CN115616615A - PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method - Google Patents

PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method Download PDF

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CN115616615A
CN115616615A CN202211237254.6A CN202211237254A CN115616615A CN 115616615 A CN115616615 A CN 115616615A CN 202211237254 A CN202211237254 A CN 202211237254A CN 115616615 A CN115616615 A CN 115616615A
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王磊
周海涛
付文举
刘季
张鹏
路莹
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707 Research Institute Of China Shipbuilding Corp
Wuhan University WHU
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707 Research Institute Of China Shipbuilding Corp
Wuhan University WHU
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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
    • G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
    • 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
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • 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

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Abstract

The invention provides a PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method, which relates to the technical field of satellite navigation positioning and aims to solve the problem that single-frequency observation data cannot effectively inhibit ionosphere errors.A technical scheme adopted is that a ground device receives a navigation signal from a GPS/BDS-3 satellite, a broadcast ephemeris is corrected by PPP-B2B real-time enhanced correction number played by a Beidou No. three GEO satellite, and real-time single-frequency precision single-point positioning is completed in the ground device by adopting a PPP-B2B real-time single-frequency precision single-point positioning algorithm model; the method comprises the steps of acquiring high-precision real-time GPS/BDS-3 real-time precise orbit and clock error data through PPP-B2B enhanced correction data broadcast by a GEO satellite, getting rid of the distance limitation of a reference station, and realizing the real-time decimeter positioning effect by using a single receiver; the indistinguishable clock error and ionized layer parameters are converted into equivalent ionized layer parameters in an equivalent parameter conversion mode, so that the influence of the ionized layer on single-frequency PPP is estimated and deducted in real time, and a real-time decimeter-level positioning result is obtained.

Description

PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method
Technical Field
The invention relates to the technical field of satellite navigation positioning, in particular to a PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method.
Background
Global Navigation Satellite Systems (GNSS) are currently in widespread use, and the demand for satellite positioning is developing towards high accuracy. However, the standard positioning service precision provided by GNSS is in the range of 10 meters to meter, and the precision requirement of precision positioning cannot be met. Two main technical means for realizing real-time precise positioning are satellite-based reinforcement and foundation reinforcement. The foundation reinforcement is realized by laying a dense reference station network on the ground, and the action distance of a single station is about 20 kilometers. Therefore, the high-precision positioning service depends on the arrangement of the reference station, and the high-precision positioning service cannot be realized on the ocean. The satellite-based augmentation is to use a regional or global tracking station network to resolve the precise orbit and clock correction of the satellite, to transmit the correction information to the user in real time through the communication satellite, and to use the correction information broadcast by the satellite and to use the linear combination of the dual-frequency observation values to eliminate the influence of the ionosphere, thereby realizing the real-time decimeter-level dynamic positioning precision. Currently, satellite-level augmentation services are mainly provided by GNSS service providers, such as Tianbao corporation in the united states, huigung corporation in the netherlands, and Hodgy and Zhonghaida corporation in China. The Beidou III which is independently researched and developed in China not only integrates navigation and communication functions, but also has various service capabilities of positioning navigation time service, satellite-based reinforcement, foundation reinforcement, precise single-point positioning, short message communication, international search and rescue and the like. The PPP-B2B signal is used as a data broadcasting channel, the precise orbit and clock error correction numbers of the Beidou satellite III and other GNSS satellites are broadcasted through the Beidou satellite III GEO satellite, the orbit and clock error of the broadcast ephemeris are corrected, high-precision GPS/BDS-3 real-time precise orbit and clock error information can be obtained in real time, and dynamic decimeter-level and static centimeter-level precise positioning service can be provided for China and surrounding areas.
Chinese patent CN202010036792.3 discloses a PPP-RTK positioning method based on non-differential observation model and rank-deficiency elimination, which adopts the technical scheme that the method comprises the following steps: selecting pseudo-range and phase observation data of a global or regional tracking station network of a GNSS system; constructing a single-system multi-frequency original observation equation by using observation data; and (3) re-integrating the parameters in the original observation equation by using an S-basis rank deficiency elimination theory, eliminating the mathematical rank deficiency in the original observation equation, and obtaining a new observation equation. The design is based on multi-frequency-point pseudo range and phase observation data of a global or regional GNSS tracking station network, a full-rank non-difference non-combined full-parameter estimation model is constructed by utilizing an S-basis rank elimination deficiency theory, unified estimation of positioning enhancement parameters such as satellite clock difference, space atmosphere delay and basic frequency satellite phase deviation is realized, PPP-RTK high-precision positioning enhancement service is provided, and meanwhile, the service requirements of traditional positioning modes such as PPP and RTK can be backwards compatible; the existing precise PPP real-time positioning service is mainly a double-frequency or multi-frequency measurement type receiver, and in the technical scheme, aiming at a PPP-RTK positioning method of a non-difference observation model, an S-basis rank deficiency elimination theory is introduced to process parameters, so that the problem of how to utilize multi-frequency data to carry out PPP-RTK positioning is mainly solved. At present, the PPP real-time positioning service of the single-frequency receiver in the low-cost mass market is not deeply researched, and the main reason is that the ionosphere error cannot be effectively inhibited by single-frequency observation data.
