CN115616615A - A low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b - Google Patents

Abstract

The present invention provides a low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b, relates to the technical field of satellite navigation and positioning, aims to solve the problem that single-frequency observation data cannot effectively suppress ionospheric errors, and adopts a technical solution Yes, the ground equipment receives the navigation signal from the GPS/BDS-3 satellite, and corrects the broadcast ephemeris through the PPP-B2b real-time enhanced correction number broadcast by the Beidou-3 GEO satellite, and uses the PPP-B2b correction number in the ground equipment Real-time single-frequency precise point positioning algorithm model to complete real-time single-frequency precise point positioning; through the PPP-B2b enhanced correction data broadcast by GEO satellites to obtain high-precision real-time GPS/BDS-3 real-time precise orbit and clock error data, get rid of The distance limit of the reference station, using a single receiver to achieve real-time decimeter-level positioning effect; the indiscriminate clock error and ionospheric parameters are converted into equivalent ionospheric parameters by means of equivalent parameter conversion, so as to estimate and deduct the ionospheric pair in real time The impact of frequency PPP can be obtained to obtain real-time decimeter-level positioning results.

Description

A low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b

technical field

The invention relates to the technical field of satellite navigation and positioning, in particular to a PPP-B2b enhanced low-cost single-frequency GNSS receiver precision positioning method.

Background technique

The global satellite navigation and positioning system (GNSS) has been widely used at present, and people's demand for satellite positioning is developing towards high precision. However, the accuracy of standard positioning services provided by GNSS is at the level of tens of meters to meters, which is far from meeting the accuracy requirements of precise positioning. There are two main technical means to achieve real-time precise positioning, namely, satellite-based augmentation and ground-based augmentation. Ground enhancement is achieved by laying a dense network of reference stations on the ground, and the distance of a single station is about 20 kilometers. Therefore, its high-precision positioning service depends on the deployment of reference stations, and cannot achieve high-precision positioning services on the ocean. Satellite-based augmentation is to use regional or global tracking station network to solve the satellite's precise orbit and clock error correction number, and transmit the correction book information to the user in real time through the communication satellite. The user end uses the correction number information broadcast by the satellite, and then uses the dual The linear combination of frequency observations eliminates the influence of the ionosphere, thereby achieving real-time decimeter-level dynamic positioning accuracy. At present, star augmentation services are mainly provided by various GNSS service providers, such as Trimble in the United States, Fugro in the Netherlands, UniStrong and China Hi-Target in China, etc. The Beidou-3 independently developed by my country not only integrates navigation and communication functions, but also has various service capabilities such as positioning and navigation timing, satellite-based augmentation, ground-based augmentation, precise point positioning, short message communication, and international search and rescue. Among them, the PPP-B2b signal is used as a data broadcasting channel to broadcast the precise orbit and clock error correction numbers of Beidou-3 and other GNSS satellites through the Beidou-3 GEO satellite, and correct the orbit and clock error of the broadcast ephemeris, which can obtain high-speed data in real time. The high-precision GPS/BDS-3 real-time precise orbit and clock error information can provide dynamic decimeter-level and static centimeter-level precise positioning services for my country and surrounding areas.

Chinese patent CN202010036792.3 discloses a PPP-RTK positioning method based on non-difference observation model and rank-deficiency elimination. The adopted technical solution includes the following steps: select the pseudorange and phase observation of the GNSS system global or regional tracking station network Data; use the observation data to construct the original observation equation of single system and multiple frequencies; use the S-basis rank deficiency theory to reintegrate the parameters in the original observation equation, eliminate the mathematical rank deficiency in the original observation equation, and obtain a new observation equation . This design is based on the global or regional GNSS tracking station network multi-frequency point pseudo-range and phase observation data, and uses the S-basis rank-deficiency theory to construct a full-rank, non-difference, and non-combined full-parameter estimation model, which realizes the satellite clock error, space atmosphere Unified estimation of positioning enhancement parameters such as delay and basic frequency satellite phase deviation, while providing PPP-RTK high-precision positioning enhancement services, can be backward compatible with the service requirements of traditional positioning modes such as PPP and RTK; the current precise PPP real-time positioning services mainly It is a dual-frequency or multi-frequency measurement receiver. In the above technical solution, for the PPP-RTK positioning method of the non-difference observation model, the S-basis rank deficiency theory is introduced to process the parameters, and the main solution is how to use multi-frequency data for PPP-RTK positioning. RTK positioning. At present, there is no in-depth study on the PPP real-time positioning service of single-frequency receivers in the low-cost mass market. The main reason is that single-frequency observation data cannot effectively suppress ionospheric errors.

