CN109597105B - GPS/GLONASS tightly-combined positioning method considering deviation between carrier systems - Google Patents

GPS/GLONASS tightly-combined positioning method considering deviation between carrier systems Download PDF

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CN109597105B
CN109597105B CN201811523438.2A CN201811523438A CN109597105B CN 109597105 B CN109597105 B CN 109597105B CN 201811523438 A CN201811523438 A CN 201811523438A CN 109597105 B CN109597105 B CN 109597105B
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glonass
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CN109597105A (en
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高旺
潘树国
闻贺
刘力玮
赵越
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Southeast 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
    • G01S19/421—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system
    • G01S19/425—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system by combining or switching between signals derived from different satellite radio beacon positioning systems
    • 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
    • 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 a GPS/GLONASS tight combination positioning method considering the deviation between carrier systems. Firstly, re-parameterizing three parameters of receiver clock error, hardware delay and single-difference ambiguity in a GPS system and a GLONASS system to construct an interstation single-difference integer ambiguity resolvable model; on the basis, a GPS is used as a reference system, an estimated model of the deviation between the carrier systems is constructed, and the time-varying characteristics of the carrier systems are subjected to statistical analysis; based on the characteristic, a random walk process with small spectrum density is adopted to perform time domain modeling on the deviation between systems, and a GPS and GLONASS tightly-combined positioning model is established. The positioning result shows that the positioning precision can be obviously improved by adopting an intersystem tight combination die, and the improvement on the shielding environment with few visible satellites is especially obvious.

Description

GPS/GLONASS tightly-combined positioning method considering deviation between carrier systems
Technical Field
The invention relates to a multisystem fusion Navigation positioning technology, in particular to a GPS/GLONASS tight combination positioning method considering deviation between carrier systems, and belongs to the technical field of GNSS (Global Navigation Satellite System) positioning and Navigation.
Background
With the modernization of existing GNSS (global navigation satellite system), more satellites are available for precise positioning. The combined use of the satellite systems can significantly improve the positioning accuracy and reliability of the GNSS, especially in the environment with serious sheltering. For centimeter-level real-time dynamic RTK positioning, two models are mainly used: one is that each system selects a loose combination model of respective reference stars, namely an intra-system differential model; and the other system selects a tightly combined model of a common reference star, namely an intersystem difference model. If the differential intersystem bias can be handled correctly, the intersystem differential model is beneficial to adding a large amount of redundant observation information, thereby being beneficial to positioning in a severe observation environment in which satellite signals are easily blocked.
In recent years, CDMA (code division multiple access) systems, such as the tight-matched model between GPS, BDS, galileo and QZSS, have been extensively studied. However, for GLONASS adopting FDMA (frequency division multiple access), an intra-system loose combination model is generally adopted, which is not favorable for better exerting the advantages of multi-GNSS fusion positioning.
Disclosure of Invention
The technical problem to be solved by the invention is as follows:
in order to exert the advantages of multi-GNSS fusion positioning, a GPS/GLONASS tightly combined positioning method considering the deviation between carrier systems is provided.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a GPS/GLONASS tight combination positioning method considering deviation between carrier systems, which comprises the following steps:
step 1, re-parameterizing three parameters of receiver clock error, hardware delay and single-difference ambiguity in a GPS and GLONASS system to construct an interstation single-difference integer ambiguity resolvable model;
step 2, constructing an estimated model of the deviation between carrier systems by taking a GPS as a reference system, and carrying out statistical analysis on the time-varying characteristics of deviation parameters between the carrier systems;
and 3, performing time domain modeling on the deviation between the systems by adopting a random walk process based on the model and the analysis result in the step 2 to obtain a GPS and GLONASS tight combination model, and performing multi-epoch continuous positioning.
