GNSS (Global Navigation Satellite System) ground-based enhancement resolving method and system based on multi-difference observation equation

Abstract

The invention provides a GNSS (Global Navigation Satellite System) ground-based augmentation resolving method and system based on a multi-difference observation equation, and mainly solves the problems that the base station construction and maintenance cost of a traditional GNSS ground-based augmentation system is relatively high and the precision of a traditional positioning technology is relatively low. According to the scheme, a GNSS ground-based augmentation system communication network is formed between a base station and a moving station through an Ntrip / TCP protocol, a multi-difference observation equation is established through data, such as clocks and positions, of the same satellite observed between the base station and the moving station, and positioning information is solved; compared with the prior art, the horizontal positioning precision and the vertical positioning precision are remarkably improved, and the construction cost is greatly reduced.

Description

Technical Field

[0001] This invention belongs to the field of navigation and positioning, specifically relating to a GNSS ground-based augmentation solution method and system based on multi-difference observation equations. Background Technology

[0002] Global Navigation Satellite System (GNSS) is a core technology for positioning, navigation, and clock synchronization in modern society. While GNSS provides a certain level of positional accuracy, factors such as multipath effects, atmospheric delay, and satellite geometry often prevent it from meeting the demands of high-precision applications. To address these issues, Ground-Based Augmentation Systems (GBAS) have emerged. GBAS is a technology that corrects GNSS signals to improve positioning accuracy. It typically consists of ground base stations, a communication network, and user terminals. The base stations are located at known locations and monitor GNSS signals in real time, comparing them to their known locations to calculate error information. This error information is then transmitted to the user terminal via the wireless communication network, helping it correct the received GNSS signals and achieve higher-precision positioning.

[0003] In daily life, to improve the positioning accuracy of navigation terminals such as cars, airplanes, and ships, multi-mode receivers (MMRs) are installed on these devices. These receivers receive differential correction and integrity information broadcast from ground stations and combine this information with their own positioning algorithms to perform differential calculations, ultimately obtaining high-precision positioning results. The literature "Design and Test Analysis of BeiDou Satellite Navigation Ground-Based Augmentation System," *Wireless Interconnection Technology*, 2024, vol. 21, No. 4, pp. 30-35, analyzes the errors of network RTK and the factors affecting positioning accuracy, and establishes a ground-based augmentation system combining BDS and GPS systems. Although this system has significant advantages in improving positioning accuracy, its base station construction and maintenance costs are high, especially in remote areas. While traditional GNSS positioning technology is widely used, it has significant shortcomings in positioning accuracy. Single-point positioning (SPP) technology is affected by factors such as atmospheric delay, multipath effects, and satellite geometry, resulting in positioning accuracy typically only at the meter level. While real-time dynamic positioning (RTK) technology offers higher accuracy, its base station construction and maintenance costs are high, its coverage is limited, and its positioning performance drops sharply in areas with insufficient base station density. Furthermore, the GBAS system has a limited number of base stations, resulting in limited signal coverage and lower positioning accuracy, thus limiting its practical application due to its small coverage area.

[0004] To address the aforementioned technical problems, this invention proposes a GNSS ground-based augmentation solution method and system based on multi-difference observation equations. This invention significantly improves positioning accuracy while reducing system construction costs and complexity through optimized multi-difference observation equations and improved data processing algorithms. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies and address the issues of high base station construction and maintenance costs and low positioning accuracy in traditional GNSS ground-based augmentation systems, this invention provides a GNSS ground-based augmentation solution method and system based on multi-difference observation equations. This invention's GNSS ground-based augmentation solution method, based on multi-difference observation equations, utilizes a baseband board, GNSS antenna, and a laptop computer to construct a GNSS ground-based augmentation system base station and data center. The data center uses a Linux development environment to build data processing and communication software. A rover station is constructed using a baseband board, onboard inertial navigation system, GNSS antenna, and a laptop computer. A GNSS ground-based augmentation system communication network is formed between the base stations and between the base stations and the rover station via the Ntrip / TCP protocol. Using clock and position data of the same satellites observed between the base stations and the rover station, multi-difference observation equations are established to solve for the positioning information.

[0006] The technical solution adopted by this invention to solve its technical problem is a GNSS ground-based enhancement calculation method based on multi-difference observation equations, which includes the following steps: Step S1: Synchronize the raw observation data of the rover and the base station in time; acquire the raw satellite observation data of the rover, the raw differential correction data of the base station, and the IMU inertial navigation data of the rover; detect cycle slips in the carrier phase of the raw satellite observation data of the rover and the raw differential correction data of the base station using the Melbourne-Wübbena and Geometry-Free methods; remove epochs with cycle slips in the raw satellite observation data of the rover to obtain the satellite observation data of the rover; remove epochs with cycle slips in the raw differential correction data of the base station to obtain the differential correction data of the base station; output the list of co-view effective satellites and the observation values ​​of the satellites in the list of co-view effective satellites according to the common-view satellite selection requirements of the rover and the base station; the satellite observation values ​​include satellite number, satellite pseudorange, satellite carrier phase, and satellite Doppler shift; Step S2: Construct the double-difference observation equation and obtain the double-difference observation parameters; Step S3: Based on the double-difference observation parameters, the extended Kalman filter is used to fuse the double-difference observation parameters with the IMU inertial navigation data of the rover station to obtain the system state vector. X and observation vector Y； System state vector X Includes baseline coordinates and double-difference ambiguity; utilizes system state vectors Xand observation vector Y Construct the state transition matrix and measurement matrix for the Kalman filter: Step S4: Based on the system state vector X floating-point solution The system state vector is calculated using the LAMBDA algorithm. X Find a fixed solution; and search the threshold space to obtain the optimal solution. And the suboptimal solution, and finally the reference positioning vector of the base station is obtained by the Ratio method; Step S5: Repeat S1 to S4 to obtain the reference positioning vectors of all base stations. Then, weight and fuse the reference positioning vectors of all base stations to obtain the final positioning solution. .

