A positioning solution method and device based on a third-generation Beidou satellite, and a medium

Abstract

This invention relates to a positioning calculation method, equipment, and medium based on BeiDou-3 satellites, belonging to the field of satellite positioning technology. The method includes the following steps: obtaining the geocentric coordinates of the BeiDou-3 satellites, the precise coordinates of the reference station, the approximate coordinates of the rover station, and the pseudorange and carrier phase observations of both relative to the satellites; inputting the geocentric coordinates and the coordinates of the reference and rover stations into a common-view satellite selection algorithm to obtain a common-view satellite set and select a reference satellite; calculating the double-difference pseudorange and double-difference carrier phase observations relative to the reference satellite using the observations from the reference and rover stations, and constructing a linearized observation equation; performing least-squares estimation using a weighted matrix to obtain the floating-point solution and its covariance matrix, and combining this with the approximate rover station coordinates to obtain the fixed solution rover station coordinates. This invention solves the problem of decreased positioning accuracy caused by the difficulty in completely eliminating tropospheric delay in complex environments such as long baselines and urban canyons by introducing double-difference tropospheric residual correction.

Description

Technical Field

[0001] This invention relates to a positioning calculation method, equipment, and medium based on BeiDou-3 satellites, belonging to the field of satellite positioning technology. Background Technology

[0002] With the full network deployment and official service launch of the BeiDou-3 satellite navigation system, its high-precision positioning, navigation, and timing capabilities, provided globally, have been widely applied in fields such as surveying and mapping, precision agriculture, intelligent transportation, UAV navigation, and deformation monitoring. In real-time dynamic positioning technology, the base station and rover simultaneously observe BeiDou-3 satellites, using pseudorange and carrier phase observations to form a double-difference observation equation to eliminate or reduce satellite orbit errors, satellite clock errors, receiver clock errors, and most atmospheric propagation delay errors. However, in complex observation environments, such as when the distance between the rover and base station is long or when located in undulating terrain areas like urban canyons or mountainous regions, residual tropospheric delay cannot be completely eliminated by a simple double-difference combination, thus affecting the estimation accuracy of floating-point solutions and the efficiency of integer ambiguity fixation.

[0003] In existing technologies, elevation angle weighting or empirical models are typically used to weight observations, but these methods fail to fully consider the spatial differences in tropospheric delay between the base station and the rover. This results in residual tropospheric errors significantly impacting the reliability and convergence speed of positioning results, especially in scenarios with long baselines or large elevation differences. Therefore, a high-precision positioning solution method specifically tailored to the characteristics of the BeiDou-3 satellite system is urgently needed to meet the growing demand for precise positioning applications. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a positioning calculation method, equipment, and medium based on BeiDou-3 satellites.

[0005] The technical solution of the present invention is as follows: On the one hand, this invention provides a positioning calculation method based on BeiDou-3 satellites, including the following steps: Obtain the geocentric coordinates of the BeiDou-3 satellite, the precise coordinates of the base station, the approximate coordinates of the rover station, the pseudorange and carrier phase observations of the BeiDou-3 satellite from the base station, and the pseudorange and carrier phase observations of the BeiDou-3 satellite from the rover station. The geocentric coordinates, precise coordinates, and approximate coordinates are used as inputs to the common-view satellite selection algorithm, which outputs a set of satellites that meet the common-view conditions, and selects a BeiDou-3 satellite from the set as a reference satellite. Based on the pseudorange and carrier phase observations of the BeiDou-3 satellite from the base station and the pseudorange and carrier phase observations of the BeiDou-3 satellite from the rover station, we obtain the double-difference pseudorange and carrier phase observations between the BeiDou-3 satellite and the reference satellite. A linearized observation equation is constructed based on the aforementioned double-difference pseudorange observations and double-difference carrier phase observations; Obtain the weight matrix, and estimate the floating-point solution of the linearized observation equation using the least squares method based on the weight matrix; The fixed solution rover coordinates are obtained based on the floating-point solution, the covariance matrix of the floating-point solution, and the approximate coordinates of the rover station.

[0006] Preferably, the geocentric coordinates, precise coordinates, and approximate coordinates are used as inputs to the common-view satellite selection algorithm. The specific steps are as follows: The coordinate difference between the BeiDou-3 satellite and the base station in the geocentric coordinate system is obtained based on the precise coordinates of the base station and the geocentric coordinates of the BeiDou-3 satellite. Based on the coordinate difference between the BeiDou-3 satellite and the reference station in the geocentric coordinate system, the projections of the BeiDou-3 satellite in the north direction, the east direction, and the vertical upward direction at the reference station are obtained. The elevation angle of the BeiDou-3 satellite observed at the reference station is obtained based on the projection of the BeiDou-3 satellite in the north direction, the projection in the east direction, and the vertical upward projection. The coordinate difference between the BeiDou-3 satellite and the rover in the geocentric coordinate system is obtained based on the approximate coordinates of the rover station and the geocentric coordinates of the BeiDou-3 satellite. Based on the coordinate difference between the BeiDou-3 satellite and the rover station in the geocentric coordinate system, the projections of the BeiDou-3 satellite in the north direction, the east direction, and the vertical upward direction at the rover station are obtained. The elevation angle of the BeiDou-3 satellite observed at the mobile station is obtained based on the projections of the BeiDou-3 satellite in the north, east, and vertical directions at the mobile station. Set an elevation angle threshold, and based on the elevation angle threshold, the elevation angle of the BeiDou-3 satellites observed at the rover station, and the elevation angle of the BeiDou-3 satellites observed at the base station, select a set of satellites that meet the common viewing condition.

