Single-base station PPP-RTK positioning method and equipment

Abstract

The present invention discloses a single-base station PPP-RTK positioning method and device. The method first obtains satellite-side error corrections and atmospheric delay corrections based on different solution models according to acquired single-base station observation data, single-base station precise coordinates, and ephemeris data. The satellite-side error corrections include satellite clock corrections and satellite orbit error corrections, and the atmospheric delay corrections include ionospheric delay corrections and tropospheric delay corrections of a first frequency. The atmospheric delay difference between the single base station and the user is calculated based on an empirical model, and the atmospheric delay difference is then substituted into the atmospheric delay correction to obtain an atmospheric delay correction that can be used for the user. The user's observation value is obtained to construct a PPP-RTK observation equation to eliminate the error term related to the single base station. The satellite-side error corrections and atmospheric delay corrections are substituted into the user-side PPP-RTK observation equation to achieve single-base station PPP-RTK positioning.

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), high-precision GNSS positioning has been widely used in fields such as autonomous driving and surveying and mapping. Traditional GNSS high-precision positioning technologies primarily include Real-Time Kinematic (RTK) and Precise Point Positioning (PPP). RTK relies on multiple ground-based base stations with known coordinates. Using a short-baseline differential model and carrier phase observations to fix integer ambiguities, it is commonly used for centimeter-level high-precision positioning. However, because its differential principle relies on a close distance between the base station and the user, it has significant coverage limitations in large-scale, remote areas, or mobile applications. Furthermore, RTK systems are expensive to build and maintain, rely on stable data transmission links, and have limited deployment flexibility. To overcome the limited spatial coverage and deployment complexity of RTK systems, PPP has emerged. PPP utilizes real-time precise orbit and clock information provided by GNSS service organizations (such as the IGS) to achieve decimeter- to centimeter-level positioning accuracy worldwide without relying on closely located base stations. However, PPP often suffers from long convergence times and poor stability due to its inability to quickly fix integer ambiguities in its model. This can take up to tens of minutes, especially in dynamic environments. To balance the wide-area capabilities of PPP with the fast convergence of RTK, PPP-RTK positioning technology has been proposed in recent years. This technology combines the advantages of PPP and RTK.

[0003] Existing PPP-RTK methods rely on a large network of base stations deployed regionally or nationwide. Server-based modeling and analysis generate ionospheric corrections, tropospheric corrections, and satellite hardware delay information. State-space representation (SSR) is then used to broadcast high-precision correction information to users, enabling rapid fixation of whole-cycle ambiguities. Representative solutions include the European Space Agency's Galileo HAS system and China's high-precision CORS network (such as Qixun Positioning and Huace), which provide centimeter-level real-time PPP-RTK services. While these methods offer a balance of accuracy and speed, their system architecture relies heavily on a multi-base station network and centralized server computing, resulting in high deployment and maintenance costs and poor system robustness and flexibility. These methods are particularly difficult to adapt to the demands of rapid, high-precision positioning in remote, outdoor, and mobile scenarios. Summary of the Invention

[0004] In response to the above-mentioned problems, the present invention proposes a single-base station PPP-RTK positioning method and device to meet the positioning needs of users in scenarios with 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 purpose is achieved through the following technical solutions:

[0006] The present invention first provides a single-base station PPP-RTK positioning method, comprising 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, respectively; estimate the satellite clock correction in the IF combination equation under inter-satellite single difference, and estimate the satellite orbit error correction in the GNSS raw observation equation, wherein the satellite clock correction and the 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, wherein the atmospheric delay correction includes the ionospheric delay correction and the tropospheric delay correction of the first frequency; then calculate the atmospheric delay difference between the single base station and the user, and generate an atmospheric delay correction available to the user based on the atmospheric delay difference; generate a correction product from the satellite-side correction and the atmospheric delay correction available to the user and broadcast it to the user;

[0009] Step S3: The user obtains ephemeris data, receives GNSS observation data and the correction products broadcasted in step S2;

[0010] Step S4: The ephemeris data, GNSS observation data and correction products obtained in step S3 are introduced into the single-base PPP-RTK positioning equation at the user end and solved to achieve single-base PPP-RTK positioning.

[0011] Furthermore, step S1 specifically includes the following sub-steps:

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

[0013] Step S12: Downloading ephemeris data from Wuhan University Data Center;

[0014] Step S13: Using the GNSS observation data and ephemeris data from multiple days before the positioning day, the GNSS observation data and ephemeris data are input into the positioning software, and positioning is solved in PPP mode to obtain the coordinates of a single base station. The coordinates obtained for multiple days are averaged to represent the precise coordinates of the base station.

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

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

[0017] First, the original GNSS observation equation is:

[0018] (1),

[0019] in, and Represents satellites To a single base station No. Frequency pseudorange observations and carrier phase observations; Indicates satellite To a single base station The geometric distance; and Represents a single base station and satellite clock difference; Indicates satellite The orbit error of For satellite To a single base station Tropospheric delay; Indicates satellite To a single base station ionospheric delay of the first frequency; and Respectively represent Frequency pseudorange observations at a single base station and satellite Hardware deviation; and Respectively represent Frequency carrier phase observations at a single base station and satellite Hardware deviation; Indicates satellite To a single base station No. The ambiguity parameters of the carrier phase observations of the frequency; and Observation noise for pseudorange and phase observations, respectively; and Represents the first frequency and the The wavelength of the carrier observation signal of the frequency; the unit of the above symbols is m;

[0020] Based on the original GNSS observation equation of formula (1), the satellite Perform intersatellite single difference processing for the reference satellite to eliminate the station-related error terms, including , and , after processing, only the error terms related to satellite and frequency remain in the observation equation, and the inter-satellite single difference equation is as follows:

[0021] (2),

[0022] in, Indicates satellite and reference satellites To a single base station No. Pseudorange observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. Carrier phase observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates satellite and reference satellites Clock error under the intersatellite single error; Indicates satellite and reference satellites Orbit error under intersatellite single difference; Indicates satellite and reference satellites To a single base station Tropospheric delay under intersatellite single difference; Indicates satellite and reference satellites To a single base station The first frequency ionospheric delay under the inter-satellite single difference; Indicates the Frequency pseudorange observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates the Frequency carrier phase observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates satellite and reference satellites To a single base station No. The ambiguity parameters of the carrier phase observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of pseudorange observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of the carrier phase observation value under the inter-satellite single difference of frequency; the unit of the above symbols is m;

