GNSS multi-path error correction method based on distance correlation modeling

Abstract

The invention relates to a GNSS (Global Navigation Satellite System) multi-path error correction method based on distance correlation modeling, which comprises the following steps of: resolving GNSS original data, and extracting to obtain a satellite position set and a residual error corresponding to the set; generating a uniformly distributed satellite position set on a unit hemispherical surface, calculating a variance-covariance matrix, and constructing a multi-path delay calculation model of the set; obtaining a currently observed to-be-calibrated satellite position set on a unit spherical surface, calculating a variance-covariance matrix, and constructing a multi-path delay calculation model of the set; the observation value of the set is corrected based on multi-path delay obtained through calculation of a multi-path delay calculation model of the set; the invention relates to an error correction method for modeling GNSS multi-path distance correlation characteristics by using least square configuration and a covariance function, which is suitable for multi-path suppression in high-precision GNSS positioning.

Description

Technical Field

[0001] The present invention relates to the field of satellite positioning technology, and in particular to a GNSS (Global Navigation Satellite System) multipath error correction method based on distance correlation modeling. Background Art

[0002] Multipath is a key error source in GNSS positioning. It can cause centimeter-level delays in phase observations, and its impact is directly related to the reflective environment surrounding the station. This systematic error can significantly reduce positioning accuracy, particularly in millimeter-level high-precision applications. Existing multipath mitigation methods based on spatial autocorrelation (such as stellar filtering and hemispherical grid methods) still have significant limitations: they fail to establish a quantitative representation of spatial correlation, while their use of discretized approximations leads to a loss of continuity information. This mismatch between theoretical modeling and actual physical properties has become a major bottleneck restricting the accuracy of multipath correction. Summary of the Invention

[0003] In response to the technical problems existing in the prior art, the present invention provides a GNSS multipath error correction method based on distance correlation modeling. The error correction method utilizes least squares configuration (LSC) and covariance function to model the GNSS multipath distance correlation characteristics, which is suitable for multipath suppression in high-precision GNSS positioning (such as PPP and RTK).

[0004] According to a first aspect of the present invention, a GNSS multipath error correction method based on distance correlation modeling is provided, comprising: Step 1: Solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual ; Step 2: Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; Step 3: Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model ; Step 4: Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0005] On the basis of the above technical solution, the present invention can also make the following improvements.

[0006] Optionally, the set constructed in step 2 The calculation model of multipath delay is: ,in , , is the standard deviation of white noise, is the identity matrix.

[0007] Optionally, the set constructed in step 3 The multipath delay calculation model is: .

[0008] Optionally, the variance-covariance matrix in step 2 and step 3 is: ; in, and Represents two points in the set, represents the empirical covariance function .

[0009] Optionally, the empirical covariance function The calculation formula is: ; in, and are the areas of the two blocks on the unit sphere, for and The arc distance between and Represent points and point The multipath delay value at .

[0010] Optionally, the process of obtaining the empirical covariance function includes: Step 11: Set the arc length range on the unit sphere Divide into set intervals; Step 12, calculate the arc distance between any two points and determine the interval to which the arc belongs; Step 13: Use the calculated covariance value as the covariance corresponding to the median of each interval to construct the empirical covariance function ; Step 14: When the areas of the intervals are equal, count the number of arc distances n in each interval and calculate the covariance ; Step 15: construct the variance-covariance matrix based on the empirical covariance function, and ensure the non-singularity of the variance-covariance matrix by fitting the parameters of the analytical positive definite covariance function.

[0011] Optionally, the residual in step 1 The calculation formula is: ; in, is the variance-covariance matrix of the double-difference residuals; is the conversion matrix from single-difference residuals to double-difference residuals; is the double difference residual vector; is the regularization parameter; is the identity matrix, The number of rows is equal to The number of elements.