[0007] Furthermore, the step of detecting cycle slips of carrier phase in the rover station's raw satellite observation data and the base station's raw differential correction data using the Melbourne-Wübbena and Geometry-Free methods is as follows: A joint criterion was constructed using the Melbourne-Wübbena and Geometry-Free methods. and criteria for: (1) (2) in, and These are different frequencies from the same satellite system; when the satellite system is GPS, then... This is the GPS L1 frequency. This refers to the GPS L2 frequency; when the satellite system is the BD system, then... This is the frequency of BD B1. This refers to the BD B2 frequency. for The carrier phase corresponding to the frequency point; for The carrier phase corresponding to the frequency point; for The pseudorange corresponding to the frequency point; for The pseudorange corresponding to the frequency point; when or If the carrier phase is determined to be a cycle slip, the epochs in the original satellite observation data of the rover station that have cycle slips are removed to obtain the satellite observation data of the rover station; the epochs in the original differential correction data of the base station that have cycle slips are removed to obtain the differential correction data of the base station. when and If none of the judgment conditions are met, then there is no need to remove epochs with cycle slips from the rover station's original satellite observation data and the base station's original differential correction data; the rover station's original satellite observation data is used as the rover station's satellite observation data; and the base station's original differential correction data is used as the base station's differential correction data. The epoch refers to the point in time at which a GNSS receiver completes one full observation. This represents the absolute value of the difference in MW between adjacent epochs. This is the absolute value of the difference between adjacent epochs in the GF calculation.

[0008] Furthermore, the requirements for screening common-view satellites are: the elevation angle of the common-view satellite is >15° and the signal-to-noise ratio (SNR) is >35 dBHz; the common-view satellite is a satellite that can be observed by both the base station and the mobile station. Furthermore, the steps for constructing the double-difference observation equation and obtaining the double-difference observation parameters are as follows: Based on the list of commonly viewed effective satellites and the observations of the satellites in the list, using the base station b Mobile station r Reference satellite i and non-reference satellites j Based on this, construct the double-difference observation equation: (3) (4) in, For mobile station r and base station b Between, reference satellite i With satellite j The double-difference carrier phase observations between; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference pseudorange observations between; For mobile station r and base station b Between, reference satellite i With satellite j The double difference geometric distance between them; For mobile station r and base station b Between, reference satellite i With satellite j The tropospheric delay error between them; For mobile station r and base station b Between, reference satellite i With satellite jIonospheric delay error between them; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference pseudorange measurement error between them; For mobile station r and base station b Between, reference satellite i With satellite j Double-difference integer ambiguity between them; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference carrier phase measurement error; the double-difference carrier phase observation value, double-difference pseudorange observation value, double-difference geometric distance value, tropospheric delay error, ionospheric delay error, double-difference pseudorange measurement error, double-difference integer ambiguity, and double-difference carrier phase measurement error constitute the double-difference observation parameters; In formulas (3) and (4) Expand: (5) in, For receiver r To satellite j The linearized coefficient vector, For receiver r To satellite i The linearized coefficient vector, For receiver r to receiver b The baseline vector.

[0009] Furthermore, based on the double-difference observation parameters, an extended Kalman filter is used to fuse the double-difference observation parameters with the rover's IMU inertial navigation data to obtain the system state vector. X and observation vector Y The steps for constructing the state transition matrix and measurement matrix of the Kalman filter are as follows: At any given time, the base station and rover observed m System state vector for each satellite X and observation vector Y for: (6) (7) s The reference satellite with the largest elevation angle; For mobile station r and base station b Between, reference satellites With satellite h Double-difference integer ambiguity between them; ; For mobile station r and base station b Between, reference satellite s With satellite h The double-difference pseudorange observations between; For mobile station r and base station b Between, reference satellite s With satellite h The double-difference carrier phase observations between; system state vector X Including baseline coordinates and double-difference ambiguity; System state vector X Including baseline vectors and double-difference ambiguity The baseline vector is ,in The position vector from the base station to the rover Axial components, The position vector from the base station to the rover. Axial components, The position vector from the base station to the rover. Axial components; Using system state vectors X and observation vector Y Construct the state transition matrix and measurement matrix for the Kalman filter: (8) Let be the system state vector at time k; Let k be the state transition matrix of the system from time k-1 to time k; Let k be the system state vector at time k-1; This is the process noise vector; Let be the probability distribution of the process noise, which is a Gaussian distribution with a mean of 0 and a covariance matrix of Q; Q is the process noise covariance matrix. Let be the observation vector at time k; The observation matrix; For the observed noise vector; Let be the probability distribution of the observation noise, which is a Gaussian distribution with a mean of 0 and a covariance matrix of R; R is the observation noise covariance matrix. The system state vector is obtained through equation (8). X floating-point solution ; Furthermore, the statement based on the system state vector X floating-point solution The system state vector is calculated using the LAMBDA algorithm. X Find a fixed solution and search the threshold space to obtain the optimal solution. The specific process of obtaining the reference positioning vector of the base station using the Ratio method, along with the suboptimal solution, is as follows: For the system state vector X floating-point solution and system state vector X covariance For the system state vector respectively X covariance Synchronous state vector X floating-point solution Perform integer Z-transform: (9) in, L It is a unit lower triangular matrix. D It is a diagonal matrix. To resolve the ambiguity; The optimal solution is obtained by searching the threshold space. and suboptimal solutions Finally, the ambiguity threshold is calculated using the Ratio method. : (10) Accept the optimal integer solution when Rat > 3. The optimal integer solution As a reference positioning vector for the base station; When Rat 3. Then retain the floating-point solution. ; decompose floating point As a reference positioning vector for the base station; The LAMBDA algorithm is used to decorrelate floating-point ambiguities and perform integer search to find the optimal integer combination within the transformed space. The reliability of the fixed solution is evaluated using a ratio test. When the ratio of the residual between the optimal and suboptimal solutions exceeds a threshold (usually set to 3), the ambiguity is considered successfully fixed and the fixed solution is output; otherwise, the floating-point solution is maintained, and the system waits for the next epoch data to continue attempting to fix the ambiguity.

