Single base station PPP-RTK positioning method and device

Abstract

The invention discloses a single base station PPP-RTK (point-to-point protocol-real-time kinematic) positioning method and equipment. The method comprises the following steps: firstly, according to acquired single base station observation data, single base station accurate coordinates and ephemeris data, satellite end error corrections and atmospheric delay corrections are respectively obtained based on different resolving models, and the satellite end error corrections comprise satellite clock error corrections and satellite orbit error corrections; the atmospheric delay correction number comprises an ionosphere delay correction number and a troposphere delay correction number of the first frequency; calculating an atmospheric delay difference between the single base station and the user based on an empirical model, and substituting the atmospheric delay difference into the atmospheric delay correction number to obtain an atmospheric delay correction number which can be used for the user; obtaining observation values of users to construct a PPP-RTK observation equation so as to eliminate error terms related to a single base station; and the satellite end error correction number and the atmospheric delay correction number are substituted into a user end PPP-RTK observation equation, so that single base station PPP-RTK positioning can be realized.

Description

Technical Field

[0001] The present invention belongs to the field of satellite navigation technology, and in particular relates to a PPP-RTK positioning method, device, computing equipment and computer-readable storage medium assisted by single base station information enhancement. Background Art

[0002] With the rapid development of the global navigation satellite system (GNSS), GNSS high-precision positioning is widely used in fields such as autonomous driving and surveying. Traditional GNSS high-precision positioning technologies mainly include real-time kinematic positioning (RTK) and precise point positioning (PPP). RTK technology relies on multiple ground base stations with known coordinates. Through a short baseline differential model, it uses carrier phase observations to fix integer ambiguities and is often used in centimeter-level high-precision positioning scenarios. However, since its differential principle relies on the close distance between the base station and the user, it has significant coverage limitations in large areas, remote areas or mobile applications. In addition, the construction and maintenance costs of the RTK system are high, and it needs to rely on a stable data transmission link, which has poor deployment flexibility. In order to overcome the insufficient spatial coverage and deployment complexity of the RTK system, PPP came into being. PPP receives real-time precise orbit and clock information provided by GNSS service organizations (such as IGS) without relying on close-range base stations, and can achieve decimeter-level to centimeter-level positioning accuracy worldwide. However, PPP usually has the problem of long convergence time and poor stability because it fails to quickly fix the integer ambiguity in its model. In particular, the convergence time can even be as long as tens of minutes in a dynamic environment. In order to take into account the wide-area capability of PPP and the fast convergence of RTK, the PPP-RTK positioning technology that combines the advantages of PPP and RTK has been proposed in recent years.

[0003] The existing PPP-RTK method relies on a large number of base station networks deployed in the region or nationwide. It generates ionospheric corrections, tropospheric corrections, satellite hardware delays and other information through server modeling and analysis, and uses the State Space Representation (SSR) model to broadcast high-precision correction information to users, thereby achieving rapid fixation of integer ambiguities. Representative solutions include the European Space Agency's Galileo HAS system and China's high-precision CORS network (such as Qianxun Location, Huace, etc.), which can provide centimeter-level real-time PPP-RTK services. Although this type of method takes into account both accuracy and speed, its system architecture is highly dependent on multi-base station networks and central server computing, with high deployment and maintenance costs, poor system robustness and flexibility, and is particularly difficult to adapt to the needs of fast and high-precision positioning in remote, outdoor and mobile scenarios. Summary of the Invention

[0004] In view of the above existing problems, the present invention proposes a single-base station PPP-RTK positioning method and device to meet the positioning needs of users in the scenario of only a single base station, aiming to solve the problems of traditional PPP-RTK requiring multiple base stations and high deployment and maintenance costs.

[0005] The above object is achieved by the following technical solutions:

[0006] The present invention first provides a single-base station PPP-RTK positioning method, including the following steps:

[0007] Step S1: Obtain single-base station GNSS observation data, single-base station precise coordinates, and ephemeris data;

[0008] Step S2: Substitute the precise coordinates and ephemeris data of the single base station obtained in Step S1 into the IF combination equation under inter-satellite single difference, the GNSS raw observation equation, and the GF combination equation under inter-satellite single difference; estimate the satellite clock error correction number in the IF combination equation under inter-satellite single difference, and estimate the satellite orbit error correction number in the GNSS raw observation equation. The satellite clock error correction number and the satellite orbit error correction number are collectively referred to as satellite-side correction numbers; estimate the atmospheric delay correction number in the GF combination equation under inter-satellite single difference. The atmospheric delay correction number includes the ionospheric delay correction number and the tropospheric delay correction number at the first frequency; then calculate the atmospheric delay difference between the single base station and the user, and generate an atmospheric delay correction number available for the user according to this atmospheric delay difference; generate a correction number product from the satellite-side correction numbers and the atmospheric delay correction number available for the user and broadcast it to the user;

[0009] Step S3: The user obtains ephemeris data, receives GNSS observation data, and the correction number product broadcast in Step S2;

[0010] Step S4: Substitute the ephemeris data, GNSS observation data, and correction number product obtained in Step S3 into the single-base station PPP-RTK positioning equation at the user side and perform a solution to achieve single-base station PPP-RTK positioning.

[0011] Further, Step S1 specifically includes the following sub-steps:

[0012] Step S11: Place the single base station in an open environment and continuously receive GNSS observation data;

[0013] Step S12: Download ephemeris data from the data center of Wuhan University;

[0014] Step S13: Using the GNSS observation data and ephemeris data of multiple days before the positioning day, input the GNSS observation data and ephemeris data into the positioning software, perform positioning calculation in the PPP mode to obtain the coordinates of the single base station, and average the coordinates obtained for multiple days to represent the accurate coordinates of the base station.

[0015] Further, step S2 specifically includes the following sub-steps:

[0016] Step S21: Construct an inter-satellite single-difference equation;

[0017] First, the GNSS raw observation equation is: (1), where and respectively represent the pseudo-range observation value and carrier-phase observation value of the th frequency from satellite to the single base station ; represents the geometric distance from satellite to the single base station ; and respectively represent the clock biases of the single base station and satellite ; represents the orbit error of satellite ; is the tropospheric delay from satellite to the single base station ; represents the ionospheric delay of the th frequency from satellite to the single base station and respectively represent the hardware biases of the th frequency pseudo-range observation value at the single base station and satellite ; and respectively represent the hardware biases of the th frequency carrier-phase observation value at the single base station and satellite ; represents the ambiguity parameter of the th frequency carrier-phase observation value from satellite to the single base station ; and respectively represent the observation noises of the pseudo-range and phase observations; and respectively represent the first frequency and the The wavelength of the carrier observation signal of the frequency; the units of the above symbols are all m;