[0012] According to a second aspect of the present invention, there is provided a GNSS multipath error correction system based on distance correlation modeling, comprising: an original data acquisition module, a module for constructing a calculation model of the multipath delay of a standard set, a module for constructing a calculation model of the multipath delay of a set to be calibrated, and a correction calculation module; The raw data acquisition module is used to solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual ; The calculation model construction module of the multipath delay of the standard set is used to generate a uniformly distributed satellite position set on a unit hemisphere. , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; The construction module of the calculation model of the multipath delay of the set to be calibrated is used to obtain the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model ; The correction calculation module is used to calculate the Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0013] According to a third aspect of the present invention, an electronic device is provided, comprising a memory and a processor, wherein the processor is configured to implement the steps of a GNSS multipath error correction method based on distance correlation modeling when executing a computer management program stored in the memory.

[0014] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, on which a computer management program is stored. When the computer management program is executed by a processor, the steps of the GNSS multipath error correction method based on distance correlation modeling are implemented.

[0015] The present invention provides a GNSS multipath error correction method, system, electronic device, and storage medium based on distance correlation modeling, which achieves high-precision compensation by accurately modeling the spatial autocorrelation characteristics of multipath errors. An innovative distance covariance function model is constructed, and a least squares configuration estimator is used to directly calculate the multipath correction value for any spatial position, breaking through the limitations of traditional grid discretization methods. Modeling is done using uniform isotropic covariance functions such as Markov functions, which only rely on the distance between points and maintain rotational symmetry. This not only simplifies the calculation process, but also more completely preserves the spatial continuity characteristics of multipath errors. This provides a new theoretical framework and technical approach for the accurate modeling and compensation of GNSS multipath errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flowchart of GNSS multipath error correction based on distance correlation modeling provided by the present invention; Figure 2 A schematic diagram of horizontal plane reflection geometry provided by an embodiment of the present invention; Figure 3 A structural block diagram of a GNSS multipath error correction system based on distance correlation modeling provided by the present invention; Figure 4 A schematic diagram of the hardware structure of a possible electronic device provided by the present invention; Figure 5 A schematic diagram of the hardware structure of a possible computer-readable storage medium provided by the present invention. DETAILED DESCRIPTION

[0017] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0018] Figure 1 The present invention provides a flow chart of a GNSS multipath error correction method based on distance correlation modeling, such as Figure 1 As shown, the error correction method includes: Step 1: Solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual .

[0019] Step 2: Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay .

[0020] Step 3: Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model .

[0021] Step 4: Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0022] The present invention provides a GNSS multipath error correction method based on distance correlation modeling. The error correction method uses least squares configuration (LSC) and covariance function to model the GNSS multipath distance correlation characteristics. The method is suitable for multipath suppression in high-precision GNSS positioning (such as PPP and RTK).

[0023] Example 1 The embodiment 1 provided by the present invention is an embodiment of a GNSS multipath error correction method based on distance correlation modeling provided by the present invention, combined with Figure 1 It can be seen that the embodiment of the error correction method includes: Step 1: Solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual .

[0024] When multipath occurs, the signal received by the GNSS receiver is composed of the direct signal and the reflected signal. The resulting phase observation delay can be expressed by a mathematical model: (1) Where, represents phase delay; is the damping factor caused by the reflecting surface and antenna gain; Is the phase offset of the reflected signal relative to the direct signal. For a horizontal reflection surface, the phase offset It is mainly determined by the additional path length (the characteristics of the reflecting surface and the antenna phase response are secondary factors), and its expression is shown in formula (2): (2) Where, represents the additional path length; is the antenna height; is the carrier wavelength; Represents the elevation angle of the satellite at the reflection point.

[0025] The geometric relationship between the direct signal and the reflected signal is as follows: Figure 2 As shown. Due to the satellite elevation angle Over time The multipath effect will show periodic changes, and its frequency calculation formula is: (3) Obviously, the higher the antenna height, the greater the phase shift The higher the frequency of change.

[0026] The multipath effect is reflected in the residual term of GNSS data post-processing. Therefore, under the premise of ignoring other systematic errors (such as ionospheric delay, tropospheric delay, etc.), the multipath effect of the following days can be modeled and predicted using historical residual data.

