CN108387912B - Solving method for Multi-GNSS precise single-point positioning - Google Patents

Solving method for Multi-GNSS precise single-point positioning Download PDF

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CN108387912B
CN108387912B CN201810094680.6A CN201810094680A CN108387912B CN 108387912 B CN108387912 B CN 108387912B CN 201810094680 A CN201810094680 A CN 201810094680A CN 108387912 B CN108387912 B CN 108387912B
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CN108387912A (en
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叶飞
闫伟
袁运斌
张宝成
欧吉坤
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Institute of Geodesy and Geophysics of CAS
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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
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/33—Multimode operation in different systems which transmit time stamped messages, e.g. GPS/GLONASS
    • 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
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
    • G01S19/05—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing aiding data

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Abstract

A resolving method for Multi-GNSS precise single-point positioning comprises the following steps: firstly, acquiring observation values and broadcast ephemeris of stations (the stations comprise subscriber stations, clock error reference stations and position reference stations) of a regional observation network through files or a network, then constructing an observation equation of the stations, and then solving the positions of the subscriber stations; according to the method, a Multi-NAPP model of a BDS + GPS dual system is constructed, BDS and GPS satellites observed in a regional observation network are fully utilized, so that the available observation value is greatly increased, and the convergence time of precise single-point positioning is remarkably shortened. The design not only shortens the convergence time of the precise single-point positioning, but also improves the positioning precision.

Description

Solving method for Multi-GNSS precise single-point positioning
Technical Field
The invention belongs to the technical field of geodetic surveying in the subject of surveying and mapping science and technology, and particularly relates to a Multi-GNSS precise single-point positioning resolving method which is mainly suitable for shortening real-time precise single-point positioning resolving convergence time.
Background
The fast convergence of the real-time precise single-point positioning calculation becomes the bottleneck in the large-scale application aspects such as real-time precise positioning, time transfer, earth dynamics and the like. In order to obtain high-precision user position information in real time, a real-time precise satellite orbit and a precise satellite clock error product are generally adopted to fix the satellite position and the satellite clock error so as to estimate the position of a user station. The real-time precise orbit is obtained by predicting orbit parameters through an orbit integrator, and a mechanical model and an observation model of the satellite orbit cannot completely accord with the motion characteristics of the satellite, so that the predicted orbit deviation may exceed 10-20 cm along with the increase of the prediction time length within the prediction time length range, which brings an orbit error exceeding 10-20 cm to user positioning and limits the user positioning precision. Particularly, after the satellite orbit maneuver, the user is positioned by a larger orbit error.
How to improve the precision of satellite forecast orbit and satellite clock error or get rid of the strong correlation between the user station and the satellite orbit and satellite clock error is always a research hotspot in the field of GNSS real-time precise point positioning. The NAPP technology is introduced by personnel of the institute of measurement and geophysical research of the Chinese academy of sciences, and is widely applied to many domestic projects. The technology can realize precise single-point positioning within hundreds of kilometers only by depending on broadcast ephemeris and regional reference networks, and gets rid of the dependence of user stations on precise tracks and precise clock errors. Although the convergence rate of the NAPPP technology is slightly higher than the convergence rate of PPP calculation using IGS precision products, the technology only uses GPS observation values, and is affected by the number of common view satellites in the reference network, and the convergence time required for calculation is still limited.
Disclosure of Invention
The invention aims to overcome the defects and problems that BDS observed values are not fully utilized and the resolving convergence rate is low in the prior art, and provides a resolving method of Multi-GNSS precise single point positioning (Multi-NAPP) with high convergence rate.