The present invention mainly provides a method of using the PPP-B2b correction number broadcasted by the Beidou-3 GEO to correct the broadcast ephemeris orbit and clock error so as to obtain high-precision real-time precise orbit and clock error data, which can be used in the form of equivalent parameter conversion The method of parameter estimation is used to deal with ionospheric errors and provide real-time high-precision location services for single-frequency users.

Contents of the invention

In view of the problems existing in the prior art, the present invention discloses a low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b. The technical solution adopted is to use the PPP-B2b correction number to correct the orbit and clock error The method with ionospheric parameter constraints is used to deal with ionospheric errors, so as to obtain real-time decimeter-level positioning results using single-frequency observation data. The method includes satellite real-time precise orbit and clock error calculation based on PPP-B2b enhanced information, without additional The decimeter-level high-precision real-time positioning results can be obtained by using a communication link and a differential station. The real-time single-frequency precise point positioning algorithm with ionospheric parameter constraints described in the present invention uses the method of reference conversion to convert the ionosphere The parameters are converted into estimable quantities, so that the ionospheric parameter estimation realized by single-frequency observations deducts the adverse effects of the ionosphere, and obtains high-precision real-time precise single-point positioning results.

As a preferred technical solution of the present invention, this method does not need to establish additional communication links, and does not need to deploy base stations nearby to achieve decimeter-level high-precision positioning, and the real-time precise orbit and clock error of satellites based on PPP-B2b enhanced information Calculation steps include:

S201, extracting the PPP-B2b orbit and the clock error correction number information broadcast in real time by the Beidou No. 3 GEO satellite, and analyzing the PPP-B2b orbit and the clock error correction number quality situation;

S202, obtain the orbit correction number of PPP-B2b enhanced GPS/BDS-3, promptly the correction number in radial direction, normal direction and tangential direction, correct the rough GPS/BDS-3 satellite position that calculates;

S203, obtain the clock error correction number of PPP-B2b enhanced GPS/BDS-3, correct the calculated rough GPS/BDS-3 satellite clock error, and obtain high-precision GPS/BDS-3 real-time high-precision orbit and clock The difference information is used for subsequent real-time precise point positioning services.

As a preferred technical solution of the present invention, the ionospheric parameters are converted into estimable parameters by means of benchmark conversion, and reasonable approximation assumptions are used to solve the problem of determining the initial value of parameters by means of multi-epoch joint solution. The specific method is as follows :

The key to single-frequency precise point positioning lies in the elimination of ionospheric errors. Traditional single-frequency ionospheric models mainly use code-phase combination to eliminate ionospheric effects, at the cost of amplifying observation noise. The single-frequency ionospheric method described in this patent uses a method with ionospheric constraints to estimate ionospheric parameters, thereby eliminating the impact of the ionosphere on single-frequency precise positioning. For the code phase observations of N satellites, a total of 2N observation equations can be formed. In the equation, a total of 3 coordinate parameters, 2 clock error parameters, 1 troposphere parameter, N ionosphere parameters and N ambiguity parameters need to be estimated. That is 2*N+6 parameters. Obviously, the number of observation equations is less than the number of parameters, resulting in the rank deficiency of normal equations, which cannot be directly estimated. Because the receiver clock bias, ionospheric parameters, and ambiguity parameters have coupling and correlation, we use the method of reference transformation to transform the strongly correlated clock bias parameters, ionospheric parameters, and ambiguity parameters into estimable ones. The specific implementation form is to set the clock error of the first epoch as the reference, and force the constraint to be 0, then the reference offset will be absorbed by the ionospheric parameters and ambiguity parameters, resulting in biased estimates of these two types of parameters, but this Does not affect the receiver coordinate parameters we want to solve. This approach solves the rank deficiency problem between parameters. Then the observation equation can be transformed into:

分别表示第i历元的伪距和相位的观测值减去计算值(OMC)；

表示卫星到接收机的单位向量；Δx表示接收机坐标向量；

分别表示相对于第一历元接收机钟差的有偏电离层延迟和模糊度。 其余符号与前面方程表述一致。i represents the epoch label;

represent the observed value minus the calculated value (OMC) of the pseudorange and phase of the i-th epoch, respectively;

Indicates the unit vector from the satellite to the receiver; Δx indicates the coordinate vector of the receiver;

Denote the biased ionospheric delay and ambiguity, respectively, relative to the receiver clock error of the first epoch. The rest of the symbols are consistent with the expressions in the previous equations.