[0007] Preferably, the double-difference pseudorange observation is expressed by the formula: ; In the formula, Indicates the first The double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. This represents the pseudorange observations of the rover to the reference satellite. This represents the pseudorange observation value of the reference station to the reference satellite; The double-difference carrier phase observation value is expressed by the formula: ; In the formula, Indicates the first Two-difference carrier phase observations between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. This represents the carrier phase observations of the reference satellite by the rover station. This represents the carrier phase observation value of the reference satellite from the base station.

[0008] Preferably, the corrected double-difference pseudorange and double-difference carrier phase observations between the BeiDou-3 satellite and the reference satellite are obtained based on the double-difference pseudorange and carrier phase observations. The specific steps are as follows: The tropospheric delay during the observation of BeiDou-3 satellites at the reference station is obtained based on the elevation angle observed at the reference station. The tropospheric delay during the observation of BeiDou-3 satellites at the rover station is obtained based on the elevation angle observed at the rover station. Based on the tropospheric delay observed from the rover station and the tropospheric delay observed from the base station, a double-difference tropospheric residue between the BeiDou-3 satellites and the reference satellites is constructed, expressed by the formula: ; In the formula, Indicates the first The double-difference tropospheric remnants between the BeiDou-3 satellite and the reference satellite This indicates the tropospheric delay when the rover observes the reference satellite. This indicates the tropospheric delay when the base station observes the reference satellite. Indicates the observation of the base station. The tropospheric delay of a single BeiDou-3 satellite Indicates the observation of the rover station. The tropospheric delay when a BeiDou-3 satellite is in use; Based on the aforementioned double-difference tropospheric residual and double-difference pseudorange observations, the corrected double-difference pseudorange observations between the BeiDou-3 satellite and the reference satellite are obtained, expressed by the formula: ; In the formula, Indicates the first Corrected double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite; Based on the aforementioned double-difference tropospheric residual and double-difference carrier phase observations, the corrected double-difference carrier observations between the BeiDou-3 satellite and the reference satellite are obtained, expressed by the formula: ; In the formula, Indicates the first Corrected double-difference carrier observation values ​​between a BeiDou-3 satellite and a reference satellite.

[0009] Preferably, the linearized observation equation is constructed using the corrected double-difference pseudorange observations and double-difference carrier phase observations between the BeiDou-3 satellite and the reference satellite. The specific steps are as follows: The geometric distance from the base station to the BeiDou-3 satellite is obtained based on the precise coordinates of the base station and the geocentric coordinates of the BeiDou-3 satellite. The geometric distance from the rover to the BeiDou-3 satellite is obtained based on the approximate coordinates of the rover and the geocentric coordinates of the BeiDou-3 satellite. Based on the geometric distances from the base station to the BeiDou-3 satellite and the rover station to the BeiDou-3 satellite, a double-difference geometric distance approximation is constructed, expressed by the formula: ; In the formula, Indicates the first Approximate value of the double-difference geometric distance between a BeiDou-3 satellite and a reference satellite. This represents the geometric distance from the rover station to the reference satellite. This represents the geometric distance from the base station to the reference satellite. Indicates the rover station to the th The geometric distance between each BeiDou-3 satellite Indicates the distance from the base station to the 1st The geometric distance between each BeiDou-3 satellite; The double-difference carrier residual is obtained based on the double-difference geometric distance approximation and the corrected double-difference carrier observations, expressed by the formula: ; In the formula, Indicates the first The double-difference carrier residual between a BeiDou-3 satellite and a reference satellite; The double-difference carrier residual is obtained based on the double-difference geometric distance approximation and the corrected double-difference pseudorange observations, expressed by the formula: ; In the formula, Indicates the first The double-difference pseudorange residual between a BeiDou-3 satellite and a reference satellite; Construct observation residual vectors based on double-difference carrier residuals and double-difference pseudorange residuals; Obtain the unit direction vector pointing from the approximate coordinates of the rover station to the BeiDou-3 satellite. Based on this unit direction vector, construct the linearization coefficient vector of the BeiDou-3 satellite, expressed by the formula: ; In the formula, Indicates the first The linearized coefficient vector between each BeiDou-3 satellite and a reference satellite This indicates the direction from the approximate coordinates of the rover station to the... The unit direction vector of a BeiDou-3 satellite. This represents the unit direction vector from the approximate coordinates of the rover station to the reference satellite; Construct a design matrix based on the linearized coefficient vector; Construct the parameter vector to be estimated, including the rover coordinate correction vector and the double-difference integer ambiguity between the BeiDou-3 satellite and the reference satellite, expressed by the formula: ; In the formula, Represents the vector of parameters to be estimated. Represents the rover coordinate correction vector transpose, Indicates the first Double-difference integer ambiguity between a BeiDou-3 satellite and a reference satellite; Based on the estimated parameter vector, design matrix, and observed residual vector, a linearized observation equation is constructed, expressed as follows: ; In the formula, Represents the observation noise vector. Represents the residual vector of observations. This represents the design matrix.

[0010] Preferably, the weight matrix is ​​obtained, expressed by the formula: ; ; ; In the formula, Represents the weight matrix, This represents the function that constructs a diagonal matrix, where the diagonal elements of the constructed weight matrix are functions. The input parameters have 0 for off-diagonal elements. Indicates the first The weight of carrier observation values ​​between each BeiDou-3 satellite and a reference satellite Indicates the first The weight of pseudorange observations between each BeiDou-3 satellite and a reference satellite This represents the prior variance of the carrier observations. This represents the prior variance of the pseudorange observations. Indicates the first The average elevation angle of each BeiDou-3 satellite; The average elevation angle is expressed by the formula: ; In the formula, This indicates the observation at the base station. The elevation angle of each BeiDou-3 satellite This indicates the observation at the rover station. The elevation angle of a Beidou-3 satellite.