[0023] Step S22: Generate satellite clock corrections under inter-satellite single difference ;

[0024] Estimated satellite clock error It is expressed as follows:

[0025] (3),

[0026] in, represents the sum of the clock error and the absorbed pseudorange hardware bias, that is, ; represents the common reference satellite clock error; Indicates the satellite clock correction number of each satellite;

[0027] Satellite For reference satellites, perform inter-satellite single difference on Equation (3) to eliminate the common reference satellite clock error , we get the following estimated satellites and reference satellites Satellite clock error under inter-satellite single difference :

[0028] (4),

[0029] in, Indicates satellite and reference satellites The sum of the clock error under the inter-satellite single difference and the absorbed pseudorange hardware bias; Indicates satellite and reference satellites Satellite clock correction number under the inter-satellite single difference;

[0030] For the first Frequency and The observation values ​​of the two frequencies are combined by IF to obtain the IF combined observation values, as shown below:

[0031] (5),

[0032] in Indicates satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station The IF composite carrier phase observation value under the inter-satellite single difference; and Respectively represent Frequency and The frequency of the carrier wave is the wavelength of the observation signal;

[0033] Perform IF combination based on equation (2) in step S21 to eliminate ionospheric delay , using the accurate tropospheric correction model to correct the tropospheric delay The intersatellite single-difference IF combination observation equation is obtained as follows:

[0034] (6),

[0035] in, Indicates satellite and reference satellites To a single base station The hardware bias of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites To a single base station The hardware bias of the IF composite carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites With single base station The ambiguity parameters of the IF combined carrier phase observations under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF composite carrier phase observation value under the inter-satellite single difference;

[0036] Combining formula (4) and formula (6), and using OSB products to correct pseudorange hardware bias, we can get satellite and reference satellites Satellite clock correction number under inter-satellite single difference , as shown in formula (7):

[0037] (7),

[0038] Step S23: Generate satellite orbit error correction under inter-satellite single difference ;

[0039] In the GNSS original observation equation of step S21, that is, in formula (1), when the error includes , , , , , , and After being corrected by the corresponding precision products, the only remaining and , The specific expression is:

[0040] (8),

[0041] in, Indicates satellite To a single base station The geometric distance; and Represents satellites and single base station The X coordinate of the real position; and Represents satellites and single base station The Y coordinate of the actual position; and Represents satellites and single base station The Z coordinate of the real position;

[0042] For reference satellites , there are also The specific expression is as follows:

[0043] (9),

[0044] in, Indicates the reference satellite To a single base station The geometric distance; Indicates the reference satellite The X coordinate of the real position; Indicates the reference satellite The Y coordinate of the actual position; Indicates the reference satellite The Z coordinate of the real position;

[0045] According to the ephemeris data, calculate the satellite and reference satellites Compared with a single base station The azimuth and altitude angles are calculated based on the azimuth and altitude angles. The real coordinates , and , and reference satellites The real coordinates , and ; Get satellite according to ephemeris data Estimated coordinates of , and , and reference satellites Estimated coordinates of , and , so we get the satellite and reference satellites The orbit error correction number is as follows:

[0046] (10),

[0047] (11),

[0048] Get satellite by difference and reference satellites Satellite orbit error correction number under inter-satellite single difference ,as follows:

[0049] (12),

[0050] Step S24: Generate an atmospheric delay correction number under inter-satellite single difference, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency. and tropospheric delay corrections ;

[0051] For the first Frequency and The observations of the two frequencies are GF-combined to obtain the GF-combined observations, as shown below:

[0052] (13),

[0053] in Indicates satellite and reference satellites To a single base station GF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station GF combined carrier phase observation value under inter-satellite single difference;

[0054] Based on equation (2) in step S21, GF combination is performed, and the obtained GF combination observation equation is as follows:

[0055] (14),

[0056] in, Indicates satellite and reference satellites The hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites 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 satellites 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 satellites 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 satellites 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 observation signal;

[0057] When no cycle slip occurs, the , and is considered as a constant term. Therefore, by taking advantage of the fact that the ionospheric delay correction values ​​of the pseudorange and carrier phase observations are equal in value but opposite in sign, we add Equation (14) and take the average value in the continuous arc segment for smoothing to weaken the observation noise of the pseudorange and carrier phase observations. Value:

[0058] (15),

[0059] Where, For continuous arc segments Take the mean;

[0060] Corrected according to OSB products , substitute equation (15) into equation (14) to obtain the first frequency ionospheric delay correction number ,Right now:

[0061] (16),

[0062] The ionospheric delay correction number Return to the intersatellite single-difference observation equation in step S21 to obtain the tropospheric delay correction number ;

[0063] Step S25: Generate an atmospheric delay correction number under inter-satellite single difference for use by the user, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency under inter-satellite single difference for use by the user. and tropospheric delay corrections ;

[0064] Calculate the atmospheric delay difference between the base station and the user, and bring the atmospheric delay difference into the ionospheric delay correction number of the first frequency under the inter-satellite single difference in step S24. and tropospheric delay corrections Generate the ionospheric delay correction number of the first frequency under the inter-satellite single difference for user use and tropospheric delay corrections ,in Indicates the user end;

[0065] In terms of ionospheric delay, based on the Klobuchar model, the model value of the ionospheric delay correction number of the first frequency of a single base station is calculated and the model value of the ionospheric delay correction for the user's first frequency In terms of the troposphere, based on the Saastamoinen model, the model value of the tropospheric delay correction number of a single base station is calculated and the model value of the user's tropospheric delay correction ;

[0066] The correction number after compensation is written as:

[0067] (17),

[0068] (18),

[0069] in and Indicates the ionospheric delay correction and tropospheric delay correction for the first frequency available to the user; and It represents the ionospheric delay correction number and the tropospheric delay correction number of the first frequency generated based on the single base station in step S24.

[0070] Furthermore, for the satellite clock error correction number obtained in step S22 The moving average method is used to reduce observation noise and obtain satellite clock corrections. The specific method is as follows:

[0071] (19),

[0072] in and Respectively represent the epoch and Satellite clock corrections extracted in real time based on inter-satellite single differences; Indicates the number of valid epochs; and Respectively represent the epoch and The accuracy of satellite clock corrections extracted in real time using inter-satellite single differences; Indicates the epoch satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates the epoch satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates that before the moving average method is used, The satellite clock correction number under the inter-satellite single difference is corresponding to the formula (7) .