Because the number of parameters is greater than the number of observation equations, the normal equation is rank deficient. Assuming that the receiver position, tropospheric parameters, and ambiguity parameters do not change in the initial two epochs, then the observation equations of the initial two epochs are combined, assuming that there are N satellites in each epoch, then there are 4N pseudoranges and phases in total observation equation. At the same time, the unknown parameters include 3 position parameters, one intersystem bias parameter (ISB), one receiver clock error parameter, one troposphere parameter, N ambiguity parameters, and 2N ionospheric parameters, a total of 3N+6 unknowns. Then as long as the number of available satellites of GPS/BDS-3 is greater than 6, the problem of rank deficiency of the observation equation can be solved, and the initial troposphere and ambiguity parameters can be solved.

As a preferred technical solution of the present invention, the time-dependent characteristics of the ionosphere are used to solve the ionosphere parameters through a method with ionosphere constraints, so that the adverse effects of the ionosphere are deducted from the single-frequency precise point positioning, and further real-time Decimeter-level high-precision positioning results, the specific method is as follows:

Considering that the tropospheric wet delay has random walk characteristics and the ambiguity parameters have constant characteristics, taking the tropospheric wet delay and ambiguity parameters of the previous epoch as the constraints of the current epoch can solve the rank deficit problem of the observation equation and realize the Continuous parameter solution estimates for epochs.

Assuming that there are N observing satellites in the last epoch, then there are N equations constrained by the ambiguity parameters, and at the same time, one constraint on the troposphere is added, resulting in a total of N+1 constraint equations. At the same time, there are M observation satellites in the current epoch, so there are 2M observation equations in total, plus constraint equations, there are 2M+N+1 equations in total. At the same time, the parameters of the current epoch include 3 position parameters, 1 receiver clock difference parameter, 1 ISB parameter, 1 troposphere parameter, M ionosphere parameters, and M ambiguity parameters, totaling 2M+6 parameters. Then as long as 2M+N+1>2M+6, that is, N is greater than 5, that is, there are at least 6 available GPS/BDS-3 satellites, the least square method can be used to continuously solve the position and reception of each epoch. Clock difference, ISB, ionosphere, troposphere, ambiguity parameters. It shows that the number of GPS/BDS-3 satellites available as a constraint in the last epoch must reach 6, and at the same time, the establishment of the observation equation will not be affected by the loss of satellites or the addition of new satellites in the current epoch, which effectively solves the problem of observing satellites during the observation process. The problem of dropping stars and adding new satellites.

Therefore, the new observation equations are reconstructed into N+1 virtual observation equations (constraint equations) of the last epoch and 2M pseudorange/phase observation equations of the current epoch. The reconstructed observation equations and parameters in single-frequency precise point positioning are:

I_i，

为上个历元对流层、模糊度参数的虚拟观测值及其方差-协方差矩阵；A_i,L_i,

分别为当前历元的设计矩阵、OMC值和和对应的观测方差-协方 差矩阵。

I _i ,

are the virtual observation values of troposphere and ambiguity parameters and their variance-covariance matrix in the last epoch; A _i , L _i ,

are the design matrix, OMC value and corresponding observation variance-covariance matrix of the current epoch, respectively.

The location parameters can be solved in real time by least squares estimation. At the same time, it should be noted that the ionospheric parameters exist in the pseudorange and phase observation equations, then the DCB correction in the pseudorange observations will be absorbed into the ionospheric parameters, and because the ionosphere is related to the ambiguity parameters, the DCB parameters will be further absorbed by the ambiguity parameters, resulting in biased estimates of the resolved ionospheric parameters and ambiguity parameters, but this does not affect the estimation of the position parameters.

Beneficial effects of the present invention: the present invention acquires high-precision real-time GPS/BDS-3 real-time precision orbit and clock error data through the PPP-B2b enhanced correction data broadcast by GEO satellites, thereby getting rid of the distance limitation of reference stations and realizing real-time Decimeter-level positioning effect; the present invention converts indistinguishable clock error and ionospheric parameters into equivalent ionospheric parameters by means of equivalent parameter conversion, thereby deducting the impact of the ionosphere on single-frequency PPP through real-time estimation, and then obtaining real-time Decimeter-level positioning results. Traditional single-frequency precise point positioning mainly eliminates the ionosphere through code-phase combination, but the positioning effect is not good due to the amplification of observation noise; the present invention solves the problem of determining the initial value of parameters by using reasonable assumptions and joint calculation of multi-epoch observation values The problem of rank deficiency in real-time, so as to avoid the instability of parameter calculation, provide technical support for real-time single-frequency high-precision applications.

Description of drawings

In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the accompanying drawings that are required in the description of the specific embodiments or prior art. Throughout the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, elements or parts are not necessarily drawn in actual scale.