[0018] Based on the GNSS raw observation equation in Equation (1), select a satellite as the reference satellite for inter-satellite single-difference processing to eliminate the station-related error terms, including , and . Only the error terms related to the satellite and frequency remain in the processed observation equation. The inter-satellite single-difference equation is as follows: (2), where represents the pseudo-range observation value under the inter-satellite single-difference of the th frequency from the satellite to the reference satellite to the single base station ; represents the carrier phase observation value under the inter-satellite single-difference of the th frequency from the satellite to the reference satellite to the single base station ; represents the geometric distance under the inter-satellite single-difference from the satellite to the reference satellite to the single base station ; represents the clock difference under the inter-satellite single-difference between the satellite and the reference satellite ; represents the orbit error under the inter-satellite single-difference between the satellite and the reference satellite ; represents the tropospheric delay under the inter-satellite single-difference from the satellite to the reference satellite to the single base station ; represents the ionospheric delay of the first frequency under the inter-satellite single-difference from the satellite to the reference satellite to the single base station ; represents the hardware bias under the inter-satellite single-difference of the pseudo-range observation value of the th frequency between the satellite and the reference satellite ; represents the hardware bias under the inter-satellite single-difference of the carrier phase observation value of the th frequency between the satellite and the reference satellite ; represents the satellite and the reference satellite to a single base station the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference of the representing the satellite and the reference satellite to a single base station the observation noise of the pseudorange observation value under the inter-satellite single difference of the representing the satellite and the reference satellite to a single base station the observation noise of the carrier phase observation value under the inter-satellite single difference of the

[0019] Step S22: Generate the satellite clock error correction number under the inter-satellite single difference ;

[0020] The estimated satellite clock error is expressed as follows: (3), where represents the sum of the clock error and the absorbed pseudorange hardware bias, that is ; represents the common reference satellite clock error; represents the satellite clock error correction number of each satellite;

[0021] Taking the satellite as the reference satellite, perform an inter-satellite single difference on Equation (3) to eliminate the common reference satellite clock error , and obtain the following estimated satellite and the reference satellite satellite clock error under the inter-satellite single difference: (4), where represents the sum of the clock error and the absorbed pseudorange hardware bias under the inter-satellite single difference of the satellite and the reference satellite ; represents the satellite clock error correction number under the inter-satellite single difference of the satellite and the reference satellite ;

[0022] Perform an IF combination on the observation values of the frequency and the frequency to obtain the IF combination observation value, as shown below: (5), where Denote the satellite and the reference satellite to the single base station the inter-satellite single-difference IF combined pseudorange observation value; Denote the satellite and the reference satellite to the single base station the inter-satellite single-difference IF combined carrier phase observation value; and respectively denote the wavelengths of the carrier observation signals at the th frequency and the th frequency;

[0023] Based on Equation (2) in Step S21, perform IF combination to eliminate the ionospheric delay , and use the precise tropospheric correction model to correct the tropospheric delay , and the obtained inter-satellite single-difference IF combined observation equation is as follows: (6), wherein, denotes the hardware bias of the inter-satellite single-difference IF combined pseudorange observation value of the satellite and the reference satellite to the single base station ; denotes the hardware bias of the inter-satellite single-difference IF combined carrier phase observation value of the satellite and the reference satellite to the single base station ; denotes the ambiguity parameter of the inter-satellite single-difference IF combined carrier phase observation value of the satellite and the reference satellite with the single base station ; denotes the observation noise of the inter-satellite single-difference IF combined pseudorange observation value of the satellite and the reference satellite ; denotes the observation noise of the inter-satellite single-difference IF combined carrier phase observation value of the satellite and the reference satellite ;

[0024] Combine Equation (4) and Equation (6), and use the OSB product to correct the pseudorange hardware bias, that is, obtain the satellite clock error correction number of the inter-satellite single-difference of the satellite and the reference satellite , as shown in Equation (7): (7),

[0025] Step S23: Generate the satellite orbit error correction under the inter-satellite single difference ;

[0026] In the GNSS raw observation equation of step S21, that is, formula (1), when the errors include , , , , , , and are all corrected by the corresponding precise products, the remaining and , The specific expression of is: (8), where represents the geometric distance from satellite to the single base station ; and respectively represent the X coordinates of the true positions of satellite and the single base station ; and respectively represent the Y coordinates of the true positions of satellite and the single base station ; and respectively represent the Z coordinates of the true positions of satellite and the single base station ;

[0027] For the reference satellite , there is also The specific expression of, as follows: (9), where represents the geometric distance from the reference satellite to the single base station ; represents the X coordinate of the true position of the reference satellite ; represents the Y coordinate of the true position of the reference satellite ; represents the Z coordinate of the true position of the reference satellite ;

[0028] According to the ephemeris data, calculate the satellite and the reference satellite relative to the single base station The azimuth and elevation angles, and then calculate the true coordinates of the satellite according to the azimuth and elevation angles respectively The true coordinates , and , and the true coordinates of the reference satellite The true coordinates , and ; Obtain the estimated coordinates of the satellite The estimated coordinates , and , and the estimated coordinates of the reference satellite The estimated coordinates , and , so the orbit error correction numbers of the satellite and the reference satellite are obtained as follows: (10), (11),

[0029] Take the difference to obtain the satellite orbit error correction number under the inter-satellite single difference of the satellite and the reference satellite as follows: as follows: (12),

[0030] Step S24: Generate the atmospheric delay correction number under the inter-satellite single difference, and the atmospheric delay correction number includes the ionospheric delay correction number at the first frequency and the tropospheric delay correction number ;

[0031] Perform GF combination on the observation values of the two frequencies of the th frequency and the th frequency to obtain the GF combination observation value as follows: (13), where represents the GF combination pseudorange observation value under the inter-satellite single difference from the satellite and the reference satellite to the single base station ; represents the GF combination carrier phase observation value under the inter-satellite single difference from the satellite and the reference satellite to the single base station ;

[0032] Based on Equation (2) in Step S21, perform GF combination to obtain the following GF combination observation equation: (14), where represents the hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference between the satellite and the reference satellite ; represents the hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference between the satellite and the reference satellite ; represents the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference between the satellite and the reference satellite and the single base station at the frequency; represents the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference between the satellite and the reference satellite and the single base station at the frequency; represents the observation noise of the GF combined pseudorange observation value under the inter-satellite single difference from the satellite to the reference satellite to the single base station ; represents the observation noise of the GF combined carrier phase observation value under the inter-satellite single difference from the satellite to the reference satellite to the single base station ; , and respectively represent the wavelengths of the carrier observation signals at the frequency, the frequency and the frequency;

[0033] When there is no cycle slip, within the continuous arc segment, , and are considered as constant terms. Therefore, by using the characteristic that the ionospheric delay corrections of the pseudorange and carrier phase observation values are equal in value and opposite in sign, add equation (14) and take the mean within the continuous arc segment for smoothing to weaken the observation noises of the pseudorange and carrier phase observation values and determine value: (15), where is to take the mean of within the continuous arc segment;

[0034] Correct according to the OSB product , substituting Equation (15) into Equation (14), the ionospheric delay correction for the first frequency is obtained , that is: (16), Bringing this ionospheric delay correction back to the inter-satellite single-difference observation equation in step S21, the tropospheric delay correction is obtained ;

[0035] Step S25: Generate the atmospheric delay correction for inter-satellite single-difference available for users, and the atmospheric delay correction includes the ionospheric delay correction for the first frequency under inter-satellite single-difference available for users and the tropospheric delay correction ;

[0036] Calculate the atmospheric delay difference between the base station and the user, and substitute this atmospheric delay difference into the ionospheric delay correction for the first frequency under inter-satellite single-difference in step S24 and the tropospheric delay correction to generate the ionospheric delay correction for the first frequency under inter-satellite single-difference available for users and the tropospheric delay correction , where represents the user side;

[0037] In terms of ionospheric delay, based on the Klobuchar model, calculate the model value of the ionospheric delay correction for the first frequency of a single base station and the model value of the ionospheric delay correction for the first frequency of the user ; In terms of the troposphere, based on the Saastamoinen model, calculate the model value of the tropospheric delay correction of a single base station and the model value of the tropospheric delay correction of the user ;

[0038] The compensated correction is written as: (17), (18), where and represent the ionospheric delay correction and the tropospheric delay correction for the first frequency available for users; and represent the ionospheric delay correction and the tropospheric delay correction for the first frequency generated based on a single base station in step S24.

