Crowdsourcing ionospheric delay data processing method and device based on space-time rearrangement verification

Abstract

This application discloses a crowdsourced ionospheric delay data processing method and apparatus based on spatiotemporal rearrangement verification, relating to the field of satellite navigation and positioning technology. The method includes: acquiring ionospheric delay observations from multiple stations; using each station as a target station, detecting and removing outlier observations based on the residuals between the target station and adjacent stations; calculating predicted values ​​based on the time-series model of the target station, and detecting and removing outlier observations based on the residuals between the predicted and observed values; calculating the initial local variance of observations within the spatiotemporal neighborhood of the target station, randomly rearranging the observations within each spatiotemporal neighborhood, calculating the rearranged local variance, detecting and removing outlier observations based on the comparison results of the variances after each rearrangement; and outputting ionospheric delay data with outlier observations removed. This application can support wide-area PPP-RTK services to achieve centimeter-level positioning accuracy, significantly shortening the initial convergence time and providing a reliable data foundation for ionospheric monitoring.

Description

Technical Field

[0001] This application relates to the field of satellite navigation and positioning technology, and in particular to a crowdsourced ionospheric delay data processing method and apparatus based on spatiotemporal rearrangement verification. Background Technology

[0002] Precise point positioning (PPP) can provide high-precision positioning services, but its initial convergence time is relatively long, typically requiring tens of minutes to achieve centimeter-level accuracy. One of the fundamental reasons for the slow convergence of PPP lies in the way ionospheric delay is handled: in PPP processing, ionospheric delay is usually estimated as a parameter along with other parameters. Its strong spatiotemporal variation makes it difficult for the estimation process to converge quickly, and its strong correlation with ambiguity directly affects the recovery of the integer properties of ambiguity, thus limiting the positioning accuracy and convergence speed of PPP.

[0003] To accelerate the convergence speed of precise point positioning (PPP-RTK), some related technologies employ a fusion of PPP-RTK and real-time kinematic positioning. This method utilizes a regional reference station network to provide ionospheric delay correction information, constraining the user's ionospheric error and significantly shortening the convergence time. However, the performance of PPP-RTK is highly dependent on the accuracy and coverage of the regional reference station network's corrections. It suffers from strong dependence on reference station density and difficulty in deploying sufficient reference stations in areas with weak infrastructure, thus hindering the achievement of wide-area, high-precision services.

[0004] In recent years, the widespread deployment of consumer-grade GNSS devices (such as smartphones, vehicle-mounted receivers, and drones) has provided a data foundation for building crowdsourced ionospheric sensing networks. However, the diverse types of crowdsourced devices and the complex observation environments have led to a prevalence of outliers, gross errors, and spatial clustering errors in the extracted ionospheric delay data. Existing anomaly detection methods (such as residual thresholding and polynomial fitting) can identify obvious gross errors, but their detection capabilities are insufficient when faced with complex patterns such as spatially clustered anomalies and local systematic biases. Furthermore, they rely on manually set thresholds, lack statistical significance testing mechanisms, and have poor adaptability.

[0005] Therefore, there is currently a lack of a method for processing ionospheric delay data that has the ability to perform statistical significance tests, adapt to complex spatiotemporal structures, and automatically identify abnormal patterns, in order to improve the quality of crowdsourced ionospheric data and support high-precision, wide-area PPP-RTK services and ionospheric monitoring applications. Summary of the Invention

[0006] This application provides a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification to overcome the shortcomings of the aforementioned related technologies. The technical solution is as follows: In a first aspect, this application provides a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification, comprising: Acquire observations of ionospheric delay from multiple stations at each time step; Each station is taken as the target station. The first abnormal observation value of the target station is detected and removed based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station. A time series model is obtained by fitting the observations of the target station at each time step. The second abnormal observations of the target station are detected and removed based on the second residual between the predicted values ​​and the observed values ​​at each time step obtained from the time series model. The spatial neighborhood formed by the target station and its first-order neighboring stations is determined by using a spherical Delaunay triangulation. The spatiotemporal neighborhood is constructed by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. Calculate the initial local variance of all observations in each spatiotemporal neighborhood; randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance; The third outlier observation of the target station is detected and removed based on the comparison between the rearranged local variance after each random rearrangement and the initial local variance. The output is ionospheric delay data that has been filtered out for all outlier observations.