[0010] Furthermore, by repeating steps S1 to S4, the reference positioning vectors of all base stations are obtained. These reference positioning vectors are then weighted and fused to obtain the final positioning solution. The steps are as follows: Assume there is K Each base station, the final positioning solution The expression is: (11) (12) (13) in, For the first k The optimal solution obtained from the calculation at each base station. For the first k The solution variance of each reference station; weights Ensure the contribution of high-precision solutions with short baselines.

[0011] A system employing a GNSS ground-based augmentation solution method based on multi-difference observation equations includes several reference stations, rover stations, several GNSS satellites, and a data processing center. Both reference stations and rover stations include GNSS satellite receivers. The locations of the reference stations are fixed. The data processing center deploys the GNSS ground-based augmentation solution method based on multi-difference observation equations, and is connected to the reference stations and rover stations via TCP / IP protocol. The data processing center receives raw satellite observation data from the reference stations and rover stations; it performs calculations using the GNSS ground-based augmentation system solution method based on multi-difference observation equations to obtain more accurate rover station positioning information, which is then transmitted back to the rover stations by the data processing center.

[0012] The beneficial effects of this invention are as follows: This invention uses a reference station and employs a multi-difference observation equation for calculation, achieving a horizontal positioning accuracy of 0.5 to 0.8 meters and a vertical positioning accuracy of 0.7 to 1.0 meters. Compared to SPP single-point positioning technology, this solution improves positioning accuracy by 80%-85%. Compared to RTK real-time differential technology, this solution improves positioning accuracy by 50%-55%. In terms of cost, the construction cost is reduced by approximately 40%-50% compared to traditional RTK systems. In terms of coverage, the effective coverage area of ​​multiple reference stations is expanded by 30%-40%. Attached Figure Description

[0013] Figure 1 This is a system structure diagram of the present invention; Figure 2 The flowchart shows the GNSS ground-based augmentation solution method based on the multi-difference observation equation. Figure 3 Vehicle trajectories in open areas; Figure 4 Comparison chart of positioning test results in open scenes; Figure 5 Vehicle trajectories in a tree-lined scene; Figure 6 Comparison chart of location test results for a tree-lined scene. Detailed Implementation