[0039] Furthermore, for the satellite clock error correction Reduce the observation noise by the moving average method to obtain the satellite clock error correction, and the specific method is as follows: (19), where and respectively represent the satellite clock error corrections under the inter-satellite single difference extracted in real time at epochs and ; represents the number of valid epochs; and respectively represent the precisions of the satellite clock error corrections under the inter-satellite single difference extracted in real time at epochs and ; represents the IF combined pseudorange observation values under the inter-satellite single difference from satellite to the single base station and the reference satellite at epoch ; represents the geometric distance under the inter-satellite single difference from satellite to the single base station and the reference satellite at epoch ; represents the satellite clock error correction under the inter-satellite single difference at epoch before adopting the moving average method, corresponding to in formula (7).

[0040] Furthermore, the specific steps of step S3 are as follows:

[0041] Step S31: The user continuously receives GNSS observation data and downloads ephemeris data from the data center of Wuhan University;

[0042] Step S32: The user receives two types of corrections broadcast by the single base station, namely the satellite-side corrections under the inter-satellite single difference and the atmospheric delay corrections available for the user. The satellite-side corrections include the satellite clock error correction and the satellite orbit error correction ; the atmospheric delay corrections available for the user include the first frequency ionospheric delay correction and the tropospheric delay correction under the inter-satellite single difference, and provides the two types of corrections to S4.

[0043] Furthermore, step S4 includes:

[0044] Step S41: Preprocess the corrections mentioned in step S32 , , and ;

[0045] Preprocess the corrections broadcast by a single base station, and perform outlier detection and rejection on , , and in sequence, and finally provide the valid data to S42;

[0046] Step S42: Initialize the user - end filter;

[0047] Calculate the initial position and velocity of the user - end through GNSS SPP, set the initial variance - covariance matrix and process noise matrix of each parameter of the filtering system, and enter S43;

[0048] Step S43: Construct the inter - satellite single - difference PPP - RTK positioning equation for the user - end, and select the satellite with the highest elevation angle as the reference satellite: (20), where the subscript U represents the user - end;

[0049] Step S44: Process the main error terms;

[0050] On the basis of step S43, process the main error terms, including the hardware bias of the frequency pseudorange observation in the inter - satellite single - difference between satellite and the reference satellite , the hardware bias of the frequency carrier - phase observation in the inter - satellite single - difference between satellite and the reference satellite , the clock error in the inter - satellite single - difference between satellite and the reference satellite , the orbit error in the inter - satellite single - difference between satellite and the reference satellite , the tropospheric delay in the inter - satellite single - difference from satellite to the user - end and the reference satellite , the first - frequency ionospheric delay in the inter - satellite single - difference from satellite to the user - end and the reference satellite where and are corrected by the OSB product. For phase observations, the phase hardware bias and to the user - end in the inter - satellite single - difference, and the first - frequency ionospheric delay , where and are corrected by the OSB product. For phase observations, the phase hardware bias After correction, the integer property of the ambiguity is restored; , , and are respectively corrected using the correction numbers , , and ;

[0051] Step S45: Filtering and calculation;

[0052] Based on step S44, the remaining error terms in formula (20) are and , where: , Therefore, the parameters to be estimated are the user's position ( , , ) and the ambiguity parameter under the inter-satellite single difference . Different stochastic models are established according to the properties of the parameters, and the Kalman filter is used to calculate all the parameters to be estimated, and the position information of the current epoch is output.

[0053] The present invention also provides a single-base station PPP-RTK positioning device, including:

[0054] A memory for storing a computer program;

[0055] A processor for calling the computer program stored in the memory and executing the single-base station PPP-RTK positioning method listed in any of the above manners according to the obtained program.

[0056] The present invention also provides a computer-readable storage medium, and the computer-readable storage medium stores a computer-executable program, and the computer-executable program is used to make a computer execute the single-base station PPP-RTK positioning method listed in any of the above manners.

[0057] The beneficial effects of the present invention compared with the prior art are:

[0058] The existing PPP-RTK positioning technology balances accuracy and speed. However, it relies on the support of a large-scale base station network to obtain correction information generated by multiple base stations (such as satellite clock error and orbit error corrections, atmospheric delay corrections, etc.). The system construction cost is high, the deployment is complex, and it is difficult to be flexibly applied in remote areas or temporary scenarios. In the implementation of the present invention, by constructing a single-base station PPP-RTK solution model, based only on the observation data of a single base station, the accurate coordinates of the single base station, and ephemeris data, the satellite-side error corrections and atmospheric delay corrections can be calculated. The satellite-side error corrections include satellite clock error corrections and satellite orbit error corrections, and the atmospheric delay corrections include ionospheric delay corrections and tropospheric delay corrections at the first frequency, and are broadcast to the user terminal in real time to achieve auxiliary enhancement of the user's PPP-RTK solution. Through the solution of the present invention, the limitations of the existing PPP-RTK positioning technology, such as relying on the support of a large-scale base station network, high system construction cost, and complex deployment, can be avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow schematic diagram of a single-base station PPP-RTK positioning method and device of the present invention. The single-base station part generates satellite-side error corrections and atmospheric delay corrections for use by the user terminal based on information such as single-base station observation data, accurate coordinates of the single base station, and ephemeris data. The satellite-side error corrections include satellite clock error corrections and satellite orbit error corrections, and the atmospheric delay corrections include ionospheric delay corrections and tropospheric delay corrections at the first frequency; the user terminal part implements the positioning method of single-base station PPP-RTK based on the corresponding corrections generated by the single base station;

[0060] Figure 2 It is an experimental device of a single base station for a static experimental scheme;

[0061] Figure 3 It is a dynamic experimental scheme. The red trajectory in the figure is the driving route, and the lower part of the figure shows the device on the vehicle;

[0062] Figure 4 It is a sequence diagram of single-difference clock error corrections for some satellites, where G19 is used as the reference satellite for all; Figure 4 In it, (a), (b), (c), (d), (e), (f), (g), and (h) are the sequence diagrams of clock error corrections for satellites G04, G05, G06, G09, G11, G12, G14, and G20 respectively;

[0063] Figure 5 It is a sequence diagram of single-difference clock error corrections for all GPS satellites;

[0064] Figure 6 It is the positioning error of the traditional model and the proposed model, Figure 6Among them, (a), (b), (c), and (d) are the positioning error maps in the E, N, U, and 3D directions, respectively.