The invention mainly provides a method for correcting a broadcast ephemeris orbit and clock error by using a PPP-B2B correction number broadcasted by Beidou No. three GEO so as to obtain high-precision real-time precise orbit and clock error data, and the ionosphere error is processed by using a parameter estimation mode through an equivalent parameter conversion mode so as to provide real-time high-precision position service for a single-frequency user.
Disclosure of Invention
In view of the problems in the prior art, the invention discloses a PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method, which adopts the technical scheme that a PPP-B2B correction number is adopted to correct an orbit and a clock error, and an ionosphere error is processed by a method with ionosphere parameter constraint, so that a real-time decimeter-level positioning result is obtained by utilizing single-frequency observation data.
As a preferred technical scheme of the invention, the method can realize decimeter-level high-precision positioning without additionally establishing a communication link and arranging a base station nearby, and the satellite real-time precision orbit and clock error calculation step based on PPP-B2B enhanced information comprises the following steps:
s201, extracting PPP-B2B orbit and clock correction number information broadcast by a Beidou No. three GEO satellite in real time, and analyzing the quality conditions of the PPP-B2B orbit and the clock correction number;
s202, acquiring a PPP-B2B enhanced GPS/BDS-3 orbit correction number, namely the correction numbers in the radial direction, the normal direction and the tangential direction, and correcting the roughly calculated GPS/BDS-3 satellite position;
and S203, acquiring a clock difference correction number of the PPP-B2B enhanced GPS/BDS-3, correcting the clock difference of the rough GPS/BDS-3 satellite obtained by calculation, and obtaining high-precision GPS/BDS-3 real-time high-precision orbit and clock difference information for subsequent real-time precise single-point positioning service.
As a preferred technical scheme of the invention, the ionospheric parameters are converted into the estimable parameters by a benchmark conversion mode, and the initial parameter value determination problem is solved by a multi-epoch joint solution mode by using a reasonable approximate hypothesis, wherein the specific method comprises the following steps:
the key of single-frequency precise single-point positioning lies in the elimination of ionosphere errors, and the traditional single-frequency ionosphere model mainly utilizes a code phase combination mode to eliminate ionosphere influence at the cost of amplifying observation noise. The single-frequency ionosphere method estimates ionosphere parameters by using a method accompanied with ionosphere constraints, thereby eliminating the influence of the ionosphere on single-frequency precise positioning. 2N observation equations can be formed for code phase observation values of N satellites, and 3 coordinate parameters, 2 clock error parameters, 1 troposphere parameter, N ionosphere parameters and N ambiguity parameters, namely 2 + N +6 parameters, are estimated in the equations. Obviously, the number of observation equations is less than the number of parameters, which results in rank deficiency of normal equations and cannot be directly estimated. Because the receiver clock error, the ionospheric parameters and the ambiguity parameters have coupling and correlation, the strongly correlated clock error parameters, the ionospheric parameters and the ambiguity parameters are converted into estimable quantities by adopting a reference transformation mode. The specific implementation form is that the clock difference of the first epoch is used as a reference, the constraint is forced to be 0, and then the reference offset can be absorbed by ionosphere parameters and ambiguity parameters, so that the estimates of the two types of parameters have bias, but the bias does not affect the receiver coordinate parameters to be solved. This approach solves the rank deficiency problem between parameters. Then the observation equation can be converted into:
Figure BDA0003880482250000041
i represents an epoch reference number;
Figure BDA0003880482250000042
subtracting a calculated value (OMC) from observed values respectively representing a pseudo range and a phase of an ith epoch;
Figure BDA0003880482250000043
a unit vector representing the satellite to the receiver; Δ x represents a receiver coordinate vector;
Figure BDA0003880482250000044
respectively representing biased ionospheric delay and ambiguity with respect to the first epoch receiver clock error. The remaining symbols are consistent with the previous equation representation.
Because the number of the parameters is larger than that of the observation equations, the normal equations are rank deficient. Assuming that the receiver position, troposphere parameters and ambiguity parameters are unchanged in the initial two epochs, the observation equations of the initial two epochs are synchronized, and assuming that there are N satellites in each epoch, there are 4N pseudorange and phase observation equations in total. Meanwhile, the unknown parameters comprise 3 position parameters, one intersystem deviation parameter (ISB), one receiver clock error parameter, one troposphere parameter, N ambiguity parameters and 2N ionosphere parameters, and the total number of the unknown parameters is 3N + 6. The problem of rank deficiency of the observation equation can be solved as long as the number of available satellites of the GPS/BDS-3 is more than 6, and the initial troposphere and ambiguity parameters can be solved.