In order to achieve the above purpose, the technical solution of the invention is as follows: a resolving method for Multi-GNSS precise single-point positioning comprises the following steps:
A. acquiring a station observation value and a broadcast ephemeris of a regional observation network through a file or a network, wherein the station comprises a user station, a clock error reference station and a position reference station;
B. constructing observation equations for stations
a. The following combined ionospheric elimination observation model was constructed:
Figure GDA0002271244560000021
Figure GDA0002271244560000022
Figure GDA0002271244560000023
Figure GDA0002271244560000024
in equations (1) to (4), P and L represent differences between observed values and calculated values of pseudoranges and phases, respectively, μ represents a unit vector of a line of sight direction, u represents a receiver of a subscriber station, s and k represent PRNs of satellites, G and C represent GPS and BDS, respectively, Δ u represents a user position correction number, Δ s and Δ k represent ephemeris errors, respectively, and cdtuIndicating subscriber station receiver clock error, cdtG，sAnd cdtC，kRespectively representing the satellite clock offsets for GPS satellite S and BDS satellite k,
Figure GDA0002271244560000025
and
Figure GDA0002271244560000026
which represents the hardware delay of the receiver and,
Figure GDA0002271244560000027
Figure GDA0002271244560000028
and
Figure GDA0002271244560000029
representing satellite hardware delay, M representing the tropospheric projection function, zpd representing tropospheric delay,
Figure GDA00022712445600000210
and
Figure GDA00022712445600000211
representing an ambiguity parameter, epsilon representing white noise;
b. eliminating the correlation between the parameters in the pseudo range and the phase observation equation through parameter reforming, and defining the following equation:
Figure GDA00022712445600000212
Figure GDA0002271244560000031
Figure GDA0002271244560000032
Figure GDA0002271244560000033
in formula (7), ISBC-GRepresenting the intersystem offset between the GPS and BDS, equations (1) -4 are expressed as follows:
Figure GDA0002271244560000034
Figure GDA0002271244560000035
Figure GDA0002271244560000036
Figure GDA0002271244560000037
c. respectively constructing observation equations of clock error reference station, position reference station and user station
By using
Figure GDA0002271244560000038
Representing the receiver clock offset of the clock offset reference station m and R representing the rover selected as the position reference station, the observation equations for the clock offset reference station, the position reference station and the subscriber station are as follows:
the observation equation of the clock error reference station is as follows:
Figure GDA0002271244560000039
Figure GDA00022712445600000310
Figure GDA0002271244560000041
Figure GDA0002271244560000042
the observation equation of the position reference station is:
Figure GDA0002271244560000043
Figure GDA0002271244560000044
Figure GDA0002271244560000045
Figure GDA0002271244560000046
the observation equation for the subscriber station is:
Figure GDA0002271244560000047
Figure GDA0002271244560000048
Figure GDA0002271244560000051
Figure GDA0002271244560000052
C. determining the position of a subscriber station
The unknowns being estimated are:
Figure GDA0002271244560000053
in the step c, a full-rank Multi-GNSS precise single-point positioning resolving model is deduced, the clock error reference is a reference station equipped with an atomic clock, and the position reference is the position coordinates of a fixed reference station.
Compared with the prior art, the invention has the beneficial effects that:
according to the resolving method for the precise single-point positioning of the Multi-GNSS, the BDS and the GPS satellites observed in the regional observation network are fully utilized, so that the available observation value is greatly increased, and the convergence time of the precise single-point positioning is obviously shortened. Therefore, the invention shortens the convergence time of the precise point positioning.
Drawings
FIG. 1 is a schematic diagram of a station in an embodiment of the invention.
Fig. 2 shows the dynamic positioning results simulated by the subscriber station ali in an embodiment of the invention.
Fig. 3 is a diagram of the dynamic positioning results simulated by subscriber station MRO1 in an embodiment of the present invention.
Figure 4 is a dynamic positioning result of a subscriber station NNOR simulation in an embodiment of the present invention.
Fig. 5 is a result of dynamic positioning of a PERT simulation of a subscriber station in an embodiment of the invention.
Fig. 6 shows a result of dynamic positioning simulated by the subscriber station PARK in the embodiment of the present invention.
Fig. 7 is a precision statistic of all subscriber stations in an embodiment of the invention.
Fig. 8 is a percentage convergence speed improvement for all subscriber stations in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following description and embodiments in conjunction with the accompanying drawings.