[0065] Figure 7 The positioning errors of the traditional model and the proposed model in the first 1000 epochs after 00:40, 06:00, 12:00, and 18:00 of GPS time Figure 7 Among them, (a), (b), (c), and (d) are the positioning error maps in the E, N, U, and 3D directions, respectively. Specific implementation manner

[0066] To make the purpose, implementation manner, and advantages of this application clearer, the following will clearly and completely describe the exemplary implementation manner of this application in combination with the accompanying drawings in the exemplary embodiments of this application. Obviously, the described exemplary embodiments are only a part of the embodiments of this application, rather than all the embodiments.

[0067] The embodiments of the present invention provide a single-base station PPP-RTK positioning method and device. The specific flowchart is as Figure 1 shown, including two parts: a single base station and a user terminal, specifically including:

[0068] Step S1: Obtain the GNSS observation data, precise coordinates, and ephemeris data of the single base station;

[0069] Specifically, the step S1 includes:

[0070] Step S11: Place the single base station in an open environment and continuously receive GNSS observation data;

[0071] To verify the effectiveness of the proposed single-base station PPP-RTK positioning method, two static data sets and one dynamic vehicle data set were collected. As Figure 2 and Figure 3 shown, they are the collection scenarios of the static data set and the dynamic data set respectively. Here, the static data set is taken as an example for introduction. Figure 2 Shown is the experimental device of the single base station, including the geodetic receiver P5 and the geodetic choke ring antenna C220GR. The experimental device is placed on the roof of a high-rise building and acts as a base station server (abbreviated as HHD1) to broadcast enhanced information such as satellite clock difference corrections and atmospheric error corrections.

[0072] The static data set of HHD1 was collected on June 1, 2023 at a sampling interval of 1 second. The precise coordinates of HHD1 were pre-determined using the static solutions of multi-day data processing before the positioning day, specifically see step S13. During data processing, the cut-off elevation angle was set to 20°, and the reference satellite was determined by the satellite with the highest elevation angle.

[0073] Step S12: Download ephemeris data from the data center of Wuhan University;

[0074] Step S13: Use the GNSS observation data and ephemeris data of multiple days before the positioning day, and calculate through the PPP mode to obtain the precise coordinates of a single base station;

[0075] Input the GNSS observation data and ephemeris data into the positioning software, and perform positioning solution in the PPP mode to obtain the coordinates of the single base station. Calculate the average value of the coordinates of multiple days to represent the precise coordinates of the base station. The positioning software in this embodiment uses RTKLIB software.

[0076] Step S2: Substitute the precise coordinates of the single base station and the ephemeris data obtained in Step S1 into the ionospheric-free (IF) combination equation, the GNSS raw observation equation, and the geometry-free (GF) combination equation under inter-satellite single difference respectively; Estimate the satellite clock error correction number in the IF combination equation under inter-satellite single difference, and estimate the satellite orbit error correction number in the GNSS raw observation equation. The satellite clock error correction number and the satellite orbit error correction number are collectively referred to as satellite-side correction numbers; Estimate the atmospheric delay correction number in the GF combination equation under inter-satellite single difference. The atmospheric delay correction number includes the ionospheric delay correction number and the tropospheric delay correction number of the first frequency; Subsequently, calculate the atmospheric delay difference between the single base station and the user, and generate an atmospheric delay correction number available for the user according to this atmospheric delay difference; Generate a correction number product from the satellite-side correction number and the atmospheric delay correction number available for the user and broadcast it to the user;

[0077] Specifically, Step S2 includes:

[0078] Step S21: Construct an inter-satellite single difference equation;

[0079] First, the GNSS raw observation equation is: (1), Where, and respectively represent the pseudo-range observation value and the carrier phase observation value of the th frequency from the satellite to the single base station ; represents the geometric distance from the satellite to the single base station ; and respectively represent the clock errors of the single base station and the satellite ; represents the orbit error of the satellite ; For a satellite to a single base station tropospheric delay; Indicates the satellite to a single base station ionospheric delay of the first frequency; and respectively represent the frequency pseudorange observation value at the single base station and the satellite hardware deviation; and respectively represent the frequency carrier phase observation value at the single base station and the satellite hardware deviation; Indicates the satellite to a single base station the frequency carrier phase observation value ambiguity parameter; and respectively the observation noise of the pseudorange and phase observations; and respectively represent the wavelengths of the carrier observation signals of the first frequency and the frequency; The units of the above symbols are all m;

[0080] Based on the GNSS raw observation equation in Equation (1), select the satellite as the reference satellite for inter-satellite single-difference processing to eliminate the station-related error terms, including , and , and only the error terms related to the satellite and frequency remain in the processed observation equation. The inter-satellite single-difference equation is as follows: (2), where Indicates the satellite and the reference satellite to the single base station the frequency inter-satellite single-difference pseudorange observation value; Indicates the satellite and the reference satellite to the single base station the frequency inter-satellite single-difference carrier phase observation value; Indicates the satellite and the reference satellite to the single base station inter-satellite single-difference geometric distance; Indicates the satellite and the reference satellite Clock error under the inter-satellite single difference; Denote satellite and reference satellite Orbit error under the inter-satellite single difference; Denote satellite and reference satellite to a single base station Tropospheric delay under the inter-satellite single difference; Denote satellite and reference satellite to a single base station First frequency ionospheric delay under the inter-satellite single difference; Denote the Frequency pseudorange observation value at satellite and reference satellite Hardware bias under the inter-satellite single difference; Denote the Frequency carrier phase observation value at satellite and reference satellite Hardware bias under the inter-satellite single difference; Denote satellite and reference satellite to a single base station The Frequency ambiguity parameter of the carrier phase observation value under the inter-satellite single difference; Denote satellite and reference satellite to a single base station The Observation noise of the pseudorange observation value under the inter-satellite single difference of the Frequency; Denote satellite and reference satellite to a single base station Observation noise of the carrier phase observation value under the inter-satellite single difference of the

[0081] Step S22: Generate the satellite clock error correction number under the inter-satellite single difference ;

[0082] When estimating the satellite clock error, to avoid rank deficiency, a specific clock offset needs to be selected as a reference, which will result in a common reference satellite clock error . Then, due to the linear correlation between the satellite clock error and the ambiguity parameter, the ambiguity parameter can be separated by using the pseudorange observation value. After the ambiguity parameter converges, the satellite clock error correction number of each satellite appears. At the same time, due to the satellite clock error and the pseudorange hardware bias The linear correlation between, the pseudorange hardware bias is absorbed into the satellite clock bias . Therefore, the estimated satellite clock bias is expressed as follows: (3), where represents the sum of the clock bias and the absorbed pseudorange hardware bias, that is ; represents the common reference satellite clock bias; represents the satellite clock bias correction for each satellite;

[0083] Taking satellite as the reference satellite, the inter-satellite single difference is performed on Equation (3) to eliminate the common reference satellite clock bias , and the following estimated satellite and reference satellite satellite clock bias under the inter-satellite single difference is obtained : (4), where represents the sum of the clock bias and the absorbed pseudorange hardware bias under the inter-satellite single difference between satellite and reference satellite ; represents the satellite clock bias correction under the inter-satellite single difference between satellite and reference satellite ;

[0084] The IF combination means eliminating the ionospheric delay by using the correlation of different frequency ionospheric delays, performing a linear combination on the observations of the th frequency and the th frequency to form the IF combination observations. in Equation (2) represents the pseudorange observation under the inter-satellite single difference of the th frequency from satellite to the single base station , and in Equation (2) represents the carrier phase observation under the inter-satellite single difference of the th frequency from satellite to the single base station . Similarly, there can be the pseudorange observation under the inter-satellite single difference of the th frequency from satellite to the single base station , and the pseudorange observation under the inter-satellite single difference of the th frequency from satellite to the single base station and reference satellite with the single base station At the carrier phase observation value under the inter-satellite single difference at the . For the observations at the frequency and the frequency, an IF combination of the observations at these two frequencies can obtain the IF combination observation value, as shown below: (5), where represents the IF combination pseudorange observation value under the inter-satellite single difference from satellite to the reference satellite to the single base station ; represents the IF combination carrier phase observation value under the inter-satellite single difference from satellite to the reference satellite to the single base station ; and respectively represent the wavelengths of the carrier observation signals at the frequency and the frequency.