[0073] Furthermore, the step S3 specifically includes the following:

[0074] Step S31: The user continues to receive GNSS observation data and downloads ephemeris data from the Wuhan University Data Center;

[0075] Step S32: The user receives two types of correction numbers broadcast by a single base station, namely, the satellite-side correction number under the inter-satellite single difference and the atmospheric delay correction number available to the user. The satellite-side correction number includes the satellite clock correction number under the inter-satellite single difference. and satellite orbit error corrections The atmospheric delay correction number available to users includes the first frequency ionospheric delay correction number under the inter-satellite single difference and tropospheric delay corrections , and provide two types of correction numbers to S4.

[0076] Furthermore, the step S4 includes:

[0077] Step S41: Pre-process the correction data mentioned in step S32 , , and ;

[0078] Pre-process the corrections broadcast by a single base station. , , and Detect and eliminate outliers in sequence, and finally provide valid data to S42;

[0079] Step S42: Initializing the user-side filter;

[0080] 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;

[0081] Step S43: Construct the user-side inter-satellite single-difference PPP-RTK positioning equation and select the satellite with the highest elevation angle As a reference satellite:

[0082] (20),

[0083] Among them, the subscript U represents the user end;

[0084] Step S44: processing the main error terms;

[0085] Based on step S43, the main error terms are processed, including the Frequency pseudorange observations on satellite and reference satellites Hardware bias under intersatellite single difference , No. Frequency carrier phase observations on satellite and reference satellites Hardware bias under intersatellite single difference ,satellite and reference satellites Clock error under intersatellite single error ,satellite and reference satellites Orbit error under intersatellite single difference ,satellite and reference satellites To the user side Tropospheric delay under intersatellite single difference ,satellite and reference satellites To the user side The first frequency ionospheric delay under the intersatellite single difference ,in and Corrected by OSB products, for phase observation, phase hardware deviation After being corrected, the integer nature of the ambiguity is restored; 、 、 and Use correction numbers respectively , , and make corrections;

[0086] Step S45: filtering and solving;

[0087] Based on step S44, the only remaining error term in formula (20) is and ,in:

[0088] ,

[0089] Therefore, the parameters to be estimated are the user's position ( , , ) and the ambiguity parameters under intersatellite single difference , different random 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.

[0090] The present invention also provides a single-base station PPP-RTK positioning device, comprising:

[0091] memory for storing computer programs;

[0092] The processor is configured to call the computer program stored in the memory and execute the PPP-RTK positioning method for a single base station listed in any of the above-mentioned ways according to the obtained program.

[0093] The present invention also provides a computer-readable storage medium, which stores a computer-executable program, and the computer-executable program is used to enable a computer to execute the PPP-RTK positioning method applied to a single base station listed in any of the above methods.

[0094] The beneficial effects of the present invention compared to the prior art are:

[0095] Existing PPP-RTK positioning technology strikes a balance between accuracy and speed, but it relies on a large-scale base station network to obtain correction information generated by multiple base stations (such as satellite clock and orbit error corrections, atmospheric delay corrections, etc.). This results in high system construction costs and complex deployment, making it difficult to flexibly apply in remote areas or temporary scenarios. The present invention constructs a single-base station PPP-RTK solution model. Based solely on observation data, precise coordinates, and ephemeris data from a single base station, it calculates satellite-side error corrections and atmospheric delay corrections. The satellite-side error corrections include satellite clock error corrections and satellite orbit error corrections, while the atmospheric delay corrections include first-frequency ionospheric delay corrections and tropospheric delay corrections. These corrections are then broadcast to user terminals in real time, providing auxiliary enhancements to the user's PPP-RTK solution. The present invention overcomes the limitations of existing PPP-RTK positioning technology, such as its reliance on a large-scale base station network, high system construction costs, and complex deployment. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 This is a flow chart of a single-base station PPP-RTK positioning method and device according to the present invention. The single-base station portion generates satellite-side error corrections and atmospheric delay corrections for use by a user terminal based on single-base station observation data, precise coordinates of the single base station, and ephemeris data. The satellite-side error corrections include satellite clock corrections and satellite orbit error corrections, and the atmospheric delay corrections include ionospheric delay corrections and tropospheric delay corrections of a first frequency. The user terminal implements a single-base station PPP-RTK positioning method based on the corresponding corrections generated by the single base station.

[0097] Figure 2 The experimental setup of a single base station for a static experimental scheme;

[0098] Figure 3 This is a dynamic experimental scheme. The red track in the figure is the driving route, and the lower half of the figure shows the equipment installed on the vehicle;

[0099] Figure 4This is a sequence diagram of single-difference clock correction numbers for some satellites, where G19 is used as the reference satellite. Figure 4 In the figure, (a), (b), (c), (d), (e), (f), (g), and (h) are the clock correction sequence diagrams of G04, G05, G06, G09, G11, G12, G14, and G20 satellites, respectively;

[0100] Figure 5 It is a sequence diagram of single difference clock correction numbers of all GPS satellites;

[0101] Figure 6 is the positioning error of the traditional model and the proposed model, Figure 6 In the figure, (a), (b), (c) and (d) are the positioning error maps in the E, N, U and 3D directions, respectively.

[0102] Figure 7 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 GPS time, Figure 7 (a), (b), (c) and (d) are the positioning error maps in the E, N, U and 3D directions respectively. DETAILED DESCRIPTION

[0103] In order to make the purpose, implementation mode and advantages of the present application clearer, the exemplary implementation mode of the present application will be clearly and completely described below in conjunction with the drawings in the exemplary embodiments of the present application. Obviously, the described exemplary embodiments are only part of the embodiments of the present application, not all of the embodiments.