[0011] Preferably, the floating-point solution of the linearized observation equation is estimated using the least squares method based on the weight matrix, and the specific steps are as follows: The normal equation matrix is ​​constructed based on the design matrix and the weight matrix, and is expressed by the following formula: ; In the formula, Representation of the normal equation matrix, Design matrix Transpose of; The free term vector of the normal equation is constructed based on the design matrix, weight matrix, and observation residual vector, and is expressed by the formula: ; In the formula, Representation of the free term vector of the equation; The floating-point solution of the parameter vector to be estimated is obtained based on the normal equation matrix and the free term vector of the normal equation, expressed by the following formula: ; In the formula, Represents the vector of parameters to be estimated Floating-point solution; The floating-point solution includes the coordinate correction estimate vector of the rover coordinate correction vector and the floating-point estimate of the double-difference integer ambiguity, expressed by the formula: ; In the formula, Represents the rover coordinate correction vector Coordinate correction estimation vector transpose, Indicates double-difference integer ambiguity The floating-point estimate; The covariance matrix of the floating-point solution is constructed based on the normal equation matrix, and is expressed by the following formula: ; In the formula, This represents the covariance matrix of the floating-point solution.

[0012] Preferably, the fixed solution rover coordinates are obtained based on the floating-point solution, the covariance matrix of the floating-point solution, and the approximate coordinates of the rover station. The specific steps are as follows: The floating-point ambiguity vector is extracted from the floating-point solution, expressed by the following formula: ; In the formula, Represents a floating-point ambiguity vector; Extracting the floating-point ambiguity covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ; In the formula, Represents the floating-point ambiguity covariance matrix; Extracting the coordinate correction ambiguity covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ; In the formula, This represents the coordinate correction ambiguity covariance matrix; The LAMBDA algorithm is used to obtain a fixed ambiguity vector based on the floating-point ambiguity vector and the floating-point ambiguity covariance matrix, expressed by the formula: ; In the formula, Represents a fixed ambiguity vector; The rover coordinate correction vector corresponding to the fixed solution is obtained based on the coordinate correction estimation vector, the coordinate correction ambiguity covariance matrix, and the fixed ambiguity vector, expressed by the formula: ; In the formula, This represents the rover coordinate correction vector corresponding to the fixed solution; The rover coordinates of the fixed solution are obtained based on the rover coordinate correction vector corresponding to the fixed solution and the approximate coordinates of the rover, expressed by the formula:

[0013] In the formula, This represents the coordinates of the fixed solution rover station.

[0014] In another aspect, the present invention also provides an electronic device having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the positioning calculation method based on BeiDou-3 satellites as described in any embodiment of the present invention.

[0015] In another aspect, the present invention also provides a computer-readable storage medium for storing one or more programs, which, when executed by one or more processors, enable the one or more processors to implement the positioning calculation method based on BeiDou-3 satellites as described in any embodiment of the present invention.

[0016] The present invention has the following beneficial effects: 1. This invention effectively solves the problem of decreased positioning accuracy caused by the difficulty in completely eliminating tropospheric delay in complex environments such as long baselines, large elevation differences, or urban canyons by introducing double-difference tropospheric residual correction.

[0017] 2. This invention calculates the elevation angles of a satellite at both ends of the observation station, filters out a set of satellites that meet the common-view criteria, and selects the satellite with the largest elevation angle as the reference satellite. This selection strategy ensures that the reference satellite has optimal observation geometry and signal quality, reducing the impact of multipath effects and atmospheric errors at low elevation angles. Simultaneously, the average elevation angle is incorporated as a weighting criterion when constructing the weight matrix, ensuring a reasonable weight distribution between high-precision carrier observations and low-precision pseudorange observations, thus improving the robustness of parameter estimation.

[0018] 3. This invention uses the LAMBDA algorithm for integer ambiguity search and combines it with the covariance matrix information of the floating-point solution to achieve efficient ambiguity fixation. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the implementation of the method in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0022] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0023] The terms “comprising” and “including” indicate the presence of the described feature, whole, step, operation, element and / or component, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0024] The term “and / or” refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes these combinations.

[0025] Example 1: See Figure 1 This embodiment provides a positioning calculation method based on BeiDou-3 satellites, including the following steps: S1. Obtain the geocentric coordinates of the BeiDou-3 satellite (calculated from the ephemeris parameters of the BeiDou-3 satellite), the precise coordinates of the base station, the approximate coordinates of the rover station, the pseudorange observations and carrier phase observations of the BeiDou-3 satellite from the base station, and the pseudorange observations and carrier phase observations of the BeiDou-3 satellite from the rover station. The approximate coordinates of the rover station are obtained using the pseudorange single-point positioning method.