[0085] Based on Equation (2) in step S21, an IF combination is performed to eliminate the ionospheric delay , and the tropospheric delay is corrected using an accurate tropospheric correction model , and the obtained inter-satellite single difference IF combination observation equation is as follows: (6), where , and have the same meanings as in Equation (2), represents the hardware bias of the IF combination pseudorange observation value under the inter-satellite single difference from satellite to the reference satellite to the single base station ; represents the hardware bias of the IF combination carrier phase observation value under the inter-satellite single difference from satellite to the reference satellite to the single base station ; represents the ambiguity parameter of the IF combination carrier phase observation value under the inter-satellite single difference between satellite and the reference satellite and the single base station ; represents the observation noise of the IF combination pseudorange observation value under the inter-satellite single difference between satellite and the reference satellite ; represents satellite and the reference satellite Observation noise of the IF combined carrier phase observation value under the inter-satellite single difference;

[0086] Combine Equation (4) and Equation (6), and use the Observable-specific Bias (OSB) product to correct the pseudorange hardware bias, which is generally very small and can be ignored or regarded as a random term here, thus obtaining the satellite and the reference satellite satellite clock difference correction number under the inter-satellite single difference , as shown in Equation (7): (7),

[0087] Since the satellite clock difference correction number remains constant over a certain arc segment, the observation noise is reduced by the method of moving average to obtain the final satellite clock difference correction number , and the specific method is as follows: (19), where and respectively represent the satellite clock difference correction numbers under the inter-satellite single difference extracted in real time at epochs and ; represents the number of valid epochs; and respectively represent the precisions of the satellite clock difference correction numbers under the inter-satellite single difference extracted in real time at epochs and ; represents the IF combined pseudorange observation value under the inter-satellite single difference from satellite to the single base station and the reference satellite at epoch ; represents the geometric distance under the inter-satellite single difference from satellite to the single base station and the reference satellite at epoch ; represents the satellite clock difference correction number under the inter-satellite single difference at epoch before adopting the moving average method, which can correspond to in Equation (7). For the sake of simple representation in the moving average method, here we uniformly use to represent the satellite clock difference correction number under the inter-satellite single difference;

[0088] In terms of experimental analysis, first, the amplitude and stability of the obtained satellite clock difference correction number are evaluated in the time domain; then, the broadcast interval of the satellite clock difference correction number is analyzed and given.

[0089] Combined with Figure 4 , it shows the sequence diagrams of the satellite clock bias corrections of satellites G04, G05, G06, G09, G11, G12, G14, and G20 with G19 as the reference satellite. It is expected to be used as one of the evaluation indicators to analyze the values and evaluate the accuracy. It can be found that the expectations of the extracted satellite clock bias correction sequences of G04, G05, G06, G09, G11, G12, G14, and G20 are 11.17, 9.88, 12.40, 9.67, 8.98, 6.37, 10.67, and 0.03 nanoseconds respectively. The clock bias corrections of each extracted satellite are non-negligible and inconsistent, indicating that the satellite clock bias corrections still have satellite specificity. In addition, the extracted satellite clock bias correction sequences after convergence have high stability within a certain observation arc.

[0090] Combined with Figure 5 , it further shows the sequence diagrams of all the obtained satellite clock bias corrections, where the jumps in the satellite clock bias correction sequences are caused by the changes in the reference satellite. It should be noted that the clock bias correction sequence of each satellite is offset by 10 nanoseconds to separate the sequence. Similarly, in the case of the same reference satellite, the clock bias correction sequences of each satellite after convergence maintain high stability for a certain period of time. Therefore, this verifies the feasibility of the broadcast satellite clock bias corrections.

[0091] Step S23: Generate the satellite orbit error correction under the inter-satellite single difference ;

[0092] In the GNSS raw observation equation in step S21, that is, formula (1), when , , , , , , and and other errors are corrected by the corresponding precise products, respectively, so the remaining and , The specific expressions of are as follows: (8), where represents the geometric distance from satellite to the single base station ; and respectively represent the X coordinates of the true positions of satellite and the single base station ; and respectively represent the satellite and the single base station for the Y coordinate of the true position; and respectively represent the satellite and the single base station for the Z coordinate of the true position;

[0093] For the reference satellite , there is also the specific expression as follows: (9), where represents the geometric distance from the reference satellite to the single base station ; represents the X coordinate of the true position of the reference satellite ; represents the Y coordinate of the true position of the reference satellite ; represents the Z coordinate of the true position of the reference satellite ;

[0094] Since , and the single base station of the true position , and are known, two spheres can be obtained with the true position of the single base station , and as the centers, and with and as the radii respectively. Still, the true coordinates of the satellite and the reference satellite cannot be determined. However, according to the ephemeris data, the azimuth and elevation angles of the satellite and the reference satellite relative to the single base station can be calculated. Therefore, the true coordinates of the satellite , and , as well as the true coordinates of the reference satellite , and can be calculated respectively according to their respective azimuth and elevation angles.

[0095] According to the ephemeris data, the estimated coordinates of the satellite can also be obtained, and , and the reference satellite 's estimated coordinates , and , so the satellite and the reference satellite 's orbit error correction numbers are as follows: (10), (11), Taking the difference can obtain the satellite and the reference satellite 's satellite orbit error correction number under the inter-satellite single difference, as follows: (12)

[0096] Step S24: Generate the atmospheric delay correction number under the inter-satellite single difference. The atmospheric delay correction number includes the ionospheric delay correction number of the first frequency and the tropospheric delay correction number ;

[0097] The GF combination means subtracting two observations of the same type but different frequencies to obtain the GF combination observation value, thereby eliminating the error terms independent of frequency. in formula (2) represents the pseudo-range observation value of the inter-satellite single difference of satellite and reference satellite to the single base station at the th frequency. in formula (2) represents the carrier phase observation value of the inter-satellite single difference of satellite and reference satellite to the single base station at the th frequency. Similarly, there can be the pseudo-range observation value of the inter-satellite single difference of satellite and reference satellite to the single base station at the th frequency , the carrier phase observation value of the inter-satellite single difference of satellite and reference satellite with the single base station at the th frequency . Performing the GF combination on the observations of the th frequency and the th frequency can obtain the GF combination observation value as follows: (13), Among them represents a satellite and the reference satellite to a single base station under the inter-satellite single difference of the GF combined pseudorange observation value; represents a satellite and the reference satellite to a single base station under the inter-satellite single difference of the GF combined carrier phase observation value.