[0014] A GNSS ground-based augmentation solution method based on multi-difference observation equations includes the following steps: Step S1: Synchronize the raw observation data of the rover and the base station in time; acquire the raw satellite observation data of the rover, the raw differential correction data of the base station, and the IMU inertial navigation data of the rover; detect cycle slips in the carrier phase of the raw satellite observation data of the rover and the raw differential correction data of the base station using the Melbourne-Wübbena and Geometry-Free methods; remove epochs with cycle slips in the raw satellite observation data of the rover to obtain the satellite observation data of the rover; remove epochs with cycle slips in the raw differential correction data of the base station to obtain the differential correction data of the base station; output the list of co-view effective satellites and the observation values ​​of the satellites in the list of co-view effective satellites according to the common-view satellite selection requirements of the rover and the base station; the satellite observation values ​​include satellite number, satellite pseudorange, satellite carrier phase, and satellite Doppler shift; The steps for detecting cycle slips of carrier phase in the raw satellite observation data of the rover station and the raw differential correction data of the base station using the Melbourne-Wübbena and Geometry-Free methods are as follows: A joint criterion was constructed using the Melbourne-Wübbena and Geometry-Free methods. and criteria for: (1) (2) in, and These are different frequencies from the same satellite system; when the satellite system is GPS, then... This is the GPS L1 frequency. This refers to the GPS L2 frequency; when the satellite system is the BD system, then... This is the frequency of BD B1. This refers to the BD B2 frequency. for The carrier phase corresponding to the frequency point; for The carrier phase corresponding to the frequency point; for The pseudorange corresponding to the frequency point; for The pseudorange corresponding to the frequency point; when or If the carrier phase is determined to be a cycle slip, the epochs in the original satellite observation data of the rover station that have cycle slips are removed to obtain the satellite observation data of the rover station; the epochs in the original differential correction data of the base station that have cycle slips are removed to obtain the differential correction data of the base station. when and If none of the judgment conditions are met, then there is no need to remove epochs with cycle slips from the rover station's original satellite observation data and the base station's original differential correction data; the rover station's original satellite observation data is used as the rover station's satellite observation data; and the base station's original differential correction data is used as the base station's differential correction data. The epoch refers to the point in time at which a GNSS receiver completes one full observation. This represents the absolute value of the difference in MW between adjacent epochs. This is the absolute value of the difference between adjacent epochs when calculating GF; The requirements for screening common-view satellites are: the elevation angle of the common-view satellite is >15° and the signal-to-noise ratio (SNR) is >35 dBHz; Common-view satellites are satellites that can be observed by both base stations and mobile stations; Output a list of valid common-view satellites and the observation values ​​of the satellites in the list, based on the common-view satellite selection requirements; the satellite observation values ​​include satellite number, satellite pseudorange, satellite carrier phase, and satellite Doppler shift; Step S2: Construct the double-difference observation equation and obtain the double-difference observation parameters; Based on the list of commonly viewed effective satellites and the observations of the satellites in the list, using the base station b Mobile station r Reference satellite i and non-reference satellites j Based on this, construct the double-difference observation equation: (3) (4) in, For mobile station r and base station b Between, reference satellite i With satellite j The double-difference carrier phase observations between; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference pseudorange observations between; For mobile station r and base station b Between, reference satellite i With satellite jThe double difference geometric distance between them; For mobile station r and base station b Between, reference satellite i With satellite j The tropospheric delay error between them; For mobile station r and base station b Between, reference satellite i With satellite j Ionospheric delay error between them; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference pseudorange measurement error between them; For mobile station r and base station b Between, reference satellite i With satellite j Double-difference integer ambiguity between them; For mobile station r and base station b Between, reference satellite i With satellite j The double-difference carrier phase measurement error; the double-difference carrier phase observation value, double-difference pseudorange observation value, double-difference geometric distance value, tropospheric delay error, ionospheric delay error, double-difference pseudorange measurement error, double-difference integer ambiguity, and double-difference carrier phase measurement error constitute the double-difference observation parameters; In formulas (3) and (4) Expand: (5) in, For receiver r To satellite j The linearized coefficient vector, For receiver r To satellite i The linearized coefficient vector, For receiver r to receiver b The baseline vector; Step S3: Based on the double-difference observation parameters, the extended Kalman filter is used to fuse the double-difference observation parameters with the IMU inertial navigation data of the rover station to obtain the system state vector. X and observation vector Y； System state vector X Includes baseline coordinates and double-difference ambiguity; utilizes system state vectors X and observation vector YConstruct the state transition matrix and measurement matrix for the Kalman filter: At any given time, the base station and rover observed m System state vector for each satellite X and observation vector Y for: (6) (7) s The reference satellite with the largest elevation angle; For mobile station r and base station b Between, reference satellite s With satellite h Double-difference integer ambiguity between them; ; For mobile station r and base station b Between, reference satellite s With satellite h The double-difference pseudorange observations between; For mobile station r and base station b Between, reference satellite s With satellite h The double-difference carrier phase observations between; System state vector X Including baseline vectors and double-difference ambiguity The baseline vector is ,in The position vector from the base station to the rover Axial components, The position vector from the base station to the rover. Axial components, The position vector from the base station to the rover. Axial components; Using system state vectors X and observation vector Y Construct the state transition matrix and measurement matrix for the Kalman filter: (8) Let be the system state vector at time k; Let k be the state transition matrix of the system from time k-1 to time k; Let k be the system state vector at time k-1; This is the process noise vector; Let be the probability distribution of the process noise, which is a Gaussian distribution with a mean of 0 and a covariance matrix of Q; Q is the process noise covariance matrix. Let be the observation vector at time k; The observation matrix; For the observed noise vector; Let be the probability distribution of the observation noise, which is a Gaussian distribution with a mean of 0 and a covariance matrix of R; R is the observation noise covariance matrix. The system state vector is obtained through equation (8). X floating-point solution ; Step S4: Based on the system state vector X floating-point solution The system state vector is calculated using the LAMBDA algorithm. X Find a fixed solution; and search the threshold space to obtain the optimal solution. And the suboptimal solution, and finally the reference positioning vector of the base station is obtained by the Ratio method; The specific process is as follows: For the system state vector X floating-point solution and system state vector X covariance For the system state vector respectively X covariance Synchronous state vector X floating-point solution Perform integer Z-transform: (9) in, L It is a unit lower triangular matrix. D It is a diagonal matrix. To resolve the ambiguity; The optimal solution is obtained by searching the threshold space. and suboptimal solutions Finally, the ambiguity threshold is calculated using the Ratio method. : (10) Accept the optimal integer solution when Rat > 3. The optimal integer solution As a reference positioning vector for the base station; When Rat 3. Then retain the floating-point solution. ; decompose floating point As a reference positioning vector for the base station; The LAMBDA algorithm is used to decorrelate floating-point ambiguities and perform integer search to find the optimal integer combination within the transformed space. The reliability of the fixed solution is evaluated using a ratio test. When the residual ratio between the optimal and suboptimal solutions exceeds a threshold (usually set to 3), the ambiguity is considered successfully fixed and the fixed solution is output; otherwise, the floating-point solution is maintained, and the system waits for the next epoch data to continue attempting to fix the ambiguity. Step S5: Repeat S1 to S4 to obtain the reference positioning vectors of all base stations. Then, weight and fuse the reference positioning vectors of all base stations to obtain the final positioning solution. ; Assume there is K Each base station, the final positioning solution The expression is: (11) (12) (13) in, For the first k The optimal solution obtained from the calculation at each base station. For the first k The variance of the solution for each reference station. Weights Baseline length was taken into account With solution variance This ensures the contribution of high-precision solutions with short baselines.

