Semi-spherical adaptive grid division method for modeling multi-path error of MHGM

Abstract

The application provides a semi-sphere adaptive grid division method for MHGM multi-path error modeling, comprising the following steps: obtaining a high-resolution multi-path error prior model as prior information by using non-difference residuals, and obtaining the spatial distribution characteristics of the multi-path error at a survey station; establishing a fixed grid division MHGM model on the survey station, extracting an AMR initial grid, obtaining the prior model value in the grid, setting to-be-estimated parameters at the corner points of the grid, and obtaining the relationship between the prior model value and the coordinates by using a bilinear interpolation method; setting the grid corner points as a to-be-estimated parameter matrix, the corresponding bilinear interpolation coefficient matrix as a design matrix, and the prior model value as an observation value matrix, so as to obtain the estimated value of the parameter matrix and the corresponding residual vector; traversing the residual vector, and considering that the grid can be divided when the absolute value is greater than the corresponding threshold value; stopping the division when the preset condition is met for any grid, or taking the grid as four congruent grids; and outputting the semi-sphere adaptive grid division result after the division is completed.

Description

Technical Field

[0001] This invention belongs to the field of global satellite navigation systems, and specifically relates to an adaptive grid partitioning method for the semi-celestial spatial domain used for multi-path error modeling of MHGM (multi-point hemispherical grid model). Background Technology

[0002] Higher demands have been placed on the accuracy of GNSS navigation and positioning. In recent years, with the research of various scholars on high-precision GNSS data processing methods, the error terms in most GNSS precision data processing have been significantly reduced. However, because multipath error is highly correlated with the station environment, it is difficult to eliminate through differential algorithms and lacks a suitable theoretical model for description. Multipath error has become one of the main error sources affecting high-precision GNSS data processing, and it also limits the application of GNSS in many scenarios.

[0003] In order to weaken the influence of multipath effect, the following measures can generally be taken: select a station location with good observation environment and avoid obstacles, reflectors and radiation sources as much as possible; use special hardware equipment, such as chokes and diameter reduction plates [1]. In addition, multipath error can be weakened by data processing algorithms. The sidereal filtering method in the time domain [2-3], the lookup table, multipath stacking map and multipath hemispherical map in the spatial domain are currently widely used. These methods model multipath error in the spatial domain. The theoretical basis is that the multipath error caused by different satellite signals of the same frequency depends only on the position of the satellite in the sky and is not related to the observation time and the specific satellite. By fitting the trend of multipath error in the hemispherical grid, Wang (2019) further proposed a multipath hemispherical map based on trend-surface analysis (T-MHM) [4].

[0004] In addition, Wang (2020) used the double-difference residuals after ambiguity fixation to establish a multi-point hemispherical grid model (MHGM) that can fuse data from multiple systems [5]. This method uses the double-difference observation residuals of the fixed ambiguity period as known quantities, establishes a hemispherical grid model of multipath error at each station, parameterizes and solves the grid points, and finally obtains the prior model of multipath error for each station. This method uses least squares to smooth the multipath error effect in the direction of adjacent signals and adds additional constraints to ensure the stability of the fitting results, further improving the accuracy of multipath error modeling. At the same time, the use of double-difference residuals avoids the influence of other non-multipath errors in the modeling process, and there is no need to perform "zero mean" constraint mapping processing on the double-difference residuals. Therefore, it can obtain a better multipath error correction effect than existing modeling methods. However, when establishing the MHGM model, since the hemispherical grid is first established with the antenna phase center of each station as the origin, the hemispherical grid is divided into grids according to the elevation angle and azimuth angle. Then, the hemisphere is divided into grids at certain intervals, and the size of the grid interval determines the density of the hemisphere grid. At the same time, the denser the grid division, the more detailed the description of multipath error by MHGM, and vice versa. However, dividing the grid points at a fixed resolution will bring more estimation parameters. As the number of stations increases, MHGM will have difficulty coping with the computational resource consumption caused by the estimation of more parameters. Moreover, the impact of multipath error on different stations is not the same. It is unreasonable to use the same division scheme for all stations, which further exacerbates the waste of computational resources in the model estimation process. These have become the bottleneck problems of MHGM when applied to a large number of stations[6].

[0005] See Figure 1 The specific implementation method for hemispherical grid division in MHGM modeling is as follows. The starting and ending range of the hemispherical azimuth angle for each station is 0° to 360°, the minimum elevation angle is set to E0, and the maximum elevation angle is set to E1. A grid point parameter is also set in the zenith direction. The interval for hemispherical division can be set as d. e d a (Under normal circumstances, the same), d e and d a The magnitude of the value determines the density of the hemispherical grid. Smaller grid intervals result in more parameters to be estimated at each grid point, consuming more computational resources, but also leading to a higher level of model refinement. The following relationship exists between the hemispherical grid settings and the number of MHGM parameters N to be estimated for a single station:

[0006]

[0007] In the process of solving the MHGM model, considering the cutoff elevation angle setting during GNSS data processing and the smaller impact of multipath error when the elevation angle is high, while also taking into account the computational resource consumption during parameter estimation, the semi-celestial grid division parameters are typically set as follows: E0 = 5°, E1 = 85°, d e =d a =2°, meaning the grid resolution is 2°×2°. Combining with formula (1), the number of grid point parameters N to be estimated for a single station is 7381. As the number of stations involved in the calculation increases, this fixed-division MHGM model faces an excessive number of parameters to be estimated, leading to an exponential increase in computational resource consumption. This affects the computational efficiency of multipath error modeling, making it unsuitable for applications such as overall multipath error modeling with multiple stations. The table below shows the memory consumption during parameter estimation at different resolutions as the number of stations increases. It is evident that the memory consumption during MHGM parameter estimation increases significantly with both resolution and the number of stations.

