to eliminate the influence of IFDB on RTK ambiguity resolution. The method determines a single-difference ambiguity search space through a traditional carrier phase pseudorange (CMC) subtracting method, and determines an optimal single-difference ambiguity value by using the search criterion of maximizing the ambiguity suboptimal solution and optimal solution ratio. The method utilizes the optimal single-difference ambiguity value to correct the IFDB, so that the positioning performance of the GNSS tight combination facing the non-overlapping frequency can be optimal. Compared with the traditional GNSS tight combination method facing non-overlapping frequencies, the method can obtain better satellite navigation positioning performance under the urban canyon environment with limited satellite collection. The invention is further described below with reference to the accompanying drawings.
Example 1:
step 1: and constructing a GNSS pseudo-range and carrier phase single-difference observation equation, and performing linearization processing on the equation by using the approximate position of the station.
The base station and the mobile station simultaneously track the BDS and Galileo satellites s. The single difference operation between stations can eliminate the correlation error of the satellite terminal. And meanwhile, only under the condition of a short baseline, the atmospheric delay error is ignored in the model. The single-difference observation model may be expressed as,
Figure GDA0003675176850000041
wherein s is different satellite numbers, B refers to BDS, E refers to Galileo; p and phi represent the single difference residual quantity of the observed quantity minus the calculated quantity of the pseudo range and the carrier phase; x represents a position increment vector, and the corresponding geometric matrix is u; t represents a receiver clock difference; d and delta respectively represent hardware delay errors of the pseudo range and the carrier phase; z is the ambiguity value; λ represents a wavelength; e and epsilon correspond to the pseudorange and carrier phase observed noise, respectively.
Step 2: in a system initialization stage, establishing a DISB estimation model, and determining a calibration value of the DISB by using data of specified initialization time;
in the initial stage of the system, the calibration value of the DISB needs to be determined by using a specified time arc segment. Therefore, from the single-difference observations given in step 1, construct the DISB estimation model as
Figure GDA0003675176850000042
Wherein
Figure GDA0003675176850000043
d BE DISB representing corresponding pseudoranges; delta BE Indicating the DISB for the corresponding carrier phase.
Figure GDA0003675176850000044
Referred to herein as IFDB. Equation (2) estimates the pseudorange and the carrier phase DISB as parameters. Due to the fact thatThe DISB has long-term stability, so the mean value of the estimated sequence in a specified time arc segment is taken as the calibration value of the DISB. In the invention, the appointed time arc segment is set to be 30 s.
And step 3: and constructing a CMC combined observed quantity, determining a central ambiguity value of a single-difference ambiguity search space of a reference satellite by a near-rounding method, and determining the boundary of the search space according to the prior pseudo-range observation precision.
Constructing CMC combined observed quantity by using pseudo-range of reference satellite and carrier phase single-difference observed quantity, and determining central ambiguity value of search space of CMC combined observed quantity by using nearest rounding method
Figure GDA0003675176850000051
Wherein [ ·] round "means a round-up operation. In order to be able to cover the true single-difference ambiguity value, in the present invention, assuming a pseudorange observation error of 10m, the corresponding search space boundary will be set to N for 50 cycles. Thus, the single-differenced ambiguity search space for the reference satellite
Figure GDA0003675176850000052
Can be expressed as
Figure GDA0003675176850000053
Wherein
Figure GDA0003675176850000054
A set of integers is represented that is,
Figure GDA0003675176850000055
is the central ambiguity value.
And 4, step 4: and (3) constructing a DISB correction model by using the DISB calibration value determined in the step (2).
Substituting the DISB calibration value determined in the step 2 and the candidate IFDB correction quantity as known quantities into the left side of the formula to obtain a corresponding DISB correction model of
Figure GDA0003675176850000056
And 5: and executing traversal operation on the single-difference ambiguity search space, generating an IFDB correction sequence, sequentially substituting the IFDB correction sequence into the DISB correction model, executing an LAMBDA ambiguity fixing algorithm, and counting the value of the ratio of the suboptimum ambiguity to the optimal value.
By traversing IFDB correction quantity determined by the search space of the ambiguity, 2N ambiguity suboptimum and optimal ratio values can be obtained.
Figure GDA0003675176850000057
Wherein "| · |" represents quadratic operation; z is a radical of min The ambiguity optimal solution is obtained; z is a radical of sec The ambiguity is a suboptimal solution;
Figure GDA0003675176850000058
expressed as a degree of ambiguity
Figure GDA0003675176850000059
The covariance of (a).
