CN110441805B - Long-baseline three-frequency ambiguity resolution method based on unequal measurement variance - Google Patents

Long-baseline three-frequency ambiguity resolution method based on unequal measurement variance Download PDF

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CN110441805B
CN110441805B CN201910828674.3A CN201910828674A CN110441805B CN 110441805 B CN110441805 B CN 110441805B CN 201910828674 A CN201910828674 A CN 201910828674A CN 110441805 B CN110441805 B CN 110441805B
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陈飞强
王耀鼎
刘文祥
刘哲
王飞雪
楼生强
李峥嵘
李井源
黄龙
牟卫华
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National University of Defense Technology
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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

Abstract

The invention provides a long-baseline three-frequency ambiguity resolution method based on unequal measurement variance, which solves the problem that when the combined coefficient is calculated by taking the minimum combined noise as an optimal target, the combined coefficient is not optimal and the combined noise is larger because the difference of pseudo-range noise of different frequency points is not considered in the conventional method. The invention considers the fact that pseudo-range noise of different frequency points is different, introduces the condition into the combination coefficient calculation, minimizes the combined noise, reduces the number of required epochs when using the ambiguity detection quantity of the second and third combinations of multi-epoch smoothing, reduces the requirement on data continuity, and has great significance for improving the success rate of fixing the three-frequency ambiguity and further finally improving the positioning accuracy.

Description

Long-baseline three-frequency ambiguity resolution method based on unequal measurement variance
Technical Field
The invention relates to the technical field of high-precision data processing of satellite navigation systems, in particular to a three-frequency ambiguity resolution method under a long baseline condition.
Background
Ambiguity resolution is the basis for high-precision data processing of satellite navigation systems such as Precision Point Position (PPP), Real-time Kinematic (RTK), and the like. At present, a satellite navigation system represented by Beidou and GPS can broadcast three-frequency navigation signals, the three-frequency navigation signals bring information redundancy for ambiguity resolution, and the success rate of ambiguity resolution is improved.
Under the long baseline condition, because the spatial correlation of the ionosphere is weakened, and the ionosphere residual after double differences is larger, the pseudo-range observed quantity is generally added into an observation combination under the long baseline condition so as to meet the constraint of no geometry and no ionosphere. Due to the introduction of the pseudo range, the noise after combination is large, and therefore when the combination coefficient is constrained, the minimum noise after combination is taken as a constraint criterion on the basis of meeting the constraint of no geometry and no ionosphere. At present, when combined noise is calculated, pseudo range noise on three frequency points is generally assumed to be the same, but in an actual environment, the pseudo range noise of the three frequency points is obviously different because code loop parameters, front-end bandwidths, multipath effects and the like of a receiver at different frequency points are different. For the Beidou system, the pseudo range noise on B1I and B2I is significantly greater than B3I. For the GPS system, the pseudorange noise at L1 and L2 is significantly greater than the pseudorange noise at L5.
Therefore, at present, the combined noise calculated on the premise that the pseudo-range noise of the three frequency points is the same is not the actual combined noise, and the calculated combined coefficient is not the optimal combined coefficient, so that the difference of the pseudo-range measurement variance on different frequency points needs to be considered to determine the optimal combined coefficient.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a long-baseline three-frequency ambiguity resolution method based on unequal measurement variance. The method provided by the invention can reduce the combined noise and provide the fixed success rate of the ambiguity.
Under the long baseline condition, the calculation of the combined coefficient of the three-frequency ambiguity resolution generally takes the minimum noise after combination as the optimal target on the premise of meeting the constraint of no geometry and no ionosphere. In the traditional method, when the combined noise is calculated, the pseudo-range noise of three frequency points is assumed to be the same, and the fact that the pseudo-range noise on different frequency points is different due to different code loop bandwidths, front end bandwidths, multipath effects and the like of different frequency points is not considered, so that the calculated combined coefficient is not a real optimal coefficient, and the calculated combined noise is not the minimum. The invention can calculate the optimal combination coefficient by considering the fact that pseudo-range noises on different frequency points are different, reduce the combination noise and improve the fuzzy degree fixing success rate.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a long-baseline three-frequency ambiguity resolution method based on unequal measurement variance comprises the following steps:
(1) the satellite navigation system broadcasts a three-frequency navigation signal, 3 frequency point pseudo ranges of the three-frequency navigation signal at the time t and carrier phases of three frequency points are given, and pseudo range noise of each frequency point is extracted;
(2) calculating pseudo-range noise standard deviation of each frequency point;
(3) given the carrier coefficients of the first combination, calculating the ambiguity of the first combination;
(4) given the carrier coefficients of the second combination, calculating the ambiguity of the second combination;
(5) given the carrier coefficients of the third combination, calculating the ambiguity of the third combination;
(6) and recovering the ambiguity of the three frequency points.