As a preferred technical scheme of the invention, the time-related characteristic of an ionosphere is utilized, ionosphere parameters are solved by a method attached with ionosphere constraint, so that the adverse influence of the ionosphere is deducted from single-frequency precise single-point positioning, and a real-time decimeter-level high-precision positioning result is further obtained, and the specific method comprises the following steps:
considering that the troposphere wet delay has the random walk characteristic and the ambiguity parameter has the constant characteristic, the troposphere wet delay and the ambiguity parameter of the previous epoch are taken as the constraint of the current epoch, the rank deficiency problem of the observation equation can be solved, and the continuous parameter solution estimation of each epoch is realized.
Assuming that there are N observation satellites in the last epoch, the ambiguity parameter constraint has N equations, and simultaneously, the addition of 1 convection layer constraint generates N +1 constraint equations. Meanwhile, the current epoch has M observation satellites, and then has 2M observation equations, plus constraint equations, and has 2M + N +1 equations. Meanwhile, the parameters of the current epoch include 3 position parameters, 1 receiver clock error parameter, 1 ISB parameter, 1 troposphere parameter, M ionosphere parameters and M ambiguity parameters, and the total number is 2M +6 parameters. Then as long as 2M + N +1 >. The number of the available GPS/BDS-3 satellites with the last epoch as the constraint is required to reach 6, and meanwhile, the satellite dropping of the current epoch or the newly added satellite does not influence the establishment of the observation equation, so that the problems of the satellite dropping and the newly added satellite of the observation satellite in the observation process are effectively solved.
Thus, the new observation equations are reconstructed as N +1 virtual observation equations (constraint equations) for the last epoch and 2M pseudorange/phase observation equations for the current epoch. The observation equation and parameters reconstructed in the single-frequency precise single-point positioning are respectively as follows:
Figure BDA0003880482250000051
Figure BDA0003880482250000052
Figure BDA0003880482250000056
I i ，
Figure BDA0003880482250000054
the virtual observed values of the troposphere and the ambiguity parameter of the previous epoch and a variance-covariance matrix thereof are obtained; a. The i ,L i ,
Figure BDA0003880482250000055
Respectively a design matrix, an OMC value and a corresponding observation variance-covariance matrix of the current epoch.
The position parameters can be solved in real time by least squares estimation. Meanwhile, it should be noted that the ionospheric parameters exist in the pseudo-range and phase observation equations, DCB corrections in the pseudo-range observations are absorbed into the ionospheric parameters, and meanwhile, because the ionospheric parameters are correlated with the ambiguity parameters, the DCB parameters are further absorbed by the ambiguity parameters, so that the resolved ionospheric parameters and the ambiguity parameters are biased estimates, but the estimation of the position parameters is not affected.
The invention has the beneficial effects that: the invention obtains high-precision real-time GPS/BDS-3 real-time precise orbit and clock error data through PPP-B2B enhanced correction data broadcast by a GEO satellite, thereby getting rid of the distance limitation of a reference station and realizing the real-time decimeter-level positioning effect by using a single receiver; the invention converts the indistinguishable clock difference and ionized layer parameters into equivalent ionized layer parameters in an equivalent parameter conversion mode, thereby deducting the influence of the ionized layer on single-frequency PPP through real-time estimation and further obtaining a real-time decimeter-level positioning result. The traditional single-frequency precise single-point positioning mainly eliminates an ionosphere through code phase combination, but amplifies observation noise to cause poor positioning effect; according to the method, through reasonable assumption, the problem of rank deficiency in parameter initial value determination is solved by using multi-epoch observation value combined calculation, so that unstable parameter calculation is avoided, and technical support is provided for real-time single-frequency high-precision application.
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In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings used in the detailed description or the prior art description will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a schematic diagram of the framework of the present invention;
FIG. 2 is a schematic diagram of a single-frequency precise single-point positioning algorithm based on PPP-B2B correction number according to the present invention;
FIG. 3 is a flow chart of the present invention for correcting the orbit and clock error of the ephemeris broadcast using the PPP-B2B enhanced correction number broadcast by the big Dipper GEO No. three;
FIG. 4 is an algorithm flow chart of the single-frequency precise single-point positioning algorithm of PPP-B2B correction number of the present invention;
FIG. 5 is a diagram of a single frequency GPS/BDS-3 dynamic positioning result applied in the present invention.