As described above, a GPS/GLONASS tightly combined positioning method considering the offset between carrier systems further includes: in the step 1, the three parameters of receiver clock error, hardware delay and single-difference ambiguity in the GPS and GLONASS systems are re-parameterized to construct an interstation single-difference integer ambiguity resolvable model, which comprises the following steps:
step 1.1, establishing an interstation single difference observation model in the GPS and GLONASS systems:
assuming that m GPS satellites and n GLONASS satellites are observed together, for a short base line, neglecting the influence of atmospheric delay, the interstation single-difference observation model is expressed as:
Figure BDA0001903791010000021
Figure BDA0001903791010000022
Figure BDA0001903791010000023
Figure BDA0001903791010000024
the formula (1) and the formula (2) are a single difference carrier observation equation and a pseudo-range observation equation between GPS stations, respectively, and the formula (3) and the formula (4) are a single difference carrier observation equation and a pseudo-range observation equation between GLONASS stations, respectively. In the formula (I), the compound is shown in the specification,
Figure BDA0001903791010000025
represents the observation value of single-difference carrier wave among GPS satellite stations, the unit is meter, wherein the superscript s =1 G ，2 G ，…，m G Denotes the GPS satellite number, and the subscript j denotes the frequency point;
Figure BDA0001903791010000026
represents the satellite distance of single difference station between GPS satellite stations, and Δ dT represents the clock difference of single difference receiver between stations, λ j，G Representing the wavelength, Δ δ, of GPS satellite signals j，G Represents the hardware delay of single difference carrier wave between terminal stations of the GPS satellite receiver,
Figure BDA0001903791010000027
representing the single-difference ambiguity between GPS satellite stations,
Figure BDA0001903791010000028
representing the single difference carrier measurement noise between GPS satellite stations,
Figure BDA0001903791010000029
represents an inter-station single-difference pseudorange observation, Δ d, of a GPS satellite j，G Represents the hardware delay of single difference pseudo range between GPS satellite receiver terminal stations,
Figure BDA00019037910100000210
representing single difference pseudo range measurement noise between GPS satellite stations;
Figure BDA00019037910100000211
represents the observed value of single difference carrier wave among GLONASS satellite stations in meters, wherein the superscript q =1 R ，2 R ，…，n R Denotes the GLONASS satellite number, and the subscript j denotes the frequency point;
Figure BDA00019037910100000212
representing the single difference station inter-station satellite distance between the GLONASS satellite stations,
Figure BDA00019037910100000213
denotes the GLONASS satellite wavelength, Δ δ j，R Representing the hardware delay of the single difference carrier between the GLONASS satellite receiver terminals,
Figure BDA00019037910100000214
representing the single-difference ambiguity between GLONASS satellite stations,
Figure BDA00019037910100000215
representing the single difference carrier measurement noise between GLONASS satellite stations,
Figure BDA00019037910100000216
represents the observed value of the single-differenced pseudo-range between GLONASS satellite stations, delta d j，R Represents the hardware delay of single differenced pseudo range between GLONASS satellite receiver terminal stations,
Figure BDA00019037910100000217
represents the code offset between the stations of the GLONASS satellite,
Figure BDA00019037910100000218
representing single difference pseudorange measurement noise between GLONASS satellite stations;
step 1.2, constructing an inter-station single-difference observation model according to the step 1.1, re-parameterizing three parameters of receiver clock difference, hardware delay and single-difference ambiguity and performing parameter decorrelation to obtain an inter-station single-difference integer ambiguity resolvable model as follows:
for GPS, delta dT, delta in the model of single difference observation between stations j，G ，
Figure BDA00019037910100000219
And (3) having correlation, and performing parameter decorrelation on the re-parametrization of the correlation to obtain a full rank observation equation as follows:
Figure BDA0001903791010000031
Figure BDA0001903791010000032
wherein:
Figure BDA0001903791010000033
Figure BDA0001903791010000034
the formula (5) and the formula (6) are full rank observation equations obtained after single difference between stations in the GPS system is re-parameterized,
Figure BDA0001903791010000035
represents the inter-station single-difference ambiguity of the GPS system reference satellite,
Figure BDA0001903791010000036
representing double-differenced ambiguities of the GPS system;
for GLONASS, since each satellite in the FDMA system has a different wavelength and there is an inter-frequency code bias between different frequencies, the observation equation of GLONASS re-reference is as follows:
Figure BDA0001903791010000037
Figure BDA0001903791010000038
the equation (9) and the equation (10) are the observation equations obtained after single difference between stations in the GLONASS system is re-parameterized, wherein in the equation,
Figure BDA0001903791010000039
representing the wavelengths of the GLONASS reference stars,
Figure BDA00019037910100000310
representing the interstation single-difference ambiguity of the GLONASS system reference star;
rewriting formula (9) to the following form:
Figure BDA00019037910100000311
as can be seen from equation (11), since the whole-cycle ambiguity of the reference star is unknown, equation (11) is still a rank-deficient equation; for this purpose, a second reference satellite is selected, and parameterization is carried out again to obtain the following observation equation:
Figure BDA00019037910100000312
wherein:
Figure BDA00019037910100000313
the observation equations for the other satellites are thus obtained as follows:
Figure BDA00019037910100000314
wherein:
Figure BDA00019037910100000315
in the formula (16), when | k 1 -k 2 When the value of | =1,
Figure BDA0001903791010000041
are integers.