In the invention, the satellite navigation system is a global positioning system capable of broadcasting three-frequency navigation signals. The satellite navigation system can be a Global Positioning System (GPS), a Glonass satellite navigation system, a Beidou satellite navigation system and other satellite navigation systems capable of broadcasting three-frequency navigation signals.
In the step (1), pseudo range noise of each frequency point is extracted according to a formula (1):
MPind＝ρind-(a0φ1+b0φ2+c0φ3) (1)
wherein, MPindWherein ind is 1,2,3, f is the three frequency points to be extracted1,f2,f3Pseudo-range noise at frequency points. RhoindWherein iD is 1,2,3, and f is the frequency of three frequencies respectively1,f2,f3And (4) frequency point pseudorange. Phi is a1,φ2,φ3Respectively three frequencies are respectively f1,f2,f3The frequency point is the carrier phase in meters. a is0,b0,c0Respectively three frequencies are respectively f1,f2,f3And (5) coefficients corresponding to the frequency points.
In the formula (1), a0,b0,c0Calculated from equation (2):
Figure BDA0002189934540000031
wherein f is1,f2,f3Frequencies of three frequency points, alpha, respectively0,β0For the introduced auxiliary coefficients, they are calculated together from equation (2).
In the step (2), the pseudo-range noise standard deviation of each frequency point is calculated according to a formula (3):
Figure BDA0002189934540000032
wherein the content of the first and second substances,
Figure BDA0002189934540000033
indicating that the calculated three frequency points are respectively f1,f2,f3And pseudo range noise standard deviation of frequency points. MP (moving Picture experts group)indFor the three frequency points to be extracted are respectively f1,f2,f3The pseudo-range noise at the frequency point is calculated by the formula (1). N represents the number of epochs required to compute the pseudorange noise standard deviation, typically 50, and h and g represent the respective epochs.
Calculating the frequencies f according to the formula (4)1,f2Compared with the frequency of f3The amplification ratio of the pseudo-range noise standard deviation of the frequency point is as follows:
Figure BDA0002189934540000034
wherein the content of the first and second substances,
Figure BDA0002189934540000041
for pseudo-range noise standard deviation, the calculation is performed by equation (3)
In step (3) of the present invention, the ambiguity of the first combination is calculated according to formula (5):
Figure BDA0002189934540000042
where c is the speed of light. (i, j, k) is the carrier coefficient of the first combination, and is (0, -1, 1). Lambda [ alpha ]ijkFor the first combined wavelength as shown in equation (5), calculated from equation (6):
Figure BDA0002189934540000043
(a1,b1,c1) As pseudo-range coefficients, calculated by equation (7):
Figure BDA0002189934540000044
wherein σρ3The pseudo-range noise standard deviation is calculated by formula (3). Lambda [ alpha ]1Representing frequency point f1Wavelength of carrier phase of c/f1。α1,β1For the introduced auxiliary coefficients, they are calculated together from equation (7).
In step (4) of the present invention, the ambiguity of the second combination is calculated according to formula (8):
Figure BDA0002189934540000045
wherein λ ismntFor the second combined wavelength, by formula(9) And (3) calculating:
Figure BDA0002189934540000051
(m, n, t) is the carrier coefficient of the second combination, which is (1, -1, 0); (i, j, k) is the carrier coefficient of the first combination, and is (0, -1, 1).
NijkCombined ambiguity for the first set of combinations, defined as Nijk＝iN1+jN2+kN3，N1,N2,N3Respectively three frequency points f1,f2,f3Ambiguity of, NijkIs L calculated by the formula (5)1And taking the rounded value.
a2,b2,c2,d2Coefficients, which are respectively corresponding terms, are calculated by equation (10):
Figure BDA0002189934540000052
wherein alpha is2,β2For the introduced auxiliary coefficients, they are calculated together by equation (10);
Figure BDA0002189934540000053
is the carrier phase variance in meters, taken to be 0.0009.