[0008] Table 1 Computational resource consumption for different numbers of stations at different resolutions

[0009]

[0010]

[0011] The key to reducing the number of grid divisions in the MHGM method without affecting the improvement effect of the multipath model is to reduce the computational resource consumption of the MHGM method and enhance its practical application value in large-scale GNSS observation networks.

[0012] This invention addresses the shortcomings of existing technologies (such as patent documents CN109541647A and CN114488228A) by further improving the grid partitioning method: the original MHGM method's medium-interval grid partitioning consumes a lot of memory resources and therefore needs adjustment. This invention proposes an adaptive unequal-interval grid partitioning scheme. Based on the specific observation environment, the grid partitioning scheme is adaptively adjusted using a prior model. If the observation environment is good, it is not necessary to make the grid partitioning fine; if the observation environment is poor, it can be further refined. This reduces the number of unnecessary grid partitions and lowers memory usage.

[0013] References

[0014] [1] Fan Xiaoyan, Zhou Qian. A review of research on multipath effect in GPS measurement [J]. Chinese Journal of Engineering Geophysics, 2010, 7(03): 382-386

[0015] [2]Agnew DC,Larson K M.Finding the repeat times of the GPSconstellation[J].GPS solutions,2007,11(1):71-76

[0016] [3] Chen Dezhong, Ye Shirong, Liu Yanyan, et al. Application analysis of GPS multipath error based on observation range [J]. Journal of Wuhan University (Information Science Edition), 2014, 39(2):147-151

[0017] [4]Wang Z,Chen W,Dong D,et al.Multipath mitigation based on trendsurface analysis applied to dual-antenna receiver with common clock[J].GPSSolutions,2019,23(4):1-15

[0018] [5]Wang Y, Zou

[0019] [6]Tang W, Wang Y, Zou X, et al.Visualization of GNSS multipath effects and its potential application in IGS data processing[J]. Journal of Geodesy, 2021,95(9):103.

[0020] [7]Moore M, Watson C, King M, et al. Empirical modeling of site-specific errors in continuous GPS data[J]. Journal of Geodesy, 2014,88:887-900. Summary of the Invention

[0021] To address the shortcomings of the existing technologies, this invention proposes a semi-celestial adaptive grid partitioning method for MHGM multipath error modeling.

[0022] To achieve the above objectives, the technical solution proposed in this invention is a hemispherical adaptive grid partitioning method for MHGM multipath error modeling, comprising the following steps:

[0023] Step 1: Use non-differential residuals to obtain a high-resolution multipath error prior model as prior information to obtain the spatial distribution characteristics of multipath errors at the station.

[0024] Step 2: Establish a fixed grid division MHGM model on the station, extract the initial grid of AMR, and set the corresponding grid as a Class I grid;

[0025] Step 3: Traverse each Level I grid and determine whether the grid needs to be further subdivided using an adaptive criterion. This is achieved through the following processing steps:

[0026] Obtain the prior model value P contained within the grid, and the coordinates corresponding to that model value within the grid.

[0027] The parameters to be estimated, Q1, Q2, Q3 and Q4, are set at the four corner points of the grid. Based on their coordinates in the grid, the relationship between them and the prior model value P is obtained by bilinear interpolation.

[0028] The values ​​Q at the four corner points of the grid are set as the parameter matrix X to be estimated, the corresponding bilinear interpolation coefficient matrix is ​​the design matrix A, and the prior model values ​​P form the observation matrix Y. The estimated values ​​of the parameter matrix X are obtained according to the least squares principle. and the corresponding residual vector v;

[0029] Traverse the residual vector v. If there is a case in the residual vector v where the absolute value is greater than the corresponding threshold k, then the level I grid is considered to be further divided into level II grids.

[0030] Step 4: For any grid, if the preset conditions are met, stop the grid division and proceed to Step 6; otherwise, proceed to Step 5.

[0031] Step 5: If adaptive meshing is required, repeat steps 3-4. Take the midpoint of the elevation angle and azimuth angle of the Level I grid and divide it into four congruent Level II grids. Continue in this manner to divide the grid into multiple levels.

[0032] Step 6: After the division is completed, output the semi-celestial adaptive grid division result.

[0033] Moreover, the multipath error prior model adopts the ESM model.

[0034] Furthermore, the implementation of step 1 includes the following steps:

[0035] Step 1.1: Establish a planar polar coordinate system with the antenna phase center as the center, and divide the coordinate system into grids at fixed intervals in the elevation and azimuth directions;

[0036] Step 1.2: For any station participating in the solution, distribute the residuals of the undifferentiated phase observations after fixing the ambiguity of each satellite to the corresponding grid according to the azimuth and elevation angles;

[0037] Step 1.3: Take the average value of the residuals in each grid to obtain the multipath error prior model of the station.