[0098] Based on Equation (2) in Step S21, perform GF combination to eliminate most of the terms independent of frequency, and the obtained GF combined observation equation is as follows: (14), where has the same meaning as in Equation (2), represents the hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference of the satellite and the reference satellite ; represents the hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite ; represents the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite with the single base station at the frequency; represents the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite with the single base station at the frequency; represents the observation noise of the GF combined pseudorange observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station ; represents the observation noise of the GF combined carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station ; , and respectively represent the wavelengths of the carrier observation signals at the frequency, the frequency, and the frequency.

[0099] When there is no cycle slip, within the continuous arc segment , and are considered as constant terms. Therefore, by taking advantage of the property that the ionospheric delay corrections of pseudorange and carrier phase observations are equal in magnitude and opposite in sign, adding the two equations in Equation (14) and taking the mean value for smoothing within a continuous arc segment, the observation noises of pseudorange and carrier phase observations can be reduced, and value can be determined.

[0100] (15), wherein, is the mean value of within a continuous arc segment. According to the OSB product correction , substituting Equation (15) into Equation (14), the ionospheric delay correction of the first frequency can be obtained, that is: (16), Bringing this ionospheric delay correction back to the inter-satellite single-difference observation equation in step S21, the tropospheric delay correction can be obtained.

[0101] Step S25: Generate the atmospheric delay corrections under inter-satellite single-difference for user use, and the atmospheric delay corrections include the ionospheric delay correction of the first frequency and the tropospheric delay correction under inter-satellite single-difference for user use, where represents the user side.

[0102] Calculate the atmospheric delay difference between the base station and the user, and substitute this atmospheric delay difference into the ionospheric delay correction of the first frequency and the tropospheric delay correction under inter-satellite single-difference in step S24 to generate the ionospheric delay correction of the first frequency and the tropospheric delay correction under inter-satellite single-difference for user use, where represents the user side.

[0103] In terms of ionospheric delay, based on the Klobuchar model, calculate the model value of the ionospheric delay correction of the first frequency of a single base station and the model value of the ionospheric delay correction of the first frequency of the user. In terms of the troposphere, based on the Saastamoinen model, calculate the model value of the tropospheric delay correction of a single base station and the model value of the tropospheric delay correction of the user.

[0104] The compensated correction is written as: (17), (18), where and represent the ionospheric delay correction and tropospheric delay correction of the first frequency available for users; and represent the ionospheric delay correction and tropospheric delay correction of the first frequency generated based on a single base station in step S24.

[0105] Step S3: The user obtains ephemeris data, receives GNSS observation data and the correction product broadcast in step S2;

[0106] Specifically, step S3 includes:

[0107] Step S31: The user continuously receives GNSS observation data and downloads ephemeris data from the Wuhan University Data Center;

[0108] Step S32: The user receives two types of corrections broadcast by a single base station, namely the satellite - side correction under inter - satellite single - difference and the atmospheric delay correction available for users. The satellite - side correction includes the satellite clock error correction under inter - satellite single - difference and the satellite orbit error correction ; The atmospheric delay correction available for users includes the ionospheric delay correction of the first frequency under inter - satellite single - difference and the tropospheric delay correction , and provides the two types of corrections to S4.

[0109] Step S4: Substitute the ephemeris data, GNSS observation data and correction product obtained in step S3 into the single - base - station PPP - RTK positioning equation at the user end and perform calculations to achieve single - base - station PPP - RTK positioning.

[0110] Specifically, step S4 includes:

[0111] Step S41: Pre - process the corrections mentioned in step S32 , , and ;

[0112] Pre - process the corrections broadcast by a single base station, detect and eliminate outliers for , , and in sequence, and finally provide the valid data to S42;

[0113] Step S42: Initialize the client filter;

[0114] Calculate the approximate position, velocity, single base station clock offset, etc. of the client through GNSS SPP, set the initial variance-covariance matrix and process noise matrix of each parameter of the filtering system, and enter S43;

[0115] Step S43: Construct the PPP-RTK positioning equation of the client and select the satellite with the highest elevation angle as the reference satellite: (20), where the subscript U represents the client, and the meanings of the symbols in formula (20) are similar to those in formula (2), but here they represent the values of the client.

[0116] Step S44: Process the main error terms;

[0117] On the basis of step S43, process the main error terms. Processing the main error terms includes the hardware bias of the pseudorange observation value at the frequency under the inter-satellite single difference between the satellite and the reference satellite , the hardware bias of the carrier phase observation value at the frequency under the inter-satellite single difference between the satellite and the reference satellite , the clock offset under the inter-satellite single difference between the satellite and the reference satellite , the orbit error under the inter-satellite single difference between the satellite and the reference satellite , the tropospheric delay under the inter-satellite single difference from the satellite to the client , the first frequency ionospheric delay under the inter-satellite single difference from the satellite to the client , where and are corrected by the OSB product. For phase observations, after the phase hardware bias is corrected, the integer property of the ambiguity is restored; , , , , and use the correction numbers , , and make corrections.

[0118] Step S45: Filtering and calculation;

[0119] Based on step S44, the remaining error terms in formula (20) are and , where: , Therefore, the parameters to be estimated are the user's position ( , , ) and the ambiguity parameter under the inter-satellite single difference . Different stochastic models are established according to the nature of the parameters, and the Kalman filter is used to calculate all the parameters to be estimated, and the position information of the current epoch is output.

[0120] Taking the static experiment as an example, the effectiveness of the proposed single-base PPP-RTK model is carefully verified in terms of positioning accuracy and re-convergence time.

[0121] Combined with Figure 6 and Figure 7 , where Figure 6 describes the positioning errors of the single-base PPP-RTK model and the traditional model proposed by HHD1 on June 1, 2023 in the east (East, E), north (North, N), up (Up, U) and three-dimensional (3-Dimensional, 3D) directions. Figure 7 Further shows the positioning errors of the first 1000 epochs after GPS times 00:40, 06:00, 12:00 and 18:00 to better emphasize the advantages of the single-base PPP-RTK model. It can be found from Figure 6 and Figure 7 that the positioning errors of the single-base PPP-RTK model in the initial period are smaller than those of the traditional model in the E, N, U and 3D directions. However, after the (re-)convergence period, there is not much difference between the two solutions. This is because the unprocessed satellite clock difference corrections will be absorbed into the pseudorange residuals after each (re-)convergence period of the traditional model.

[0122] In summary, a single-base PPP-RTK positioning method and device of the present invention make full use of the information of a single base station to generate enhanced information such as PPP-RTK positioning satellite clock difference corrections and atmospheric error corrections, provide positioning services for users in special scenarios, and significantly enrich the application scenarios of PPP-RTK positioning.