Detailed Description
The technical scheme of the invention is clearly and completely described in the following with reference to the accompanying drawings. In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships indicated on the basis of drawings, only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Moreover, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases by those skilled in the art.
Example 1
As shown in figure 1, the invention discloses a PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method, which adopts the technical scheme that ground equipment receives a navigation signal from a GPS/BDS-3, broadcast ephemeris is corrected through a PPP-B2B real-time enhanced correction number broadcast by a Beidou three-number GEO satellite, and finally real-time single-frequency precision single-point positioning application is completed in the ground equipment.
As shown in fig. 2, the PPP-B2B modified real-time single-frequency precise single-point positioning algorithm model includes the following steps:
s1, a single-point positioning technology based on pseudo-range observed values;
s2, calculating a satellite real-time precise orbit and a clock error based on PPP-B2B enhancement information;
s3, observation data preprocessing and error model calculation;
and S4, a real-time single-frequency precise single-point positioning algorithm based on the PPP-B2B correction number.
In S1, a pseudo-range observation value-based point positioning technology comprises the following steps:
in S101, checking received GPS/BDS-3 satellite pseudo-range observation data, eliminating non-pseudo-range data, calculating the altitude angle of each satellite, and eliminating satellite observation data with low altitude angles;
in S102, the broadcast ephemeris is an extrapolation result of a ground analysis center, and the real-time position and clock error information of the GPS/BDS-3 satellite with poor precision can be obtained through the calculation of the broadcast ephemeris;
in S103, the pseudo range observation data of the GPS/BDS-3 is linearized by Taylor expansion, and the ionosphere and the convection layer are obtained through model calculation. Constructing an observation equation of parameters related to the clock error of the position and the ground equipment, and obtaining the position and the clock error result of the ground equipment meeting the precision index through least square iterative calculation;
in S104, the positioning result is further determined, and whether pseudorange residual information satisfies a requirement is analyzed, if so, the positioning result is usable, otherwise, the positioning result is not usable.
S101-S104 are firstly carried out in each epoch, so that the initial approximate position of the ground receiver at the current moment can be obtained, and initial coordinates are provided for subsequent real-time precise positioning.
As shown in fig. 3, it is a flowchart for correcting the orbit and clock error of the ephemeris by using the PPP-B2B enhanced correction number broadcast by the beidou No. three GEO.
S2, calculating the real-time precise orbit and clock error of the satellite based on the PPP-B2B enhancement information, and solving the real-time precise coordinate and clock error data of the GPS/BDS-3 satellite required by real-time high-precision positioning, comprising the following steps:
s201, extracting PPP-B2B orbit and clock correction number information broadcast by a Beidou No. three GEO satellite in real time, and analyzing the quality conditions of the PPP-B2B orbit and the clock correction number;
s202, acquiring a PPP-B2B enhanced GPS/BDS-3 orbit correction number, namely the correction numbers in the radial direction, the normal direction and the tangential direction, and correcting the roughly calculated GPS/BDS-3 satellite position;
the track correction information includes parameters for the radial, tangential and normal components of the track correction vector δ O. The orbit correction values are used to calculate satellite position correction vectors deltaX in combination with satellite position vectors X calculated using broadcast ephemeris broadcast . The calculation formula for correction is:
X orbit ＝X broadcast -δX
X orbit representing the satellite positions corrected by the orbit correction text; x broadcast The satellite position calculated by the broadcast ephemeris is represented, and the IOD of the satellite position is matched with the IODN of the orbit correction message; δ X represents the satellite position correction. The calculation formula of the satellite position correction δ X is as follows:
Figure BDA0003880482250000081
Figure BDA0003880482250000082
e along ＝e cross ×e radial
δX＝[e radial e along e cross ]·δO
r＝X broadcast representing a broadcast ephemeris satellite position vector;
Figure BDA0003880482250000083
representing broadcast ephemeris satellite velocity vector e i Representing a direction unit vector, i = { radial impact cross } corresponds to radial, tangential, normal, respectively; δ O represents the track correction vector obtained in the PPP information, in order radial, tangential, normal components. S203, acquiring a clock error correction number of the PPP-B2B enhanced GPS/BDS-3, and correcting the clock error of the rough GPS/BDS-3 satellite obtained by calculation.
The clock error correction message includes parameters that are correction parameters relative to the broadcast ephemeris clock error. The use method of the correction parameters comprises the following steps:
Figure BDA0003880482250000091
t broadcast representing satellite clock error parameters obtained by calculating broadcast ephemeris; t is t satellite The satellite clock error obtained by correcting telegraph text through the clock error is represented; c represents the speed of light; c 0 The clock correction parameters obtained in the PPP-B2B text are shown. After each epoch acquires the rough satellite coordinates and clock error of the GPS/BDS-3 through the broadcast ephemeris, the satellite orbit and clock error of the broadcast ephemeris are corrected by using the PPP-B2B real-time precise correction number to obtain high-precision GPS/BDS-3 real-time high-precision orbit and clock error information for subsequent real-time precise single-point positioning service.