[0038] Furthermore, the method for obtaining the relationship between the bilinear interpolation and the prior model value P is as follows:

[0039]

[0040] The coordinates of the four corner points of Q1, Q2, Q3 and Q4 are denoted as (x0, y0), (x1, y0), (x1, y1) and (x0, y1) respectively.

[0041] Furthermore, if any of the following conditions are met, the preset conditions are considered satisfied, the division stops, and the process proceeds to step 6; otherwise, the process proceeds to step 5.

[0042] (a) The number of prior model values ​​P contained in the grid is less than the corresponding preset threshold n0;

[0043] (b) In the residual vector v after least squares estimation within the grid, the absolute value of all elements is less than or equal to k;

[0044] (c) The grid has been divided to the set minimum grid size.

[0045] Furthermore, it is used to adaptively adjust the fineness of the semi-celestial grid in different regions according to the actual distribution of multipath error effects around the station, thereby reducing the number of grid point parameters to be estimated in the MHGM method, reducing the computational resource consumption during MHGM modeling, and realizing the correction of multipath effect errors in the observations.

[0046] On the other hand, the present invention also provides a semi-celestial adaptive grid partitioning system for MHGM multipath error modeling, which is used to implement the semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described above.

[0047] Moreover, it includes the following modules,

[0048] The first module is used to obtain a high-resolution multipath error prior model as prior information by using non-differential residuals to obtain the spatial distribution characteristics of multipath errors at the station.

[0049] The second module is used to establish a fixed grid division MHGM model on the station, extract the initial grid of AMR, and set the corresponding grid as a Class I grid.

[0050] The third module iterates through each Level I grid, using adaptive criteria to determine whether the grid needs further subdivision. This is achieved through the following processing steps.

[0051] Obtain the prior model value P contained within the grid, and the coordinates corresponding to that model value within the grid.

[0052] The parameters to be estimated, Q1, Q2, Q3 and Q4, are set at the four corner points of the grid. Based on their coordinates in the grid, the relationship between them and the prior model value P is obtained by bilinear interpolation.

[0053] The values ​​Q at the four corner points of the grid are set as the parameter matrix X to be estimated, the corresponding bilinear interpolation coefficient matrix is ​​the design matrix A, and the prior model values ​​P form the observation matrix Y. The estimated values ​​of the parameter matrix X are obtained according to the least squares principle. and the corresponding residual vector v;

[0054] Traverse the residual vector v. If there is a case in the residual vector v where the absolute value is greater than the corresponding threshold k, then the level I grid is considered to be further divided into level II grids.

[0055] The fourth module is used to stop mesh generation and command the sixth module to work when preset conditions are met for any mesh; otherwise, it commands the fifth module to work.

[0056] The fifth module is used to repeat the work of the third and fourth modules when adaptive meshing is required. It takes the midpoint of the level I grid in the elevation and azimuth directions and divides it into four congruent level II grids, and so on, to divide the multi-level grid.

[0057] The sixth module is used to output the semi-celestial adaptive grid division results after the division is completed.

[0058] Alternatively, it may include a processor and a memory, the memory being used to store program instructions, and the processor being used to call the stored instructions in the memory to execute a semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described above.

[0059] Alternatively, it may include a readable storage medium storing a computer program that, when executed, implements a semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described above.

[0060] This invention can significantly reduce the number of grid point parameters to be estimated, effectively reducing the consumption of computational resources such as memory, CPU, and time in the multipath error modeling process of the MHGM method.

[0061] The present invention is simple and convenient to implement, highly practical, and solves the problems of low practicality and inconvenience in actual application of related technologies. It can improve user experience and has significant market value. Attached Figure Description

[0062] Figure 1 A diagram illustrating the equal-interval grid division of the hemispherical sphere in existing technologies;

[0063] Figure 2 This is a schematic diagram of adaptive grid partitioning implemented using the AMR clustering method according to an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of the prior model values ​​in an embodiment of the present invention, wherein (a) represents the distribution of the prior model values ​​in a certain level of grid; and (b) represents the prior model value P at any point in the grid.

[0065] Figure 4 This is a flowchart of the hemispherical adaptive grid partitioning process based on AMR clustering according to an embodiment of the present invention.

[0066] Figure 5 This is a schematic diagram showing the distribution of monitoring stations as sources of experimental data in an embodiment of the present invention.

[0067] Figure 6 This is a schematic diagram of the ESM model at each station in an embodiment of the present invention, wherein each part provides the ESM modeling result model at 7 stations.

[0068] Figure 7 This is a schematic diagram of adaptive grid division according to an embodiment of the present invention, including the number of MHGM parameters on station 0052 after adaptive division and the corresponding adaptive grid division scheme when the threshold k is 0.1cm, 0.5cm and 0.9cm respectively.

[0069] Figure 8 This is a schematic diagram showing the number of parameters to be estimated in the MHGM model at each station under different k values ​​in an embodiment of the present invention.