The full rank observation equation for GLONASS carrier phase can thus be derived as follows:
Figure BDA0001903791010000042
the method for tightly combining and positioning GPS/GLONASS considering the offset between carrier systems as described above further comprises: in the step 2, a GPS is used as a reference system, an inter-carrier system deviation estimable model is constructed, and statistical analysis is performed on time-varying characteristics thereof, which specifically includes:
after the carrier phase full-rank observation equation in the GPS and GLONASS systems is obtained in the step 2, only the receiver clock error of the GPS is estimated by taking the GPS system as a reference system, and the order is made
Figure BDA0001903791010000043
And
Figure BDA0001903791010000044
the difference value of (2) is a deviation parameter between carrier systems; the carrier intersystem deviation estimable model is obtained as follows:
Figure BDA0001903791010000045
wherein, the deviation parameters between the carrier systems are as follows:
Figure BDA0001903791010000046
the method for tightly combining and positioning GPS/GLONASS considering the offset between carrier systems as described above further comprises: the spectral density of the random walk process in the step 3 is 0.05 × 0.05cycle 2 /h。
The method for tightly combining and positioning GPS/GLONASS considering the offset between carrier systems as described above further comprises: in the step 3, a time domain modeling is performed on the intersystem deviation by adopting a random walk process to obtain a tight combination positioning and filtering model of GPS and GLONASS, and the method comprises the following steps:
step 3.1, performing time domain modeling on the deviation between the systems by adopting a random walk process;
and 3.2, constructing a GPS and GLONASS tightly combined positioning filtering model, and performing multi-epoch continuous positioning.
The method for tightly combining and positioning GPS/GLONASS considering the offset between carrier systems as described above further comprises: the step 3.1 specifically comprises the following steps:
for inter-system deviation delta GR And performing time domain modeling by adopting a random walk model with smaller spectral density, wherein the formula is as follows:
Figure BDA0001903791010000051
where k represents the epoch, w represents the process noise,
Figure BDA0001903791010000052
is the variance of w and is,
Figure BDA0001903791010000053
spectral density of w 0.05X 0.05cycle 2 /h。
The method for tightly combining and positioning GPS/GLONASS considering the offset between carrier systems as described above further comprises: step 3.2 the step of multi-epoch continuous positioning includes:
step 3.2.1 State prediction
Using estimated or filtered initial value X of previous time k-1 Obtaining the predicted state vector at the next momentX k，k-1 ：
X k，k-1 ＝Φ k，k-1 X k-1 (22)
Meanwhile, the predicted state vector X can be obtained according to the error propagation law k，k-1 Of the covariance matrix Q k，k-1 ：
Figure BDA0001903791010000054
Step 3.2.2, calculating the filter gain
Calculating a filtered gain matrix K according to the predicted variance information and the observation model of the current epoch k ：
Figure BDA0001903791010000055
Step 3.2.3, valuation update
Using a filter gain matrix K k Combined with the observation vector L at the current moment k For the filtered estimate X k，k Perform the update
X k，k ＝X k，k-1 +K k (L k -A k X k，k-1 ) (25)
Simultaneous pair variance covariance matrix Q k，k Perform the update
Q k.k ＝(I-K k A k )Q k，k-1 (26)
And repeatedly executing the three steps at the next moment to realize continuous resolving of the positioning result and obtain a multi-epoch continuous positioning result.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
(1) The invention adopts GPS and GLONASS to carry out carrier difference tight combination positioning, thereby overcoming the defect that the carrier difference tight combination positioning can be carried out only in a CDMA system in the prior research;
(2) The method can reduce the parameters to be estimated, is favorable for enhancing the stability of the observation model in a shielding environment, and improves the positioning precision and reliability.
