Optimal observation station topological configuration design method for atmospheric delay measurement in GNSS network area

Abstract

The invention discloses a GNSS network area atmospheric delay measurement optimal observation station topological configuration design method. According to the method, dynamic refined site selection of a candidate site area is realized by implementing multi-stage space division on a target terrain, and an optimal observation station topological configuration capable of realizing maximization of regional atmosphere delay inversion precision is intelligently screened out in combination with a Hash table rapid retrieval mechanism. According to the method, a reference based on data can be provided for site selection of the GNSS monitoring station under the complex terrain condition on site, meanwhile, the huge calculation amount needed by a traditional traversal method is greatly reduced through the Hash table, and the method is more reasonable than a method which only depends on design drawings and does not conduct experience verification.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and atmospheric remote sensing technology. This method innovatively integrates regional division strategy and global optimization algorithm, and focuses on solving the problem of optimizing the selection of station network topology in complex terrain environment. It can provide a high-precision reference station network layout scheme for atmospheric parameter inversion. Background Technology

[0002] GNSS-based tropospheric delay inversion is an important application in meteorology and atmospheric science. Compared to traditional observation methods, GNSS-based tropospheric delay inversion technology demonstrates significant technical value due to its continuous operation capability, cost-effectiveness, and real-time atmospheric information acquisition capabilities. This technology can provide high spatiotemporal resolution tropospheric delay data, effectively supporting the construction of atmospheric correction models for measurement equipment systems. This has important engineering significance for improving the performance indicators of measurement equipment in various application scenarios.

[0003] To achieve high-precision tropospheric delay inversion, multiple GNSS monitoring stations need to be deployed in the target area. In this context, optimizing the location deployment of these GNSS monitoring stations is particularly important, as the geometric configuration of the network topology directly affects the quality of the tropospheric delay parameter inversion. Therefore, there is an urgent need to develop a GNSS network topology design method that combines theoretical innovation with engineering practicality to meet the pressing demand for high-precision tropospheric delay correction from local measurement equipment arrays.

[0004] However, due to practical factors such as construction costs and complex terrain, a brute-force exhaustive search method is not feasible. For example, if there are 80 potential sites in a 2km × 2km area, and 20 GNSS stations are to be built, then... One GNSS network configuration. Even if we calculate the regional atmospheric delay accuracy for one GNSS network configuration per second, it would still require 1.12 × 10⁻⁶. 11 Therefore, this invention innovatively introduces a global fast search mechanism using a hash table. By establishing a mapping function, it achieves intelligent filtering of site combinations, randomly selecting effective combinations from all candidate sites for accuracy evaluation, thus greatly improving search efficiency while avoiding redundant calculations. Summary of the Invention

[0005] To address the aforementioned technical challenges, this invention proposes a method for designing the optimal station topology configuration for GNSS network regional atmospheric delay measurement. This method achieves dynamic and refined site selection of candidate station areas through multi-level spatial division of the target terrain. Combined with a fast hash table retrieval mechanism, it intelligently selects the optimal station topology configuration that maximizes the accuracy of regional atmospheric delay inversion.

[0006] The technical solution of this invention is as follows:

[0007] A method for designing the optimal station topology configuration for regional atmospheric delay measurement in a GNSS network, comprising:

[0008] Step 1: Candidate Area Analysis and Preliminary Division: Based on project requirements and station construction specifications (such as ease of construction and unobstructed environment), candidate geographical areas for GNSS station deployment are determined, and preliminary spatial grid division is performed to provide a basic framework for subsequent refined site selection. i. Analyze the terrain features of the target area to determine the overall area suitable for constructing GNSS monitoring stations.

[0009] ii. Divide the determined site area into regular grid sub-regions (for example, divide a 30m × 30m area into a basic sub-region). Figure 1 】

[0010] The second step is to determine the objective function: establish the observation equation, clarify the objective function to be optimized (maximize the accuracy of tropospheric delay estimation), and define a complete observation model that includes various error sources.

[0011] i. Establish system observation equations that include observations from all proposed deployment sites.