[0070] Figure 9 The adaptive MHGM models for stations SEP1 and K708 in this embodiment of the invention are shown below. From top to bottom, they are the MHGM models obtained with a fixed resolution of 2°×2° and adaptive parameter k values ​​of 0.1cm, 0.5cm, and 0.9cm, respectively. Detailed Implementation

[0071] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0072] Existing traditional methods utilize unequal residuals for multipath modeling, resulting in low memory consumption and fast computation. However, this approach is inherently flawed because the obtained unequal residuals are not necessarily all multipath errors. For example, they may contain orbital errors, clock errors, or baseline errors when mapping double-difference residuals to unequal residuals. Therefore, while the modeling is effective, its accuracy is not optimal. This invention breaks with convention by using the somewhat inaccurate unequal residual modeling results as a priori model for grid partitioning, adaptively partitioning the grid, and then using the MHGM method to model multipath errors through double-difference observation residuals.

[0073] To address the problem of excessive computational resource consumption (memory, CPU, and time) in multi-station overall modeling of GNSS multipath error due to the large number of grid point parameters when using the MHGM method, this invention proposes an adaptive mesh refinement (AMR) clustering method for adaptive grid division of the hemispherical sphere. By setting appropriate adaptive criteria, the prior distribution information of multipath error effects in the spatial domain at the station is utilized. Unequal interval resolution is used to merge regions with small changes in multipath error influence and to finely divide regions with large changes in multipath error influence, thereby reducing the number of grid point parameters to be estimated and lowering the computational resource consumption in the MHGM modeling process. The prior distribution information of multipath error effects in the spatial domain at the station is obtained using existing multipath error correction models based on non-differential residuals (e.g., ESM) (Moore et al. 2014). Although the accuracy of such models is lower than MHGM, the model building process is relatively simpler and the computational resource consumption is lower.

[0074] Example 1

[0075] See Figure 4 The hemispherical spatial domain adaptive grid partitioning method for MHGM multipath error modeling provided in this embodiment of the invention specifically includes the following steps:

[0076] Step 1: Use non-differential residuals to obtain a high-resolution multipath error prior model (e.g., ESM) as prior information to obtain the spatial distribution characteristics of multipath errors at the station (Moore et al. 2014).

[0077] In practice, a multipath error prior model can be selected as prior information as needed, with the preferred recommendation being the Empirical Site Model (ESM).

[0078] Step 1.1: Establish a planar polar coordinate system with the antenna phase center as the center, and divide the coordinate system into grids at fixed intervals in the elevation and azimuth directions;

[0079] Step 1.2: For any station participating in the solution, distribute the residuals of the undifferentiated phase observations after fixing the ambiguity of each satellite to the corresponding grid according to the azimuth and elevation angles;

[0080] Step 1.3: Take the average value of the residuals in each grid to obtain the multipath error prior model of the station.

[0081] Step 2: Establish a fixed grid division MHGM model on the station, that is, use a larger grid division interval, still divide the hemisphere with a fixed interval, extract the initial grid of AMR, and set the corresponding grid as a level I grid. The level I grid is the initial division, and the grid interval value is relatively large.

[0082] Step 3: Traverse each Level I grid and determine whether the grid needs to be further subdivided using an adaptive criterion; the implementation includes the following processing.

[0083] Step 3.1: Obtain the ESM prior model value P contained in the grid, and the coordinates (x,y) of the model value within the grid;

[0084] The specific extraction of the ESM prior model value P is based on existing technologies and will not be elaborated upon in this invention: Moore et al. 2014, ESM. When using other multipath error prior models, the corresponding values ​​can also be extracted.

[0085] Step 3.2: Set the parameters to be estimated Q1, Q2, Q3 and Q4 at the four corner points of the grid. Based on their coordinates in the grid, use bilinear interpolation to obtain the relationship with the prior model value P.

[0086]

[0087] See Figure 3 The coordinates of the four corner points of Q1, Q2, Q3 and Q4 are denoted as (x0, y0), (x1, y0), (x1, y1) and (x0, y1) respectively. Part (a) is the distribution of the prior model values ​​in a certain level of grid; part (b) is the prior model value P of any point in the grid.

[0088] Step 3.3: Set the values ​​Q of the four corner points of the grid as the parameter matrix to be estimated, the corresponding bilinear interpolation coefficient matrix as the design matrix A, and the prior model values ​​P to form the observation matrix Y. According to the least squares principle, the estimated values ​​of the parameter matrix X can be obtained.

[0089]

[0090] The corresponding residual vector is:

[0091]

[0092] Step 3.4: Traverse the residual vector v. If there is a case in the residual vector v where the absolute value is greater than the corresponding threshold k, then the level I grid is considered to be further divided into level II grids.

[0093] In practice, a threshold k for the maximum allowable residual observation can be preset as needed. If the maximum residual within the grid exceeds this threshold, it indicates significant inconsistency in the multipath error effects in different directions within the grid, thus requiring further refinement of the grid.

[0094] Step 4: For any grid, if one of the following conditions is met, the meshing can be stopped and proceed to step 6; otherwise, proceed to step 5.

[0095] (a) The number of prior model values ​​P contained in the grid is less than the corresponding preset threshold n0; in specific implementation, n0 can be taken as an empirical value, and it is recommended to take a preferred value of n0. Where d is the grid resolution;

[0096] (b) In the residual vector v after least squares estimation within the grid, the absolute value of all elements is less than or equal to k;

[0097] (c) The grid has been divided to the set minimum grid size.