In step (5) of the present invention, the ambiguity of the third combination is calculated according to formula (11):
Figure BDA0002189934540000054
wherein λ isuvwFor the third combined wavelength, calculated by equation (12):
Figure BDA0002189934540000061
(u, v, w) is the carrier coefficient of the third combination, which is (0, 1, 0); (m, n, t) is the carrier coefficient of the second combination, which is (1, -1, 0); (i, j, k) is the carrier coefficient of the first combination, which is (0, -1, 1).
NmntCombined ambiguity for the second set of combinations, defined as Nmnt＝mN1+nN2+tN3，NmntIs represented by the result L of equation (8)2Averaging over 10 epochs and rounding.
a3,b3,c3,d3,e3Coefficients, which are respectively corresponding terms, are calculated by equation (13):
Figure BDA0002189934540000062
α3,β3for the introduced auxiliary coefficients, they are calculated together from equation (13).
In step (6), the ambiguity of each frequency point is recovered according to a formula (14):
Figure BDA0002189934540000063
wherein N is1,N2,N3Respectively three frequencies of f1,f2,f3Ambiguity of frequency point, int (L)1) As a result of the single epoch rounding of equation (5),
Figure BDA0002189934540000064
the result of rounding the result after averaging the results of 10 epochs for equation (8),
Figure BDA0002189934540000065
the results of 200 epochs are averaged for equation (11) and rounded.
Compared with the prior art, the method has the following obvious advantages:
1. the invention considers the fact that the pseudo range noise of different frequency points is different, and applies the fact to the calculation process of the combination coefficient, thereby reducing the combination noise
2. The invention reduces the combination noise, thereby reducing the number of required epochs and reducing the requirement on data continuity when smoothing the ambiguity detection quantity of the second and third combinations by using multiple epochs.
Drawings
FIG. 1 is a block diagram of a three-frequency ambiguity resolution of the present invention under long baseline conditions.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings.
Referring to fig. 1, the invention provides a long-baseline three-frequency ambiguity resolution method based on unequal measurement variance, aiming at satellite navigation systems such as a Global Positioning System (GPS), a glonass satellite navigation system and a Beidou satellite navigation system which can broadcast three-frequency navigation signals, and the method comprises the following steps:
(1) extracting pseudo range noise of each frequency point according to formula (1):
MPind＝ρind-(a0φ1+b0φ2+c0φ3) (1)
wherein, MPindFor the three frequencies to be extracted are respectively f1,f2,f3Pseudo-range noise of frequency points, pindFor three frequencies respectively being f1,f2,f3The frequency point pseudorange, where ind is 1,2,3, represents the frequency point, phi1,φ2,φ3Respectively three frequencies are respectively f1,f2,f3Carrier phase with frequency point in meter0,b0,c0Respectively three frequencies are respectively f1,f2,f3And (5) coefficients corresponding to the frequency points.
a0,b0,c0Calculated from equation (2):
Figure BDA0002189934540000081
wherein f is1,f2,f3Frequencies of three frequency points, alpha, respectively0,β0For the introduced auxiliary coefficients, they are calculated together from equation (2).
(2) Calculating the pseudo-range noise standard deviation of each frequency point according to the formula (3):
Figure BDA0002189934540000082
wherein the content of the first and second substances,
Figure BDA0002189934540000083
indicating that the calculated three frequency points are respectively f1,f2,f3And pseudo range noise standard deviation of frequency points. MP (moving Picture experts group)indFor the three frequency points to be extracted are respectively f1,f2,f3The pseudo-range noise at the frequency point is calculated by the formula (1). N represents the number of epochs required to compute the pseudorange noise standard deviation, typically 50, and h and g represent the respective epochs.
Calculating the frequencies f according to the formula (4)1,f2Compared with the frequency of f3The amplification ratio of the pseudo-range noise standard deviation of the frequency point is as follows:
Figure BDA0002189934540000084
wherein the content of the first and second substances,
Figure BDA0002189934540000085
the pseudo-range noise standard deviation is calculated by formula (3).
(3) The ambiguity of the first combination is calculated according to equation (5):
Figure BDA0002189934540000086
where c is the speed of light and (i, j, k) is the carrier coefficient of the first combination, which is taken to be (0, -1, 1), respectively. Lambda [ alpha ]ijkFor the first combined wavelength, calculated by equation (6):
Figure BDA0002189934540000091
(a1,b1,c1) As pseudo-range coefficients, calculated by equation (7):
Figure BDA0002189934540000092
wherein σρ3Calculated as the pseudo-range noise standard deviation by equation (3), λ1Representing frequency point f1Wavelength of carrier phase of c/f1。α1,β1For the introduced auxiliary coefficients, they are calculated together from equation (7).