[0026] S2. Using the geocentric coordinates, precise coordinates, and approximate coordinates as input to the common-view satellite selection algorithm, the algorithm outputs a set of satellites that meet the common-view criteria. The specific steps are as follows: S201. Based on the precise coordinates of the reference station and the geocentric coordinates of the BeiDou-3 satellite, obtain the coordinate difference between the BeiDou-3 satellite and the reference station in the geocentric coordinate system, including... Axis coordinate difference Axis coordinate difference and Difference between axial coordinates; The The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a reference station in the geocentric coordinate system Axis coordinate difference Indicates the first The BeiDou-3 satellite in the geocentric coordinate system Axis coordinates (obtained through the geocentric coordinates of BeiDou-3 satellites). Indicates the reference station in the geocentric coordinate system Axis coordinates (obtained through precise coordinates from the base station); The The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a reference station in the geocentric coordinate system Axis coordinate difference Indicates the first The BeiDou-3 satellite in the geocentric coordinate system Axis coordinates (obtained through the geocentric coordinates of BeiDou-3 satellites). Indicates the reference station in the geocentric coordinate system Axis coordinates (obtained through precise coordinates from the base station); The The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a reference station in the geocentric coordinate system Axis coordinate difference Indicates the first The BeiDou-3 satellite in the geocentric coordinate system Axis coordinates (obtained through the geocentric coordinates of BeiDou-3 satellites). Indicates the reference station in the geocentric coordinate system Axis coordinates (obtained through precise coordinates from the base station); S202. Based on the coordinate difference between the BeiDou-3 satellite and the reference station in the geocentric coordinate system, obtain the projection of the BeiDou-3 satellite in the north direction, the projection in the east direction, and the vertical upward projection at the reference station. The projection of the BeiDou-3 satellite in the north direction at the reference station is expressed by the formula: ; In the formula, Indicates the first The projection of a BeiDou-3 satellite onto the north side of the base station, i.e., the northward component in the station-centered coordinate system. Indicates the geodetic latitude of the base station. Indicates the geodetic longitude of the base station; The projection of the BeiDou-3 satellite in the east direction at the reference station is expressed by the formula: ; In the formula, Indicates the first The projection of a BeiDou-3 satellite onto the reference station in the east direction, i.e., the eastward component in the station center coordinate system; The vertical upward projection of the BeiDou-3 satellite at the base station is expressed by the formula: ; In the formula, Indicates the first The vertical upward projection of a BeiDou-3 satellite at the base station, i.e., the zenith direction component in the station center coordinate system; S203. The elevation angle of the BeiDou-3 satellite observed at the reference station is obtained based on the projections of the BeiDou-3 satellite in the north, east, and vertical directions at the reference station, expressed by the formula: ; In the formula, This indicates the observation at the base station. The elevation angle of a BeiDou-3 satellite; S204. Based on the approximate coordinates of the rover and the geocentric coordinates of the BeiDou-3 satellite, obtain the coordinate difference between the BeiDou-3 satellite and the rover in the geocentric coordinate system, including... Axis coordinate difference Axis coordinate difference and Difference between axial coordinates; The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a mobile station in the geocentric coordinate system Axis coordinate difference Represents the position of the rover in the geocentric coordinate system Axis coordinates (obtained through approximate coordinates of the rover station); The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a mobile station in the geocentric coordinate system Axis coordinate difference Represents the position of the rover in the geocentric coordinate system Axis coordinates (obtained through approximate coordinates of the rover station); The difference between the axes coordinates is expressed by the formula: ; In the formula, Indicates the first A BeiDou-3 satellite and a mobile station in the geocentric coordinate system Axis coordinate difference Represents the position of the rover in the geocentric coordinate system Axis coordinates (obtained through approximate coordinates of the rover station); S205. Based on the coordinate difference between the BeiDou-3 satellite and the rover station in the geocentric coordinate system, obtain the projections of the BeiDou-3 satellite in the north direction, the east direction, and the vertical upward direction at the rover station. The projection of the BeiDou-3 satellite in the north direction at the rover station is expressed by the formula: ; In the formula, Indicates the first The projection of a BeiDou-3 satellite onto the north side of the rover station, i.e., the northward component in the station-center coordinate system. Indicates the geodetic latitude of the rover station. Indicates the geodetic longitude of the rover station; The projection of the BeiDou-3 satellite in the east direction at the mobile station is expressed by the formula: ; In the formula, Indicates the first The projection of a BeiDou-3 satellite onto the eastward direction at the mobile station, i.e., the eastward component in the station center coordinate system; The vertical upward projection of the BeiDou-3 satellite at the mobile station is expressed by the formula: ; In the formula, Indicates the first The vertical upward projection of a BeiDou-3 satellite at the mobile station, i.e., the zenith direction component in the station-center coordinate system; S206. Based on the projections of BeiDou-3 satellites onto the rover station in the north, east, and vertical directions, the elevation angle of the observed BeiDou-3 satellites at the rover station is obtained, expressed by the formula: ; In the formula, This indicates the observation at the rover station. The elevation angle of a BeiDou-3 satellite; S207. Set an elevation angle threshold. Based on the elevation angle threshold, the elevation angles of the BeiDou-3 satellites observed at the rover station, and the elevation angles of the BeiDou-3 satellites observed at the base station, select a set of satellites that meet the common-view condition, expressed by the formula: ; In the formula, This refers to a set of satellites that meet the criteria for common visibility. This indicates the elevation angle threshold.

[0027] S3. The BeiDou-3 satellite with the highest elevation angle observed at the rover station from the satellite array is taken as the reference satellite, expressed by the formula: ; In the formula, Indicates the reference satellite identifier, This indicates the index of BeiDou-3 satellites that achieve the largest elevation angle observed at the mobile station. .

[0028] S4. Based on the pseudorange and carrier phase observations of the BeiDou-3 satellite from the base station and the pseudorange and carrier phase observations of the BeiDou-3 satellite from the rover station, obtain the double-difference pseudorange and carrier phase observations between the BeiDou-3 satellite and the reference satellite. The double-difference pseudorange observations are expressed by the formula: ; In the formula, Indicates the first The double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. This represents the pseudorange observations of the rover to the reference satellite. This represents the pseudorange observation value of the reference station to the reference satellite; The double-difference carrier phase observation value is expressed by the formula: ; In the formula, Indicates the first Two-difference carrier phase observations between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. This represents the carrier phase observations of the reference satellite by the rover station. This represents the carrier phase observation value of the reference satellite from the base station.