Fig. 1 is a schematic diagram of the framework of the present invention;

Fig. 2 is a schematic diagram of the single-frequency precise point positioning algorithm based on the PPP-B2b correction number of the present invention;

Fig. 3 is the flow chart that the present invention utilizes the PPP-B2b enhancement correction number that No. 3 GEO of Big Dipper broadcasts to correct the track and the clock difference of the broadcast ephemeris;

Fig. 4 is the algorithm flowchart of the single-frequency precise point positioning algorithm of the PPP-B2b correction number of the present invention;

Fig. 5 is a schematic diagram of the single-frequency GPS/BDS-3 dynamic positioning result applied in the present invention.

detailed description

The technical solutions of the present invention will be clearly and completely described below in conjunction with 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. The indicated orientation or positional relationship is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific orientation, or in a specific orientation. construction and operation, therefore, should not be construed as limiting the invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and should not be construed as indicating or implying relative importance.

In the description of the present invention, it should be noted that unless otherwise specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection. Connected, or integrally connected; it can be mechanically connected or electrically connected; it can be directly connected or indirectly connected through an intermediary, and it can be the internal communication of two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood in specific situations.

Example 1

As shown in Figure 1, the present invention discloses a low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b. The technical solution adopted is that ground equipment receives navigation signals from GPS/BDS-3, The PPP-B2b real-time enhanced correction broadcasted by the GEO satellite corrects the broadcast ephemeris, and finally completes the real-time single-frequency precise point positioning application in the ground equipment.

As shown in Figure 2, the real-time single-frequency precise point positioning algorithm model of PPP-B2b correction number includes the following steps:

S1, single-point positioning technology based on pseudo-range observations;

S2, satellite real-time precise orbit and clock error calculation based on PPP-B2b enhanced information;

S3, observation data preprocessing and error model calculation;

S4, real-time single-frequency precise point positioning algorithm based on PPP-B2b corrections.

In S1, the single-point positioning technology based on pseudo-range observations includes the following steps:

In S101, the received GPS/BDS-3 satellite pseudo-range observation data is checked, and no pseudo-range data is removed, and the elevation angle of each satellite is calculated simultaneously, and the satellite observation data of low elevation angle are removed;

In S102, the broadcast ephemeris is the extrapolation result of the ground analysis center, and the real-time position and clock error information of GPS/BDS-3 satellites with poor accuracy can be obtained through broadcast ephemeris calculation;

In S103, the pseudo-range observation data of GPS/BDS-3 is Taylor expanded and linearized, and the ionosphere and troposphere are obtained through model calculation. Construct the observation equation about the parameters of the position and the clock error of the ground equipment, and obtain the position and clock error results of the ground equipment that meet the accuracy index through the least squares iterative calculation;

In S104, the above positioning result is further judged to analyze whether the pseudorange residual information meets the requirements. If the requirements are met, it means that the positioning result is available, otherwise it is not available.

In each epoch, S101-S104 is first performed to obtain the initial rough position of the ground receiver at the current moment, and provide initial coordinates for subsequent real-time precise positioning.

As shown in Figure 3, it is a flow chart of the present invention utilizing the PPP-B2b enhanced correction number broadcasted by Beidou-3 GEO to correct the orbit and the clock error of the broadcast ephemeris.

S2, satellite real-time precise orbit and clock error calculation based on PPP-B2b enhanced information, satellite real-time precise orbit and clock error calculation based on PPP-B2b enhanced information, to solve the GPS/BDS-3 satellite real-time precision required for real-time high-precision positioning Coordinate and clock data, including the following steps:

S201, extracting the PPP-B2b orbit and the clock error correction number information broadcast in real time by the Beidou No. 3 GEO satellite, and analyzing the PPP-B2b orbit and the clock error correction number quality situation;

S202, obtain the orbit correction number of PPP-B2b enhanced GPS/BDS-3, promptly the correction number in radial direction, normal direction and tangential direction, correct the rough GPS/BDS-3 satellite position that calculates;

The parameters included in the orbit correction information are the radial, tangential and normal components of the orbit correction vector δO. The orbit correction value is used to calculate the satellite position correction vector δX, and at the same time, the satellite position vector X _broadcast calculated by using the broadcast ephemeris is also used. The corrected calculation formula is:

X _orbit ＝X _broadcast -δX

X _orbit represents the satellite position corrected by the orbit correction message; X _broadcast represents the satellite position calculated by the broadcast ephemeris, and its IOD matches the IODN of the orbit correction message; δX represents the satellite position correction. The calculation formula of satellite position correction δX is as follows:

e _along ＝e _cross ×e _radial

δX＝[e _radial e _along e _cross ]·δO

表示广播星历卫星 速度矢量e_i表示方向单位矢量，i＝{radial along cross}分别对应径向、切向、法 向；δO表示PPP信息中获得的轨道改正矢量，顺序为径向、切向、法向分量。 S203，获取PPP-B2b增强GPS/BDS-3的钟差改正数，对计算得到的粗略 GPS/BDS-3卫星钟差进行修正。r=X _broadcast represents the broadcast ephemeris satellite position vector;