[0098] Step 5: If adaptive meshing is required, repeat steps 3-4. Take the midpoint of the Level I grid in the elevation and azimuth directions, and divide it into four congruent Level II grids. Continue this process to create multi-level grids. Figure 2 );

[0099] Step 6, after the division is complete, the final grid only contains parent classes and no child classes (e.g., Figure 2 Medium grids (grid 2-5, grid 6, etc.) are components of adaptive grid generation. The MHGM model sets an estimated parameter at each grid point after generation (e.g., at the four vertices corresponding to a square), so the more grids there are, the more estimated parameters there are at each grid point.

[0100] Compared to the fixed-interval grid division mode, for regions where multipath error changes are not significant, the adaptive grid division result obtained by AMR clustering can avoid the phenomenon of too many grid points in the fixed division mode, reduce the number of parameters to be estimated by the MHGM method, and solve the problem of computational resource consumption in multi-station MHGM model estimation. At the same time, it can achieve a more detailed parameterized description for regions where multipath error changes are significant, and finally realize adaptive dynamic grid division modeling.

[0101] Example 2

[0102] Based on the hemispherical spatial domain adaptive grid partitioning method for MHGM multipath error modeling provided in Example 1, the following steps are further performed to correct the error caused by multipath effects in the observations:

[0103] Step 7: Using the obtained double-difference observation residuals as observations, construct the normal equations corresponding to the parameters of the semi-sky grid point model, specifically including:

[0104] Step 7.1: Using the residual information of the double-difference observations corresponding to the fixed time period of ambiguity, and based on the elevation angle and azimuth angle of satellites j and k at stations m and n in the record, map the residual of this data record to the half-sky grid of the two stations involved.

[0105] Step 7.2: Set a parameter to be estimated at each grid point obtained after adaptive grid division in “Example 1”, and use the observation equation from step 7.1 as the observation equation. Construct the normal equation using the residuals of double-difference observations between satellites at different stations over a period of time.

[0106] Step 7.3: Based on the normal equations obtained in Step 7.2, if the data records are insufficient, some grid point parameters to be estimated may not be involved in the observation equations in Step 7.2. In this case, a rank deficiency will inevitably occur when solving the normal equations. To solve this problem and to ensure the rationality of solving the grid point parameters, additional constraints need to be added to the grid point parameters. Considering that the numerical values ​​of multipaths have a certain range, the size of the grid point parameters can be constrained first.

[0107] Step 7.4: While adding constraints to the size of the grid point parameters, considering that the grid point parameters of the multi-path hemispherical grid point model established in the same environment will not theoretically undergo too many abrupt changes, constraints are imposed on the variation values ​​between grid point parameters (including constraints in the longitude and latitude directions).

[0108] Step 8: Obtain the normal equations, solve for the model parameters of the half-day spherical grid points at each station, and use the model to correct the errors caused by multipath effects in subsequent observations.

[0109] Compared with existing technologies, the advantages and technical effects of this invention are as follows:

[0110] 1. The MHGM method using the fixed-interval grid division mode does not fully consider the spatial distribution characteristics of the multipath error effect around the station. In areas where the multipath effect changes slowly, there is over-division of grids and too many grid point parameter estimation problems.

[0111] 2. This invention fully utilizes the superior performance of MHGM compared to ESM in multipath error modeling, while ESM is faster than MHGM in modeling, and effectively reduces the consumption of computational resources such as memory, CPU, and time when using the MHGM method.

[0112] For ease of implementation and reference, the following supporting measured data analysis results are provided:

[0113] 1) Experimental data and solution strategy

[0114] To verify the effectiveness of this method in multi-station scenarios, seven stations were established in the experiment. The locations of these seven stations are distributed as follows: Figure 5 As shown. Five of the seven stations are located on the roof of building A, and two are located on the roof of building B. The straight-line distance between buildings A and B is approximately 310 meters.

[0115] Table 2 Station Configuration Information

[0116]

[0117] The specific configuration information of the above stations is shown in the table above. Two metal baffles were installed in the northwest and southeast directions of station SEP1 to simulate strong multipath interference. Stations SEP2 and SEP3 are located on a smooth, fixed platform. Station UB4B is surrounded by significant building obstruction and reflection. The remaining stations are in relatively normal observation environments. During the experiment, 14 days of data were collected from day 015 to day 028 of 2021, including data from GPS, Galileo, and BDS. The L1, E1, and B1I frequencies were used for data processing and modeling, respectively. The first 10 days were used to establish a multipath error correction model, and the last 4 days were used to verify the effectiveness of the model correction and evaluate the improvement effects on various indicators such as observation residuals and positioning results under different schemes.

[0118] Based on the known station coordinates, the station coordinates are fixed during data processing. Using PANDA software, the residual values ​​of each satellite at each station after ambiguity fixation can be obtained. Since the baselines between stations are short, these residual values ​​can effectively reflect the multipath error interference experienced by each station. A polar coordinate system is established with the antenna phase center of each station as the origin. A grid with a resolution of 0.5°×0.5° is established in the elevation and azimuth directions. The non-differential residuals of each satellite at each station are indexed into the grid corresponding to that satellite according to the elevation and azimuth angles. After all non-differential residuals have been allocated, the entire grid is traversed, and the average value of the accumulated non-differential residuals within each grid is taken, which can further eliminate the influence of noise on the residual values ​​within the grid. After obtaining the single-day ESM models for each station from 015 to 024 through the above steps, the single-day models can be further superimposed to obtain the final ESM prior models for each station. Figure 6 The model values ​​at each station are visualized, with each section providing the ESM modeling results for the seven stations.