S3: observation data preprocessing and error model calculation, elimination of observation data of GPS/BDS-3 which does not meet the calculation requirement, providing 'clean' observation data for subsequent precise single-point positioning service, and simultaneously providing directly-calculated error source information for subsequent precise single-point positioning variance construction by calculating a modelable error, the method comprises the following steps:
s301, further checking the GPS/BDS-3 observation data, eliminating observation data without phase observation information in the observation value, simultaneously calculating the satellite altitude again, and eliminating the satellite observation data with low altitude.
And S302, performing cycle slip detection and clock error detection on the GPS/BDS-3 observation data, and marking satellites with cycle slip and clock error.
And S303-S306, performing correction calculation by adopting corresponding error models for tide correction, relativistic correction, satellite antenna phase winding correction and PCO/PCV correction.
And S306, calculating the dry delay and the wet delay coefficient of the troposphere by using the error model.
The invention adopts a GPT2 model to model the convection layer delay. The GPT2 model is a meteorological parameter model established based on the profile data of the global monthly average air pressure, air temperature, specific humidity of ERA-Interim 2001-2010, which can provide the coefficients of the air pressure, temperature, humidity vertical decreasing rate, specific humidity and VMF1 dry-wet projection functions on the global grid points with a resolution of 5 ° or 1 °, and the time variation of each meteorological parameter on each grid point is expressed by a trigonometric function containing the annual period and the semiannual period:
Figure BDA0003880482250000101
in the formula A 0 ，A 1 ，A 2 ，B 1 ，B 2 The calculation is carried out in advance, and the calculation is stored in a file in a grid form and can be directly called.
A 0 ，A 1 ，A 2 ，B 1 ，B 2 Model coefficients of air temperature, air pressure and specific humidity respectively represent constant deviation, cosine harmonic terms of annual period and half-annual period and sine harmonic terms of annual period and half-annual period.
In the vertical direction, the scholars assume that the temperature in the vicinity of the earth follows a linear variation with altitude, while the vertical variation of the barometric pressure is expressed by an exponential function and the meteorological parameters are highly corrected using the following formula:
T＝T 0 +dT·dh
P＝P 0 ×exp{-c×dh}/100
c＝g m ×dMtr/(R g ×T v )
g m ＝9.784×(1.0-2.66×10 -3 cos(2×lat)-2.8×10 -7 h g )
T v ＝T 0 ×(1+0.6077Q)
e＝Q×P/(0.622+0.378Q)
T 0 ，P 0 respectively the air temperature and the air pressure on the grid points, T and P respectively the temperature and the air pressure when the dh height is increased by the grid points, and Dt is the vertical decreasing rate of the temperature; q is specific humidity; e is the water gas pressure; g m Is gravity acceleration, and the value in GPT2 model is 9.80665m/s 2 (ii) a dMtr and R g Respectively atmospheric molar mass and gasNumber of 28.965X 10 - 3 kg/mol，8.3143J/K/mol。
When the GPT2 model is used, the latitude, longitude and geodetic height of the measuring station and the reduced julian day of the observation time are input, the model searches weather parameters close to the measuring station in the grid file according to the coordinates of the measuring station, the weather parameters on grid points are reduced to the height of the measuring station by using the formula, and finally, the weather parameters at the positions of the station points are obtained by using bilinear interpolation. The zenith tropospheric delays at the rover position can be calculated taking into account the weather parameters at the rover position calculated using the GPT2 model, substituting into the simplified saastanmonen model:
ZHD＝22.2754×P/g m
ZWD＝22.2754×(1255/T+0.5)×e/g m
s4, correcting the broadcast ephemeris through the PPP-B2B real-time precise orbit and clock error correction number based on a PPP-B2B correction number real-time single-frequency precise single-point positioning algorithm to obtain precise GPS/BDS-3 real-time precise satellite orbit and clock error information, and estimating real-time high-precision position information of the ground receiver in real time by utilizing Kalman filtering, wherein the method comprises the following steps:
s401, carrying out 'clean' observation data after the previous processing, simultaneously obtaining GPS/BDS-3 real-time precise satellite orbit and clock error data which are corrected by PPP-B2B enhanced information, and linearizing the observed value.