[0029] S5. Based on the aforementioned double-difference pseudorange observations, double-difference carrier phase observations, the elevation angle of the BeiDou-3 satellite observed at the rover station, and the elevation angle of the BeiDou-3 satellite observed at the base station, obtain the corrected double-difference pseudorange observations and double-difference carrier phase observations between the BeiDou-3 satellite and the reference satellite. The specific steps are as follows: S501. The tropospheric delay of the BeiDou-3 satellite observation at the reference station is obtained based on the elevation angle observed at the reference station, expressed by the formula: ; In the formula, Indicates the observation of the base station. The tropospheric delay of a single BeiDou-3 satellite Indicates atmospheric pressure. Represents absolute temperature. Indicates water vapor pressure; S502. The tropospheric delay during the observation of BeiDou-3 satellites by the rover station is obtained based on the elevation angle observed at the rover station, expressed by the formula: ; In the formula, Indicates the observation of the rover station. The tropospheric delay when a BeiDou-3 satellite is in use; S503. Based on the tropospheric delay observed from the rover station and the tropospheric delay observed from the base station, a double-difference tropospheric residue between the BeiDou-3 satellite and the reference satellite is constructed, expressed by the formula: ; In the formula, Indicates the first The double-difference tropospheric remnants between the BeiDou-3 satellite and the reference satellite This indicates the tropospheric delay when the rover observes the reference satellite. This indicates the tropospheric delay when the base station observes the reference satellite; S504. Based on the double-difference tropospheric residual and double-difference pseudorange observations between BeiDou-3 satellites and reference satellites, the corrected double-difference pseudorange observations between BeiDou-3 satellites and reference satellites are obtained, expressed by the formula: ; In the formula, Indicates the first Corrected double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite; S505. Based on the double-difference tropospheric residual and double-difference carrier phase observations between BeiDou-3 satellites and reference satellites, the corrected double-difference carrier observations between BeiDou-3 satellites and reference satellites are obtained, expressed by the formula: ; In the formula, Indicates the first Corrected double-difference carrier observation values ​​between a BeiDou-3 satellite and a reference satellite.

[0030] S6. Based on the geocentric coordinates of the BeiDou-3 satellite, the precise coordinates of the base station, and the approximate coordinates of the rover station, construct an approximate double-difference geometric distance between the BeiDou-3 satellite and the reference satellite. Then, construct a linearized observation equation using the corrected double-difference pseudorange observations and double-difference carrier phase observations between the BeiDou-3 satellite and the reference satellite, as well as the approximate geometric distance. The specific steps are as follows: S601. Based on the precise coordinates of the base station and the geocentric coordinates of the BeiDou-3 satellite, the geometric distance from the base station to the BeiDou-3 satellite is obtained, expressed by the formula: ; In the formula, Indicates the distance from the base station to the 1st The geometric distance between each BeiDou-3 satellite Indicates the precise coordinates of the base station. Indicates the first Topographic coordinates of a BeiDou-3 satellite Denotes the Euclidean norm; S602. Based on the approximate coordinates of the rover station and the geocentric coordinates of the BeiDou-3 satellite, the geometric distance from the rover station to the BeiDou-3 satellite is obtained, expressed by the formula: ; In the formula, Indicates the rover station to the th The geometric distance between each BeiDou-3 satellite Represents the approximate coordinates of the rover station; S603. Based on the geometric distance from the base station to the BeiDou-3 satellite and the geometric distance from the rover station to the BeiDou-3 satellite, a double-difference geometric distance approximation is constructed, expressed by the formula: ; In the formula, Indicates the first Approximate value of the double-difference geometric distance between a BeiDou-3 satellite and a reference satellite. This represents the geometric distance from the rover station to the reference satellite. Indicates the geometric distance from the base station to the reference satellite; S604. The double-difference carrier residual is obtained based on the double-difference geometric distance approximation and the corrected double-difference carrier observation, expressed by the formula: ; In the formula, Indicates the first The double-difference carrier residual between a BeiDou-3 satellite and a reference satellite; S605. Based on the approximate double-difference geometric distance and the corrected double-difference pseudorange observations, the double-difference carrier residual is obtained, expressed by the formula: ; In the formula, Indicates the first The double-difference pseudorange residual between a BeiDou-3 satellite and a reference satellite; S606. Construct the observation residual vector based on the double-difference carrier residual and the double-difference pseudorange residual, expressed by the formula: ; In the formula, Represents the residual vector of observations. This indicates the number of satellite pairs consisting of BeiDou-3 satellites and a reference satellite. Representing vectors Transpose of; S607. Obtain the unit direction vector from the approximate coordinates of the rover station to the BeiDou-3 satellite, expressed by the formula: ; In the formula, This indicates the direction from the approximate coordinates of the rover station to the... The unit direction vector of a BeiDou-3 satellite; S608. Construct the linearization coefficient vector of the BeiDou-3 satellite based on the unit direction vector, expressed by the formula: ; In the formula, Indicates the first The linearization coefficient vector between each BeiDou-3 satellite and the reference satellite, including... Axial component, Axial direction components and Axial component, This represents the unit direction vector from the approximate coordinates of the rover station to the reference satellite; S609. Based on the linearized coefficient vector and the carrier wavelength of the BeiDou-3 satellite, construct the carrier observation row vector between the BeiDou-3 satellite and the reference satellite, expressed by the formula: ; In the formula, Indicates the first Row vector of carrier observation values ​​between a BeiDou-3 satellite and a reference satellite This represents the carrier wavelength of the BeiDou-3 satellite, with a value of 0.192. S610. Based on the linearized coefficient vector, construct the pseudorange observation row vector between the BeiDou-3 satellite and the reference satellite, expressed by the formula: ; In the formula, Indicates the first The pseudorange observation row vector between a BeiDou-3 satellite and a reference satellite; S611. Construct a design matrix based on the row vector of the carrier observations and the row vector of the pseudorange observations, expressed by the formula: ; In the formula, Represents the design matrix; S612. Construct the parameter vector to be estimated, including the rover coordinate correction vector and the double-difference integer ambiguity between the BeiDou-3 satellite and the reference satellite, expressed by the formula: ; In the formula, Represents the vector of parameters to be estimated. Represents the rover coordinate correction vector transpose, Indicates the first Double-difference integer ambiguity between a BeiDou-3 satellite and a reference satellite; S613. Based on the estimated parameter vector, design matrix, and observed residual vector, construct a linearized observation equation, expressed as follows: ; In the formula, This represents the observation noise vector.