[0104] The embodiment of the present invention provides a single base station PPP-RTK positioning method and device, the specific flow chart is as follows Figure 1 As shown, it includes two parts: a single base station and a user terminal, specifically including:

[0105] Step S1: Obtain single-base station GNSS observation data, single-base station precise coordinates and ephemeris data;

[0106] Specifically, step S1 includes:

[0107] Step S11: placing the single base station in an open environment and continuously receiving GNSS observation data;

[0108] In order to verify the effectiveness of the proposed single-base PPP-RTK positioning method, two static datasets and one dynamic vehicle dataset were collected. Figure 2 and Figure 3 The following are the scenarios for collecting static and dynamic datasets. Here, we take the static dataset as an example. Figure 2The figure shows a single-base experimental setup consisting of a geodetic receiver P5 and a geodetic choke antenna C220GR. The experimental setup is placed on the roof of a high-rise building and acts as a base station server (abbreviated as HHD1), broadcasting augmentation information such as satellite clock corrections and atmospheric error corrections.

[0109] The static dataset for HHD1 was collected on June 1, 2023, with a sampling interval of 1 second. The precise coordinates of HHD1 were predetermined using a static solution processed from multiple days of data prior to the current fix date, as detailed in step S13. During data processing, the cutoff elevation angle was set to 20°, and the reference satellite was determined by the satellite with the highest elevation angle.

[0110] Step S12: Downloading ephemeris data from Wuhan University Data Center;

[0111] Step S13: Using the GNSS observation data and ephemeris data of multiple days before the positioning day, the precise coordinates of the single base station are obtained by calculation in PPP mode;

[0112] Input GNSS observation data and ephemeris data into the positioning software and perform positioning calculation in PPP mode to obtain the coordinates of a single base station. The coordinates calculated over multiple days are averaged to represent the precise coordinates of the base station. The positioning software in this embodiment uses RTKLIB software.

[0113] Step S2: Substitute the precise coordinates and ephemeris data of the single base station obtained in step S1 into the ionospheric-free (IF) combination equation under inter-satellite single difference, the GNSS raw observation equation, and the geometry-free (GF) combination equation under inter-satellite single difference, respectively; estimate the satellite clock correction in the IF combination equation under inter-satellite single difference, and estimate the satellite orbit error correction in the GNSS raw observation equation. The satellite clock correction and the 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 the tropospheric delay correction of the first frequency; then calculate the atmospheric delay difference between the single base station and the user, and generate an atmospheric delay correction available to the user based on the atmospheric delay difference; generate a correction product from the satellite-side correction and the atmospheric delay correction available to the user and broadcast it to the user;

[0114] Specifically, step S2 includes:

[0115] Step S21: constructing an inter-satellite single-difference equation;

[0116] First, the original GNSS observation equation is:

[0117] (1),

[0118] in, and Represents satellites To a single base station No. Frequency pseudorange observations and carrier phase observations; Indicates satellite To a single base station The geometric distance; and Represents a single base station and satellite clock difference; Indicates satellite The orbit error of For satellite To a single base station Tropospheric delay; Indicates satellite To a single base station ionospheric delay of the first frequency; and Respectively represent Frequency pseudorange observations at a single base station and satellite Hardware deviation; and Respectively represent Frequency carrier phase observations at a single base station and satellite Hardware deviation; Indicates satellite To a single base station No. The ambiguity parameters of the carrier phase observations of the frequency; and Observation noise for pseudorange and phase observations, respectively; and Represents the first frequency and the The wavelength of the carrier observation signal of the frequency; the unit of the above symbols is m;

[0119] Based on the original GNSS observation equation of formula (1), the satellite Perform intersatellite single difference processing for the reference satellite to eliminate the station-related error terms, including , and , after processing, only the error terms related to satellite and frequency remain in the observation equation, and the inter-satellite single difference equation is as follows:

[0120] (2),

[0121] in, Indicates satellite and reference satellites To a single base station No. Pseudorange observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. Carrier phase observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates satellite and reference satellites Clock error under the intersatellite single error; Indicates satellite and reference satellites Orbit error under intersatellite single difference; Indicates satellite and reference satellites To a single base station Tropospheric delay under intersatellite single difference; Indicates satellite and reference satellites To a single base station The first frequency ionospheric delay under the inter-satellite single difference; Indicates the Frequency pseudorange observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates the Frequency carrier phase observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates satellite and reference satellites To a single base station No. The ambiguity parameters of the carrier phase observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of pseudorange observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of the carrier phase observation value under the inter-satellite single difference of frequency; the unit of the above symbols is m.

[0122] Step S22: Generate satellite clock corrections under inter-satellite single difference ;

[0123] When estimating satellite clock errors, in order to avoid rank deficiency, a specific clock offset needs to be selected as a reference, which will lead to the common reference satellite clock error Then, due to the linear correlation between satellite clock errors and ambiguity parameters, the ambiguity parameters can be separated by using pseudorange observations. After the ambiguity parameters converge, the satellite clock error correction number for each satellite is At the same time, due to the satellite clock error and pseudorange hardware bias Linear correlation between pseudorange hardware bias Absorbed into satellite clock error Therefore, the estimated satellite clock error It is expressed as follows:

[0124] (3),

[0125] in, represents the sum of the clock error and the absorbed pseudorange hardware bias, that is, ; represents the common reference satellite clock error; Indicates the satellite clock correction number of each satellite;

[0126] Satellite For reference satellites, perform inter-satellite single difference on Equation (3) to eliminate the common reference satellite clock error , we get the following estimated satellites and reference satellites Satellite clock error under inter-satellite single difference :

[0127] (4),

[0128] in, Indicates satellite and reference satellites The sum of the clock error under the inter-satellite single difference and the absorbed pseudorange hardware bias; Indicates satellite and reference satellites Satellite clock correction number under the inter-satellite single difference;

[0129] IF combination is to use the correlation of ionospheric delays at different frequencies to eliminate them. Frequency and The frequency observations are linearly combined to form the IF combination observations. Indicates satellite and reference satellites To a single base station No. The pseudo-range observation value under the inter-satellite single difference of frequency, the formula (2) Indicates satellite and reference satellites To a single base station No. The carrier phase observation value under the inter-satellite single difference of frequency. and reference satellites To a single base station In the Pseudorange observations under inter-satellite single difference of frequency ,satellite and reference satellites With single base station In the Carrier phase observations under inter-satellite single difference of frequency . Frequency and The IF combination of the two frequency observations can be used to obtain the IF combination observations, as shown below:

[0130] (5),

[0131] in Indicates satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station The IF composite carrier phase observation value under the inter-satellite single difference; and Respectively represent Frequency and The frequency of the carrier wave is the wavelength of the observation signal.