[0027] Single Difference (SD) residuals are used in the baseline solution model and can be derived from Double Difference (DD) residuals. is the double difference residual vector, then the single difference residual is calculated as: (4) Where, is the variance-covariance (VC) matrix of the double-difference residuals; is the transformation matrix from single-difference residual to double-difference residual, and satisfies .matrix There is a rank deficiency problem. Therefore, The method of imposing zero-sum constraints to eliminate rank deficiency. It should be noted that the zero-sum constraint may introduce additional error effects, so although it is not an ideal method, it is a compromise solution for deriving single-difference residuals. Therefore, Equation (4) can be rewritten as: (5) Where, is the regularization parameter; is the identity matrix, whose number of rows is equal to The number of elements.

[0028] Zero-difference (ZD) residuals can be directly obtained and used for precise point positioning. Both the single-difference residuals in the baseline solution model and the zero-difference residuals in the PPP model can be considered as a superposition of multipath delay and white noise. In practical applications, the zero-difference residuals of PPP are also affected by satellite orbit errors, clock errors, and atmospheric delay errors, which can reduce the accuracy of multipath calculations.

[0029] In a possible embodiment, the residual in step 1 is The calculation formula is: .

[0030] in, is the variance-covariance matrix of the double-difference residuals; is the conversion matrix from single-difference residuals to double-difference residuals; is the double difference residual vector, ; is the regularization parameter; is the identity matrix, The number of rows is equal to The number of elements.

[0031] Step 2: Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay .

[0032] In a possible embodiment, the set constructed in step 2 The calculation model of multipath delay is: ,in , , is the standard deviation of white noise, is the identity matrix. Since the trend should be absorbed by the estimated parameters in data processing, the trend term is ignored in equation (9) and equation (10) is used instead.

[0033] Step 3: Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model .

[0034] Least Squares Collocation (LSC) can be considered a combination of least squares adjustment and least squares prediction. Assuming that the observation value consists of three parts: trend term, signal term, and noise term, the vector-matrix expression of its observation equation is: (6) Where, is the observation vector; Design matrix for trend model; is the unknown trend parameter; represents the signal vector consisting of spatially autocorrelated system errors; is a randomly distributed white noise. Assume that the other signals at the prediction point are vectors , although it is related to the signal There are spatial differences, but the two are correlated, so the solution of equation (6) and the unknown signal vector The solution is based on the minimization principle of least squares configuration: (7) Where, It is noise The variance-covariance matrix of ; It's a signal The variance-covariance matrix of . Parameters and The estimated value of can be expressed by the following formula: (8) (9) Where, Indicates measured values The VC matrix of , Indicates the prediction point signal and measuring point signals Without considering the trend, the LSC solution can be simplified to: (10) When the trend cannot be ignored, equations (8) and (9) should be used to obtain the signal.

[0035] In a possible embodiment, the set constructed in step 3 The multipath delay calculation model is: .

[0036] Although the least squares collocation method can use a variety of covariance functions, based on the modeling framework of the grid method, the present invention uses a homogeneous and isotropic covariance function. This type of covariance function shows that the covariance of any two point observations can be expressed as a distance function ,in is the distance between two points, and For all non-negative distances are defined. Assume two points and The distance is , and its covariance can be expressed as: (11) Covariance function It has the following basic properties: When the distance between two points is When , the covariance reaches its maximum value. When the distance tends to infinity, the spatial correlation between points disappears and the covariance tends to zero. Based on this property, the variance-covariance matrix of signal terms (such as multipath error) between multiple points can be constructed. If given The corresponding variance-covariance matrix can be calculated as follows: (12) Where, Represents the number of spatial points involved in the calculation. Obviously, and are equal because the distance between the two points is symmetrical. In practical applications, the covariance function is usually expressed in analytical form to avoid singularity problems in the variance-covariance matrix. Commonly used analytical functions include Gaussian function, Markov function, and Hivonen function.

[0037] In addition, when the observed data is in numerical form, the empirical covariance function (ECVF) can be calculated and expressed by numerical methods. Assume that the areas of the two blocks on the unit sphere are and , the arc distance between them is For any function on these two blocks and , the calculation formula of the empirical covariance function is as follows: (13) When the areas of the regions are uniform or approximately equal, the covariance function can be simplified to an unweighted form.

[0038] (14) In the multipath delay calculation, let 、 ,in and Represent points and point The present invention adopts equal-weight observation, so the calculation is performed using formula (14).