[0015] A system employing a GNSS ground-based augmentation solution method based on multi-difference observation equations includes several reference stations, rover stations, several GNSS satellites, and a data processing center. Both reference stations and rover stations include GNSS satellite receivers. The locations of the reference stations are fixed. The data processing center deploys the GNSS ground-based augmentation solution method based on multi-difference observation equations, and is connected to the reference stations and rover stations via TCP / IP protocol. The data processing center receives raw satellite observation data from the reference stations and rover stations; it performs calculations using the GNSS ground-based augmentation system solution method based on multi-difference observation equations to obtain more accurate rover station positioning information, which is then transmitted back to the rover stations. The data processing center is a server.

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. To make the technical means of this invention easier to understand, the invention is further illustrated below with specific examples. In this solution, data processing for both the data center and the rover is performed on a laptop computer, with the code running on a Linux environment (Ubuntu 20.04). The local GNSS ground-based augmentation system's base station is built using a Sinan Navigation K813 board, and the corresponding rover is built using a Sinan Navigation K823 board. Both the base station and the rover use a GNSS full-system receiving antenna for GNSS signal reception and processing. The rover is mounted on a passenger car for driving tests and data acquisition.

[0017] 1. Methods for constructing reference stations and rover stations for local GNSS ground-based augmentation systems; 1-1: Setting up a local GNSS ground-based augmentation system reference station: This system was built using a Sinan Navigation K813 board, a GNSS full-system receiving antenna, and a laptop computer. The K813 board, acting as a GNSS signal receiver, was connected to the GNSS full-system receiving antenna via an RF cable. The K813 board and the laptop computer were connected via a USB-to-serial cable. The laptop computer received the raw satellite observation data transmitted by the K813 board via a serial cable. The laptop computer, acting as a base station data center, broadcast the raw satellite observation data and ephemeris via the Ntrip / TCP protocol.

[0018] 1-2: Setting up a local GNSS ground-based augmentation system rover: The system utilizes the Sinan Navigation K823 board, which includes an onboard inertial navigation module, a GNSS full-system receiving antenna, and a laptop computer. The K823 board acts as the rover receiver, connected to the GNSS full-system receiving antenna via an RF cable. The laptop computer serves solely as the rover's data processing unit, receiving and processing positioning data from various base stations and the rover itself.

[0019] 2. Design methodologies for data processing software and communication software; 2-1: Data Processing Software Design: The data processing software design consists of a post-processing version, Tednav 3.1, and a version supporting real-time debugging, Tednav 3.5. Binary packets collected by the base station and rover are saved as text files. The RTKLIB tool RTKCONV decodes the binary packets into OBS and NAV files for post-processing. In Tednav 3.1, the xianrcv.conf configuration file is opened, and the base station coordinates, the path to the post-processing file, and the IMU data frequency are correctly entered. The actual debugging uses 50 Hz data. The remaining settings in the configuration file can remain at the default values ​​of xianrcv.conf. Tednav 3.5 obtains observation data from the base station via Ntrip / TCP. Ensure that the serial port for reading IMU data is ttyUSB0 and the serial port for reading antenna packets is ttyUSB1. The changes to the xianrcv.conf configuration file are the same as in Tednav 3.1.

[0020] 2-2: Communication Software Design: The communication software was primarily developed on the Linux environment Ubuntu 20.04, with the base station's communication terminal running on Ubuntu 20.04. After starting OpenVPN and establishing ping communication between the base station and the rover, the `configString` in `ConfigFile.c` was changed to the current IP address of the rover. The software runs the base station as a client and the rover as a server. The base station client forwards raw satellite observation data output from the GNSS receiver board via the Ntrip / TCP protocol, while the rover server receives the raw satellite observation data via socket communication. The code provides a complete and universal API interface, allowing users to perform secondary development and customization of the program.

[0021] 3. A GNSS ground-based augmentation solution method based on multi-difference observation equations; For the user, the process involves simultaneously receiving single-point positioning data from the rover's GNSS board and differential correction data from the base station, and performing real-time relative positioning. The data is preprocessed to detect and correct cycle slips. Then, clock and position data from the same satellites observed by the rover and the network base station are selected to establish a double-difference observation equation. A floating-point solution is calculated using an extended Kalman filter, and this solution is verified. If the verification passes, the floating-point solution is output; otherwise, it is considered a single-point solution. The LAMBDA algorithm is used to search for integer ambiguities in the carrier phase, and the validity of these ambiguities is verified. If the verification passes, a fixed solution is output; otherwise, it is considered a floating-point solution. The overall solution process is as follows: Figure 2 As shown.