Drawings
FIG. 1 is a flow chart of the method.
FIG. 2 is a schematic diagram of a zero baseline and a short baseline for analyzing bias between GPS and GLONASS carrier systems.
FIG. 3 is a diagram of the offset time series between GPS-GLONASS carrier systems under different conditions.
FIG. 4 is a comparison graph of the 3-day positioning deviations in the directions of N, E, U for the GPS + GLONASS loose combination and the GPS + GLONASS tight combination in the simulated occlusion environment (8 visible satellites).
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
it will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
FIG. 1 shows a flow chart of the method of the present invention. As shown in FIG. 1, the present invention provides a tight-coupled GPS/GLONASS positioning method considering the deviation between carrier systems, comprising the following steps:
step 1, re-parameterizing three parameters of receiver clock error, hardware delay and single-error ambiguity in a GPS and GLONASS system to construct an interstation single-error integer ambiguity resolvable model;
step 2, constructing an estimated model of the deviation between carrier systems by taking a GPS as a reference system, and carrying out statistical analysis on the time-varying characteristics of deviation parameters between the carrier systems;
and 3, performing time domain modeling on the deviation between the systems by adopting a random walk process based on the model and the analysis result in the step 2 to obtain a GPS and GLONASS tight combination model, and performing multi-epoch continuous positioning.
In the step 1, the three parameters of receiver clock error, hardware delay and single-difference ambiguity in the GPS and GLONASS systems are re-parameterized to construct an interstation single-difference integer ambiguity resolvable model, which comprises the following steps:
step 2.1, constructing an interstation single difference observation model in the GPS and GLONASS systems:
assuming that m GPS satellites and n GLONASS satellites are observed together, for a short baseline, the effect of atmospheric delay can be ignored, and the model of single-difference observation between stations can be expressed as:
Figure BDA0001903791010000061
Figure BDA0001903791010000062
Figure BDA0001903791010000071
Figure BDA0001903791010000072
the formula (1) and the formula (2) are a single difference carrier observation equation and a pseudo-range observation equation between GPS stations, respectively, and the formula (3) and the formula (4) are a single difference carrier observation equation and a pseudo-range observation equation between GLONASS stations, respectively. In the formula (I), the compound is shown in the specification,
Figure BDA0001903791010000073
(superscript s =1 G ，2 G ，…，m G Representing a GPS satellite, subscript j representing a frequency point) represents a single difference carrier observation (meters) between GPS satellite stations,
Figure BDA0001903791010000074
showing the satellite distance of single difference station between GPS satellite stations, delta dT showing the clock difference of single difference receiver between stations, lambda j，G Representing the wavelength, delta, of GPS satellite signals j，G Indicating single difference between GPS satellite receiver terminalsThe hardware delay of the carrier wave is delayed,
Figure BDA0001903791010000075
representing the single-difference ambiguity between GPS satellite stations,
Figure BDA0001903791010000076
representing the single difference carrier measurement noise between GPS satellite stations,
Figure BDA0001903791010000077
represents an inter-station single-difference pseudorange observation, Δ d, of a GPS satellite j，G Represents the hardware delay of single difference pseudo range between GPS satellite receiver terminal stations,
Figure BDA0001903791010000078
representing single difference pseudo range measurement noise between GPS satellite stations;
Figure BDA0001903791010000079
(superscript q = 1) R ，2 R ，…，n R Representing GLONASS satellites, subscript j representing a frequency point) represents single difference carrier observations (meters) between GLONASS satellites,
Figure BDA00019037910100000710
representing the single difference station inter-station satellite distance between the GLONASS satellite stations,
Figure BDA00019037910100000711
denotes the GLONASS satellite wavelength, Δ δ j，R Represents the hardware delay of single difference carrier wave between the GLONASS satellite receiver terminal stations,
Figure BDA00019037910100000712
representing the single-difference ambiguity between GLONASS satellite stations,
Figure BDA00019037910100000713
representing the single difference carrier measurement noise between GLONASS satellite stations,
Figure BDA00019037910100000714
representing single differences between GLONASS satellite stationsPseudorange observations, Δ d j，R Represents the hardware delay of the homodyne pseudoranges between the GLONASS satellite receiver terminals,
Figure BDA00019037910100000715
represents the code offset between the stations of the GLONASS satellite,
Figure BDA00019037910100000716
representing the single differenced pseudorange measurement noise between GLONASS satellite stations.