[0007] In one alternative to the first aspect, acquiring the observations of ionospheric delay from multiple stations at each time step includes: For each station, precise single-point positioning observation data of the station at each time moment is acquired, and the oblique path ionospheric delay of the station at the corresponding time moment is calculated based on the precise single-point positioning observation data. Extract the latitude and longitude data of the puncture point corresponding to the precise single-point positioning observation data and the elevation angle of the observation satellite, and convert the oblique path ionospheric delay into the vertical ionospheric delay at the corresponding time. The vertical ionospheric delay is output as the observed value of the ionospheric delay at the corresponding time of the station.

[0008] In one alternative embodiment of the first aspect, the step of detecting and removing the first abnormal observation of the target station based on the first residual of the observations of all adjacent stations within a preset range of the target station at the same time includes: The preset range is determined based on a preset radius with the target station as the center, and adjacent stations falling within the preset range are identified. The geodetic distance between each adjacent station and the target station is calculated. Based on the geodetic distance, the weighted interpolation weights of the observations of the corresponding adjacent stations are determined. Based on the weighted interpolation weights, the observations of each adjacent station are weighted and interpolated to obtain the interpolation result. The first residual is calculated based on the absolute value of the difference between the interpolation result and the observation value of the target station; If the ratio of the first residual to the first standard deviation of the observation value of each adjacent station within the preset range is greater than the first preset threshold, then the observation value of the target station at the corresponding time is the first abnormal observation value with spatial dimension anomaly. Remove all first outlier observations.

[0009] In one alternative embodiment of the first aspect, the step of detecting and removing second abnormal observations of the target station based on the second residual between the predicted value and the observed value obtained at each time step using a time-series model includes: Extract the observation values ​​of the target station at each moment within a preset time window, and calculate the predicted values ​​at each moment within the preset time window based on the time series model; The absolute value of the difference between each observed value and the predicted value at the corresponding time is calculated to obtain the second residual; If the ratio of the second residual to the second standard deviation of the observation value at each moment within the preset time window is greater than the second preset threshold, then the observation value of the target station at the corresponding moment is the second abnormal observation value with an abnormal time dimension. Remove all second outlier observations.

[0010] In one alternative embodiment of the first aspect, determining the spatial neighborhood of the target station and its first-order neighboring stations using a spherical Delaunay triangulation includes: Construct a spherical Delaunay triangulation with the puncture point corresponding to the target station and the puncture points corresponding to any two other stations as vertices, such that there are no puncture points outside the vertices of the spherical triangles within the circumscribed circle of each spherical triangle in the spherical Delaunay triangulation. Extract each spherical triangle from the constructed triangulation network, determine the first-order neighboring stations directly connected to the target station based on the vertices of the spherical triangles, and construct a spatial neighborhood containing the target station and the first-order neighboring stations. The process of extracting observations from each station within a spatial neighborhood based on a sliding time window to construct a spatiotemporal neighborhood includes: A sliding time window is constructed using three adjacent sampling times on the time axis. The observations of the target station and the first-order neighboring station are extracted at each sampling time. The observation corresponding to the sampling time in the middle of the three sampling times of the target station is used as the observation to be examined, and the corresponding spatiotemporal neighborhood is constructed.

[0011] In one alternative embodiment of the first aspect, the detection and removal of third outlier observations of the target station based on the comparison between the rearranged local variance after each random rearrangement and the initial local variance includes: After each random rearrangement, the size of the rearranged local variance is compared with the initial local variance, and the total number of times the rearranged local variance is less than or equal to the initial local variance is accumulated. The significance test value is calculated based on the total number of times. If the significance test value is greater than the significance level, the observation to be tested in the current spatiotemporal neighborhood is determined to be the third abnormal observation value. Remove all third-anomaly observations in the spatiotemporal neighborhood.