[0119] from Figure 6 As can be seen, except for SEP1 and UB4B stations, the ESM model values ​​of the other stations are mostly close to zero. 2) The adaptively gridded MHGM model is established, and the values ​​between adjacent grids are relatively consistent, with interference only present in a small area at low elevation angles. Due to the influence of the baffle, SEP1 station has significant multipath error interference in the azimuth angles of 75°–150° and 250°–325°, and this disturbance area is also relatively consistent with the installation azimuth of the baffle. UB4B station has multipath error interference caused by surrounding buildings, with significant disturbance in the azimuth angle range of 240°–320°, and also some blank areas caused by signal obstruction. The visualization model results of each station show that the ESM model can reflect the multipath error interference areas present at the station well. The ESM model can be used as a clustering dataset (prior distribution information of the spatial domain at the station) to adaptively divide the MHGM model grid at the station.

[0120] Based on the 0.5°×0.5° ESM model at each station, and combined with the adaptive grid partitioning method described in this invention, the MHGM model at each station can be further established. In the experiments presented in this paper, the semi-celestial grid partitioning parameters are set as follows: B0 = 5°, B1 = 85°. Three levels of grids, I, II, and III, are defined for the MHGM model, with level I grids having a resolution of 8°×8°, level II grids having a resolution of 4°×4°, and level III grids having a resolution of 2°×2°. When performing adaptive grid partitioning, for any level of grid, if its resolution is d×d, then to meet the requirements of least squares parameter estimation, the prior model value density threshold n0 of the ESM is set as follows:

[0121]

[0122] n0 is the minimum threshold that, assuming an average of one prior observation per grid cell in an ESM grid with a resolution of 0.5° × 0.5°, the grid must contain at least 64 ESM prior model values. Otherwise, the grid with too few prior model values ​​is classified as a low-density grid and will not be further subdivided.

[0123] As can be seen from the above formula, the decision threshold k of the objective function during adaptive partitioning is an important factor affecting the partitioning of the MHGM model and ultimately the number of parameter estimates. Figure 7 The diagram shows the number of MHGM parameters on station 0052 after adaptive grid partitioning when the threshold k is set to 0.1cm, 0.5cm, and 0.9cm, respectively.

[0124] from Figure 7 It can be seen that as the value of k increases, the number of 8°×8° Level I grids at station 0052 is constantly increasing, and the adaptive grid division strategy is gradually merging areas where multipath error changes are relatively mild. Meanwhile, Level II and Level III grids are mostly concentrated in low-elevation-angle areas susceptible to multipath error. This shows that the adaptive grid division is reasonable in its selection of areas requiring refinement, consistent with the multipath error influence around the station.

[0125] This paper's experiment evaluated the adaptive scheme by setting nine k values ​​with 0.1cm intervals between 0.1cm and 0.9cm. The results were compared with a scheme where all stations used a fixed 2°×2° grid division to study the impact of different k values ​​on adaptive grid division and the number of parameters to be estimated in the MHGM model. After adaptive grid division, the changes in the number of MHGM parameters to be estimated at seven stations were statistically analyzed, such as... Figure 8 As shown.

[0126] It can be seen that as the value of k increases, the number of parameters to be estimated in MHGM decreases. Combined with... Figure 6The ESM model values ​​displayed for each station reveal that the five stations operating under normal observation conditions with relatively weak multipath error influence in the ESM model exhibit consistent parameter change trends. However, the stations SEP1 and UB4B (represented by short lines and dots in the figure, respectively), which are more severely affected by multipath error, show significantly different trends. When setting the same k value, due to the influence of strong multipath error interference sources around the stations, the adaptive partitioning results in more detailed partitioned regions for the two stations, leading to significantly higher estimated parameters for SEP1 and UB4B compared to other stations. It's important to note that since SEP1 simulates a strong multipath interference environment, the changes in estimated parameters for SEP1 under different k values ​​do not represent the environments of most stations. The changes in estimated parameters for the vast majority of stations should be similar to... Figure 8 A dotted line diagram with straight lines connecting the dots.

[0127] 3) Comparison of observed residuals and localization results for different experimental strategies

[0128] The adaptive MHGM models for different k values ​​at each station were obtained by overlaying 10 days of data from day 015 to day 024 of 2021. Due to space limitations, Figure 9 The visualization of the MHGM model under different adaptive parameters is shown for SEP1, which is severely affected by multipath errors, and K708, a station in a normal observation environment. The MHGM model under different k values ​​is also compared with... Figure 6 It can be observed that in the adaptive MHGM model, the abnormal area of ​​SEP1 station, which is greatly affected by multipath, is basically consistent with the ESM model. The interference in the low elevation angle area of ​​K708 is also consistent with ESM. This also shows that it is reasonable and feasible to use the ESM model as the prior value for adaptive mesh generation.