Step 2.2, according to the interstation single-difference observation model constructed in the step 2.1, three types of parameters including receiver clock difference, hardware delay and single-difference ambiguity are re-parameterized and subjected to parameter decorrelation, and an interstation single-difference integer ambiguity resolvable model can be obtained as follows:
for GPS, due to the Δ dT, Δ δ in the inter-station single difference observation model j，G ，
Figure BDA00019037910100000717
The method has correlation, so the method needs to be re-parameterized for parameter decorrelation to obtain a full rank observation equation as follows:
Figure BDA00019037910100000718
Figure BDA00019037910100000719
wherein:
Figure BDA00019037910100000720
Figure BDA00019037910100000721
the formula (5) and the formula (6) are full rank observation equations obtained after single difference between stations in the GPS system is re-parameterized,
Figure BDA0001903791010000081
represents the interstation single-difference ambiguity of the GPS system reference star,
Figure BDA0001903791010000082
representing the double-differenced ambiguity of the GPS system.
For GLONASS, since each satellite in the FDMA system has a different wavelength and there is an inter-frequency code bias between different frequencies, the observation equation of GLONASS re-reference is as follows:
Figure BDA0001903791010000083
Figure BDA0001903791010000084
the formula (9) and the formula (10) are observation equations obtained after single-difference re-parametrization between stations in the GLONASS system, in the formula,
Figure BDA0001903791010000085
representing the wavelengths of the GLONASS reference stars,
Figure BDA0001903791010000086
representing the interstation single-difference ambiguity of the GLONASS system reference star.
Rewriting formula (9) to the following form:
Figure BDA0001903791010000087
as can be seen from equation (11), since the whole-cycle ambiguity of the reference star is unknown, equation (11) is still a rank-deficient equation. For this purpose, a second reference satellite is selected, and the observation equation obtained by carrying out parameterization again is as follows:
Figure BDA0001903791010000088
wherein:
Figure BDA0001903791010000089
the observation equations for the other satellites are thus obtained as follows:
Figure BDA00019037910100000810
wherein:
Figure BDA00019037910100000811
in the formula (16), when | k 1 -k 2 When the value of | =1,
Figure BDA00019037910100000812
are integers.