[0012] Formula (1) defines the method for calculating the omnidirectional tropospheric delay value centered on the location of each candidate GNSS station:

[0013]

[0014] In the formula, P IF and Φ IF Ionospherically-free combined observations representing pseudorange and carrier phase respectively; c·dt represents the geometric distance calculated from the spatial coordinates of satellite s and receiver r. r dtr is the GNSS receiver clock offset, where c is the speed of light, and dtr is...; Represents the tropospheric delay term; e represents the product of wavelength and ambiguity in an ionospherically unaffected combination. P and e Φ These correspond to the observation noise of pseudorange and carrier phase, respectively.

[0015]

[0016] Among them, P1, P2, ..., P n and Φ1, Φ2, ..., Φ n These represent the pseudorange and phase observations from the n GNSS stations to be deployed, respectively, with each item containing multiple satellite measurements; δ1, δ2, ..., δ n This represents the coordinate relationship between the various stations, corresponding to the estimated parameters x1, x2, ..., x... n(If the site coordinates have been accurately determined, this parameter can be removed); the coefficient c represents the speed of light and is used to adjust the receiver clock error terms dt1, dt2, ..., dt. n Perform dimensional normalization; transform factors τ1, τ2, ..., τ n The tropospheric delay at the reference measuring device is mapped to the corresponding delay at each GNSS station to compensate for the measured values; τ1, τ2, ..., τ n Multiplied by the tropospheric delay parameter T at the reference measuring device k The tropospheric delay of the GNSS monitoring station can be obtained, where T k It is a vector representing the tropospheric delay in different directions. λ and N are the wavelength and ambiguity parameters, respectively, and are used only in the phase observation equation.

[0017] The elevation deviation, horizontal displacement, and surrounding terrain obstruction effects between the GNSS antenna phase center and the reference measurement equipment all significantly affect the accuracy of tropospheric delay estimation. This invention innovatively constructs three types of error models: 1) a horizontal distance deviation model, 2) an elevation difference correction model, and 3) a terrain obstruction quantification model, to quantify and analyze the impact mechanisms of planar distance, elevation difference, and obstruction effects on delay inversion accuracy.

[0018] ii. Construct a triple spatial error quantization model

[0019] a) Horizontal distance error model

[0020] The horizontal displacement error components can be mathematically represented by the Gaussian function model in Kriging interpolation theory, as shown in the following formula (3):

[0021]

[0022] The horizontal spacing between the GNSS antenna and the measurement equipment antenna is represented by h; parameters a and b refer to the Nugget and distance parameters in Kriging interpolation, respectively. It is generally believed that a plane distance of 20 to 60 km will cause a tropospheric delay compensation error of 0.52 to 0.77 mm, and this error satisfies the Gaussian model of Kriging interpolation. Therefore, a = 20 km and b = 0.77 mm can be considered respectively.

[0023] b) Elevation difference error model

[0024] The atmospheric variations caused by vertical elevation differences introduce more significant model errors, which can be characterized by the exponential relationship of formula (4):

[0025]

[0026] Where v is the height difference between the phase center of the receiver antenna and the measuring equipment. Compared with the horizontal direction, the elevation difference has a greater impact on atmospheric compensation. This is because the gradient changes of meteorological parameters such as temperature, humidity, and air pressure are more significant in the vertical direction. It is generally believed that a 200m elevation difference will cause a 0.2mm vertical atmospheric delay compensation error. Therefore, c = 0.2mm and d = 200m can be assumed.

[0027] Therefore, the pseudorange and carrier phase observation error model ε in this invention P and ε Φ It covers the error ε(h) caused by horizontal distance and the error ε(v) caused by elevation difference:

[0028]

[0029] in, and These represent the pseudorange and carrier phase observation errors of the traditional model. As can be seen from the above formulas, the topological location of the GNSS monitoring station will affect the values ​​of ε(h) and ε(v).