[0012] In one alternative to the first aspect, after the output has been filtered to remove ionospheric delay data from all outlier observations, the method further includes: The vertical total electron content at the puncture point corresponding to each station is calculated based on the ionospheric delay after all outlier observations have been removed. The total vertical electron content of each neighboring station is selected based on the user's real-time location. The total vertical electron content is then interpolated based on the distance between the user and each neighboring station to obtain the total vertical electron content at the user's location.

[0013] Secondly, this application also provides a crowdsourced ionospheric delay data processing device based on spatiotemporal rearrangement verification, comprising: The crowdsourced data acquisition unit is used to acquire observations of ionospheric delay from multiple stations at each time point; The outlier detection unit is used to take each station as the target station and detect and remove the first outlier observation value of the target station based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station. The outlier detection unit is also used to fit a time series model based on the observations of the target station at each time moment, and to detect and remove the second outlier observations of the target station based on the second residual between the predicted value and the observed value at each time moment obtained based on the time series model. The outlier detection unit is also used to determine the spatial neighborhood formed by the target station and its first-order neighboring stations using a spherical Delaunay triangulation, and to construct a spatiotemporal neighborhood by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. The outlier detection unit is also used to calculate the initial local variance of all observations in each spatiotemporal neighborhood; it is also used to randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance. The outlier detection unit is also used to detect and remove the third outlier observation of the target station based on the comparison results of the rearranged local variance after each random rearrangement and the initial local variance. The crowdsourced ionospheric delay data output unit is used to output ionospheric delay data after removing all outlier observations.

[0014] Thirdly, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification provided by the first aspect of this application or any implementation thereof.

[0015] Fourthly, this application also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification provided by the first aspect of this application or any implementation thereof.

[0016] The beneficial effects of the technical solution provided in this application include at least the following: 1) Crowdsourcing was used to obtain ionospheric data, which expanded the sources of ionospheric data, reduced the cost of data acquisition, and reduced the dependence of PPP-RTK technology on regional reference stations; 2) The rearrangement test method was adopted to improve the quality of crowdsourced ionospheric data, supporting high-precision, wide-area PPP-RTK services and ionospheric monitoring applications.

[0017] 1) Crowdsourcing of ionospheric data effectively expands data sources and reduces the reliance of PPP-RTK technology on regional reference stations, solving the problem that traditional methods struggle to deploy sufficient reference stations in areas with weak infrastructure.

[0018] 2) To address the issues of outliers, gross errors, and spatial clustering errors caused by the diverse types of crowdsourced equipment and complex observation environments, this application innovatively adopts a spatiotemporal rearrangement test technique. By constructing a sliding time window and a neighborhood model of a spherical Delaunay triangulation network, combined with residual analysis and local variance test, it achieves automatic identification and removal of multiple types of outlier observations.

[0019] 3) This application significantly improves the detection capability of anomalous patterns under complex spatiotemporal structures through a statistical significance test mechanism, with a data quality improvement rate of over 30%. The high-precision ionospheric delay data output by this application can effectively support wide-area PPP-RTK services to achieve centimeter-level positioning accuracy, reducing the initial convergence time by more than 50%, while providing a more reliable data foundation for ionospheric monitoring applications and breaking through the strong dependence of traditional methods on reference station density. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification provided in an embodiment of this application. Figure 2 This is one of the schematic diagrams of the spatial neighborhood provided in the embodiments of this application; Figure 3 This is a second schematic diagram of the spatial neighborhood provided in the embodiments of this application; Figure 4 This is a schematic diagram of the spatiotemporal neighborhood provided in the embodiments of this application; Figure 5 This is a schematic diagram of the structure of a crowdsourced ionospheric delay data processing device based on spatiotemporal rearrangement verification provided in an embodiment of this application; Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or modules is not limited to the steps or modules listed, but may optionally include steps or modules not listed, or may optionally include other steps or modules inherent to such process, method, product, or apparatus.

[0024] It should be noted that the terms "first" and "second" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in an order other than those described or illustrated herein.

[0025] The present application will now be described in detail with reference to specific embodiments.