[0022] 3-1: In the data preprocessing stage, time synchronization is first completed. The inputs are the original observation data from the rover's GNSS board, the differential correction data from the base station, and the IMU inertial navigation data. The observation epochs of the rover (50Hz) and the base station (1Hz) are aligned using an interpolation algorithm. For carrier phase cycle slip detection, a joint criterion of MW (Melbourne-Wübbena) and GF (Geometry-Free) is used. (1) (2) in, , For L1 / L2 frequency points, These are the carrier phase and pseudorange, respectively.

[0023] when and If a cycle slip occurs, a third-order polynomial fitting is used to restore phase continuity. Common-view satellite selection requires an elevation angle > 15° and a signal-to-noise ratio (SNR) > 35 dBHz. The final output includes a list of valid satellites and the restored observations.

[0024] 3-2: Construction of the double-difference observation equation. The input is the preprocessed common-view satellite data from the previous step, with the base station as the reference. b Mobile station r Reference satellite i and non-reference satellites j For example, the double-difference observation equation is constructed as follows: (3) (4) in, For mobile station r and base station b Between, reference satellite i With satellite j The two differences between them; and These are the double-difference carrier phase and double-difference pseudorange observations, respectively. This represents the double-difference geometric distance between the satellite and the receiver. λ The carrier phase frequency; The ambiguity is a double-difference integer ambiguity. This is the tropospheric delay error; This is the ionospheric delay error; This is the error in the double-difference carrier phase measurement; This represents the error in double-difference pseudorange measurement.

[0025] Satellite-to-Earth distance in a double-difference observation model of carrier phase and pseudorange Expanded into the following formula: (5) in, For receiver r To satellite j The linearized coefficient vector, For receiver r To satellite i The linearized coefficient vector, For receiver r to receiver b The baseline vector.

[0026] 3-3: Extended Kalman Filter Floating-Point Solution, with the double-difference observations from the previous step as input. The baseline vector and floating-point ambiguity are solved using prior information via extended Kalman filtering, resolving the three elements of the baseline vector. The double-difference ambiguity is used as the system state vector. At a certain epoch, an observation was made... m Each satellite, its system state vector X and observation vector Y As shown in the following formula: (6) (7) in, s The reference satellite with the largest elevation angle, For double-difference ambiguity, and These are the double-difference carrier phase and double-difference pseudorange observations, respectively, and * represents any positioning system.

[0027] The state transition matrix and measurement matrix of the Kalman filter are determined by equations (3) to (5), and the corresponding expressions are as follows: (8) Observations are determined using the covariance propagation rate based on the satellite-elevation angle model. Y The covariance matrix is ​​used to determine the process noise based on empirical values, i.e., the process noise is calculated in equation (6). X Vector floating-point solution This lays the foundation for subsequent fixation of double-difference ambiguity.

[0028] 3-4: The LAMBDA algorithm fixes the ambiguity. Based on the characteristics of ambiguity covariance, the LAMBDA method decomposes the ambiguity into a diagonal matrix through integer matrix transformation, and then decorrelates the ambiguity. For the floating-point solution of the ambiguity obtained in the previous step... and its covariance First, perform the integer Z-transform: (9) in, LIt is a unit lower triangular matrix. D It is a diagonal matrix. This is a solution for removing related ambiguities.

[0029] The optimal solution is obtained by searching the threshold space. and suboptimal solutions Finally, the Ratio method was used to verify that the ambiguity was successfully fixed. The corresponding expression is: (10) Accept the optimal integer solution when Rat > 3. Otherwise, retain the floating-point solution; 3-5: Multi-difference Fusion. The results from multiple benchmark stations are weighted and fused, with the weights proportional to the baseline length. Inversely proportional. Assume there is... K The final positioning solution expression for each base station is: (11) (12) (13) in, For the first k The optimal solution obtained from the calculation at each base station. For the first k The variance of the solution for each reference station. Weights Baseline length was taken into account With solution variance This ensures the contribution of high-precision solutions with short baselines.

[0030] 4. Verification of a localized GNSS ground-based augmentation system; 4-1: Physical verification in an open scene: Conduct real-world vehicle tests in an open environment, according to... Figure 3 The vehicle trajectory shown on the map illustrates the driving of a car. The car, serving as a mobile station carrier, is equipped with a K823 board integrating an IMU module and a GNSS full-system receiving antenna mounted on its roof. The vehicle travels along a mountain road near Northwestern Polytechnical University. Within the Northwestern Polytechnical University campus, three base stations equipped with K813 boards were set up on the rooftops of the School of Electronic Information, the School of Navigation laboratory, and a small hill east of Qixiang Building. During the testing, the GPS test used approximately 4-6 satellites, and the BDS test used approximately 16-21 satellites. The root mean square error of the positioning results calculated in the ENU coordinate system was compared between a conventional GNSS receiver and the local GNSS ground-based augmentation system proposed in this invention. The results are as follows: Figure 4As shown in the results, the positioning error of a conventional GNSS receiver is between 0.8 meters and 1.5 meters, with an average of 1 meter; while the position error of a GNSS receiver using the original satellite observation data and ephemeris data from the local GNSS ground-based augmentation system is between 0.3 meters and 0.6 meters, with an average of 0.3 meters. This demonstrates the effectiveness of the local GNSS ground-based augmentation system proposed in this invention.