A resolving method for Multi-GNSS precise single-point positioning comprises the following steps:
A. acquiring a station observation value and a broadcast ephemeris of a regional observation network through a file or a network, wherein the station comprises a user station, a clock error reference station and a position reference station;
B. constructing observation equations for stations
a. The following combined ionospheric elimination observation model was constructed:
Figure GDA0002271244560000061
Figure GDA0002271244560000062
Figure GDA0002271244560000063
Figure GDA0002271244560000064
in equations (1) to (4), P and L represent differences between observed values and calculated values of pseudoranges and phases, respectively, μ represents a unit vector of a line of sight direction, u represents a receiver of a subscriber station, s and k represent PRNs of satellites, G and C represent GPS and BDS, respectively, Δ u represents a user position correction number, Δ s and Δ k represent ephemeris errors, respectively, and cdtuIndicating subscriber station receiver clock error, cdtG，sAnd cdtC，kRespectively representing the satellite clock offsets for GPS satellite s and BDS satellite k,
Figure GDA0002271244560000065
and
Figure GDA0002271244560000066
which represents the hardware delay of the receiver and,
Figure GDA0002271244560000067
Figure GDA0002271244560000068
and
Figure GDA0002271244560000069
representing satellite hardware delay, M representing the tropospheric projection function, zpd representing tropospheric delay,
Figure GDA00022712445600000610
and
Figure GDA00022712445600000611
representing an ambiguity parameter, epsilon representing white noise;
b. eliminating the correlation between the parameters in the pseudo range and the phase observation equation through parameter reforming, and defining the following equation:
Figure GDA0002271244560000071
Figure GDA0002271244560000072
Figure GDA0002271244560000073
Figure GDA0002271244560000074
in formula (7), ISBC-GRepresenting the intersystem offset between the GPS and BDS, equations (1) -4 are expressed as follows:
Figure GDA0002271244560000075
Figure GDA0002271244560000076
Figure GDA0002271244560000077
Figure GDA0002271244560000078
c. respectively constructing observation equations of clock error reference station, position reference station and user station
By using
Figure GDA0002271244560000079
Representing the receiver clock offset of the clock offset reference station m and R representing the rover selected as the position reference station, the observation equations for the clock offset reference station, the position reference station and the subscriber station are as follows:
the observation equation of the clock error reference station is as follows:
Figure GDA00022712445600000710
Figure GDA0002271244560000081
Figure GDA0002271244560000082
Figure GDA0002271244560000083
the observation equation of the position reference station is:
Figure GDA0002271244560000084
Figure GDA0002271244560000085
Figure GDA0002271244560000086
Figure GDA0002271244560000087
the observation equation for the subscriber station is:
Figure GDA0002271244560000088
Figure GDA0002271244560000091
Figure GDA0002271244560000092
Figure GDA0002271244560000093
C. determining the position of a subscriber station
The unknowns being estimated are:
Figure GDA0002271244560000094
in the step c, a full-rank Multi-GNSS precise single-point positioning resolving model is deduced, the clock error reference is a reference station equipped with an atomic clock, and the position reference is the position coordinates of a fixed reference station.
The principle of the invention is illustrated as follows:
with the rapid development of the Beidou satellite navigation system in China, particularly in the Asia-Pacific region, compared with a single GPS, the number of visible satellites at the same cut-off height angle is greatly increased, so that how to fully and effectively utilize the observation values of the BDS and the GPS to provide better precise single-point positioning service for users is realized, thereby enhancing the competitiveness of the BDS and increasing the living space of the BDS, and the method is a direction worthy of long-term research.
The design specifically relates to a method for resolving real-time precise single-point positioning of a GPS (global positioning system) assisted by an observation value of a Multi-satellite navigation system, a Multi-NAPP (navigation satellite protocol) model of a BDS + GPS dual system is constructed by the method, a resolving method for achieving Multi-GNSS precise single-point positioning (Multi-NAPP) based on a broadcast ephemeris and a regional reference network with higher convergence speed is provided, the method fully utilizes BDS and GPS satellites observed in the regional observation network, the available observation value is greatly increased, and the convergence time of the precise single-point positioning is remarkably shortened.