[0030] c) Occlusion quantification analysis model

[0031] The terrain and object obstruction effect in the GNSS signal propagation path significantly reduces the accuracy of tropospheric delay inversion. These obstructions reduce the number of visible satellites and decrease the geometric distribution of observations, thus affecting the quality and reliability of tropospheric delay estimation. To quantitatively characterize the spatial obstruction relationship between the measurement equipment (obstruction) and the receiver antenna, this invention employs a parameterized model based on the elevation angle α and azimuth angle β in the celestial coordinate system of the receiver antenna center:

[0032]

[0033] Among them, H0 and H rec R0 represents the height of the obstruction and the receiver antenna, respectively; D represents the horizontal distance between the receiver antenna and the obstruction; and R0 represents the radius of the obstruction.

[0034] d) Construct an objective function with the accuracy of tropospheric delay estimation as its core: integrating the three error sources

[0035] The accuracy index for calculating neutral atmospheric delay can be simplified as follows:

[0036]

[0037] in Let be the variance-covariance matrix of the estimator x, used to characterize the atmospheric estimation accuracy. A is the design matrix, composed of the coefficients in formula (1), reflecting the geometric relationship between the GNSS receiver and the satellite. Q yyLet be the pseudorange and carrier phase observation variance covariance matrix, i.e.:

[0038]

[0039] Obstructions that block navigation satellite signals reduce the number of observations and compromise the integrity of matrix A. It can be seen that errors caused by planar distance, differences caused by elevation variations, and obstruction are all reflected in formula (7), constructing a comprehensive error model that integrates spatial displacement, vertical gradient, and signal obstruction as three error sources.

[0040] Step 3: Global topology optimization search based on hash table. Figure 2 To obtain the optimal configuration: Using an efficient hash table search algorithm, global optimization is performed on all candidate station location combinations in the defined sub-region grid (e.g., 30m×30m) to maximize the objective function (Equation 7) and obtain the optimal station topology configuration at the current grid scale.

[0041] Step 4, Grid Refinement: By further refining the spatial grid, the search process is repeatedly optimized at a finer scale to improve the location accuracy. Based on the optimal configuration obtained in Step 3, or within the initially divided sub-regions, the grid is further subdivided (for example, the original 30m×30m sub-region is subdivided into smaller units of 10m×10m).

[0042] Step 5: Perform a global topology optimization search again to obtain the optimal configuration. On the fine grid defined in Step 4, search for and determine the optimal station topology configuration at this scale.

[0043] You can repeat the process 4-5 times to further refine the website.

[0044] Beneficial effects:

[0045] 1. Data-driven approach replaces experience-driven approach: Currently, most GNSS station network design principles in the field rely on the experience of technical personnel. The mathematical models of formulas (1)-(8) provide objective basis for station layout, reduce human experience bias, and improve the reliability and rationality of configuration design schemes.

[0046] 2. A high-efficiency global search algorithm based on hash tables is proposed: Existing search techniques mostly employ traversal search or heuristic algorithms, which have high computational complexity and are prone to getting trapped in local optima. This invention, through gridded region partitioning and a hash table search strategy, can reduce computational complexity while ensuring global optima;

[0047] 3. A comprehensive three-dimensional spatial error model with strong scalability is established: This model comprehensively considers three main spatial error sources affecting the accuracy of tropospheric delay estimation (horizontal displacement, elevation difference, and signal obstruction), establishes quantitative error models for each, and integrates them into the observation model. This optimization approach and framework can also be applied to station design scenarios requiring comprehensive optimization of multiple factors, such as meteorological station networks, seismic monitoring arrays, and 5G base station planning. Attached Figure Description

[0048] Figure 1 The search method uses a hash table.

[0049] Figure 2 The process for optimizing GNSS station topology based on hash tables;

[0050] Figure 3 , for the terrain of the application scenario;

[0051] Figure 4 For the deployment of radar and infrastructure;

[0052] Figure 5 The areas designated as candidate GNSS station construction sites;

[0053] Figure 6 The cumulative error of the horizontal range and vertical difference of 12 radars in a single GNSS network topology;

[0054] Figure 7 The total obstructed airspace spanning 12 radars within a single GNSS network topology;

[0055] Figure 8 The cumulative tropospheric delay error of 12 radars in a single GNSS network topology;

[0056] Figure 9 Local optimization of GNSS station topology;

[0057] Figure 10 The area centered on each locally optimal GNSS station is used for candidate location selection;

[0058] Figure 11 The second step is to calculate the cumulative error of the horizontal range and vertical difference of 12 radars in a single GNSS network topology.