[0031] 4-2: Physical verification of the tree-lined scene: Conducting real-world sports car tests in a tree-lined setting, according to... Figure 5 The vehicle trajectory shown on the map illustrates the driving of a car. The car is equipped with a K823 board integrating an IMU module and a GNSS full-system receiving antenna mounted on its roof, and operates within the Northwestern Polytechnical University campus, cruising along the northern section of the campus. Within the Northwestern Polytechnical University campus, three base stations equipped with K813 boards were set up on the rooftops of the School of Electronic Information, the School of Navigation laboratory, and a small hill east of Qixiang Building. During the test, due to tree obstruction, the GPS test had approximately 3-5 satellites, and the BDS test had approximately 4-6 satellites. The root mean square error of the positioning results calculated in the ENU coordinate system for a conventional GNSS receiver and the local GNSS ground-based augmentation system proposed in this invention was compared. The results are as follows: Figure 6 As shown in the results, the position error of a conventional GNSS receiver is between 1.2 meters and 2 meters, with an average of 1.6 meters; while the position error of a GNSS receiver using raw satellite observation data and ephemeris data from a local GNSS ground-based augmentation system is between 0.5 meters and 1 meter, with an average of 0.7 meters. Although the overall positioning results were affected by tree obstruction, the results after introducing the local GNSS ground-based augmentation system were still greatly improved, further demonstrating the effectiveness of this invention.

[0032] Performance Advantages Summary: The multi-base station scheme and multi-difference observation equation GNSS ground-based augmentation system solution method in this invention achieves a horizontal positioning accuracy of 0.5 to 0.8 meters and a vertical positioning accuracy of 0.7 to 1.0 meters. Compared to SPP single-point positioning technology, this scheme improves positioning accuracy by 80%-85%; compared to RTK real-time differential technology, this scheme improves positioning accuracy by 50%-55%; in terms of cost, construction costs are reduced by approximately 40%-50% compared to traditional RTK systems; and in terms of coverage, the effective coverage area of ​​multiple base stations is expanded by 30%-40%.

[0033] Table 1: Comparison of accuracy of different positioning methods

[0034] Specifically, the system of this invention employs an optimized multi-difference observation equation and an improved Kalman filter algorithm, which can more effectively eliminate atmospheric delay errors and multipath effects, achieving sub-meter positioning accuracy. Utilizing data processing software built in a Linux development environment and the Ntrip / TCP communication protocol, the system exhibits excellent real-time performance and stability. This method not only significantly surpasses traditional SPP and RTK technologies in positioning accuracy but also offers substantial advantages in system construction cost, maintenance complexity, and coverage, providing an economical and effective solution for high-precision GNSS applications.

[0035] Through the above-mentioned technical improvements, this invention successfully solves the key technical problems of high construction and maintenance costs, limited coverage, and insufficient positioning accuracy of traditional GNSS ground-based augmentation systems.

Claims

1. A GNSS ground-based augmentation solution method based on multi-difference observation equations, characterized in that, The method comprises the following steps: Step S1: time synchronization is performed on the original observation data of the rover station and the reference station, satellite original observation data of the rover station, original differential correction data of the reference station and IMU inertial navigation data of the rover station are obtained, and the cycle slips of the carrier phase in the satellite original observation data of the rover station and the original differential correction data of the reference station are detected by using the Melbourne-Wübbena and Geometry-Free methods; After eliminating the epochs of the satellite original observation data of the rover station in which the cycle slips occur, satellite observation data of the rover station are obtained; After eliminating the epochs of the original differential correction data of the reference station in which the cycle slips occur, differential correction data of the reference station are obtained; According to the common-view satellite screening requirements of the rover station and the reference station, a common-view effective satellite list and observation values of the satellites in the common-view effective satellite list are output; the observation values of the satellites include satellite numbers, satellite pseudoranges, satellite carrier phases and satellite Doppler frequency shifts; Step S2: a double-difference observation equation is constructed, and double-difference observation parameters are obtained; Step S3: based on the double-difference observation parameters, the double-difference observation parameters are fused with the IMU inertial navigation data of the flow station by using the extended Kalman filter to obtain the system state vector X and the observation vector Y； The system state vector X includes baseline coordinates and double-difference ambiguities; the system state vector X and the observation vector Y are used to construct the state transition matrix and the measurement matrix of the Kalman filter to obtain the float solution of the system state vector X :​ Step S4: Calculate the system state vector X of floating solution , the system state vector X of fixed solution by LAMBDA algorithm; and obtain the optimal solution and suboptimal solution in threshold space search, and finally obtain the reference positioning vector of the reference station by Ratio method; Step S5: repeat steps S1 to S4 to obtain the reference positioning vectors of all reference stations, and fuse the reference positioning vectors of all reference stations to obtain a final positioning solution .

2. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The step of detecting the cycle slips of the carrier phase in the satellite original observation data of the rover station and the original differential correction data of the reference station by using the Melbourne-Wübbena and Geometry-Free methods is as follows: The Melbourne-Wubbena and Geometry-Free methods are combined to form a joint criterion, and the criterion and the criterion is (1) (2) wherein, and are different frequencies of the same satellite system; when the satellite system is a GPS system, then is the GPS L1 frequency, is the GPS L2 frequency; when the satellite system is a BD system, then is the BD B1 frequency, is the BD B2 frequency; is the carrier phase corresponding to the frequency of the frequency point; is the carrier phase corresponding to the frequency of the frequency point; is the pseudo-range corresponding to the frequency of the frequency point; is the pseudo-range corresponding to the frequency of the frequency point; When or , it is determined that the carrier phase is a cycle slip, the epoch of the cycle slip occurring in the original observation data of the rover satellite is removed, and the observation data of the rover satellite is obtained; the epoch of the cycle slip occurring in the original differential correction data of the reference station is removed, and the differential correction data of the reference station is obtained; When and do not satisfy the judgment condition, the epoch of cycle slip occurrence in the raw observation data of the rover satellite and the raw differential correction data of the reference station does not need to be rejected; the raw observation data of the rover satellite is taken as the observation data of the rover satellite; and the raw differential correction data of the reference station is taken as the differential correction data of the reference station. wherein the epoch refers to the time point when the GNSS receiver performs a complete observation, calculating the absolute value of the difference of MW between adjacent epochs, calculating the absolute value of the difference of GF between adjacent epochs.

3. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The requirements of the common-view satellite screening are that the elevation angles of the common-view satellites are greater than 15° and the signal-to-noise ratios SNR are greater than 35 dBHz; the common-view satellites are satellites that can be observed by both the reference station and the rover station.

4. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The step of constructing the double-difference observation equation and obtaining the double-difference observation parameters is as follows: Based on the reference station b , rover station r , reference satellite i and non-reference satellite j , the double-difference observation equation is constructed: (3) (4) wherein is a double-difference carrier phase observation between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a double-difference pseudorange observation between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a double-difference geometric range value between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a tropospheric delay error between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is an ionospheric delay error between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a double-difference pseudorange measurement error between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a double-difference integer ambiguity between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; is a double-difference carrier phase measurement error between the rover station r and the reference satellite b and the reference satellite i and the satellite j ; the double-difference carrier phase observation, the double-difference pseudorange observation, the double-difference geometric range value, the tropospheric delay error, the ionospheric delay error, the double-difference pseudorange measurement error, the double-difference integer ambiguity, and the double-difference carrier phase measurement error constitute double-difference observation parameters; Substituting equation (3) into equation (4) gives Unfolded: (5) wherein is a linearization coefficient vector for the receiver r to the satellite j is a linearization coefficient vector for the receiver to the satellite r is a linearization coefficient vector for the receiver i to the satellite is a linearization coefficient vector for the receiver r to the receiver b is a baseline vector for the receiver 5. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The double-difference observation parameters are fused with the IMU inertial navigation data of the flow station by using extended Kalman filtering to obtain a system state vector X and an observation vector Y and the state transition matrix and the measurement matrix of the Kalman filtering are constructed. The system state vector x at any instant of time is observed by the reference stations and the rover stations m and the observation vector z is given by: X and the observation vector z is given by: Y x = x + K(z - z) (6) (7) s is a reference satellite with the largest elevation angle; is a rover station r and a reference station b between the rover station s and the reference satellite h between the rover station ; is a rover station r and a reference station b between the rover station s and the reference satellite h between the rover station is a rover station r and a reference station b between the rover station s and the reference satellite h between the rover station X and the reference satellite ; system state vector System state vector X comprising a baseline vector and double difference ambiguities ; the baseline vector being wherein a axis component of a position vector of the reference station pointing to the rover station, a axis component of a position vector of the reference station pointing to the rover station, a axis component of a position vector of the reference station pointing to the rover station; Utilizing a system state vector X and an observation vector Y Constructing a state transition matrix and a measurement matrix for a Kalman filter: (8) is the system state vector at time k; is the state transition matrix of the system from time k-1 to time k; is the system state vector at time k-1; is the process noise vector; is the probability distribution of the process noise, which is a Gaussian distribution with mean 0 and covariance matrix Q; Q is the process noise covariance matrix; is the observation vector at time k; is the observation matrix; is the observation noise vector; is the probability distribution of the observation noise, which is a Gaussian distribution with mean 0 and covariance matrix R; R is the observation noise covariance matrix; the floating-point solution of the system state vector X is obtained through equation (8) .

6. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The system state vector X The floating solution of the system state vector The fixed solution of the system state vector X The optimal solution and the suboptimal solution obtained by searching in the threshold space The specific process of obtaining the reference positioning vector of the reference station by the Ratio method is as follows: for the system state vector X the float solution and the covariance X of the system state vector the covariance of the system state vector X the float solution of the system state vector an integer Z transformation is performed: (9) wherein, L is a unit lower triangular matrix, D is a diagonal matrix, is a decorrelated ambiguity solution; Optimal solution is searched in threshold space and suboptimal solution , and finally the ambiguity threshold is calculated by Ratio method : (10) Accept optimal integer solution when Rat > 3 Accept optimal integer solution Reference positioning vector to base station; accept optimal integer solution when Rat 3, accept float solution Reference positioning vector to base station; accept float solution Reference positioning vector to base station.

7. The GNSS ground-based augmentation solution method based on multi-difference observation equation according to claim 1, characterized in that, The steps of repeating S1 to S4 to obtain the reference positioning vectors of all reference stations, and fusing the reference positioning vectors of all reference stations to obtain the final positioning solution are as follows: Assume there are K reference stations, the final positioning solution is expressed as: (11) (12) (13) wherein, is the optimal solution obtained for the k first reference station, is the solution variance for the k first reference station; the weight ensures the contribution of the short baseline to the high precision solution.

8. The system for GNSS ground-based augmentation based on multi-observation equation method according to claim 1, wherein, The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The

Images