Example (b):
a resolving method for Multi-GNSS precise single-point positioning comprises the following steps:
A. acquiring a station observation value and a broadcast ephemeris of a regional observation network through a file or a network, wherein the station comprises a user station, a clock error reference station and a position reference station;
B. constructing observation equations for stations
a. The following deionization layer combination (IF) observation model was constructed:
Figure GDA0002271244560000101
Figure GDA0002271244560000102
Figure GDA0002271244560000103
Figure GDA0002271244560000104
in equations (1) to (4), P and L represent O-C (observed value minus calculated value) residuals of pseudo ranges and phases, respectively, μ represents a unit vector of a line-of-sight direction, u represents a receiver of a subscriber station, s and k represent PRN of a satellite, G and C represent GPS and BDS, respectively, Δ u represents a subscriber position correction number, Δ s and Δ k represent ephemeris error, respectively, cdtuIndicating subscriber station receiver clock error, cdtG，sAnd cdtC，kRespectively representing the satellite clock offsets for GPS satellite s and BDS satellite k,
Figure GDA0002271244560000105
and
Figure GDA0002271244560000106
which represents the hardware delay of the receiver and,
Figure GDA0002271244560000107
and
Figure GDA0002271244560000108
representing satellite hardware delay, M representing the tropospheric projection function, zpd representing tropospheric delay,
Figure GDA0002271244560000109
and
Figure GDA00022712445600001010
representing an ambiguity parameter, epsilon representing white noise;
b. eliminating the correlation between the parameters in the pseudo range and the phase observation equation through parameter reforming, and defining the following equation:
Figure GDA00022712445600001011
Figure GDA0002271244560000111
Figure GDA0002271244560000112
Figure GDA0002271244560000113
in formula (7), ISBC-GRepresenting the intersystem offset between the GPS and BDS, equations (1) -4 are expressed as follows:
Figure GDA0002271244560000114
Figure GDA0002271244560000115
Figure GDA0002271244560000116
Figure GDA0002271244560000117
c. respectively constructing observation equations of clock error reference station, position reference station and user station
In the formula (9) to the formula (12), Δ u is correlated with Δ s and Δ k,
Figure GDA0002271244560000118
and
Figure GDA0002271244560000119
and therefore, a proper position reference and a clock difference reference must be selected; in the implementation process of the design, a reference station provided with an atomic clock is selected as a clock error reference, and the position coordinates of the fixed reference station are used as a position reference;
by using
Figure GDA00022712445600001110
Representing the receiver clock offset of the clock offset reference station m and R representing the rover selected as the position reference station, the observation equations for the clock offset reference station, the position reference station and the subscriber station are as follows:
the observation equation of the clock error reference station is as follows:
Figure GDA0002271244560000121
Figure GDA0002271244560000122
Figure GDA0002271244560000123
Figure GDA0002271244560000124
the observation equation of the position reference station is:
Figure GDA0002271244560000125
Figure GDA0002271244560000126
Figure GDA0002271244560000127
Figure GDA0002271244560000128
the observation equation for the subscriber station is:
Figure GDA0002271244560000129
Figure GDA0002271244560000131
Figure GDA0002271244560000132
Figure GDA0002271244560000133
C. determining the position of a subscriber station
The unknowns being estimated are:
Figure GDA0002271244560000134
referring to fig. 1, CEDUs, DARW, KARR, YAR2, MOBS, SYDN, TOW2, ali, MRO1, NNOR, PERT, and PARK of the IGS MGEX are selected as test stations, wherein CEDUs of five-pointed star are clock reference stations, stations of inverted triangle, e.g., DARW, are position reference stations, and stations of circle, e.g., ali, are subscriber stations. This example analyzes the observation data (sampling rate: 30 seconds) of 11/1/2017, and it can be calculated that the distances between the ali and SYDN and the CEDU are 2011.959km and 907.624km, respectively, and in addition, the distance between the two nearest stations (NNOR and YAR2) is 236.452km, so the network covers a wide range.