[0031] S7. Construct the weight matrix, expressed by the formula: ; ; ; In the formula, Represents the weight matrix, This represents the function that constructs a diagonal matrix, where the diagonal elements of the constructed weight matrix are functions. The input parameters have 0 for off-diagonal elements. Indicates the first The weight of carrier observation values ​​between each BeiDou-3 satellite and a reference satellite Indicates the first The weight of pseudorange observations between each BeiDou-3 satellite and a reference satellite This represents the prior variance of the carrier observations. This represents the prior variance of the pseudorange observations. Indicates the first Average elevation angle and prior variance of each BeiDou-3 satellite , Based on the experience of technical personnel, such as prior variance, etc. Set to 0.01, prior variance Set to 1; The average elevation angle is expressed by the formula: .

[0032] S8. Based on the weight matrix, the floating-point solution of the linearized observation equation is estimated using the least squares method. The specific steps are as follows: S801. Construct the normal equation matrix based on the design matrix and weight matrix, expressed by the formula: ; In the formula, Representation of the normal equation matrix, Design matrix Transpose of; S802. Construct the free term vector of the normal equation based on the design matrix, weight matrix, and observation residual vector, expressed by the formula: ; In the formula, Representation of the free term vector of the equation; S803. Obtain the floating-point solution of the parameter vector to be estimated based on the normal equation matrix and the free term vector of the normal equation, expressed by the formula: ; In the formula, Represents the vector of parameters to be estimated Floating-point solution; The floating-point solution includes the coordinate correction estimate vector of the rover coordinate correction vector and the floating-point estimate of the double-difference integer ambiguity, expressed by the formula: ; In the formula, Represents the rover coordinate correction vector Coordinate correction estimation vector transpose, Indicates double-difference integer ambiguity The floating-point estimate; S804. Construct the covariance matrix of the floating-point solution based on the normal equation matrix, expressed by the formula: ; In the formula, This represents the covariance matrix of the floating-point solution.

[0033] S9. Based on the floating-point solution, the covariance matrix of the floating-point solution, and the approximate coordinates of the rover station, obtain the fixed solution rover station coordinates. The specific steps are as follows: S901. Extract the floating-point ambiguity vector from the floating-point solution, expressed by the formula: ; In the formula, Represents a floating-point ambiguity vector; S902. Extract the floating-point fuzzy covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ; In the formula, Represents the floating-point ambiguity covariance matrix; S903. Extract the coordinate correction ambiguity covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ; In the formula, This represents the coordinate correction ambiguity covariance matrix; S904. Based on the floating-point ambiguity vector and the floating-point ambiguity covariance matrix, the LAMBDA algorithm is used to obtain the fixed ambiguity vector, which is expressed by the formula: ; In the formula, Represents a fixed ambiguity vector; S905. Based on the coordinate correction estimation vector, the coordinate correction ambiguity covariance matrix, and the fixed ambiguity vector, the rover coordinate correction vector corresponding to the fixed solution is obtained, expressed by the formula: ; In the formula, This represents the rover coordinate correction vector corresponding to the fixed solution; S906. Obtain the rover coordinates of the fixed solution based on the rover coordinate correction vector corresponding to the fixed solution and the approximate coordinates of the rover, expressed by the formula:

[0034] In the formula, This represents the coordinates of the fixed solution rover station.

[0035] Example 2: This embodiment provides an electronic device that stores a computer program. When the computer program is executed by a processor, it implements the positioning calculation method based on BeiDou-3 satellites as described in any embodiment of the present invention.

[0036] Example 3: This embodiment provides a computer-readable storage medium for storing one or more programs, which, when executed by one or more processors, enable the one or more processors to implement the positioning calculation method based on BeiDou-3 satellites as described in any embodiment of the present invention.

[0037] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, A and B simultaneously, or B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, at least one of a, b, and c can represent: a, b, c, a and b, a and c, b and c, or a and b and c, where a, b, and c can be single or multiple.

[0038] Those skilled in the art will recognize that the units and algorithm steps described in the embodiments disclosed herein can be implemented using electronic hardware, computer software, or a combination of electronic hardware and software. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0039] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0040] In the several embodiments provided in this application, any function, if implemented as a software functional unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0041] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A positioning calculation method based on BeiDou-3 satellites, characterized in that, Includes the following steps: Obtain the geocentric coordinates of the BeiDou-3 satellite, the precise coordinates of the base station, the approximate coordinates of the rover station, the pseudorange and carrier phase observations of the BeiDou-3 satellite from the base station, and the pseudorange and carrier phase observations of the BeiDou-3 satellite from the rover station. The geocentric coordinates, precise coordinates, and approximate coordinates are used as inputs to the common-view satellite selection algorithm, which outputs a set of satellites that meet the common-view conditions, and selects a BeiDou-3 satellite from the set as a reference satellite. Based on the pseudorange and carrier phase observations of the BeiDou-3 satellite from the base station and the pseudorange and carrier phase observations of the BeiDou-3 satellite from the rover station, we obtain the double-difference pseudorange and carrier phase observations between the BeiDou-3 satellite and the reference satellite. A linearized observation equation is constructed based on the aforementioned double-difference pseudorange observations and double-difference carrier phase observations; Obtain the weight matrix, and estimate the floating-point solution of the linearized observation equation using the least squares method based on the weight matrix; The fixed solution rover coordinates are obtained based on the floating-point solution, the covariance matrix of the floating-point solution, and the approximate coordinates of the rover station.