(4) Calculating the ambiguity of the second combination according to equation (8):
Figure BDA0002189934540000093
wherein λ ismntFor the second combined wavelength, calculated by equation (9):
Figure BDA0002189934540000094
(m, n, t) is the carrier coefficient of the second combination, which is (1, -1, 0). (i, j, k) is the carrier coefficient of the first combination, and is (0, -1, 1).
NijkCombined ambiguity for the first set of combinations, defined as Nijk＝iN1+jN2+kN3，N1,N2,N3Respectively three frequencies of f1,f2,f3Ambiguity of frequency points, NijkHas a value of(5) Calculated L1And taking the rounded value.
a2,b2,c2,d2Coefficients, which are respectively corresponding terms, are calculated by equation (10):
Figure BDA0002189934540000101
wherein alpha is2,β2For the introduced auxiliary coefficients, they are calculated together by equation (10);
Figure BDA0002189934540000102
is the carrier phase variance in meters, taken to be 0.0009.
(5) Calculating the third combined ambiguity according to equation (11):
Figure BDA0002189934540000103
wherein λ isuvwFor the third combined wavelength, calculated by equation (12):
Figure BDA0002189934540000104
(u, v, w) is the carrier coefficient of the third combination, which is (0, 1, 0); (m, n, t) is the carrier coefficient of the second combination, is (1, -1, 0), and (i, j, k) is the carrier coefficient of the first combination, and is (0, -1, 1). N is a radical ofmntCombined ambiguity for the second set of combinations, defined as Nmnt＝mN1+nN2+tN3，NmntIs represented by the result L of equation (8)2Averaging over 10 epochs and rounding.
a3,b3,c3,d3,e3Coefficients, which are respectively corresponding terms, are calculated by equation (13):
Figure BDA0002189934540000111
wherein: alpha is alpha3,β3For the introduced auxiliary coefficients, they are calculated together from equation (13).
(6) And recovering the ambiguity of each frequency point according to the formula (14):
Figure BDA0002189934540000112
wherein N is1,N2,N3Respectively three frequencies of f1,f2,f3Ambiguity of frequency point, int (L)1) As a result of the single epoch rounding of equation (5),
Figure BDA0002189934540000113
the result of rounding the result after averaging the results of 10 epochs for equation (8),
Figure BDA0002189934540000114
the results of 200 epochs are averaged for equation (11) and rounded.
The invention solves the problem that when the minimum combined noise is used as the optimal target to calculate the combined coefficient, the combined coefficient is not optimal and the combined noise is larger because the difference of pseudo-range noise of different frequency points is not considered in the prior art. The invention considers the fact that pseudo-range noise of different frequency points is different, introduces the condition into the combination coefficient calculation, minimizes the combined noise, reduces the number of required epochs when using the ambiguity detection quantity of the second and third combinations of multi-epoch smoothing, reduces the requirement on data continuity, and has great significance for improving the success rate of fixing the three-frequency ambiguity and further finally improving the positioning accuracy.
The foregoing description of the preferred embodiments of the present invention has been included to describe the features of the invention in detail, and is not intended to limit the inventive concepts to the particular forms of the embodiments described, as other modifications and variations consistent with the principles of the present invention are also protected by the present patent. The subject matter of the present disclosure is defined by the claims, not by the detailed description of the embodiments.