[0129] Figure 9From top to bottom, the figures show the MHGM models obtained with a fixed resolution of 2°×2° and adaptive parameter k values ​​of 0.1cm, 0.5cm, and 0.9cm, respectively. As can be seen from the figures, the difference between the fixed resolution scheme and the model with a k value of 0.1cm is not significant. Furthermore, as the k value increases, the number of merged regions in the model increases significantly, but the prominent interference areas in the SEP1 station model do not change significantly. These interference areas maintain detailed mesh division under different parameters, reflecting that the adaptive MHGM model under different parameters can still describe the multipath error impact on the station relatively well. The following analysis further examines the impact of the multipath error prior model under different schemes on the residuals of double-difference observations with fixed ambiguity. In the experiment, four sets of adaptive MHGM model parameters k were set at intervals of 0.2cm, ranging from 0.1cm to 0.7cm, for verification. The correction effect of the 0.5°×0.5° ESM model, as prior information, was added for comparison.

[0130] Table 3. Verification of RMS residual changes (cm) over a fixed time period for ambiguity.

[0131]

[0132] To quantify the performance improvement of the proposed adaptive grid partitioning MHGM, Table 3 presents the residual information of double-difference observations for a fixed ambiguity period within the validation day, after multipath error correction for both uncorrected and different models. NO and ESM represent the RMS statistics for uncorrected and multipath error correction using prior ESM, respectively. Fixed represents the MHGM model with a fixed resolution of 2°×2°, and the others represent the MHGM models corresponding to the objective function threshold k. The statistical results in Table 3 show that as the threshold k increases, the multipath error correction performance of the MHGM model is slightly reduced, but it is still better than the correction performance of the ESM model.

[0133] To evaluate the improvement in computational resource consumption when using MHGM by the adaptive grid partitioning method proposed in this patent, taking the hardware used for data processing in the experiment as an example, with an i7-9700K CPU and 64GB of memory, it could only process MHGM models with a fixed resolution of 2°×2° for 12 stations under extreme conditions, with an average modeling time of approximately 26 hours. This time consumption is clearly unacceptable. If k is set to 0.7cm in the experiment, the average time consumption for 12 stations at a fixed resolution is approximately 1.6 hours. Meanwhile, the number of stations that can be processed by the same hardware increases to 49. It is evident that the adaptive grid partitioning scheme using the ESM model as prior information can effectively reduce the computational resource consumption of MHGM during model estimation, solve the problem of too many parameters to be estimated in MHGM at fixed resolutions, and realize the application service capability of the MHGM model in large-scale network data processing.

[0134] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0135] In some possible embodiments, a hemispherical adaptive grid partitioning system for MHGM multipath error modeling is provided, comprising the following modules:

[0136] The first module is used to obtain a high-resolution multipath error prior model as prior information by using non-differential residuals to obtain the spatial distribution characteristics of multipath errors at the station.

[0137] The second module is used to establish a fixed grid division MHGM model on the station, extract the initial grid of AMR, and set the corresponding grid as a Class I grid.

[0138] The third module iterates through each Level I grid, using adaptive criteria to determine whether the grid needs further subdivision. This is achieved through the following processing steps.

[0139] Obtain the prior model value P contained within the grid, and the coordinates corresponding to that model value within the grid.

[0140] The parameters to be estimated, Q1, Q2, Q3 and Q4, are set at the four corner points of the grid. Based on their coordinates in the grid, the relationship between them and the prior model value P is obtained by bilinear interpolation.

[0141] The values ​​Q at the four corner points of the grid are set as the parameter matrix X to be estimated, the corresponding bilinear interpolation coefficient matrix is ​​the design matrix A, and the prior model values ​​P form the observation matrix Y. The estimated values ​​of the parameter matrix X are obtained according to the least squares principle. and the corresponding residual vector v;

[0142] Traverse the residual vector v. If there is a case in the residual vector v where the absolute value is greater than the corresponding threshold k, then the level I grid is considered to be further divided into level II grids.

[0143] The fourth module is used to stop mesh generation and command the sixth module to work when preset conditions are met for any mesh; otherwise, it commands the fifth module to work.

[0144] The fifth module is used to repeat the work of the third and fourth modules when adaptive meshing is required. It takes the midpoint of the level I grid in the elevation and azimuth directions and divides it into four congruent level II grids, and so on, to divide the multi-level grid.

[0145] The sixth module is used to output the semi-celestial adaptive grid division results after the division is completed.

[0146] In some possible embodiments, a semi-celestial adaptive grid partitioning system for MHGM multipath error modeling is provided, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described above.

[0147] In some possible embodiments, a semi-celestial adaptive grid partitioning system for MHGM multipath error modeling is provided, including a readable storage medium on which a computer program is stored. When the computer program is executed, it implements the semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described above.

[0148] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A hemispherical adaptive grid partitioning method for multipath error modeling in MHGM, characterized in that: Includes the following steps, Step 1: Use non-differential residuals to obtain a high-resolution multipath error prior model as prior information to obtain the spatial distribution characteristics of multipath errors at the station. Step 2: Establish a fixed grid division MHGM model on the station, extract the initial grid of AMR, and set the corresponding grid as a Class I grid; Step 3: Traverse each Level I grid and determine whether the grid needs to be further subdivided using an adaptive criterion. This is achieved through the following processing steps: Obtain the prior model value P contained within the grid, and the coordinates corresponding to that model value within the grid. Set the parameters to be estimated at the four corner points of the grid. , , and Based on its coordinates within the grid, the relationship between it and the prior model value P is obtained using bilinear interpolation. Values ​​of the four corner points of the grid Let X be the parameter matrix to be estimated, A be the design matrix, and P be the prior model values ​​forming the observation matrix Y. The estimated values ​​of parameter matrix X are then obtained using the least squares principle. and the corresponding residual vector ; Traversing the residual vector If the residual vector There exists an absolute value greater than the corresponding threshold. In such cases, it is considered that the Level I grid can be further subdivided into Level II grids; Step 4: For any grid, if the preset conditions are met, stop the grid division and proceed to Step 6; otherwise, proceed to Step 5. Step 5: If adaptive meshing is required, repeat steps 3-4. Take the midpoint of the elevation angle and azimuth angle of the Level I grid and divide it into four equal Level II grids. Continue in this manner to divide the multi-level grid. Step 6: After the division is completed, output the semi-celestial adaptive grid division result.