[0039] In a possible embodiment, the variance-covariance matrix in step 2 and step 3 is a symmetric square matrix consisting of the variance matrix as the main diagonal elements and the covariance matrix as the off-diagonal elements.

[0040] In a possible embodiment, the variance-covariance matrix is: .

[0041] in, and Represents two points in the set, and C represents the empirical covariance function , , and are the areas of the two blocks on the unit sphere, for and The arc distance between and Represent points and point The multipath delay value at .

[0042] In a possible embodiment, assuming that a set of spatial points exists, the process of obtaining the empirical covariance function includes: Step 11: Set the arc length range on the unit sphere Divide into set intervals.

[0043] Step 12: Calculate the arc distance between any two points and determine the interval to which the arc belongs.

[0044] Step 13: Use the calculated covariance value as the covariance corresponding to the median of each interval to construct the empirical covariance function .

[0045] Step 14: When the areas of the intervals are equal, count the number of arc distances n in each interval and calculate the covariance .

[0046] Step 15: construct the variance-covariance matrix based on the empirical covariance function, and ensure the non-singularity of the variance-covariance matrix by fitting the parameters of the analytical positive definite covariance function.

[0047] Step 4: Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0048] In a specific implementation, the correction method may be to subtract the multipath delay from the current observation value.

[0049] LSC is used to study and mitigate multipath delays caused by the SD residuals between stations in the baseline model and the ZD residuals in the PPP model. Multipath errors are spatially correlated and are treated as signal terms in LSC, while the residuals are considered to be a superposition of multipath errors and white noise.

[0050] Since satellite positions can be mapped to the unit sphere, their spatial positions only need to be expressed by azimuth and elevation. Three position sets are defined on the unit hemisphere: Satellite position sets in GNSS data post-processing for multipath modeling , represents the reference position set of the multipath model , and the new set of observed satellite positions to be calibrated .

[0051] First, the GNSS multipath modeling data is post-processed, the GNSS raw data is solved, and the satellite position set is extracted and the corresponding residual. Then, by setting The residuals of the multipath spatial correlation model are used to establish the multipath spatial correlation model. Furthermore, the LSC method is used to calculate the reference set Finally, based on the set The model predicts the new observation set multipath error and correct it.

[0052] It should be noted that although it is possible to directly pass the collection The residuals of the set are calculated using the LSC method Multipath delay (without going through the collection ), but this study still introduces the set This is mainly due to the following two reasons: (1) Model expression completeness: collection The points are evenly distributed on the unit hemisphere, which can more comprehensively characterize the spatial distribution characteristics of multipath errors. If the point spacing is small enough, the multipath model can be completely represented by The value representation of the point.

[0053] (2) Computational efficiency optimization: When the set When the amount of data increases (for example, when using multi-day residual modeling), it is easier to calculate The multipath of the computation load will increase linearly. Indirect calculation , the amount of calculation can be kept stable, because The number of points does not change as historical data increases.

[0054] The present invention provides a GNSS multipath error correction method based on distance correlation modeling. The least squares configuration method based on the distance correlation characteristics realizes high-precision compensation by accurately modeling the spatial autocorrelation characteristics of the multipath error. This method innovatively constructs a distance covariance function model and uses a least squares configuration estimator to directly calculate the multipath correction amount at any spatial position, breaking through the limitations of the traditional grid discretization method. The modeling adopts a uniform isotropic covariance function such as the Markov function, which only depends on the distance between points and maintains rotational symmetry, which not only simplifies the calculation process, but also more completely preserves the spatial continuity characteristics of the multipath error. This method provides a new theoretical framework and technical approach for the accurate modeling and compensation of GNSS multipath errors. Specifically: (1) Continuous spatial modeling: The Markov covariance function is introduced for the first time to construct a distance autocorrelation model of multipath error. Its isotropy and rotational symmetry characteristics strictly conform to the physical propagation laws of the multipath effect, solving the problem of spatial continuity loss caused by discretization partitioning in traditional grid methods.