Claims (5)

1. A long-baseline three-frequency ambiguity resolution method based on unequal measurement variance is characterized by comprising the following steps:
(1) the satellite navigation system broadcasts three-frequency navigation signals and provides three-frequency navigation signals at t moment and 3 frequency point pseudo ranges rho thereofindAnd three frequency points f1,f2,f3Carrier phase phi of1,φ2,φ3Extracting pseudo range noise MP of each frequency pointindWherein ind ═ 1,2, 3;
(2) calculating pseudo-range noise standard deviation of each frequency point;
calculating the pseudo-range noise standard deviation of each frequency point according to the formula (3):
Figure FDA0002839424520000011
wherein: n represents the number of epochs required for calculating the standard deviation of pseudo-range noise, and h and g respectively represent the h-th epoch and the g-th epoch;
calculating the frequencies f according to the formula (4)1,f2Compared with the frequency of f3The amplification ratio of the pseudo-range noise standard deviation of the frequency point is as follows:
Figure FDA0002839424520000012
(3) given the carrier coefficients of the first combination, calculating the ambiguity of the first combination;
the ambiguity of the first combination is calculated according to equation (5):
Figure FDA0002839424520000013
wherein c is the speed of light;
λijkis as followsA combined wavelength calculated by equation (6):
Figure FDA0002839424520000014
(i, j, k) is the carrier coefficient of the first combination, which is (0, -1, 1);
(a1,b1,c1) As pseudo-range coefficients, calculated by equation (7):
Figure FDA0002839424520000021
wherein the content of the first and second substances,
Figure FDA0002839424520000024
calculating the pseudo-range noise standard deviation by a formula (3); lambda [ alpha ]1Representing frequency point f1Wavelength of carrier phase of c/f1；α1,β1The introduced auxiliary coefficient is calculated by formula (7);
(4) given the carrier coefficients of the second combination, calculating the ambiguity of the second combination;
calculating the ambiguity of the second combination according to equation (8):
Figure FDA0002839424520000022
wherein λ ismntFor the second combined wavelength, calculated by equation (9):
Figure FDA0002839424520000023
(m, n, t) is the carrier coefficient of the second combination, which is (1, -1, 0);
Nijkcombined ambiguity for the first set of combinations, defined as Nijk＝iN1+jN2+kN3，N1,N2,N3Respectively three frequencies of f1,f2,f3Ambiguity of frequency points, NijkIs L calculated by the formula (5)1Taking the value after the rounding;
a2,b2,c2,d2coefficients, which are respectively corresponding terms, are calculated by equation (10):
Figure FDA0002839424520000031
wherein alpha is2,β2The introduced auxiliary coefficient is calculated by formula (10); sigmaφ23Taking the carrier phase variance in meters as 0.0009;
(5) given the carrier coefficients of the third combination, calculating the ambiguity of the third combination;
calculating the third combined ambiguity according to equation (11):
Figure FDA0002839424520000032
wherein λ isuvwFor the third combined wavelength, calculated by equation (12):
Figure FDA0002839424520000033
(u, v, w) is the carrier coefficient of the third combination, which is (0, 1, 0);
Nmntcombined ambiguity for the second set of combinations, defined as Nmnt＝mN1+nN2+tN3，NmntIs represented by the result L of equation (8)2Averaging over 10 epochs and rounding to obtain the average value;
a3,b3,c3,d3,e3coefficients of the corresponding terms, respectively, expressed by the formula (1)3) And (3) calculating:
Figure FDA0002839424520000041
wherein alpha is3,β3The introduced auxiliary coefficient is calculated by formula (13);
(6) and recovering the ambiguity of the three frequency points.
2. The non-equal measurement variance-based long-baseline tri-band ambiguity resolution method of claim 1, wherein in step (1), the satellite navigation system is a global positioning system, a glonass satellite navigation system or a beidou satellite navigation system capable of broadcasting tri-band navigation signals.
3. The non-equal measurement variance-based long-baseline three-frequency ambiguity resolution method according to claim 1, wherein in step (1), the pseudo-range noise of each frequency point is extracted according to formula (1):
MPind＝ρind-(a0φ1+b0φ2+c0φ3) (1)
wherein, MPindWherein ind is 1,2,3, and the three frequencies to be extracted are f1,f2,f3Pseudo-range noise of frequency points; rhoindFor three frequencies respectively being f1,f2,f3A frequency point pseudo range; phi is a1,φ2,φ3Respectively three frequencies are respectively f1,f2,f3The carrier phase of the frequency point in meters is taken as the unit; a is0,b0,c0Respectively three frequencies are respectively f1,f2,f3And (5) coefficients corresponding to the frequency points.
4. The non-equal measurement variance based long-baseline three-frequency ambiguity resolution method of claim 3, wherein in equation (1), a0,b0,c0Calculated from equation (2):
Figure FDA0002839424520000051
wherein f is1,f2,f3Frequencies of three frequency points, alpha, respectively0,β0Are all introduced auxiliary coefficients.
5. The non-equal measurement variance-based long-baseline three-frequency ambiguity resolution method according to claim 1, wherein in step (6), the ambiguity of each frequency point is restored according to formula (14):
Figure FDA0002839424520000052
wherein int (L)1) As a result of the single epoch rounding of equation (5),
Figure FDA0002839424520000053
the result of rounding the result after averaging the results of 10 epochs for equation (8),
Figure FDA0002839424520000054
the results of 200 epochs are averaged for equation (11) and rounded.
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