Represents the broadcast ephemeris satellite velocity vector e _i represents the direction unit vector, i={radial along cross} corresponds to the radial direction, tangential direction, and normal direction respectively; δO represents the orbit correction vector obtained in the PPP information, and the order is radial direction, tangential direction , Normal component. S203. Obtain the clock error correction number of the PPP-B2b enhanced GPS/BDS-3, and correct the calculated rough GPS/BDS-3 satellite clock error.

The parameters included in the clock error correction message are correction parameters relative to the clock error of the broadcast ephemeris. The usage method of this correction parameter is:

t _broadcast indicates the satellite clock error parameter calculated from the broadcast ephemeris; t _satellite indicates the satellite clock error obtained through the clock error correction message; c indicates the speed of light; C ₀ indicates the clock error correction parameter obtained in the PPP-B2b message. After obtaining the rough satellite coordinates and clock error of GPS/BDS-3 through the broadcast ephemeris in each epoch, the satellite orbit and clock error of the broadcast ephemeris are corrected by using the PPP-B2b real-time precision correction number to obtain high-precision GPS/BDS-3 3 Real-time high-precision orbit and clock error information for subsequent real-time precise single-point positioning services.

S3: Observation data preprocessing and error model calculation, observation data preprocessing and error model calculation, eliminate GPS/BDS-3 observation data that do not meet the calculation requirements, and provide "clean" observation data for subsequent precise point positioning services, At the same time, by calculating the error that can be modeled, the error source information that can be directly calculated is provided for the follow-up precision single-point positioning variance construction, including the following steps:

S301, further check the GPS/BDS-3 observation data, remove the observation data without phase observation information in the observation value, calculate the satellite elevation angle again simultaneously, and reject the satellite observation data with low elevation angle.

S302. Carry out cycle slip detection and clock error detection on the GPS/BDS-3 observation data, and mark satellites with cycle slip and clock error.

S303～S306, tidal correction, relativity correction, satellite antenna phase winding correction, PCO/PCV correction can all use the corresponding error model for correction calculation.

S306, using the error model to calculate the tropospheric dry delay and wet delay coefficients.

The present invention uses the GPT2 model to model the tropospheric delay. The GPT2 model is a meteorological parameter model based on the global monthly average pressure, temperature, and specific humidity profile data of ERA-Interim from 2001 to 2010. It can provide pressure and temperature on global grid points with a resolution of 5° or 1° , humidity vertical lapse rate, specific humidity, and the coefficient of the VMF1 dry-humidity projection function. At each grid point, the time variation of each meteorological parameter is expressed by a trigonometric function including the annual cycle and the semi-annual cycle:

A ₀ , A ₁ , A ₂ , B ₁ , and B ₂ in the formula are calculated in advance and saved in a file in the form of a grid, which can be called directly.

A ₀ , A ₁ , A ₂ , B ₁ , and B ₂ are the model coefficients of air temperature, air pressure, and specific humidity, respectively representing the constant deviation, the cosine harmonic term of the annual cycle and the semi-annual cycle, and the sine harmonic term of the annual cycle and the semi-annual cycle .

In the vertical direction, scholars assume that the temperature near the earth follows a linear change with altitude, while the vertical change of air pressure is expressed by an exponential function, and the meteorological parameters are corrected for altitude with 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 are the air temperature and air pressure on the grid point respectively, T and P are the temperature and air pressure when the grid point increases dh height respectively, Dt is the vertical lapse rate of temperature; Q is the specific humidity; e is the water pressure; g _m is the gravitational acceleration, which is 9.80665m/s ² in the GPT2 model; dMtr and R _g are the atmospheric molar mass and gas constant, and their values are 28.965×10 ^{- 3} kg/mol, 8.3143J/K/ mol.