2. The positioning calculation method based on BeiDou-3 satellites according to claim 1, characterized in that, The geocentric coordinates, precise coordinates, and approximate coordinates are used as inputs to the common-view satellite selection algorithm. The specific steps are as follows: The coordinate difference between the BeiDou-3 satellite and the base station in the geocentric coordinate system is obtained based on the precise coordinates of the base station and the geocentric coordinates of the BeiDou-3 satellite. Based on the coordinate difference between the BeiDou-3 satellite and the reference station in the geocentric coordinate system, the projections of the BeiDou-3 satellite in the north direction, the east direction, and the vertical upward direction at the reference station are obtained. The elevation angle of the BeiDou-3 satellite observed at the reference station is obtained based on the projection of the BeiDou-3 satellite in the north direction, the projection in the east direction, and the vertical upward projection. The coordinate difference between the BeiDou-3 satellite and the rover in the geocentric coordinate system is obtained based on the approximate coordinates of the rover station and the geocentric coordinates of the BeiDou-3 satellite. Based on the coordinate difference between the BeiDou-3 satellite and the rover station in the geocentric coordinate system, the projections of the BeiDou-3 satellite in the north direction, the east direction, and the vertical upward direction at the rover station are obtained. The elevation angle of the BeiDou-3 satellite observed at the mobile station is obtained based on the projections of the BeiDou-3 satellite in the north, east, and vertical directions at the mobile station. Set an elevation angle threshold, and based on the elevation angle threshold, the elevation angle of the BeiDou-3 satellites observed at the rover station, and the elevation angle of the BeiDou-3 satellites observed at the base station, select a set of satellites that meet the common viewing condition.

3. The positioning calculation method based on BeiDou-3 satellites according to claim 2, characterized in that, The double-difference pseudorange observations are expressed by the following formula: ； In the formula, Indicates the first The double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Pseudo-range observation values ​​of a BeiDou-3 satellite. This represents the pseudorange observations of the rover to the reference satellite. This represents the pseudorange observation value of the reference station to the reference satellite; The double-difference carrier phase observation value is expressed by the formula: ； In the formula, Indicates the first Two-difference carrier phase observations between a BeiDou-3 satellite and a reference satellite Indicates the rover station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. Indicates the base station to the first Carrier phase observation values ​​of a BeiDou-3 satellite. This represents the carrier phase observations of the reference satellite by the rover station. This represents the carrier phase observation value of the reference satellite from the base station.

4. The positioning calculation method based on BeiDou-3 satellites according to claim 3, characterized in that, Based on the aforementioned double-difference pseudorange observations and double-difference carrier phase observations, the corrected double-difference pseudorange observations and double-difference carrier phase observations between the BeiDou-3 satellite and the reference satellite are obtained. The specific steps are as follows: The tropospheric delay during the observation of BeiDou-3 satellites at the reference station is obtained based on the elevation angle observed at the reference station. The tropospheric delay during the observation of BeiDou-3 satellites at the rover station is obtained based on the elevation angle observed at the rover station. Based on the tropospheric delay observed from the rover station and the tropospheric delay observed from the base station, a double-difference tropospheric residue between the BeiDou-3 satellites and the reference satellites is constructed, expressed by the formula: ； In the formula, Indicates the first The double-difference tropospheric remnants between the BeiDou-3 satellite and the reference satellite This indicates the tropospheric delay when the rover observes the reference satellite. This indicates the tropospheric delay when the base station observes the reference satellite. Indicates the observation of the base station. The tropospheric delay of a single BeiDou-3 satellite Indicates the observation of the rover station. The tropospheric delay when a BeiDou-3 satellite is in use; Based on the aforementioned double-difference tropospheric residual and double-difference pseudorange observations, the corrected double-difference pseudorange observations between the BeiDou-3 satellite and the reference satellite are obtained, expressed by the formula: ； In the formula, Indicates the first Corrected double-difference pseudorange observation values ​​between a BeiDou-3 satellite and a reference satellite; Based on the aforementioned double-difference tropospheric residual and double-difference carrier phase observations, the corrected double-difference carrier observations between the BeiDou-3 satellite and the reference satellite are obtained, expressed by the formula: ； In the formula, Indicates the first Corrected double-difference carrier observation values ​​between a BeiDou-3 satellite and a reference satellite.