2. The hemispherical adaptive grid partitioning method for MHGM multipath error modeling according to claim 1, characterized in that: The multipath error prior model adopts the ESM model.

3. The hemispherical adaptive grid partitioning method for MHGM multipath error modeling according to claim 1, characterized in that: Step 1 is implemented by including the following steps: Step 1.1: Establish a planar polar coordinate system with the antenna phase center as the center, and divide the coordinate system into grids at fixed intervals in the elevation and azimuth directions; Step 1.2: For any station participating in the solution, distribute the residuals of the undifferentiated phase observations after fixing the ambiguity of each satellite to the corresponding grid according to the azimuth and elevation angles; Step 1.3: Take the average value of the residuals in each grid to obtain the multipath error prior model of the station.

4. The hemispherical adaptive grid partitioning method for MHGM multipath error modeling according to claim 1, characterized in that: Obtain the ESM prior model value P contained within the mesh, and the coordinates of this model value within the mesh. Then, the relationship between the bilinear interpolation method and the prior model value P is obtained as follows: in, , , and The coordinates of the four corner points are denoted as follows: , , , .

5. The hemispherical adaptive grid partitioning method for MHGM multipath error modeling according to claim 1, characterized in that: If any of the following conditions are met, the preset conditions are considered satisfied, the division stops, and the process proceeds to step 6; otherwise, the process proceeds to step 5. (a) The number of prior model values ​​P contained in the grid is less than the corresponding preset threshold. ; (b) The residual vector within the grid after least squares estimation In the equation, the absolute value of all elements is less than or equal to 1. ; (c) The grid has been divided to the set minimum grid size.

6. The hemispherical adaptive grid partitioning method for MHGM multipath error modeling according to claim 1, 2, 3, 4, or 5, characterized in that: This method is used to adaptively adjust the fineness of the semi-celestial grid in different regions based on the actual distribution of multipath error effects around the station, thereby reducing the number of grid point parameters to be estimated in the MHGM method, reducing the computational resource consumption during MHGM modeling, and realizing the correction of multipath effect errors in the observations.

7. A hemispherical adaptive grid partitioning system for multipath error modeling in MHGM, characterized in that: This method is used to implement the hemispherical adaptive grid partitioning method for MHGM multipath error modeling as described in any one of claims 1-6.

8. The hemispherical adaptive grid partitioning system for MHGM multipath error modeling according to claim 7, characterized in that: Includes the following modules, The first module is used to obtain a high-resolution multipath error prior model as prior information by using non-differential residuals to obtain the spatial distribution characteristics of multipath errors at the station. The second module is used to establish a fixed grid division MHGM model on the station, extract the initial grid of AMR, and set the corresponding grid as a Class I grid. The third module iterates through each Level I grid, using adaptive criteria to determine whether the grid needs further subdivision. This is achieved through the following processing steps. Obtain the prior model value P contained within the grid, and the coordinates corresponding to that model value within the grid. Set the parameters to be estimated at the four corner points of the grid. , , and Based on its coordinates within the grid, the relationship between it and the prior model value P is obtained using bilinear interpolation. Values ​​of the four corner points of the grid Let X be the parameter matrix to be estimated, A be the design matrix, and P be the prior model values ​​forming the observation matrix Y. The estimated values ​​of parameter matrix X are then obtained using the least squares principle. and the corresponding residual vector ; Traversing the residual vector If the residual vector There exists an absolute value greater than the corresponding threshold. In such cases, it is considered that the Level I grid can be further subdivided into Level II grids; The fourth module is used to stop mesh generation and command the sixth module to work when preset conditions are met for any mesh; otherwise, it commands the fifth module to work. The fifth module is used to repeat the work of the third and fourth modules when adaptive meshing is required. It takes the midpoint of the level I grid in the elevation and azimuth directions and divides it into four congruent level II grids, and so on, to divide the multi-level grid. The sixth module is used to output the semi-celestial adaptive grid division results after the division is completed.

9. The hemispherical adaptive grid partitioning system for MHGM multipath error modeling according to claim 7, characterized in that: It includes a processor and a memory, the memory being used to store program instructions, and the processor being used to call the stored instructions in the memory to execute the semi-celestial adaptive grid partitioning method for MHGM multipath error modeling as described in any one of claims 1-6.

10. The hemispherical adaptive grid partitioning system for MHGM multipath error modeling according to claim 7, characterized in that: It includes a readable storage medium on which a computer program is stored, and when the computer program is executed, it implements a hemispherical adaptive grid partitioning method for MHGM multipath error modeling as described in any one of claims 1-6.

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