The simulated dynamic positioning results of five stations, ALIC, MRO1, NNOR, PERT, and PARK, were analyzed using the Multi-NAPP technique described above. Referring to fig. 2 to 6, the precision positioning solution accuracy of each station using the Multi-NAPPP technique is slightly improved and the convergence speed is significantly improved, using the BDS observation value, compared to the NAPPP technique of GPS. As can be seen from fig. 7, with the Multi-napp technique, when the positional deviation is less than 20 cm and 10 cm, respectively, and stable (i.e., 95% and 68% confidence), the RMS values are less than 4 cm and 3 cm, respectively, in the planar direction, and less than 7 cm and 6 cm, respectively, in the elevation direction, slightly higher than the napp technique of GPS; as can be seen from fig. 8, the convergence rates of ali, MRO1, NNOR, PERT, and PARK in the planar and elevation directions are improved by 16.46 and 40.94%, 78.11 and 65.24%, 91.87 and 47.54%, 77.89 and 69.54%, 11.3 and 24.78% on average. Therefore, the results show that the Multi-NAPPP technique of the present design provides a slightly improved positioning accuracy and a significantly improved convergence performance as compared to the NAPPP technique of GPS.

Claims (2)

1. A resolving method for Multi-GNSS precise single-point positioning is characterized by comprising the following steps:
A. acquiring a station observation value and a broadcast ephemeris of a regional observation network through a file or a network, wherein the station comprises a user station, a clock error reference station and a position reference station;
B. constructing observation equations for stations
a. The following combined ionospheric elimination observation model was constructed:
Figure FDA0002271244550000011
Figure FDA0002271244550000012
Figure FDA0002271244550000013
Figure FDA0002271244550000014
in equations (1) to (4), P and L represent differences between observed values and calculated values of pseudoranges and phases, respectively, μ represents a unit vector of a line of sight direction, u represents a receiver of a subscriber station, s and k represent PRNs of satellites, G and C represent GPS and BDS, respectively, Δ ll represents a user position correction number, Δ s and Δ k represent ephemeris errors, respectively, and cdtuIndicating subscriber station receiver clock error, cdtG，sAnd cdtC，kRespectively representing the satellite clock offsets for GPS satellite s and BDS satellite k,
Figure FDA0002271244550000015
and
Figure FDA0002271244550000016
which represents the hardware delay of the receiver and,
Figure FDA0002271244550000017
Figure FDA0002271244550000018
and
Figure FDA0002271244550000019
representing satellite hardware delay, M representing the tropospheric projection function, zpd representing tropospheric delay,
Figure FDA00022712445500000110
and
Figure FDA00022712445500000111
representing an ambiguity parameter, epsilon representing white noise;
b. eliminating the correlation between the parameters in the pseudo range and the phase observation equation through parameter reforming, and defining the following equation:
Figure FDA0002271244550000021
Figure FDA0002271244550000022
Figure FDA0002271244550000023
Figure FDA0002271244550000024
in formula (7), ISBC-GRepresenting the intersystem offset between the GPS and BDS, equations (1) -4 are expressed as follows:
Figure FDA0002271244550000025
Figure FDA0002271244550000026
Figure FDA0002271244550000027
Figure FDA0002271244550000028
c. respectively constructing observation equations of clock error reference station, position reference station and user station
By using
Figure FDA0002271244550000029
Representing the receiver clock offset of the clock offset reference station m and R representing the rover selected as the position reference station, the observation equations for the clock offset reference station, the position reference station and the subscriber station are as follows:
the observation equation of the clock error reference station is as follows:
Figure FDA0002271244550000031
Figure FDA0002271244550000032
Figure FDA0002271244550000033
Figure FDA0002271244550000034
the observation equation of the position reference station is:
Figure FDA0002271244550000035
Figure FDA0002271244550000036
Figure FDA0002271244550000037
Figure FDA0002271244550000038
the observation equation for the subscriber station is:
Figure FDA0002271244550000041
Figure FDA0002271244550000042
Figure FDA0002271244550000043
Figure FDA0002271244550000044
C. determining the position of a subscriber station
The unknowns being estimated are:
Figure FDA0002271244550000045
2. the method for resolving Multi-GNSS precise point-of-location as recited in claim 1, wherein: in the step c, a full-rank Multi-GNSS precise single-point positioning resolving model is deduced, the clock error reference is a reference station equipped with an atomic clock, and the position reference is the position coordinates of a fixed reference station.
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