[0055] (2) Global analytical calculation: Based on the analytical expression of the covariance function, the direct and accurate calculation of the multipath correction at any position in the hemispherical space is realized, breaking through the inherent limitation of the traditional method that relies on sky grid division, and significantly improving the computational efficiency and model adaptability.

[0056] (3) Dynamic parameter optimization: An innovative parameter adaptation mechanism is proposed, which dynamically fits key model parameters through the empirical covariance function, enabling the system to autonomously adapt to different observation environments, greatly enhancing the robustness and practicality of the method.

[0057] Example 2 Embodiment 2 provided by the present invention is an embodiment of a GNSS multipath error correction system based on distance correlation modeling provided by the present invention. Figure 3 A structural diagram of a GNSS multipath error correction system based on distance correlation modeling provided by an embodiment of the present invention, combined with Figure 3 It can be seen that the embodiment of the error correction system includes: an original data acquisition module, a calculation model construction module for the multipath delay of a standard set, a calculation model construction module for the multipath delay of a set to be calibrated, and a correction calculation module.

[0058] The raw data acquisition module is used to solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual .

[0059] The calculation model construction module of the multipath delay of the standard set is used to generate a uniformly distributed satellite position set on a unit hemisphere. , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay .

[0060] The construction module of the calculation model of the multipath delay of the set to be calibrated is used to obtain the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model .

[0061] The correction calculation module is used to calculate the Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0062] In a specific implementation, the correction method may be to subtract the multipath delay from the current observation value.

[0063] It can be understood that the GNSS multipath error correction system based on distance correlation modeling provided by the present invention corresponds to the GNSS multipath error correction method based on distance correlation modeling provided in the aforementioned embodiments. The relevant technical features of the GNSS multipath error correction system based on distance correlation modeling can refer to the relevant technical features of the GNSS multipath error correction method based on distance correlation modeling, and will not be repeated here.

[0064] See also Figure 4 , Figure 4 Schematic diagram of an embodiment of an electronic device provided by an embodiment of the present invention. Figure 4 As shown, an embodiment of the present invention provides an electronic device, including a memory 1310, a processor 1320, and a computer program 1311 stored in the memory 1310 and executable on the processor 1320. When the processor 1320 executes the computer program 1311, the following steps are implemented: solving the GNSS raw data, extracting a satellite position set and the collection The corresponding residual ; Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0065] See also Figure 5 , Figure 5 Schematic diagram of an embodiment of a computer-readable storage medium provided by the present invention. Figure 5 As shown, this embodiment provides a computer-readable storage medium 1400 on which a computer program 1411 is stored. When the computer program 1411 is executed by a processor, the following steps are implemented: solving the GNSS raw data and extracting a satellite position set. and the collection The corresponding residual ; Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

[0066] This invention is suitable for high-precision GNSS positioning in complex urban environments, especially in scenarios where GNSS receivers are subject to signal obstruction or severe multipath interference. Its main applications include: (1) Urban high-precision navigation and autonomous driving: In urban environments, GNSS signals are affected by reflectors such as buildings and bridges, resulting in severe multipath effects, which can lead to positioning errors of up to meters. Applications such as autonomous driving and drone delivery require sub-meter or even centimeter-level accuracy. Using the method of the present invention, a multipath spatial autocorrelation model is established using historical residual data to predict and correct the multipath errors of the current observation in real time, significantly improving positioning reliability.

[0067] (2) Geological disaster monitoring and infrastructure deformation analysis: Millimeter-level deformation monitoring of structures such as dams, bridges, and slopes requires long-term, stable, and high-precision GNSS data. However, multipath effects can mask the true deformation signal. At fixed monitoring stations, the spatial correlation of multipath is modeled using long-term residual data, separating multipath errors from true deformation signals and improving monitoring accuracy.

[0068] (3) UAV and robot navigation: Applicable to UAV urban mapping, logistics distribution and autonomous mobile robots, enabling them to achieve high-precision positioning in areas with severe satellite signal interference (such as urban canyons and industrial parks), thereby improving the reliability of mission execution.

[0069] The present invention can be widely used in fields that require high-precision, low-cost positioning, and improve the adaptability and practicality of GNSS technology in complex environments.