When using the GPT2 model, input the latitude, longitude, geodetic height of the station and the reduced Julian day of the observation time, the model searches for the similar meteorological parameters in the grid file according to the coordinates of the station, and uses the above formula to convert the grid points to The meteorological parameters above are reduced to the height of the station, and finally the meteorological parameters of the location of the station are obtained by bilinear interpolation. The meteorological parameters at the station location calculated using the GPT2 model can be considered into the simplified Saastanmoinen model to calculate the zenith tropospheric delay at the station location:

ZHD＝22.2754×P/g _m

ZWD＝22.2754×(1255/T+0.5)×e/g _m

S4, the real-time single-frequency precise point positioning algorithm based on the PPP-B2b correction number, the broadcast ephemeris is corrected by the PPP-B2b real-time precise orbit and clock correction number, and the precise GPS/BDS-3 real-time precise satellite orbit and clock are obtained difference information, using the Kalman filter to estimate the real-time high-precision position information of the ground receiver in real time, including the following steps:

S401, for the "clean" observation data after the previous processing, obtain the GPS/BDS-3 real-time precise satellite orbit and clock error data corrected by PPP-B2b enhanced information at the same time, and linearize the observation value.

S402. Construct a single-frequency non-difference observation equation. The linearization of GPS/BDS-3 single-frequency non-difference model can be expressed as:

ZWD_r分别表示对 流层湿延迟系数和天顶对流层延迟；λ_i,

分别表示GPS/BDS-3的L1/B1I频点 的波长及其对应的模糊度；

分别表示伪距和相位噪声.s, r, M represent the satellite, receiver and navigation system respectively; P, L represent the pseudorange and phase observation values respectively; ρ represents the geometric distance between the satellite antenna and the receiver antenna, in meters; dt _r , dt ^s represent the receiver clock error and the satellite clock error; I represents the ionospheric delay in meters;

ZWD _r represent the tropospheric wet delay coefficient and zenith tropospheric delay respectively; λ _i ,

Respectively represent the wavelength of the L1/B1I frequency point of GPS/BDS-3 and its corresponding ambiguity;

are the pseudorange and phase noise, respectively.

S403, using the initial two epoch observation equations to obtain initial solutions of tropospheric parameters and ambiguity parameters and variance-covariance matrices thereof.

The key to single-frequency precise point positioning lies in the elimination of ionospheric errors. Traditional single-frequency ionospheric models mainly use code-phase combination to eliminate ionospheric effects, at the cost of amplifying observation noise. The single-frequency ionospheric method described in this patent uses a method with ionospheric constraints to estimate ionospheric parameters, thereby eliminating the impact of the ionosphere on single-frequency precise positioning. For the code phase observations of N satellites, a total of 2N observation equations can be formed. In the equation, a total of 3 coordinate parameters, 2 clock error parameters, 1 troposphere parameter, N ionosphere parameters and N ambiguity parameters need to be estimated. That is 2*N+6 parameters. Obviously, the number of observation equations is less than the number of parameters, resulting in the rank deficiency of normal equations, which cannot be directly estimated. Because the receiver clock error, ionospheric parameters, and ambiguity parameters have coupling and correlation, we transform the strongly correlated clock error parameters, ionospheric parameters, and ambiguity parameters into estimable ones by means of equivalent parameter conversion. The specific implementation form is to force the clock bias of the first epoch to be 0, then the clock bias offset will be absorbed by the ionospheric parameters and ambiguity parameters, resulting in biased estimates of these two types of parameters, which we call equivalent Ionospheric parameters and equivalent ambiguity parameters. But this does not affect the receiver coordinate parameters we are solving for. This approach solves the rank deficit problem between parameters. Then the observation equation can be transformed into:

分别表示第i历元的伪距和相位的观测值减去计算值(OMC)；

表示卫星到接收机的单位向量；Δx表示接收机坐标向量；

分别表示相对于第一历元接收机钟差的有偏电离层延迟和模糊度。 其余符号与前面方程表述一致。i represents the epoch label;

represent the observed value minus the calculated value (OMC) of the pseudorange and phase of the i-th epoch, respectively;

Indicates the unit vector from the satellite to the receiver; Δx indicates the coordinate vector of the receiver;

Denote the biased ionospheric delay and ambiguity, respectively, relative to the receiver clock error of the first epoch. The rest of the symbols are consistent with the expressions in the previous equations.

Because the number of parameters is greater than the number of observation equations, the normal equation is rank deficient. Assuming that the receiver position, tropospheric parameters, and ambiguity parameters do not change in the initial two epochs, then the observation equations of the initial two epochs are combined, assuming that there are N satellites in each epoch, then there are 4N pseudoranges and phases in total observation equation. At the same time, the unknown parameters include 3 position parameters, one intersystem bias parameter (ISB), one receiver clock error parameter, one troposphere parameter, N ambiguity parameters, and 2N ionospheric parameters, a total of 3N+6 unknowns. Then as long as the number of available satellites of GPS/BDS-3 is greater than 6, the problem of rank deficiency of the observation equation can be solved, and the initial troposphere and ambiguity parameters can be solved.