Claims

1. A single-base station PPP-RTK positioning method, characterized in that, The method includes the following steps: Step S1: Obtain single-base GNSS observation data, precise coordinates of the single base, and ephemeris data; Step S2: Substitute the precise coordinates and ephemeris data of the single base obtained in Step S1 into the IF combination equation under inter-satellite single difference, the GNSS raw observation equation, and the GF combination equation under inter-satellite single difference respectively; estimate the satellite clock error correction in the IF combination equation under inter-satellite single difference, estimate the satellite orbit error correction in the GNSS raw observation equation, and the satellite clock error correction and satellite orbit error correction are collectively referred to as satellite-side corrections; estimate the atmospheric delay correction in the GF combination equation under inter-satellite single difference, and the atmospheric delay correction includes the ionospheric delay correction and tropospheric delay correction at the first frequency; then calculate the atmospheric delay difference between the single base and the user, generate the atmospheric delay correction available for the user according to the atmospheric delay difference; generate a correction product from the satellite-side corrections and the atmospheric delay correction available for the user and broadcast it to the user; Step S3: The user obtains ephemeris data, receives GNSS observation data, and the correction product broadcast in Step S2; Step S4: Substitute the ephemeris data, GNSS observation data, and correction product obtained in Step S3 into the single-base PPP-RTK positioning equation at the user side and perform the solution to achieve single-base PPP-RTK positioning.

2. The single-base station PPP-RTK positioning method according to claim 1, characterized in that, Step S1 specifically includes the following sub-steps: Step S11: Place the single base in an open environment and continuously receive GNSS observation data; Step S12: Download ephemeris data from the Data Center of Wuhan University; Step S13: Use the GNSS observation data and ephemeris data of multiple days before the positioning day, input the GNSS observation data and ephemeris data into the positioning software, perform positioning solution in the PPP mode to obtain the coordinates of the single base, and average the coordinates obtained in multiple days to represent the precise coordinates of the base station.

3. A single-base station PPP-RTK positioning method according to claim 1 or 2, characterized in that, Step S2 specifically includes the following sub-steps: Step S21: Construct an inter-satellite single difference equation; First, the GNSS raw observation equation is: （1）， Among them, and respectively represent the pseudorange observation value and the carrier phase observation value of the satellite to the single base station at the frequency; represents the geometric distance from the satellite to the single base station ; and respectively represent the clock offsets of the single base station and the satellite; represents the orbit error of the satellite; is the tropospheric delay from the satellite to the single base station ; represents the ionospheric delay of the first frequency from the satellite to the single base station ; and respectively represent the hardware biases of the pseudorange observation value of the frequency at the single base station and the satellite; and respectively represent the hardware biases of the carrier phase observation value of the frequency at the single base station and the satellite; represents the ambiguity parameter of the carrier phase observation value of the satellite to the single base station at the frequency; and respectively represent the observation noises of the pseudorange and phase observation values; and respectively represent the wavelengths of the carrier observation signals of the first frequency and the frequency; The units of the above symbols are all m; Based on the GNSS raw observation equation of Equation (1), a satellite is selected as the reference satellite for inter-satellite single-difference processing to eliminate the station-related error terms, including , and . Only the error terms related to the satellite and frequency remain in the processed observation equation. The inter-satellite single-difference equation is as follows: （2）， wherein, represents the pseudorange observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station at the th frequency; represents the carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station at the th frequency; represents the geometric distance under the inter-satellite single difference of the satellite and the reference satellite to the single base station ; represents the clock error under the inter-satellite single difference of the satellite and the reference satellite ; represents the orbit error under the inter-satellite single difference of the satellite and the reference satellite ; represents the tropospheric delay under the inter-satellite single difference of the satellite and the reference satellite to the single base station ; represents the ionospheric delay of the first frequency under the inter-satellite single difference of the satellite and the reference satellite to the single base station ; represents the hardware bias under the inter-satellite single difference of the pseudorange observation value of the th frequency between the satellite and the reference satellite ; represents the hardware bias under the inter-satellite single difference of the carrier phase observation value of the th frequency between the satellite and the reference satellite ; represents the ambiguity parameter of the carrier phase observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station at the th frequency; represents the observation noise of the pseudorange observation value under the inter-satellite single difference of the satellite and the reference satellite to the single base station at the th frequency; represents the satellite and the reference satellite to the single base station at the Observation noise of carrier phase observations under the inter-satellite single difference of frequency; the unit of the above symbols is m; Step S22: Generate satellite clock error corrections under inter-satellite single differences ; Estimated satellite clock bias Is expressed as follows: （3）， Among them, represents the sum of the clock error and the pseudo-range hardware bias of absorption, that is ; represents the common reference satellite clock error; represents the satellite clock error correction of each satellite; Using the satellite as the reference satellite, perform an inter-satellite single difference on Equation (3) to eliminate the common reference satellite clock error , and obtain the estimated satellite and the reference satellite under the inter-satellite single difference of the satellite clock error : （4）， Among them, represents the sum of the clock error and the absorbed pseudorange hardware bias under the inter-satellite single difference between the satellite and the reference satellite; ; represents the satellite clock error correction under the inter-satellite single difference between the satellite and the reference satellite ; For the frequency and the frequency, the observed values of these two frequencies are combined by IF to obtain the IF combined observed value as follows: （5）， Among them represents a satellite and a reference satellite to a single base station the inter-satellite single-difference IF combined pseudorange observation value; represents a satellite and a reference satellite to a single base station the inter-satellite single-difference IF combined carrier phase observation value; and respectively represent the wavelengths of the carrier observation signals at the th frequency and the th frequency; Based on Equation (2) in step S21, perform an IF combination to eliminate the ionospheric delay , and use an accurate tropospheric correction model to correct the tropospheric delay , and the obtained inter-satellite single-difference IF combination observation equation is as follows: （6）， Among them, represents the hardware bias of the IF combined pseudorange observation value of the inter-satellite single difference from satellite and the reference satellite to a single base station ; represents the hardware bias of the IF combined carrier phase observation value of the inter-satellite single difference from satellite and the reference satellite to a single base station ; represents the ambiguity parameter of the IF combined carrier phase observation value of the inter-satellite single difference between satellite and the reference satellite and a single base station ; represents the observation noise of the IF combined pseudorange observation value of the inter-satellite single difference between satellite and the reference satellite ; represents the observation noise of the IF combined carrier phase observation value of the inter-satellite single difference between satellite and the reference satellite ; Combining formula (4) and formula (6) and using the OSB product to correct the pseudorange hardware bias, the satellite clock bias correction number in the inter-satellite single difference between the satellite and the reference satellite is obtained, as shown in formula (7): as shown in Equation (7): （7）， Step S23: Generate the satellite orbit error correction under the inter-satellite single difference ; In the GNSS raw observation equation of step S21, that is, in formula (1), when the errors include , , , , , , and are all corrected by the corresponding precise products, the remaining and , has the following specific expressions: （8）， Among them, represents the geometric distance from the satellite to the single base station ; and respectively represent the X coordinates of the true positions of the satellite and the single base station ; and respectively represent the Y coordinates of the true positions of the satellite and the single base station ; and respectively represent the Z coordinates of the true positions of the satellite and the single base station ; For the reference satellite , there is also with the specific expression as follows: （9）， Among them, represents the geometric distance from the reference satellite to the single base station ; represents the X coordinate of the true position of the reference satellite ; represents the Y coordinate of the true position of the reference satellite ; represents the Z coordinate of the true position of the reference satellite ; Based on the ephemeris data, the satellite and the reference satellite are calculated for their azimuth and elevation angles relative to the single base station . Then, based on the azimuth and elevation angles, the true coordinates of the satellite , and are calculated, as well as the true coordinates of the reference satellite , and . The estimated coordinates of the satellite , and are obtained from the ephemeris data, and the estimated coordinates of the reference satellite , and . Thus, the orbit error correction numbers of the satellite and the reference satellite are as follows: （10）， （11）， Subtraction gives the satellite and the reference satellite satellite orbit error correction under the inter-satellite single difference as follows: （12）， Step S24: Generate the atmospheric delay correction number under the inter-satellite single difference, where the atmospheric delay correction number includes the ionospheric delay correction number at the first frequency and the tropospheric delay correction number ; For the observations of the frequency and the frequency, the GF combination is obtained for these two frequencies, and the GF combination observations are as follows: （13）， Among them represents a satellite and a reference satellite to a single base station under the inter-satellite single difference of the GF combined pseudorange observation value; represents a satellite and a reference satellite to a single base station under the inter-satellite single difference of the GF combined carrier phase observation value; Based on Equation (2) in Step S21, perform GF combination, and the obtained GF combination observation equation is as follows: （14）， in, Indicates satellite and reference satellite The hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellite The hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellite With single base station In the The ambiguity parameters of the carrier phase observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellite With single base station In the The ambiguity parameters of the carrier phase observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellite To a single base station The observation noise of the GF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellite To a single base station The observation noise of the GF combined carrier phase observation value under the inter-satellite single difference; , and Respectively represent Frequency, Frequency and The frequency of the carrier wave is the wavelength of the observed signal; When there is no cycle slip, within a continuous arc segment, , and are considered as constant terms. Therefore, by utilizing the characteristic that the ionospheric delay correction values of pseudorange and carrier phase observations are equal in value and opposite in sign, add Equation (14), and take the mean within the continuous arc segment for smoothing to weaken the observation noise of pseudorange observations and carrier phase observations, and determine value: （15）， In the formula, is to take the average value of within the continuous arc segment; Correction based on OSB products , substituting Equation (15) into Equation (14), the first-frequency ionospheric delay correction is obtained , that is: （16）， Bring the ionospheric delay correction back to the inter-satellite single-difference observation equation in step S21, and the tropospheric delay correction ; Step S25: Generate the atmospheric delay correction for the inter-satellite single difference available for users, where the atmospheric delay correction includes the ionospheric delay correction for the first frequency under the inter-satellite single difference available for users and the tropospheric delay correction ; Calculate the atmospheric delay difference between the base station and the user, and substitute the atmospheric delay difference into the ionospheric delay correction number of the first frequency under the inter-satellite single difference in step S24 and the tropospheric delay correction number to generate the ionospheric delay correction number of the first frequency under the inter-satellite single difference available for the user and the tropospheric delay correction number , where represents the user side; In terms of ionospheric delay, based on the Klobuchar model, calculate the model value of the ionospheric delay correction for the first frequency of a single base station and the model value of the ionospheric delay correction for the first frequency of the user ; In terms of the troposphere, based on the Saastamoinen model, calculate the model value of the tropospheric delay correction for a single base station and the model value of the tropospheric delay correction for the user ; The compensated correction is written as: （17）， （18）， where and represent the ionospheric delay correction and tropospheric delay correction of the first frequency available for users; and represent the ionospheric delay correction and tropospheric delay correction of the first frequency generated based on a single base station in step S24.