5. The positioning calculation method based on BeiDou-3 satellites according to claim 4, characterized in that, The linearized observation equations are constructed using the corrected double-difference pseudorange observations and double-difference carrier phase observations between BeiDou-3 satellites and reference satellites. The specific steps are as follows: The geometric distance from the base station to the BeiDou-3 satellite is obtained based on the precise coordinates of the base station and the geocentric coordinates of the BeiDou-3 satellite. The geometric distance from the rover to the BeiDou-3 satellite is obtained based on the approximate coordinates of the rover and the geocentric coordinates of the BeiDou-3 satellite. Based on the geometric distances from the base station to the BeiDou-3 satellite and the rover station to the BeiDou-3 satellite, a double-difference geometric distance approximation is constructed, expressed by the formula: ； In the formula, Indicates the first Approximate value of the double-difference geometric distance between a BeiDou-3 satellite and a reference satellite. This represents the geometric distance from the rover station to the reference satellite. This represents the geometric distance from the base station to the reference satellite. Indicates the rover station to the th The geometric distance between each BeiDou-3 satellite Indicates the distance from the base station to the 1st The geometric distance between each BeiDou-3 satellite; The double-difference carrier residual is obtained based on the double-difference geometric distance approximation and the corrected double-difference carrier observations, expressed by the formula: ； In the formula, Indicates the first The double-difference carrier residual between a BeiDou-3 satellite and a reference satellite; The double-difference carrier residual is obtained based on the double-difference geometric distance approximation and the corrected double-difference pseudorange observations, expressed by the formula: ； In the formula, Indicates the first The double-difference pseudorange residual between a BeiDou-3 satellite and a reference satellite; Construct observation residual vectors based on double-difference carrier residuals and double-difference pseudorange residuals; Obtain the unit direction vector pointing from the approximate coordinates of the rover station to the BeiDou-3 satellite. Based on this unit direction vector, construct the linearization coefficient vector of the BeiDou-3 satellite, expressed by the formula: ； In the formula, Indicates the first The linearized coefficient vector between each BeiDou-3 satellite and a reference satellite This indicates the direction from the approximate coordinates of the rover station to the... The unit direction vector of a BeiDou-3 satellite. This represents the unit direction vector from the approximate coordinates of the rover station to the reference satellite; Construct a design matrix based on the linearized coefficient vector; Construct the parameter vector to be estimated, including the rover coordinate correction vector and the double-difference integer ambiguity between the BeiDou-3 satellite and the reference satellite, expressed by the formula: ； In the formula, Represents the vector of parameters to be estimated. Represents the rover coordinate correction vector transpose, Indicates the first Double-difference integer ambiguity between a BeiDou-3 satellite and a reference satellite; Based on the estimated parameter vector, design matrix, and observed residual vector, a linearized observation equation is constructed, expressed as follows: ； In the formula, Represents the observation noise vector. Represents the residual vector of observations. This represents the design matrix.

6. The positioning calculation method based on BeiDou-3 satellites according to claim 5, characterized in that, The weight matrix is ​​obtained, expressed by the formula: ； ； ； In the formula, Represents the weight matrix, This represents the function that constructs a diagonal matrix, where the diagonal elements of the constructed weight matrix are functions. The input parameters have 0 for off-diagonal elements. Indicates the first The weight of carrier observation values ​​between each BeiDou-3 satellite and a reference satellite Indicates the first The weight of pseudorange observations between each BeiDou-3 satellite and a reference satellite This represents the prior variance of the carrier observations. This represents the prior variance of the pseudorange observations. Indicates the first The average elevation angle of each BeiDou-3 satellite; The average elevation angle is expressed by the formula: ； In the formula, This indicates the observation at the base station. The elevation angle of each BeiDou-3 satellite This indicates the observation at the rover station. The elevation angle of a Beidou-3 satellite.

7. The positioning calculation method based on BeiDou-3 satellites according to claim 6, characterized in that, The floating-point solution of the linearized observation equation is estimated using the least squares method based on the weight matrix. The specific steps are as follows: The normal equation matrix is ​​constructed based on the design matrix and the weight matrix, and is expressed by the following formula: ； In the formula, Representation of the normal equation matrix, Design matrix Transpose of; The free term vector of the normal equation is constructed based on the design matrix, weight matrix, and observation residual vector, and is expressed by the formula: ； In the formula, Representation of the free term vector of the equation; The floating-point solution of the parameter vector to be estimated is obtained based on the normal equation matrix and the free term vector of the normal equation, expressed by the following formula: ； In the formula, Represents the vector of parameters to be estimated Floating-point solution; The floating-point solution includes the coordinate correction estimate vector of the rover coordinate correction vector and the floating-point estimate of the double-difference integer ambiguity, expressed by the formula: ； In the formula, Represents the rover coordinate correction vector Coordinate correction estimation vector transpose, Indicates double-difference integer ambiguity The floating-point estimate; The covariance matrix of the floating-point solution is constructed based on the normal equation matrix, and is expressed by the following formula: ； In the formula, This represents the covariance matrix of the floating-point solution.

8. The positioning calculation method based on BeiDou-3 satellites according to claim 7, characterized in that, The fixed solution rover coordinates are obtained based on the floating-point solution, the covariance matrix of the floating-point solution, and the approximate coordinates of the rover station. The specific steps are as follows: The floating-point ambiguity vector is extracted from the floating-point solution, expressed by the following formula: ； In the formula, Represents a floating-point ambiguity vector; Extracting the floating-point ambiguity covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ； In the formula, Represents the floating-point ambiguity covariance matrix; Extracting the coordinate correction ambiguity covariance matrix from the covariance matrix of the floating-point solution, expressed by the formula: ； In the formula, This represents the coordinate correction ambiguity covariance matrix; The LAMBDA algorithm is used to obtain a fixed ambiguity vector based on the floating-point ambiguity vector and the floating-point ambiguity covariance matrix, expressed by the formula: ； In the formula, Represents a fixed ambiguity vector; The rover coordinate correction vector corresponding to the fixed solution is obtained based on the coordinate correction estimation vector, the coordinate correction ambiguity covariance matrix, and the fixed ambiguity vector, expressed by the formula: ； In the formula, This represents the rover coordinate correction vector corresponding to the fixed solution; The rover coordinates of the fixed solution are obtained based on the rover coordinate correction vector corresponding to the fixed solution and the approximate coordinates of the rover, expressed by the formula: In the formula, This represents the coordinates of the fixed solution rover station.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the positioning calculation method based on BeiDou-3 satellites as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the positioning calculation method based on BeiDou-3 satellites as described in any one of claims 1 to 8.

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