S404, use the troposphere and ambiguity parameter information to constrain, combine the observation equation of the current epoch, use least squares to estimate the current epoch receiver position, clock error parameters, ionospheric parameters, troposphere parameters, ambiguity parameters and inter-system deviation parameter. Considering that the tropospheric wet delay has random walk characteristics and the ambiguity parameters have constant characteristics, taking the tropospheric wet delay and ambiguity parameters of the previous epoch as the constraints of the current epoch can solve the rank deficit problem of the observation equation and realize the Continuous parameter solution estimates for epochs. Assuming that there are N observing satellites in the last epoch, then there are N equations constrained by the ambiguity parameters, and at the same time, one constraint on the troposphere is added, resulting in a total of N+1 constraint equations. At the same time, there are M observation satellites in the current epoch, so there are 2M observation equations in total, plus constraint equations, there are 2M+N+1 equations in total. At the same time, the parameters of the current epoch include 3 position parameters, 1 receiver clock difference parameter, 1 ISB parameter, 1 troposphere parameter, M ionosphere parameters, and M ambiguity parameters, totaling 2M+6 parameters. Then as long as 2M+N+1>2M+6, that is, N is greater than 5, that is, there are at least 6 available GPS/BDS-3 satellites, the least square method can be used to continuously solve the position and reception of each epoch. Clock difference, ISB, ionosphere, troposphere, ambiguity parameters. It shows that the number of available GPS/BDS-3 satellites used as a constraint in the last epoch must reach 6, and at the same time, the establishment of the observation equation will not be affected by the loss of satellites or the addition of new satellites in the current epoch, which effectively solves the problem of satellite observation during the observation process. The problem of dropping stars and adding new satellites.

Therefore, the new observation equations are reconstructed into N+1 virtual observation equations (constraint equations) of the last epoch and 2M pseudorange/phase observation equations of the current epoch. The reconstructed observation equations and parameters in single-frequency precise point positioning are:

I_i,

为上个历元对流层、模糊度参数的虚拟观测值及其方差-协方差矩阵；A_i,L_i,

分别为当前历元的设计矩阵、OMC值和和对应的观测方差-协方 差矩阵。

I _i ,

are the virtual observation values of troposphere and ambiguity parameters and their variance-covariance matrix in the last epoch; A _i , L _i ,

are the design matrix, OMC value and corresponding observation variance-covariance matrix of the current epoch, respectively.

The location parameters can be solved in real time by least squares estimation. At the same time, it should be noted that the ionospheric parameters exist in the pseudorange and phase observation equations, then the DCB correction in the pseudorange observations will be absorbed into the ionospheric parameters, and because the ionosphere is related to the ambiguity parameters, the DCB parameters will be further absorbed by the ambiguity parameters, resulting in biased estimates of the resolved ionospheric parameters and ambiguity parameters, but this does not affect the estimation of the position parameters.

S405, updating the variance-covariance state matrix of the troposphere parameter and the ambiguity parameter. In order to ensure the smooth progress of the solution of the observation equation in the next epoch, that is, to eliminate the rank deficiency problem of the observation equation, the tropospheric parameters and ambiguity parameters of the current epoch and their corresponding variance-covariance matrix information are extracted, and these information are submitted to the following The observation equations for each epoch are established. In this way, the receiver position parameters can be solved continuously by least squares estimation.

Repeat the steps of S101-S405, use the single-frequency GPS/BDS-3 observation data and PPP-B2b correction number for each epoch, use the constraint information of the troposphere and ambiguity to construct the observation equation, and then use the least squares to estimate the ground surface in real time Receiver real-time high-precision position information.

After correcting broadcast ephemeris with PPP-B2b precise orbit and clock error, the clock error accuracy of broadcast ephemeris is no longer applicable to the calculation of satellite orbit and clock error accuracy, and a new calculation method for satellite orbit and clock error accuracy is required:

表示卫星s的B2b改正后的轨道和钟差计算精度；URA表示PPP- B2b提供的用户测距精度指数。In the formula,

Indicates the B2b corrected orbit and clock error calculation accuracy of satellite s; URA indicates the user ranging accuracy index provided by PPP-B2b.

Then the calculation method of the observation accuracy of the satellite is:

表示观测噪声、多路径等综合误差，通过高度角定权的方式计算得到。则 观测卫星的伪距和相位观测权模型R为

Indicates the comprehensive error of observation noise, multipath, etc., and is calculated by the method of height angle weighting. Then the pseudo-range and phase observation weight model R of the observation satellite is

分别表示无电离层组合的伪距和相位观测值的噪声。

denote the noise of the pseudorange and phase observations for the ionospheric-free combination, respectively.