The full rank observation equation for GLONASS carrier phase can thus be derived as follows:
Figure BDA00019037910100000813
in the step 2, a GPS is used as a reference system, an inter-carrier system deviation estimable model is constructed, and the time-varying characteristics of the model are statistically analyzed, including the following steps:
after the carrier phase full-rank observation equation in the GPS and GLONASS systems is obtained in the step 2, the GPS system is taken as a reference system, only the receiver clock error of the GPS is estimated, and then
Figure BDA0001903791010000091
And
Figure BDA0001903791010000092
the difference can form a new parameter, which is the carrier intersystem offset parameter, so that the carrier intersystem offset estimation model can be obtained as follows:
Figure BDA0001903791010000093
wherein:
Figure BDA0001903791010000094
in the step 3, a time domain modeling is performed on the inter-system deviation by adopting a random walk process, and a GPS and GLONASS tight combination positioning filtering model is constructed, specifically:
for an estimable intersystem deviation Δ δ GR And performing time domain modeling by adopting a random walk model with smaller spectral density to absorb possible slow change, wherein the formula is as follows:
Figure BDA0001903791010000095
where k represents the epoch, w represents the process noise,
Figure BDA0001903791010000096
is the variance of w and is,
Figure BDA0001903791010000097
the spectral density of w is 0.05X 0.05cycle 2 /h。
As shown in fig. 2, the inter-carrier-system offset parameter is stable over time, and more redundancy observations can be obtained by using the stability of the inter-carrier-system offset parameter in the multi-epoch continuous positioning. The multi-epoch continuous positioning comprises the following steps:
based on a time domain modeling model of the intersystem deviation, a Kalman filtering is adopted to establish a GPS and GLONASS tightly combined positioning filtering model, namely a state equation and an observation equation shown in an equation (20) and an equation (21):
X k ＝Φ k，k-1 X k-1 +w k (20)
L k ＝A k X k +v k
in the formula, X k And X k-1 Respectively represent t k And t k-1 A state vector of a time; phi k，k-1 Denotes t k-1 Time to t k A state transition matrix of the system state at the moment; w is a k Representing a system dynamic noise vector; l is k Represents t k An observation vector of a time; a. The k A coefficient matrix which is an observation equation; v. of k To observe the noise vector. In GNSS data processing, system noise w is generally assumed k And observation noise v k Are uncorrelated and have zero mean and white Gaussian noise characteristics, i.e.
Figure BDA0001903791010000101
In the formula, Q wk And R k Respectively, a variance matrix of system noise and a variance matrix of measurement noise.
The Kalman filtering parameter estimation mainly comprises a time updating part and an observation value updating part, and the specific calculation steps are as follows:
(1) State prediction
Using estimated or filtered initial value X of previous time k-1 Obtaining the predicted state vector X at the next moment k，k-1 ：
X k，k-1 ＝Φ k，k-1 X k-1 (22)
Meanwhile, the predicted state vector X can be obtained according to the error propagation law k，k-1 Of (2) a variance covariance matrix Q k，k-1 ：
Figure BDA0001903791010000102
(2) Calculating filter gain
Calculating a filtered gain matrix K based on the predicted variance information and the observation model of the current epoch k ：
Figure BDA0001903791010000103
(3) Valuation update
Using a filter gain matrix K k Combined with the observation vector L at the current moment k For the filtered estimate X k，k Perform the update
X k，k ＝X k，k-1 +K k (L k -A k X k，k-1 ) (25)
Simultaneous update of variance-covariance matrix
Q k.k ＝(I-K k A k )Q k，k-1 (26)
And at the next moment, repeatedly executing the three steps, thereby realizing the continuous resolving of the positioning result and obtaining the multi-epoch continuous positioning result.
Figure BDA0001903791010000104
Figure BDA0001903791010000111
TABLE 1
Table 1 is the zero baseline and short baseline information used. Experimental analysis was performed using the zero baseline and the short baseline of the australian university of cotting multi-system GNSS as shown in fig. 2 and table 1, and the sequence of estimates of the inter-system bias single epoch of the GPS-GLONASS carrier can be calculated according to the above step 2, as shown in fig. 3, it can be seen that, regardless of the same receiver type or different receiver types, the inter-system bias of the carrier is relatively stable with time, the amplitude of the mean value in the three-day range is within 0.1 week, and the standard deviation is better than 0.01 week. Fig. 4 shows a comparison of positioning results when the number of visible satellites is 8 and the conventional loose combination model and the tight combination model of the present invention are used, and it can be seen that the positioning accuracy can be significantly improved by using the tight combination model, and the positioning accuracy can be improved by 13.5%, 15.0% and 46.2% in N, E, U three directions, respectively.