[0059] Figure 12 The second step involves covering the total obstructed airspace of 12 radars within a single GNSS network topology.

[0060] Figure 13 The cumulative tropospheric delay error of 12 radars in a single GNSS network topology in the second step;

[0061] Figure 14 , is the tropospheric delay accuracy of a single radar. Detailed Implementation

[0062] The present invention will now be described in detail with reference to the accompanying drawings. This description is merely illustrative and explanatory, and should not be construed as limiting the scope of protection of the present invention. Furthermore, those skilled in the art can combine the features in the embodiments described herein and in different embodiments accordingly based on the description in this document.

[0063] The proposed method for selecting the optimal GNSS station topology is illustrated using a regional radar array project as an experimental case. Due to project requirements, latitude and longitude information is omitted from the topographic map in this case study. Figure 3 As shown, a main road encircles the hills, and a mountain path leads to the summit. Lakes, reservoirs, and farmland are mainly distributed in the northeastern and southeastern regions. The specific implementation steps for GNSS topology optimization are as follows:

[0064] Step 1: Candidate Region Analysis and Preliminary Division

[0065] i. Confirm the website creation area. Figure 4 The planned locations of the radar arrays are shown. Solid purple circles indicate radar locations, with 10 radars located in the center of the island (main platform) and 2 radars located in the southern region (secondary platform).

[0066] ii. Initially divide the site area into regional grids.

[0067] a) Determining the number of candidate stations. Given that each radar unit has a design radius of 15m and occupies approximately 900 square meters, an equivalent spatial allocation was adopted for the GNSS monitoring stations. The candidate site distribution based on the available area is as follows: 80 main platforms, 20 secondary platforms, and 50 along mountain roads, totaling 150. Based on a candidate point ratio of 8:2:5, the final design includes 20 GNSS stations: 10 main stations, 3 secondary stations, and 7 along roads.

[0068] b) Figure 5 Sub-region grid division to meet the requirements of candidate GNSS site construction areas. The feasible construction areas marked with yellow solid circles in the figure are schematic ranges and not specific site locations. There are four selectable construction areas: the radar main platform and secondary platform construction area, the administrative facility area, and the area along the mountain road.

[0069] The second step is a global topology optimization search based on a hash table. A hash table is used to randomly search and generate the topology configuration. Drawing inspiration from the fast global search method using hash tables, a mapping function is established to randomly select stations from all stations for accuracy analysis, ensuring that each randomly selected station combination is unique. This yields the optimal station topology configuration at the current grid scale.

[0070] Calculate the cumulative tropospheric delay estimation accuracy of 12 radars. After determining the topology of the 20 GNSS monitoring station network, calculate the tropospheric delay accuracy of each of the 12 radar devices sequentially according to the observation equation formula (2). Record the tropospheric delay estimation accuracy of all 12 radars and use... Figure 2 The illustrated process framework was evaluated. A total of 7.5 × 10⁻⁶ was calculated. 7 The topology of one GNSS station is shown in the accompanying figures only for 2×10 stations for ease of visualization. 4 The result of each topological configuration is used as a representative.

[0071] Analysis of the current optimal configuration's triple error quantification index:

[0072] i. Visualize the effects of horizontal distance and vertical elevation to assess topology performance. Figure 6 The horizontal range error and vertical elevation difference of 12 radar systems were quantified, and their joint evaluation model is shown in the following formula:

[0073]

[0074] Where ε Φ,i These represent the phase error of a single radar. These error characteristics quantify the impact of the GNSS network topology on radar coordinate observations. For example... Figure 6 As shown, the cumulative errors of horizontal and vertical distance differences for the 12 radars range from 3 to 13 mm, with a minimum cumulative error of 3.17 mm. These errors exhibit a banded distribution, primarily influenced by the terrain constraints of the target area.