As shown in Figure 4, it represents the detailed flowchart of the real-time single-frequency precise point positioning algorithm based on PPP-B2b correction number, mainly including 4 modules, which are respectively: point positioning technology (S1) based on pseudo-range observation value; Satellite real-time precise orbit and clock error calculation based on PPP-B2b enhanced information (S2); observation data preprocessing and error model calculation (S3); real-time single-frequency precise point positioning algorithm based on PPP-B2b correction number (S4). And the specific implementation content in each module.

As shown in Fig. 5, the real-time single-frequency precise point positioning algorithm based on the PPP-B2b correction number is used for the dynamic positioning test of the IGS station MIZU. The experiment uses GPS/BDS-3 dual-system single-frequency imitation dynamic observation data. In order to analyze the enhancement effect of PPP-B2b corrections on single-frequency precise positioning, the experiment uses broadcast ephemeris (BRDC) and ex-post precise ephemeris (precise) as Compared. The results show that GPS/BDS-3 dual-system single-frequency precise positioning can quickly converge to decimeter level under the enhancement of PPP-B2b correction number. The single-frequency dynamic positioning accuracy after PPP-B2b correction is equivalent to the positioning accuracy of the post-event precision ephemeris, far higher than the positioning accuracy of the broadcast ephemeris, which can meet the needs of real-time high-precision positioning, and is a low-cost, large-scale application. The real-time precise positioning of the single-frequency receiver provides technical support.

Components not specified herein are prior art.

Although the above-mentioned specific embodiments of the present invention have been described in detail, the present invention is not limited to the above-mentioned embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various The modification or deformation without creative work is still within the protection scope of the present invention.

Claims (5)

1. A low-cost single-frequency GNSS receiver precision positioning method enhanced by PPP-B2b is characterized in that: it comprises receiving navigation signals from GPS/BDS-3 satellites by ground equipment, and the PPP-BDS broadcast by Beidou No. 3 GEO satellites The B2b real-time enhanced correction corrects the broadcast ephemeris, and the real-time single-frequency precise point positioning is completed by using the real-time single-frequency precise point positioning algorithm model of the PPP-B2b correction number in the ground equipment. 2. the low-cost single-frequency GNSS receiver precision positioning method of a kind of PPP-B2b enhancement according to claim 1 is characterized in that: based on the satellite real-time precise orbit and clock error calculation of PPP-B2b enhancement information, no additional Establishing a communication link does not require a nearby base station to achieve decimeter-level high-precision positioning. 3. the low-cost single-frequency GNSS receiver precision positioning method of a kind of PPP-B2b enhancement according to claim 2, is characterized in that: the satellite real-time precise orbit of PPP-B2b enhancement information and the clock error calculation step comprise: S201, extracting the PPP-B2b orbit and clock correction number information broadcast in real time by the Beidou-3 GEO satellite, and analyzing the quality of the PPP-B2b orbit and clock correction number; S202. Obtain the orbit correction number of the PPP-B2b enhanced GPS/BDS-3, that is, the correction number in the radial direction, normal direction and tangential direction, and correct the calculated rough GPS/BDS-3 satellite position; S203, obtain the clock error correction number of PPP-B2b enhanced GPS/BDS-3, correct the calculated rough GPS/BDS-3 satellite clock error, and obtain high-precision GPS/BDS-3 real-time high-precision orbit and clock The difference information is used for subsequent real-time precise point positioning services. 4. The low-cost single-frequency GNSS receiver precision positioning method of a kind of PPP-B2b enhancement according to claim 1 is characterized in that: utilize the mode of datum conversion, ionosphere parameter is estimated, utilize multi-epoch joint solution The initial value of the parameters is determined by means of ionospheric constraints, the ionospheric parameters are estimated using the method with ionospheric constraints, the influence of the ionosphere on single-frequency precise positioning is eliminated, and the observation equation is established. The expression of the observation equation is:

i represents the epoch label;

represent the observed value minus the calculated value (OMC) of the pseudorange and phase of the i-th epoch, respectively;

Indicates the unit vector from the satellite to the receiver; Δx indicates the coordinate vector of the receiver;

Denote the biased ionospheric delay and ambiguity, respectively, relative to the receiver clock error of the first epoch. 5. the low-cost single-frequency GNSS receiver precision positioning method of a kind of PPP-B2b enhancement according to claim 1 is characterized in that: utilize the time correlation characteristic of ionosphere, solve ionosphere by the method with ionosphere constraint Parameters, the adverse effects of the ionosphere are deducted from the single-frequency precise point positioning, and further obtain real-time decimeter-level high-precision positioning results; the tropospheric wet delay and ambiguity parameters of the previous epoch are used as the constraints of the current epoch to solve the observation A rank-deficient problem for equations that implements continuous parameter-solving estimates for each epoch.

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