The foregoing is only a partial embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (2)

1. A GPS/GLONASS tight combination positioning method considering deviation between carrier systems is characterized by comprising the following steps:
step 1, re-parameterizing three parameters of receiver clock error, hardware delay and single-difference ambiguity in a GPS and GLONASS system to construct an interstation single-difference integer ambiguity resolvable model, comprising the following steps of:
step 1.1, establishing an interstation single difference observation model in the GPS and GLONASS systems:
assuming that m GPS satellites and n GLONASS satellites are observed together, for a short base line, neglecting the influence of atmospheric delay, the interstation single-difference observation model is expressed as:
Figure FDA0003804333380000011
Figure FDA0003804333380000012
Figure FDA0003804333380000013
Figure FDA0003804333380000014
the formula (1) and the formula (2) are a single difference carrier observation equation and a pseudo-range observation equation between GPS stations, respectively, the formula (3) and the formula (4) are a single difference carrier observation equation and a pseudo-range observation equation between GLONASS stations, respectively,
Figure FDA0003804333380000015
represents the observation value of single-difference carrier wave among GPS satellite stations, and the unit is meter, wherein the superscript s =1 G ,2 G ,…,m G Denotes the GPS satellite number, and the subscript j denotes the frequency point;
Figure FDA0003804333380000016
showing the satellite distance of single difference station between GPS satellite stations, delta dT showing the clock difference of single difference receiver between stations, lambda j,G Representing the wavelength, delta, of GPS satellite signals j,G Represents the hardware delay of single difference carrier wave between terminal stations of the GPS satellite receiver,
Figure FDA0003804333380000017
representing the single-difference ambiguity between GPS satellite stations,
Figure FDA0003804333380000018
representing the single difference carrier measurement noise between GPS satellite stations,
Figure FDA0003804333380000019
represents an inter-station single-difference pseudorange observation, Δ d, of a GPS satellite j,G Represents the hardware delay of single difference pseudo range between GPS satellite receiver terminal stations,
Figure FDA00038043333800000110
representing single difference pseudo range measurement noise between GPS satellite stations;
Figure FDA00038043333800000111
represents the observed value of single difference carrier wave among GLONASS satellite stations, the unit is meter, wherein the superscript q =1 R ,2 R ,…,n R Denotes the GLONASS satellite number, and the subscript j denotes the frequency point;
Figure FDA00038043333800000112
representing the single difference station inter-station satellite distance between the GLONASS satellite stations,
Figure FDA00038043333800000113
denotes the GLONASS satellite wavelength, Δ δ j,R Represents the hardware delay of single difference carrier wave between the GLONASS satellite receiver terminal stations,
Figure FDA00038043333800000114
representing single-difference ambiguities between GLONASS satellites,
Figure FDA00038043333800000115
representing the single difference carrier measurement noise between GLONASS satellite stations,
Figure FDA00038043333800000116
represents the observed value of the single-difference pseudo range between GLONASS satellite stations, delta d j,R Represents the hardware delay of the homodyne pseudoranges between the GLONASS satellite receiver terminals,
Figure FDA00038043333800000117
represents the code offset between the stations of the GLONASS satellite,
Figure FDA00038043333800000118
representing single difference pseudorange measurement noise between GLONASS satellite stations;
step 1.2, constructing an inter-station single-difference observation model according to the step 1.1, re-parameterizing three parameters of receiver clock difference, hardware delay and single-difference ambiguity and performing parameter decorrelation to obtain an inter-station single-difference integer ambiguity resolvable model as follows:
for GPS, Δ dT, Δ δ in the model of single difference observation between stations j,G ，
Figure FDA0003804333380000021
And (3) having correlation, and performing parameter decorrelation on the re-parametrization of the correlation to obtain a full rank observation equation as follows:
Figure FDA0003804333380000022
Figure FDA0003804333380000023
wherein:
Figure FDA0003804333380000024
Figure FDA0003804333380000025
the formula (5) and the formula (6) are full rank observation equations obtained after single difference between stations in the GPS system is re-parameterized,
Figure FDA0003804333380000026
represents the interstation single-difference ambiguity of the GPS system reference star,