[0132] Perform IF combination based on equation (2) in step S21 to eliminate ionospheric delay , using the accurate tropospheric correction model to correct the tropospheric delay The intersatellite single-difference IF combination observation equation is obtained as follows:

[0133] (6),

[0134] in, 、 and The meaning of is the same as that in formula (2), Indicates satellite and reference satellites To a single base station The hardware bias of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites To a single base station The hardware bias of the IF composite carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites With single base station The ambiguity parameters of the IF combined carrier phase observations under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF composite carrier phase observation value under the inter-satellite single difference;

[0135] Combine equations (4) and (6) and use the observable-specific bias (OSB) product to correct the pseudorange hardware bias. Generally, the value is very small and can be ignored or used as a random item, that is, the satellite and reference satellites Satellite clock correction number under inter-satellite single difference , as shown in formula (7):

[0136] (7),

[0137] Since the satellite clock correction number remains constant in a certain arc segment, the moving average method is used to reduce the observation noise and obtain the final satellite clock correction number , the specific method is as follows:

[0138] (19),

[0139] in and Respectively represent the epoch and Satellite clock corrections extracted in real time based on inter-satellite single differences; Indicates the number of valid epochs; and Respectively represent the epoch and The accuracy of satellite clock corrections extracted in real time using inter-satellite single differences; Indicates the epoch satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates the epoch satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates that before the moving average method is used, The satellite clock correction number under the inter-satellite single difference can be corresponded to the formula (7) In order to simplify the representation in the moving average method, we use Indicates the satellite clock correction under inter-satellite single error;

[0140] In terms of experimental analysis, the amplitude and stability of the satellite clock correction numbers are first evaluated in the time domain; then, the broadcast interval of the satellite clock correction numbers is analyzed and given.

[0141] Combine Figure 4 , which shows the clock correction sequences for the G04, G05, G06, G09, G11, G12, G14, and G20 satellites, using G19 as the reference satellite. Expectation can be used as an evaluation metric to analyze values ​​and assess accuracy. The expectations of the extracted clock correction sequences for the G04, G05, G06, G09, G11, G12, G14, and G20 satellites are 11.17, 9.88, 12.40, 9.67, 8.98, 6.37, 10.67, and 0.03 nanoseconds, respectively. The extracted clock corrections for each satellite are non-negligible and inconsistent, indicating that satellite clock corrections are still satellite-specific. Furthermore, the extracted clock correction sequences for each satellite exhibit high stability within a specific observation arc after convergence.

[0142] Combine Figure 5 , which further shows the resulting sequence of clock corrections for all satellites, where jumps in the satellite clock correction sequence are caused by changes in the reference satellite. Notably, each satellite's clock correction sequence is offset by 10 nanoseconds to separate them. Similarly, given the same reference satellite, the converged clock correction sequence for each satellite maintains a high degree of stability over time. This demonstrates the feasibility of broadcasting satellite clock corrections.

[0143] Step S23: Generate satellite orbit error correction under inter-satellite single difference ;

[0144] In the GNSS original observation equation of step S21, that is, in formula (1), when , , , , , , and After all errors are corrected by the corresponding precision products, the only remaining and , The specific expression is:

[0145] (8),

[0146] in, Indicates satellite To a single base station The geometric distance; and Represents satellites and single base station The X coordinate of the real position; and Represents satellites and single base station The Y coordinate of the actual position; and Represents satellites and single base station The Z coordinate of the real position;

[0147] For reference satellites , there are also The specific expression is as follows:

[0148] (9),

[0149] in, Indicates the reference satellite To a single base station The geometric distance; Indicates the reference satellite The X coordinate of the real position; Indicates the reference satellite The Y coordinate of the actual position; Indicates the reference satellite The Z coordinate of the real position;

[0150] because , and single base station The real location , and It is known that two single base stations can be obtained The real location , and As the center of the circle, and Two spheres with a radius of 1, the satellite cannot be determined and reference satellites The real coordinates of the satellite can be calculated based on the ephemeris data. and reference satellites Compared with a single base station The azimuth and altitude of the satellite can be calculated based on their azimuth and altitude. The real coordinates , and , and reference satellites The real coordinates , and .

[0151] Satellite data can also be obtained based on the ephemeris data Estimated coordinates of , and , and reference satellites Estimated coordinates of , and , so we can get the satellite and reference satellites The orbit error correction number is as follows:

[0152] (10),

[0153] (11),

[0154] Satellites can be obtained by making a difference and reference satellites Satellite orbit error correction number under inter-satellite single difference ,as follows:

[0155] (12)

[0156] Step S24: Generate an atmospheric delay correction number under inter-satellite single difference, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency. and tropospheric delay corrections ;

[0157] GF combination refers to the subtraction of two observations of the same type but different frequencies to obtain the GF combination observation, which can eliminate the error terms that are not related to the frequency. Indicates satellite and reference satellites To a single base station No. The pseudo-range observation value under the inter-satellite single difference of frequency, the formula (2) Indicates satellite and reference satellites To a single base station No. The carrier phase observation value under the inter-satellite single difference of frequency. and reference satellites To a single base station In the Pseudorange observations under inter-satellite single difference of frequency ,satellite and reference satellites With single base station In the Carrier phase observations under inter-satellite single difference of frequency . Frequency and The GF combination of the two frequency observations can be obtained as follows:

[0158] (13),

[0159] in Indicates satellite and reference satellites To a single base station GF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station GF combined carrier phase observation value under inter-satellite single difference.

[0160] Based on equation (2) in step S21, GF combination is performed to eliminate most of the terms that are independent of frequency. The resulting GF combination observation equation is as follows:

[0161] (14),

[0162] in, The meaning of is the same as that in formula (2), Indicates satellite and reference satellites The hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites 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 satellites 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 satellites 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 satellites 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 observation signal.

[0163] When no cycle slip occurs, the , and Therefore, by taking advantage of the fact that the ionospheric delay corrections of the pseudorange and carrier phase observations are equal in value but opposite in sign, the two equations in equation (14) are added together and the average is taken in the continuous arc segment for smoothing, which can weaken the observation noise of the pseudorange and carrier phase observations and determine value.

[0164] (15),

[0165] Where, For continuous arc segments Take the average value. Corrected according to OSB products , by substituting equation (15) into equation (14), we can obtain the first frequency ionospheric delay correction number ,Right now:

[0166] (16),

[0167] The ionospheric delay correction number Returning to the intersatellite single-difference observation equation in step S21, the tropospheric delay correction number can be obtained. .