S402, constructing a single-frequency non-difference observation equation. The GPS/BDS-3 single frequency non-difference model linearization can be expressed as:
Figure BDA0003880482250000111
s, r, M represent satellite, receiver and navigation system, respectively; p and L respectively represent pseudo range and phase observed value; ρ represents the station-satellite geometric distance between the satellite antenna and the receiver antenna in meters; dt is r ,dt s Respectively representing a receiver clock error and a satellite clock error; i represents ionospheric delay in meters;
Figure BDA0003880482250000112
ZWD r respectively representing the convective zone wet delay coefficient and zenith convective zone delay; lambda [ alpha ] i ,
Figure BDA0003880482250000113
Respectively representing the wavelength of an L1/B1I frequency point of the GPS/BDS-3 and the corresponding ambiguity thereof;
Figure BDA0003880482250000114
respectively, pseudorange and phase noise.
And S403, obtaining initial solutions of troposphere parameters and ambiguity parameters and a variance-covariance matrix thereof by using the initial two epoch observation equations.
The key of single-frequency precise single-point positioning lies in the elimination of ionosphere errors, and the traditional single-frequency ionosphere model mainly utilizes a code phase combination mode to eliminate ionosphere influence at the cost of amplifying observation noise. The single-frequency ionosphere method disclosed by the patent estimates ionosphere parameters by using a method with ionosphere constraints, so that the influence of the ionosphere on single-frequency precise positioning is eliminated. 2N observation equations can be formed for code phase observation values of N satellites, and 3 coordinate parameters, 2 clock error parameters, 1 troposphere parameter, N ionosphere parameters and N ambiguity parameters, namely 2 + N +6 parameters, are estimated in the equations. Obviously, the number of observation equations is less than the number of parameters, which results in rank deficiency of normal equations and cannot be directly estimated. Because the receiver clock error, the ionospheric parameters and the ambiguity parameters have coupling and correlation, the strongly correlated clock error parameters, the ionospheric parameters and the ambiguity parameters are converted into estimable quantities by adopting an equivalent parameter conversion mode. The specific implementation form is that the clock error of the first epoch is constrained to be 0, so that the clock error offset can be absorbed by the ionospheric parameters and the ambiguity parameters, and the estimates of the two types of parameters have bias, which are called equivalent ionospheric parameters and equivalent ambiguity parameters. But this does not affect the receiver coordinate parameters that we are solving. This approach solves the rank deficiency problem between parameters. Then the observation equation can be converted into:
Figure BDA0003880482250000121
i represents an epoch reference;
Figure BDA0003880482250000122
subtracting a calculated value (OMC) from observed values respectively representing a pseudo range and a phase of an ith epoch;
Figure BDA0003880482250000123
a unit vector representing the satellite to the receiver; Δ x represents a receiver coordinate vector;
Figure BDA0003880482250000124
respectively representing biased ionospheric delay and ambiguity with respect to the first epoch receiver clock error. The remaining symbols are consistent with the previous equation representation.
Because the number of the parameters is larger than that of the observation equations, the normal equations are rank deficient. Assuming that the receiver position, troposphere parameters and ambiguity parameters are unchanged in the first two epochs, the observation ranges of the first two epochs are simultaneously established, and assuming that each epoch has N satellites, 4N pseudo ranges and phase observation equations are total. Meanwhile, the unknown parameters comprise 3 position parameters, one intersystem deviation parameter (ISB), one receiver clock error parameter, one troposphere parameter, N ambiguity parameters and 2N ionosphere parameters, and the total is 3N +6 unknown numbers. The problem of rank deficiency of the observation equation can be solved as long as the number of available satellites of the GPS/BDS-3 is more than 6, and the initial troposphere and ambiguity parameters can be solved.
S404, constraining by using troposphere and ambiguity parameter information, and estimating a receiver position, a clock error parameter, an ionosphere parameter, a troposphere parameter, an ambiguity parameter and an intersystem deviation parameter of the current epoch by using least square in combination with an observation equation of the current epoch. Considering that the troposphere wet delay has the random walk characteristic and the ambiguity parameter has the constant characteristic, the troposphere wet delay and the ambiguity parameter of the previous epoch are taken as the constraint of the current epoch, the rank deficiency problem of the observation equation can be solved, and the continuous parameter solution estimation of each epoch is realized. Assuming that there are N observation satellites in the last epoch, the ambiguity parameter constraint has N equations, and simultaneously, the addition of 1 convection layer constraint generates N +1 constraint equations. Meanwhile, the current epoch has M observation satellites, and then has 2M observation equations, plus constraint equations, and has 2M + N +1 equations. Meanwhile, the parameters of the current epoch include 3 position parameters, 1 receiver clock error parameter, 1 ISB parameter, 1 troposphere parameter, M ionosphere parameters and M ambiguity parameters, and the total number is 2M +6 parameters. Then as long as 2M + N +1 >. The number of the available GPS/BDS-3 satellites taking the last epoch as the constraint must reach 6, and meanwhile, the satellite drop of the current epoch or the newly added satellite does not influence the establishment of the observation equation, so that the problems of the satellite drop and the newly added satellite of the observation satellite in the observation process are effectively solved.