[0075] ii. Visualize the impact of occlusion effects to evaluate topology performance. Figure 7 The cumulative obstruction percentage of the 12 radars relative to the total observable airspace of the GNSS station is shown. For a specific GNSS monitoring station, the obstructed airspace of a single radar is determined by formula (6). Then, the total cumulative obstruction of all 12 radars is calculated using formula (10):

[0076]

[0077] Where b i,j This represents the percentage of airspace blocked by a single radar relative to a specific GNSS station. (By...) Figure 7Analysis shows that the average range of obstruction caused by the 12 radars ranged from 1.33% to 5.67%.

[0078] iii. By integrating the three evaluation criteria, the accuracy of tropospheric delay estimation is visualized, and the local optimal configuration is determined. In the parameter estimation process, by incorporating the observation error of formula (5) and combining it with the signal blocking effect described in formula (6), the accuracy of tropospheric delay estimation for a single radar under a given GNSS station topology can be determined. The cumulative tropospheric delay estimation error of 12 radars is as follows: Figure 8 As shown. The topology configuration that minimizes the cumulative tropospheric delay estimation error achieves a cumulative atmospheric delay error of 9.72 mm. The corresponding optimal GNSS station topology configuration is shown in [reference needed]. Figure 9 .

[0079] Step 3: Mesh Refinement. Based on the locally optimal topology, refine the regional mesh. Figure 9 The locally optimal configuration shown selects candidate points within a 900-square-meter area around the center of each locally optimal GNSS station, such as... Figure 10 As shown. Then, 20 candidate points for GNSS stations are randomly combined.

[0080] Step 4: Determine the optimal station topology at this scale. A hash table is used to randomly search and generate the topology. The optimal GNSS topology is searched using a hash table model system, with each 900-square-meter area further subdivided into nine 10m × 10m grids. The location of each GNSS station is restricted to these nine subgrids.

[0081] Similar to step three, we analyze the triple error quantification index of the refined optimal configuration:

[0082] i. Visualize the effects of horizontal range and vertical elevation to evaluate topology performance. Consistent with S15, the cumulative phase error of the differences in horizontal range and vertical elevation of the 12 radars is calculated using formula (9), such as... Figure 11 As shown. With Figure 6 Compared to the cumulative error of the random distribution in the middle, Figure 11 The cumulative error in the second phase exhibits a regular variation. This is because the GNSS station in the second phase is limited to a 30-square-meter area, which differs from the random selection method used in the first phase.

[0083] ii. Visualize the impact of occlusion effects to evaluate topology performance. Figure 12 The total obstructed airspace of 12 radars in a given GNSS network topology is shown, and the calculation method is given in formula (10). The obstruction percentage ranges from 40% to 65%, and the cumulative obstruction area also exhibits periodic changes, with an amplitude exceeding [missing information]. Figure 11The magnitude of the accumulated error. This phenomenon is due to the relatively close distance between the GNSS monitoring station and the radar, where even a small displacement can cause significant changes in the obstructed airspace.

[0084] iii. Calculate the cumulative tropospheric delay estimation accuracy of the 12 radars and determine the local optimal configuration. Figure 13 This shows the tropospheric delay estimation accuracy for 12 radars in a single GNSS network topology. In this step's calculation, the topology configuration that minimizes the cumulative tropospheric delay estimation error achieves a cumulative atmospheric delay error of 9.39 mm, slightly lower than the 9.72 mm recorded in the first step. The optimized GNSS station topology configuration is compared with... Figure 9 The results are consistent with those shown. The cumulative error is 9.39 mm, corresponding to 12 radars, and the tropospheric delay estimation accuracy for each radar is as follows: Figure 14 As shown.

[0085] The first step, a coarse-grained grid search, determines the optimal GNSS topology. In this stage, the cumulative atmospheric delay estimation error exhibits a random distribution, with a minimum cumulative error of 9.72 mm. The second step, based on the locally optimal GNSS topology, subdivides the region into a finer grid and repeats the search process. Due to the dense distribution of candidate points within each sub-region, the cumulative atmospheric delay estimation error shows a regular distribution. After the second step of refinement, the cumulative atmospheric delay estimation error is reduced to 9.39 mm.