[0168] Step S25: Generate an atmospheric delay correction number under inter-satellite single difference for use by the user, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency under inter-satellite single difference for use by the user. and tropospheric delay corrections ,in Indicates the user end.

[0169] Calculate the atmospheric delay difference between the base station and the user, and bring the atmospheric delay difference into the ionospheric delay correction number of the first frequency under the inter-satellite single difference in step S24. and tropospheric delay corrections Generate the ionospheric delay correction number of the first frequency under the inter-satellite single difference for user use and tropospheric delay corrections ,in Indicates the user end.

[0170] In terms of ionospheric delay, based on the Klobuchar model, the model value of the ionospheric delay correction number of the first frequency of a single base station is calculated and the model value of the ionospheric delay correction for the user's first frequency In terms of the troposphere, based on the Saastamoinen model, the model value of the tropospheric delay correction number of a single base station is calculated and the model value of the user's tropospheric delay correction .

[0171] The correction number after compensation is written as:

[0172] (17),

[0173] (18),

[0174] in and Indicates the ionospheric delay correction and tropospheric delay correction for the first frequency available to the user; and It represents the ionospheric delay correction number and the tropospheric delay correction number of the first frequency generated based on the single base station in step S24.

[0175] Step S3: The user obtains ephemeris data, receives GNSS observation data and the correction products broadcasted in step S2;

[0176] Specifically, step S3 includes:

[0177] Step S31: The user continues to receive GNSS observation data and downloads ephemeris data from the Wuhan University Data Center;

[0178] Step S32: The user receives two types of correction numbers broadcast by a single base station, namely, the satellite-side correction number under the inter-satellite single difference and the atmospheric delay correction number available to the user. The satellite-side correction number includes the satellite clock correction number under the inter-satellite single difference. and satellite orbit error corrections The atmospheric delay correction number available to users includes the first frequency ionospheric delay correction number under the inter-satellite single difference and tropospheric delay corrections , and provide two types of correction numbers to S4.

[0179] Step S4: The ephemeris data, GNSS observation data and correction products obtained in step S3 are introduced into the single-base PPP-RTK positioning equation at the user end and solved to achieve single-base PPP-RTK positioning.

[0180] Specifically, step S4 includes:

[0181] Step S41: Pre-process the correction data mentioned in step S32 , , and ;

[0182] Pre-process the corrections broadcast by a single base station. , , and Detect and eliminate outliers in sequence, and finally provide valid data to S42;

[0183] Step S42: Initializing the user-side filter;

[0184] The approximate position, velocity, and single-base station clock error of the user end are calculated through GNSS SPP, and the initial variance-covariance matrix and process noise matrix of each parameter of the filtering system are set, and then the process goes to S43;

[0185] Step S43: Construct the user-side PPP-RTK positioning equation and select the satellite with the highest elevation angle As a reference satellite:

[0186] (20),

[0187] The subscript U represents the user end. The meaning of the symbols in formula (20) is similar to that in formula (2), except that they represent the values ​​of the user end.

[0188] Step S44: processing the main error terms;

[0189] Based on step S43, the main error terms are processed. The main error terms are processed, including Frequency pseudorange observations on satellite and reference satellites Hardware bias under intersatellite single difference , No. Frequency carrier phase observations on satellite and reference satellites Hardware bias under intersatellite single difference ,satellite and reference satellites Clock error under intersatellite single error ,satellite and reference satellites Orbit error under intersatellite single difference ,satellite and reference satellites To the user side Tropospheric delay under intersatellite single difference ,satellite and reference satellites To the user side The first frequency ionospheric delay under the intersatellite single difference ,in and Corrected by OSB products, for phase observation, phase hardware deviation After being corrected, the integer nature of the ambiguity is restored; 、 、 and Use correction numbers respectively , , and Make corrections.

[0190] Step S45: filtering and solving;

[0191] Based on step S44, the only remaining error term in formula (20) is and ,in:

[0192] ,

[0193] Therefore, the parameters to be estimated are the user's position ( , , ) and the ambiguity parameters under intersatellite single difference Different random 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.

[0194] Taking static experiments as an example, the effectiveness of the proposed single-base station PPP-RTK model is carefully verified in terms of positioning accuracy and reconvergence time.

[0195] Combine Figure 6 and Figure 7 ,in Figure 6 This paper describes the positioning errors in the east (E), north (N), up (U), and 3D directions of the single-base PPP-RTK model and the traditional model proposed by HHD1 on June 1, 2023. Figure 7 The positioning errors of the initial 1000 epochs after 00:40, 06:00, 12:00 and 18:00 GPS time are further shown to better emphasize the advantages of the single-base PPP-RTK model. Figure 6 and Figure 7 As can be seen in the figure, the positioning error of the single-base PPP-RTK model in the initial phase is smaller than that of the traditional model in the E, N, U, and 3D directions. However, after the (re)convergence period, there is little difference between the two solutions. This is because the unprocessed satellite clock corrections are absorbed into the pseudorange residuals after each (re)convergence period of the traditional model.

[0196] In summary, the single-base station PPP-RTK positioning method and device of the present invention fully utilizes the information of a single base station to generate enhanced information such as PPP-RTK positioning satellite clock correction numbers and atmospheric error correction numbers, providing positioning services for users in special scenarios, and significantly enriching the application scenarios of PPP-RTK positioning.