Thus, the new observation equations are reconstructed as N +1 virtual observation equations (constraint equations) for the previous epoch and 2M pseudorange/phase observation equations for the current epoch. The observation equation and parameters reconstructed in the single-frequency precise single-point positioning are respectively as follows:
Figure BDA0003880482250000131
Figure BDA0003880482250000132
Figure BDA0003880482250000135
I i ,
Figure BDA0003880482250000134
the virtual observed values of the troposphere and the ambiguity parameter of the previous epoch and a variance-covariance matrix thereof are obtained; a. The i ,L i ,
Figure BDA0003880482250000136
Respectively a design matrix, an OMC value and a corresponding observation variance-covariance matrix of the current epoch.
The position parameters can be solved in real time by least squares estimation. Meanwhile, it should be noted that the ionospheric parameters exist in the pseudorange and phase observation equations, so that DCB corrections in pseudorange observations are absorbed into ionospheric parameters, and meanwhile, because the ionospheric and ambiguity parameters are correlated, the DCB parameters are further absorbed by the ambiguity parameters, so that the resolved ionospheric parameters and ambiguity parameters are biased estimates, but the estimation of the position parameters is not affected.
S405, updating the variance-covariance state matrix of the convection layer parameter and the ambiguity parameter. In order to ensure that the observation equation of the next epoch is solved smoothly, namely the rank deficiency problem of the observation equation is eliminated, troposphere parameters and ambiguity parameters of the current epoch and variance-covariance matrix information corresponding to the troposphere parameters are extracted, and the information is submitted to the observation equation of the next epoch for establishment. In this way, the receiver position parameters can be continuously solved by least square estimation.
And repeating the steps of S101-S405, wherein each epoch utilizes single-frequency GPS/BDS-3 observation data and PPP-B2B correction data, utilizes constraint information of troposphere and ambiguity to construct an observation equation, and then utilizes least square to estimate real-time high-precision position information of the ground receiver in real time.
After the broadcast ephemeris is corrected by adopting the PPP-B2B precision orbit and clock error, the clock error precision of the broadcast ephemeris is no longer suitable for calculating the orbit and clock error precision of a satellite end, and a new satellite orbit and clock error precision calculation mode needs to be adopted:
Figure BDA0003880482250000141
in the formula (I), the compound is shown in the specification,
Figure BDA0003880482250000142
the calculation precision of the orbit and the clock error of the satellite s after B2B correction is shown; URA represents the user ranging accuracy index provided by PPP-B2B.
Then the observation accuracy of the satellite is calculated as follows:
Figure BDA0003880482250000143
Figure BDA0003880482250000144
the expression represents the comprehensive errors such as observation noise, multipath and the like, and is obtained by calculation in a mode of altitude angle weighting. The pseudo-range and phase observation weight model R of the observation satellite is
Figure BDA0003880482250000145
Figure BDA0003880482250000146
Noise representing the pseudorange and phase observations, respectively, of the ionosphere-free combination.
As shown in fig. 4, a detailed flowchart of a real-time single-frequency precise single-point positioning algorithm based on PPP-B2B correction is shown, which mainly includes 4 modules, which are respectively: a single-point positioning technique (S1) based on pseudo-range observations; calculating the satellite real-time precise orbit and clock error based on PPP-B2B enhanced information (S2); preprocessing observation data and calculating an error model (S3); and (S4) a real-time single-frequency precise point positioning method based on the PPP-B2B correction number. And the specific implementation content in each module.
As shown in fig. 5, a dynamic positioning test is performed on the MIZU of the IGS station by using a real-time single-frequency precise single-point positioning algorithm based on PPP-B2B correction. The experiment adopts GPS/BDS-3 dual-system single-frequency simulated dynamic observation data, and in order to analyze the enhancement effect of PPP-B2B correction on single-frequency precise positioning, the experiment simultaneously utilizes broadcast ephemeris (BRDC) and post-precise ephemeris (precision) as comparison. The result shows that the GPS/BDS-3 dual-system single-frequency precise positioning can be quickly converged to a decimeter level under the enhancement of the PPP-B2B correction number. The single-frequency dynamic positioning accuracy after PPP-B2B correction is equivalent to the positioning accuracy of a post-event precise ephemeris, is far higher than the positioning accuracy of a broadcast ephemeris, can meet the requirement of real-time high-accuracy positioning, and provides technical support for the real-time precise positioning of a single-frequency receiver with low cost and large-range application.
Components not described in detail herein are prior art.
Although the present invention has been described in detail with reference to the specific embodiments, the present invention is not limited to the above embodiments, and various changes and modifications without inventive changes may be made within the knowledge of those skilled in the art without departing from the spirit of the present invention.