Figure FDA0003804333380000027
representing double-differenced ambiguities of the GPS system;
for GLONASS, since each satellite in the FDMA system has a different wavelength and there is an inter-frequency code bias between different frequencies, the observation equation of GLONASS re-reference is as follows:
Figure FDA0003804333380000028
Figure FDA0003804333380000029
the equation (9) and the equation (10) are the observation equations obtained after single difference between stations in the GLONASS system is re-parameterized, wherein in the equation,
Figure FDA00038043333800000210
representing GLONASS reference starsThe wavelength of the light emitted by the light source,
Figure FDA00038043333800000211
representing the interstation single-difference ambiguity of the GLONASS system reference star;
rewriting formula (9) to the following form:
Figure FDA00038043333800000212
as can be seen from equation (11), since the whole-cycle ambiguity of the reference star is unknown, equation (11) is still a rank-deficient equation; for this purpose, a second reference satellite is selected, and parameterization is carried out again to obtain the following observation equation:
Figure FDA00038043333800000213
wherein:
Figure FDA00038043333800000214
the observation equations for the other satellites are thus obtained as follows:
Figure FDA0003804333380000031
wherein:
Figure FDA0003804333380000032
as can be seen from the formula (15), when | k 1 -k 2 When the value of | =1,
Figure FDA0003804333380000033
is an integer;
the full rank observation equation for GLONASS carrier phase can thus be derived as follows:
Figure FDA0003804333380000034
step 2, constructing an estimated model of the deviation between the carrier systems by taking the GPS as a reference system, and carrying out statistical analysis on the time-varying characteristics of the deviation parameters between the carrier systems, wherein the statistical analysis comprises the following steps:
after the carrier phase full-rank observation equation in the GPS and GLONASS systems is obtained in the step 1, only the receiver clock error of the GPS is estimated by taking the GPS system as a reference system, and the order is made
Figure FDA0003804333380000035
And
Figure FDA0003804333380000036
the difference value of (a) is a deviation parameter between carrier systems; the carrier intersystem deviation estimable model is obtained as follows:
Figure FDA0003804333380000037
wherein, the deviation parameter between the carrier systems is:
Figure FDA0003804333380000038
and 3, based on the model and the analysis result in the step 2, performing time domain modeling on the deviation between the systems by adopting a random walk process to obtain a GPS and GLONASS tight combination model, and performing multi-epoch continuous positioning, wherein the method comprises the following steps of:
step 3.1, performing time domain modeling on the intersystem deviation by adopting a random walk process, specifically comprising the following steps:
for intersystem deviation delta GR And performing time domain modeling by adopting a random walk model with smaller spectral density, wherein the formula is as follows:
Figure FDA0003804333380000041
where k represents the epoch, w represents the process noise,
Figure FDA0003804333380000042
is the variance of w and is,
Figure FDA0003804333380000043
spectral density of w 0.05X 0.05cycle 2 /h；
Step 3.2, constructing a GPS and GLONASS tight combination positioning filtering model, and performing multi-epoch continuous positioning, wherein the method comprises the following steps:
step 3.2.1 State prediction
Using estimated or filtered initial value X of previous time k-1,k-1 Obtaining the predicted state vector X at the next moment k,k-1 ：
X k,k-1 ＝Φ k,k-1 X k-1，k-1 (22)
Meanwhile, the predicted state vector X can be obtained according to the error propagation law k,k-1 Of the covariance matrix Q k,k-1 ：
Figure FDA0003804333380000044
Step 3.2.2, calculating the filter gain
Calculating a filtered gain matrix K based on the predicted variance information and the observation model of the current epoch k ：
Figure FDA0003804333380000045
Step 3.2.3, valuation update
Using a filter gain matrix K k Combined with the observation vector L at the current moment k For the filtered estimate X k,k Perform the update
X k,k ＝X k,k-1 +K k (L k -A k X k,k-1 ) (25)
Simultaneous pair variance covariance matrix Q k,k Perform the update
Q k.k ＝(I-K k A k )Q k,k-1 (26)
And repeatedly executing the three steps at the next moment to realize continuous resolving of the positioning result and obtain a multi-epoch continuous positioning result.
2. The method of claim 1, wherein the GPS/GLONASS close-coupled positioning method is capable of considering inter-carrier-system bias, and comprises: the spectral density of the random walk process in the step 3 is 0.05 × 0.05cycle 2 /h。
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