Claims

1. A single-base station PPP-RTK positioning method, characterized in that: The method comprises the following steps: Step S1: Obtain single-base station GNSS observation data, single-base station precise coordinates and ephemeris data; Step S2: Substitute the precise coordinates and ephemeris data of the single base station obtained in step S1 into the ionosphere-free combination equation under inter-satellite single difference, referred to as the IF combination equation, the GNSS raw observation equation, and the geometry-free combination equation under inter-satellite single difference, referred to as the GF combination equation; estimate the satellite clock correction in the IF combination equation under inter-satellite single difference, and estimate the satellite orbit error correction in the GNSS raw observation equation. The satellite clock correction and the 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 the tropospheric delay correction of the first frequency; then calculate the atmospheric delay difference between the single base station and the user, and generate an atmospheric delay correction available to the user based on the atmospheric delay difference; generate a correction product from the satellite-side correction and the atmospheric delay correction available to the user and broadcast it to the user; Step S3: The user obtains ephemeris data, receives GNSS observation data and the correction products broadcasted in step S2; Step S4: The ephemeris data, GNSS observation data, and correction products obtained in step S3 are fed into the user-side single-base station precise point positioning - real-time kinematic positioning (PPP-RTK) positioning equation and solved to achieve single-base station PPP-RTK positioning. The step S4 comprises: Step S41: Pre-processing the satellite correction data including the satellite clock correction data under the inter-satellite single difference and satellite orbit error corrections The atmospheric delay correction number available to users includes the first frequency ionospheric delay correction number under the inter-satellite single difference and tropospheric delay corrections ; Pre-process the corrections broadcast by a single base station. , , and Detect and eliminate outliers in sequence, and finally provide valid data to S42; Step S42: Initializing the user-side filter; 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; Step S43: Construct the user-side inter-satellite single-difference PPP-RTK positioning equation and select the satellite with the highest elevation angle As a reference satellite: （20）， in, and Represents satellites To a single base station No. Frequency pseudorange observations and carrier phase observations; Indicates satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates satellite and reference satellites Clock error under the intersatellite single error; Indicates satellite and reference satellites Orbit error under intersatellite single difference; Indicates the Frequency pseudorange observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates the Frequency carrier phase observations on satellite and reference satellites Hardware bias under inter-satellite single difference; represents the ambiguity parameter under inter-satellite single difference; and Represents the first frequency and the The wavelength of the carrier observation signal of the frequency; the unit of the above symbols is m; the subscript U represents the user end; Step S44: processing the main error terms; Based on step S43, the main error terms are processed, including the Frequency pseudorange observations on satellite and reference satellites Hardware bias under intersatellite single difference , No. Frequency carrier phase observations on satellite and reference satellites Hardware bias under intersatellite single difference ,satellite and reference satellites Clock error under intersatellite single error ,satellite and reference satellites Orbit error under intersatellite single difference ,satellite and reference satellites To the user side Tropospheric delay under intersatellite single difference ,satellite and reference satellites To the user side The first frequency ionospheric delay under the intersatellite single difference ,in and Corrected by OSB products, for phase observation, phase hardware deviation After being corrected, the integer nature of the ambiguity is restored; 、 、 and Use correction numbers respectively , , and make corrections; Step S45: filtering and solving; Based on step S44, the only remaining error term in formula (20) is and ,in ， Therefore, the parameters to be estimated are the user's position ( , , ) and the ambiguity parameters under intersatellite single difference , different random 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.