Claims (5)

1. A PPP-B2B enhanced low-cost single-frequency GNSS receiver precision positioning method is characterized by comprising the following steps: the method comprises the steps that a ground device receives a navigation signal from a GPS/BDS-3 satellite, a broadcast ephemeris is corrected through a PPP-B2B real-time enhancement correction number played by a Beidou three-satellite GEO satellite, and real-time single-frequency precise single-point positioning is completed through a real-time single-frequency precise single-point positioning algorithm model adopting the PPP-B2B correction number in the ground device.
2. The PPP-B2B enhanced low-cost single-frequency GNSS receiver fine positioning method of claim 1, characterized in that: the satellite real-time precise orbit and clock error calculation based on PPP-B2B enhanced information can realize decimeter-level high-precision positioning without additionally establishing a communication link and arranging a base station nearby.
3. The PPP-B2B enhanced low-cost single-frequency GNSS receiver fine positioning method of claim 2, characterized in that: the satellite real-time precise orbit and clock error calculation step of PPP-B2B enhanced information comprises the following steps:
s201, extracting PPP-B2B orbit and clock correction number information broadcast by a Beidou No. three GEO satellite in real time, and analyzing the quality conditions of the PPP-B2B orbit and the clock correction number;
s202, acquiring the track correction numbers of the PPP-B2B enhanced GPS/BDS-3, namely the correction numbers in the radial direction, the normal direction and the tangential direction, and correcting the calculated coarse GPS/BDS-3 satellite position;
and S203, acquiring a clock difference correction number of the PPP-B2B enhanced GPS/BDS-3, correcting the clock difference of the rough GPS/BDS-3 satellite obtained by calculation, and obtaining high-precision GPS/BDS-3 real-time high-precision orbit and clock difference information for subsequent real-time precise single-point positioning service.
4. The PPP-B2B enhanced low-cost single-frequency GNSS receiver fine positioning method of claim 1, characterized in that: estimating ionospheric parameters by means of reference conversion, determining initial values of the parameters by means of multi-epoch combined solution, estimating the ionospheric parameters by means of a method with ionospheric constraints, eliminating the influence of the ionospheric on single-frequency precision positioning, and establishing an observation equation, wherein the expression of the observation equation is as follows:
Figure FDA0003880482240000021
i represents an epoch reference number;
Figure FDA0003880482240000022
subtracting an arithmetic value (OMC) from observed values representing a pseudo range and a phase of an ith epoch, respectively;
Figure FDA0003880482240000023
a unit vector representing the satellite to the receiver; Δ x represents a receiver coordinate vector;
Figure FDA0003880482240000024
respectively representing biased ionospheric delay and ambiguity with respect to the first epoch receiver clock error.
5. The PPP-B2B enhanced low-cost single-frequency GNSS receiver fine positioning method of claim 1, characterized in that: utilizing the time correlation characteristic of an ionized layer, solving ionized layer parameters by a method with ionized layer constraint, deducting the adverse effect of the ionized layer from single-frequency precise single-point positioning, and further obtaining a real-time decimeter-level high-precision positioning result; and (3) taking the troposphere wet delay and ambiguity parameters of the last epoch as the constraints of the current epoch, solving the rank deficiency problem of the observation equation and realizing the continuous parameter solution estimation of each epoch.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116125514A (en) * 2023-02-09 2023-05-16 广州市城市规划勘测设计研究院 Ground disaster monitoring method, device, terminal and medium based on Beidou PPP-RTK virtual observation value
CN117784179A (en) * 2024-02-23 2024-03-29 中国科学院空天信息创新研究院 PPP-B2B-based real-time space environment sensing monitoring system and method
CN118393538A (en) * 2024-03-29 2024-07-26 中国科学院上海天文台 Beidou B2B-PPP user distance precision factor refinement and user positioning stochastic model optimization method
CN118626866A (en) * 2024-08-09 2024-09-10 武汉大学 PPP-B2B satellite clock error prediction method and device, electronic equipment and storage medium

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116125514A (en) * 2023-02-09 2023-05-16 广州市城市规划勘测设计研究院 Ground disaster monitoring method, device, terminal and medium based on Beidou PPP-RTK virtual observation value
CN117784179A (en) * 2024-02-23 2024-03-29 中国科学院空天信息创新研究院 PPP-B2B-based real-time space environment sensing monitoring system and method
CN117784179B (en) * 2024-02-23 2024-04-30 中国科学院空天信息创新研究院 PPP-B2B-based real-time space environment sensing monitoring system and method
CN118393538A (en) * 2024-03-29 2024-07-26 中国科学院上海天文台 Beidou B2B-PPP user distance precision factor refinement and user positioning stochastic model optimization method
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