Step 6: in the ratio sequence generated in step 5, the single-difference ambiguity value corresponding to the maximum value is selected as the optimal solution.
And 7: and (4) substituting the optimal single-difference ambiguity resolved in the step (6) into the DISB correction model in the step (4) to obtain the optimal ambiguity and a positioning solution value.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. An improved tight combination method of GNSS facing non-overlapped frequencies is characterized in that the execution steps comprise:
the method comprises the following steps: constructing a GNSS pseudo-range and carrier phase single-difference observation equation, and performing linearization processing on the equation by using the approximate position of the station;
step two: in the system initialization stage, establishing a DISB (Differential inter-system bias) estimation model between Differential systems at a receiver end, and determining a calibration value of the DISB by using data of specified initialization time, wherein the estimation model is expressed as;
Figure FDA0003648393330000011
Figure FDA0003648393330000012
wherein s is different satellite numbers, B refers to BDS, E refers to Galileo; p and phi represent the single difference residual quantity of the observed quantity minus the calculated quantity of the pseudo range and the carrier phase; d and delta respectively represent hardware delay errors of the pseudo range and the carrier phase; x represents a position increment vector, and the corresponding geometric matrix is u;
Figure FDA0003648393330000013
t represents a receiver clock difference; d BE DISB representing corresponding pseudoranges; delta BE DISB representing the corresponding carrier phase;
Figure FDA0003648393330000014
the designation is inter-frequency difference correlation deviation IFDB (inter-frequency differential bias),
Figure FDA0003648393330000015
searching a space for single-difference ambiguity, and representing the wavelength; e and epsilon respectively correspond to the pseudo range and the observation noise of the carrier phase;
step three: constructing a Carrier-phase reduced pseudo-range CMC (Carrier-minus-code combination) combined observed quantity, determining a central ambiguity value of a single-difference ambiguity search space of a reference satellite by a near-rounding method, and determining a boundary of the search space according to a priori pseudo-range observation precision;
step four: and D, constructing a DISB correction model by using the DISB calibration value determined in the step two, wherein the correction model is represented as:
Figure FDA0003648393330000016
Figure FDA0003648393330000017
wherein
Figure FDA0003648393330000018
Representing an estimate of the IFDB;
step five: performing traversal operation on the single-difference ambiguity search space, generating an IFDB numerical sequence, sequentially substituting the IFDB numerical sequence into a DISB correction model, performing an LAMBDA ambiguity fixing algorithm, and counting the ratio value of suboptimum ambiguity to optimal ambiguity;
step six: selecting the single-difference ambiguity value corresponding to the maximum value as an optimal solution in the ratio sequence generated in the step five;
step seven: and substituting the optimal single-difference ambiguity resolved in the sixth step into the DISB correction model in the fourth step to obtain the optimal ambiguity and the positioning solution value.
2. The improved tight combination method of GNSS facing non-overlapping frequencies as claimed in claim 1, wherein the single-difference observation model in the first step is represented as:
Figure FDA0003648393330000021
Figure FDA0003648393330000022
wherein s is different satellite numbers, B refers to BDS, E refers to Galileo; p and phi represent the single difference residual quantity of the observed quantity minus the calculated quantity of the pseudo range and the carrier phase; x represents a position increment vector, and the corresponding geometric matrix is u; t represents a receiver clock difference; d and delta respectively represent hardware delay errors of the pseudo range and the carrier phase; z is the ambiguity value; λ represents a wavelength; e and epsilon correspond to the pseudorange and carrier phase observed noise, respectively.
3. The improved tight combining method for GNSS facing non-overlapped frequencies as claimed in claim 2, wherein the central ambiguity value of the search space in the third step is:
Figure FDA0003648393330000023
wherein [ ·] round "means a round-up operation;
Figure FDA0003648393330000024
is the central ambiguity value;
Figure FDA0003648393330000025
search space for single-differenced ambiguities, denoted as
Figure FDA0003648393330000026
Wherein
Figure FDA0003648393330000027
Representing an integer set, and N is a spatial search boundary.
4. The improved tight combination method of GNSS facing non-overlapped frequencies as claimed in claim 3, wherein the ambiguity suboptimal to optimal ratio value in the fifth step is expressed as:
Figure FDA0003648393330000028
wherein "| · |" represents quadratic operation; z is a radical of min The ambiguity optimal solution is obtained; z is a radical of sec The ambiguity is a suboptimal solution;
Figure FDA0003648393330000029
expressed as a degree of ambiguity
Figure FDA00036483933300000210
The covariance of (a).
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