4. The single-base station PPP-RTK positioning method according to claim 3, wherein For the satellite clock error correction obtained in step S22 The observation noise is reduced by the method of moving average to obtain the satellite clock error correction. The specific method is as follows: （19）， where and respectively represent the satellite clock error corrections under the inter-satellite single difference extracted in real time at epochs and ; represents the number of valid epochs; and respectively represent the precisions of the satellite clock error corrections under the inter-satellite single difference extracted in real time at epochs and ; represents the IF combined pseudorange observations under the inter-satellite single difference from satellite to the reference satellite and to the single base station at epoch ; represents the geometric distance under the inter-satellite single difference from satellite to the reference satellite and to the single base station at epoch ; represents the satellite clock error correction under the inter-satellite single difference at epoch before adopting the moving average method, corresponding to in formula (7).

5. The single-base station PPP-RTK positioning method according to claim 4, characterized in that The specific content of Step S3 is as follows: Step S31: The user continuously receives GNSS observation data and downloads ephemeris data from the Data Center of Wuhan University; Step S32: The user receives two types of corrections broadcast by a single base station, namely, satellite - side corrections under inter - satellite single - difference and atmospheric delay corrections available for the user. The satellite - side corrections include satellite clock error corrections and satellite orbit error corrections under inter - satellite single - difference ; The atmospheric delay corrections available for the user include the first - frequency ionospheric delay corrections and tropospheric delay corrections under inter - satellite single - difference ; and provide the two types of corrections to S4. ​ 6. A single-base station PPP-RTK positioning method according to claim 5, characterized in that Step S4 includes: Step S41: Preprocess the correction numbers mentioned in step S32 , , and ; Preprocess the corrections broadcast by a single base station, and , , and successively detect and remove outliers, and finally provide the valid data to S42; Step S42: Initialize the user-side filter; Calculate the initial position and velocity of the user side through GNSS SPP, set the initial variance-covariance matrix and process noise matrix of each parameter of the filtering system, and enter S43; Step S43: Construct the inter-satellite single-difference PPP-RTK positioning equation for the user terminal and select the satellite with the highest elevation angle as the reference satellite: （20）， Among them, the subscript U represents the user side; Step S44: Process the main error terms; Based on step S43, the main error terms are processed, including the hardware bias of the frequency pseudorange observation in the inter-satellite single difference between the satellite and the reference satellite, the hardware bias of the frequency carrier phase observation in the inter-satellite single difference between the satellite and the reference satellite, the clock error in the inter-satellite single difference between the satellite and the reference satellite, the orbit error in the inter-satellite single difference between the satellite and the reference satellite, the tropospheric delay in the inter-satellite single difference from the satellite to the user terminal, the first frequency ionospheric delay in the inter-satellite single difference from the satellite to the user terminal , where and are corrected by the OSB product. For phase observations, after the phase hardware bias is corrected, the integer property of the ambiguity is restored; , , , and are corrected using the correction numbers , , and respectively; Step S45: Perform filtering solution; Based on step S44, the only remaining error terms in formula (20) are and , where ， Therefore, the parameters to be estimated include the user's position ( , , ) and the ambiguity parameters under the inter-satellite single difference . Different stochastic models are established according to the properties of the parameters, and the Kalman filter is used to solve all the parameters to be estimated, and the position information of the current epoch is output.

7. A single-base PPP-RTK positioning device, including: A memory for storing computer programs; A processor for calling the computer programs stored in the memory and executing the single-base PPP-RTK positioning method listed in any one of claims 1-6 according to the obtained programs.

8. A computer-readable storage medium storing a computer-executable program for causing a computer to execute the single-base station PPP-RTK positioning method recited in any one of claims 1-6.

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