[0086] This completes all the steps.

[0087] The above results demonstrate that this patent can provide a data-based reference for the site selection of GNSS monitoring stations under complex terrain conditions, while significantly reducing the massive amount of computation required by traditional traversal methods by utilizing hash tables.

[0088] While it's impossible to account for all practical scenarios, this research still holds practical value. It provides at least one more reasonable approach than relying solely on design drawings without empirical validation. This patent validates the proposed topology optimization method using an example of correcting radar tropospheric delay with local GNSS monitoring stations. Furthermore, this method can be applied to various similar scenarios. For instance, when deploying seismometers for earthquake monitoring in seismically active areas, the network topology can be optimized using an objective function describing geological conditions, historical earthquake data, and body wave propagation characteristics. The optimal topology search method proposed in this study is also applicable to various fields requiring the deployment of a specified number of monitoring stations, including hydrological, ecological, agricultural, and marine monitoring.

Claims

1. A method for designing the optimal station topology configuration for regional atmospheric delay measurement in a GNSS network, characterized in that, Includes the following steps: Step 1: Candidate Area Analysis and Preliminary Division: Based on project requirements and station construction specifications (such as ease of construction and unobstructed environment), candidate geographical areas for GNSS station deployment are determined, and preliminary spatial grid division is carried out to provide a basic framework for subsequent refined site selection. The second step is to determine the objective function: establish the observation equation, clarify the objective function to be optimized (maximize the accuracy of tropospheric delay estimation), and define a complete observation model that includes various error sources; The third step is to perform a global topology optimization search based on a hash table to obtain the optimal configuration: using an efficient hash table search algorithm, a global optimization is performed on all candidate station location combinations in the defined sub-region grid to maximize the objective function and obtain the optimal station topology configuration at the current grid scale. Step 4, Grid Refinement: By further refining the spatial grid, the search process is repeatedly optimized at a finer scale to improve the location accuracy; based on the optimal configuration obtained in Step 3, or within the initially divided sub-regions, the grid is further subdivided. Step 5: Perform a global topology optimization search again to obtain the optimal configuration. On the fine grid defined in Step 4, search for and determine the optimal station topology configuration at this scale.

2. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, The first step includes: i. Analyze the terrain features of the target area to determine the overall area suitable for building a GNSS monitoring station; ii. Divide the determined website area into regular grid sub-regions.

3. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, The second step includes: i. Establish a system observation equation that includes observations from all proposed deployment sites; ii. Construct a triple spatial error quantization model.

4. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, In the second step, the horizontal distance error model is expressed as: The horizontal spacing between the GNSS antenna and the measurement equipment antenna is represented by h; parameters a and b refer to the Nugget and distance parameters in the Kriging interpolation, respectively, a = 20 km and b = 0.77 mm.

5. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, In the second step, the elevation difference error model is expressed as: Where v is the height difference between the phase center of the receiver antenna and the measuring equipment, c = 0.2 mm, and d = 200 m.

6. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, In the second step, the pseudorange and carrier phase observation error model ε P and ε Φ The errors ε(h) caused by planar distance and ε(v) caused by elevation difference are respectively expressed as: in, and This refers to the pseudorange and carrier phase observation errors of the traditional model.

7. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, In the second step, the parameterized model based on the elevation angle α and azimuth angle β in the celestial coordinate system of the receiver antenna center is expressed as follows: Among them, H0 and H rec R0 represents the height of the obstruction and the receiver antenna, respectively; D represents the horizontal distance between the receiver antenna and the obstruction; and R0 represents the radius of the obstruction.

8. The optimal station topology design method for GNSS network regional atmospheric delay measurement as described in claim 1, characterized in that, In the second step, the neutral atmospheric delay accuracy index is simplified as follows: in Let be the variance-covariance matrix of the estimator x, used to characterize the accuracy of atmospheric estimation, and A be the design matrix.

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