2. A single-base station PPP-RTK positioning method according to claim 1, characterized in that: Step S1 specifically includes the following sub-steps: Step S11: placing the single base station in an open environment and continuously receiving GNSS observation data; Step S12: downloading ephemeris data in the data center; Step S13: Using the GNSS observation data and ephemeris data from multiple days before the positioning day, the GNSS observation data and ephemeris data are input into the positioning software, and positioning is solved in PPP mode to obtain the coordinates of a single base station. The coordinates obtained for multiple days are averaged 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: constructing an inter-satellite single-difference equation; First, the original GNSS observation equation is: （1）， in, and Represents satellites To a single base station No. Frequency pseudorange observations and carrier phase observations; Indicates satellite To a single base station The geometric distance; and Represents a single base station and satellite clock difference; Indicates satellite The orbit error of For satellite To a single base station Tropospheric delay; Indicates satellite To a single base station ionospheric delay of the first frequency; and Respectively represent Frequency pseudorange observations at a single base station and satellite Hardware deviation; and Respectively represent Frequency carrier phase observations at a single base station and satellite Hardware deviation; Indicates satellite To a single base station No. The ambiguity parameters of the carrier phase observations of the frequency; and Observation noise for pseudorange and phase observations, respectively; and Represents the first frequency and the The wavelength of the carrier observation signal of the frequency; the unit of the above symbols is m; Based on the original GNSS observation equation of formula (1), the satellite Perform intersatellite single difference processing for the reference satellite to eliminate the station-related error terms, including , and , after processing, only the error terms related to satellite and frequency remain in the observation equation, and the inter-satellite single difference equation is as follows: （2）， in, Indicates satellite and reference satellites To a single base station No. Pseudorange observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. Carrier phase observation value under inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates satellite and reference satellites Clock error under the intersatellite single error; Indicates satellite and reference satellites Orbit error under intersatellite single difference; Indicates satellite and reference satellites To a single base station Tropospheric delay under intersatellite single difference; Indicates satellite and reference satellites To a single base station The first frequency ionospheric delay under the inter-satellite single difference; Indicates the Frequency pseudorange observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates the Frequency carrier phase observations on satellite and reference satellites Hardware bias under inter-satellite single difference; Indicates satellite and reference satellites To a single base station No. The ambiguity parameters of the carrier phase observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of pseudorange observations under the inter-satellite single difference of frequency; Indicates satellite and reference satellites To a single base station No. The observation noise of the carrier phase observation value under the inter-satellite single difference of frequency; the unit of the above symbols is m; Step S22: Generate satellite clock corrections under inter-satellite single difference ; Estimated satellite clock error It is expressed as follows: （3）， in, represents the sum of the clock error and the absorbed pseudorange hardware bias, that is, ; represents the common reference satellite clock error; Indicates the satellite clock correction number of each satellite; Satellite For reference satellites, perform inter-satellite single difference on Equation (3) to eliminate the common reference satellite clock error , we get the following estimated satellites and reference satellites Satellite clock error under inter-satellite single difference : （4）， in, Indicates satellite and reference satellites The sum of the clock error under the inter-satellite single difference and the absorbed pseudorange hardware bias; Indicates satellite and reference satellites Satellite clock correction number under the inter-satellite single difference; For the first Frequency and The observations of the two frequencies are combined by IF to obtain the IF combined observations, as shown below: （5）， in Indicates satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station The IF composite carrier phase observation value under the inter-satellite single difference; and Respectively represent Frequency and The frequency of the carrier wave is the wavelength of the observation signal; Perform IF combination based on equation (2) in step S21 to eliminate ionospheric delay , using the accurate tropospheric correction model to correct the tropospheric delay The intersatellite single-difference IF combination observation equation is obtained as follows: （6）， in, Indicates satellite and reference satellites To a single base station The hardware bias of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites To a single base station The hardware bias of the IF combined carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites With single base station The ambiguity parameters of the IF combined carrier phase observations under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The observation noise of the IF composite carrier phase observation value under the inter-satellite single difference; Combining formula (4) and formula (6), and using OSB products to correct pseudorange hardware bias, we can get satellite and reference satellites Satellite clock correction number under inter-satellite single difference , as shown in formula (7): （7）， Step S23: Generate satellite orbit error correction under inter-satellite single difference ; In the GNSS original observation equation of step S21, that is, in formula (1), when the error includes , , , , , , and After being corrected by the corresponding precision products, the only remaining and , The specific expression is: （8）， in, Indicates satellite To a single base station The geometric distance; and Represents satellites and single base station The X coordinate of the real position; and Represents satellites and single base station The Y coordinate of the actual position; and Represents satellites and single base station The Z coordinate of the real position; For reference satellites , there are also The specific expression is as follows: （9）， in, Indicates the reference satellite To a single base station The geometric distance; Indicates the reference satellite The X coordinate of the real position; Indicates the reference satellite The Y coordinate of the actual position; Indicates the reference satellite The Z coordinate of the real position; According to the ephemeris data, calculate the satellite and reference satellites Compared with a single base station The azimuth and altitude angles are calculated based on the azimuth and altitude angles. The real coordinates , and , and reference satellites The real coordinates , and ; Get satellite according to ephemeris data Estimated coordinates of , and , and reference satellites Estimated coordinates of , and , so we get the satellite and reference satellites The orbit error correction number is as follows: （10）， （11）， Get satellite by difference and reference satellites Satellite orbit error correction number under inter-satellite single difference ,as follows: （12）， Step S24: Generate an atmospheric delay correction number under inter-satellite single difference, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency. and tropospheric delay corrections ; For the first Frequency and The observations of the two frequencies are GF-combined to obtain the GF-combined observations, as shown below: （13）， in Indicates satellite and reference satellites To a single base station GF combined pseudorange observation value under inter-satellite single difference; Indicates satellite and reference satellites To a single base station GF combined carrier phase observation value under inter-satellite single difference; Based on equation (2) in step S21, GF combination is performed, and the obtained GF combination observation equation is as follows: （14）， in, Indicates satellite and reference satellites The hardware bias of the GF combined pseudorange observation value under the inter-satellite single difference; Indicates satellite and reference satellites The hardware bias of the GF combined carrier phase observation value under the inter-satellite single difference; Indicates satellite and reference satellites 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 satellites 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 satellites 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 satellites 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 observation signal; When no cycle slip occurs, the , and is considered as a constant term. Therefore, by taking advantage of the fact that the ionospheric delay correction values ​​of the pseudorange and carrier phase observations are equal in value but opposite in sign, we add Equation (14) and take the average value in the continuous arc segment for smoothing to weaken the observation noise of the pseudorange and carrier phase observations. Value: （15）， Where, For continuous arc segments Take the mean; Corrected according to OSB products , substitute equation (15) into equation (14) to obtain the first frequency ionospheric delay correction number ,Right now: （16）， The ionospheric delay correction number Return to the intersatellite single-difference observation equation in step S21 to obtain the tropospheric delay correction number ; Step S25: Generate an atmospheric delay correction number under inter-satellite single difference for use by the user, wherein the atmospheric delay correction number includes an ionospheric delay correction number of the first frequency under inter-satellite single difference for use by the user. and tropospheric delay corrections ; Calculate the atmospheric delay difference between the base station and the user, and bring the atmospheric delay difference into the ionospheric delay correction number of the first frequency under the inter-satellite single difference in step S24. and tropospheric delay corrections Generate the ionospheric delay correction number of the first frequency under the inter-satellite single difference for user use and tropospheric delay corrections ,in Indicates the user end; In terms of ionospheric delay, based on the Klobuchar model, the model value of the ionospheric delay correction number of the first frequency of a single base station is calculated and the model value of the ionospheric delay correction for the user's first frequency In terms of the troposphere, based on the Saastamoinen model, the model value of the tropospheric delay correction number of a single base station is calculated and the model value of the user's tropospheric delay correction ; The correction number after compensation is written as: （17）， （18）， in and Indicates the ionospheric delay correction and tropospheric delay correction for the first frequency available to the user; and It represents the ionospheric delay correction number and the tropospheric delay correction number of the first frequency generated based on the single base station in step S24.

4. A single-base station PPP-RTK positioning method according to claim 3, characterized in that: The satellite clock error correction number obtained in step S22 The moving average method is used to reduce observation noise and obtain satellite clock corrections. The specific method is as follows: （19）， in and Respectively represent the epoch and Satellite clock corrections extracted in real time based on inter-satellite single differences; Indicates the number of valid epochs; and Respectively represent the epoch and The accuracy of satellite clock corrections extracted in real time using inter-satellite single differences; Indicates the epoch satellite and reference satellites To a single base station IF combined pseudorange observation value under inter-satellite single difference; Indicates the epoch satellite and reference satellites To a single base station The geometric distance under the inter-satellite single difference; Indicates that before the moving average method is used, The satellite clock correction number under the inter-satellite single difference is corresponding to the formula (7) .

5. A single-base station PPP-RTK positioning method according to claim 4, characterized in that: The step S3 specifically includes the following: Step S31: The user continues to receive GNSS observation data and downloads ephemeris data in the data center; Step S32: The user receives two types of correction numbers broadcast by a single base station, namely, the satellite-side correction number under the inter-satellite single difference and the atmospheric delay correction number available to the user. The satellite-side correction number includes the satellite clock correction number under the inter-satellite single difference. and satellite orbit error corrections The atmospheric delay correction number available to users includes the first frequency ionospheric delay correction number under the inter-satellite single difference and tropospheric delay corrections , and provide two types of correction numbers to S4.

6. A single-base station PPP-RTK positioning device, comprising: memory for storing computer programs; A processor is used to call the computer program stored in the memory and execute the PPP-RTK positioning method applied to a single base station listed in any one of claims 1 to 5 according to the obtained program.

7. A computer-readable storage medium storing a computer-executable program, wherein the computer-executable program is used to enable a computer to execute the PPP-RTK positioning method for a single base station listed in any one of claims 1 to 5.

Images