[0070] The embodiments of the present invention provide a GNSS multipath error correction method, system, electronic device, and storage medium based on distance correlation modeling, which achieve high-precision compensation by accurately modeling the spatial autocorrelation characteristics of multipath errors. An innovative distance covariance function model is constructed, and a least squares configuration estimator is used to directly calculate the multipath correction value at any spatial position, breaking through the limitations of traditional grid discretization methods. Modeling is done using uniform isotropic covariance functions such as Markov functions, which only rely on the distance between points and maintain rotational symmetry. This not only simplifies the calculation process, but also more completely preserves the spatial continuity characteristics of multipath errors. This provides a new theoretical framework and technical approach for the accurate modeling and compensation of GNSS multipath errors.

[0071] It should be noted that, in the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0072] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0073] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0074] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0075] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0076] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0077] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A GNSS multipath error correction method based on distance correlation modeling, characterized in that: The correction method comprises: Step 1: Solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual ; Step 2: Generate a uniformly distributed set of satellite positions on the unit hemisphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; Step 3: Get the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model ; Step 4: Based on the set Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

2. The error correction method according to claim 1, wherein: The set constructed in step 2 The calculation model of multipath delay is: ,in , , is the standard deviation of white noise, is the identity matrix.

3. The error correction method according to claim 1, wherein: The set constructed in step 3 The multipath delay calculation model is: .

4. The error correction method according to claim 1, wherein: The variance-covariance matrix in step 2 and step 3 is: ; in, and Represents two points in the set, represents the empirical covariance function .

5. The error correction method according to claim 4, characterized in that: The empirical covariance function The calculation formula is: ; in, and are the areas of the two blocks on the unit sphere, for and The arc distance between and Represent points and point The multipath delay value at .

6. The error correction method according to claim 4, wherein: The process of obtaining the empirical covariance function includes: Step 11: Set the arc length range on the unit sphere Divide into set intervals; Step 12, calculate the arc distance between any two points and determine the interval to which the arc belongs; Step 13: Use the calculated covariance value as the covariance corresponding to the median of each interval to construct the empirical covariance function ; Step 14: When the areas of the intervals are equal, count the number of arc distances n in each interval and calculate the covariance ; Step 15: construct the variance-covariance matrix based on the empirical covariance function, and ensure the non-singularity of the variance-covariance matrix by fitting the parameters of the analytical positive definite covariance function.

7. The error correction method according to claim 1, wherein: The residual in step 1 The calculation formula is: ； in, is the variance-covariance matrix of the double-difference residuals; is the conversion matrix from single-difference residuals to double-difference residuals; is the double difference residual vector; is the regularization parameter; is the identity matrix, The number of rows is equal to The number of elements.

8. A GNSS multipath error correction system based on distance correlation modeling, characterized in that: The error correction system includes: an original data acquisition module, a calculation model construction module for the multipath delay of a standard set, a calculation model construction module for the multipath delay of a set to be calibrated, and a correction calculation module; The raw data acquisition module is used to solve the GNSS raw data and extract the satellite position set and the collection The corresponding residual ; The calculation model construction module of the multipath delay of the standard set is used to generate a uniformly distributed satellite position set on a unit hemisphere. , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix and the residual Construct the collection Calculation model of multipath delay ; The construction module of the calculation model of the multipath delay of the set to be calibrated is used to obtain the set of satellite positions to be calibrated currently observed on the unit sphere , calculate the set The variance-covariance matrix of each point in and the collection With the collection The variance-covariance matrix of each point between , based on the matrix ,matrix And the calculation model Construct the collection Multipath delay calculation model ; The correction calculation module is used to calculate the Multipath delay calculation model The calculated multipath delay is The observed values ​​are corrected.

9. An electronic device, characterized in that: The method comprises a memory and a processor, wherein the processor is configured to implement the steps of the GNSS multipath error correction method based on distance correlation modeling as described in any one of claims 1 to 7 when executing a computer management program stored in the memory.

10. A computer-readable storage medium, characterized in that A computer management program is stored thereon, and when the computer management program is executed by the processor, the steps of the GNSS multipath error correction method based on distance correlation modeling as described in any one of claims 1 to 7 are implemented.

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