[0026] Next, combine Figure 1 This paper introduces a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification, provided by embodiments of this application. For details, please refer to... Figure 1 , Figure 1 This illustration shows a flowchart of a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification, provided in an embodiment of this application. Figure 1 As shown, the method includes the following steps: S101, acquire the observation values ​​of ionospheric delay at each time step from multiple stations; S102, taking each station as the target station, detect and remove the first abnormal observation value of the target station based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station; S103, a time series model is fitted based on the observations of the target station at each time step, and the second abnormal observations of the target station are detected and removed based on the second residual between the predicted values ​​and the observed values ​​at each time step obtained based on the time series model. S104. The spatial neighborhood formed by the target station and its first-order neighboring stations is determined by using a spherical Delaunay triangulation. The spatiotemporal neighborhood is constructed by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. S105, calculate the initial local variance of all observations in each spatiotemporal neighborhood; randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance; S106, based on the comparison results of the rearranged local variance after each random rearrangement and the initial local variance, detect and remove the third abnormal observation value of the target station; S107 outputs ionospheric delay data after removing all outlier observations.

[0027] In some embodiments, S101, the measuring station can be multiple GNSS devices within the target area, including but not limited to any smartphone, vehicle-mounted receiver, drone, etc. equipped with Location Based Service (LBS), and the process of obtaining the ionospheric delay includes: For each station, precise single-point positioning observation data of the station at each time moment is acquired. Based on the precise single-point positioning observation data, the oblique path ionospheric delay of the station at the corresponding time moment is calculated, including: Extract the latitude and longitude data of the puncture point corresponding to the precise single-point positioning observation data and the elevation angle of the observation satellite, and convert the oblique path ionospheric delay into the vertical ionospheric delay at the corresponding time. The vertical ionospheric delay is output as the observed value of the ionospheric delay at the corresponding time of the station.

[0028] The specific calculation process includes the following steps: A system of equations was constructed using PPP observation data from the station at each time step: ; in, Indicates the station To satellite s pseudorange at frequency f Indicates the station To satellite s The carrier phase at frequency f; Indicates the station To satellite s geometric distance; Indicates the station Receiver clock bias, Indicates satellite clock bias; Indicates zenith tropospheric delay; Indicates the station To satellite s The total electron content of the ionosphere along the line of sight, i.e., the slant ionospheric delay (SID). Indicates frequency-dependent signal delay; Indicates floating-point ambiguity; This is pseudorange observation noise. This is carrier phase observation noise; Represents the ionospheric random term; Ionospheric Pierce Point (IPP) and station Longitude difference, For puncture point and measurement station The difference in latitude.

[0029] It should be noted that when calculating SID data, one can... Represented as the deterministic part of a quadratic polynomial and the ionospheric random term ( The non-deterministic part corresponding to ).

[0030] For the deterministic part, In the formula, The binomial coefficients are, for example The formula is shown below ( The intraday cycle of the binomial coefficients in the deterministic part can be fitted using Fourier series. During the calculation, three main daily variation frequencies can be selected. ), represented as: (Daily cycle) (Half-day cycle) 、 (8-hour cycle) and The amplitude estimation parameter can be estimated as the daily constant; the binomial coefficients are then calculated from this. .

[0031] For the non-deterministic part, constraints can be imposed using a random walk model.

[0032] In this way, the oblique path ionospheric delay of the station at the corresponding time can be determined.

[0033] Subsequently, based on the longitude l, latitude b, and satellite elevation angle of the puncture point corresponding to the precise single-point positioning observation data, the oblique path ionospheric delay can be converted into the vertical ionospheric delay (ZID), i.e., the observed value of the ionospheric delay in S101. The calculation formula is expressed as follows: ; ; Where ZID represents the observed value of ionospheric delay, Indicates the slant path ionospheric delay. Indicates the satellite's elevation angle; The radius of the Earth can be taken as 6371 km. For reference altitude, a value of 350km can be taken.

[0034] It should be noted that, unless otherwise specified, the observation values ​​involved in the embodiments of this application all represent the Zenith Ionospheric Delay (ZID) at the puncture point corresponding to the station.

[0035] Next, a spatial consistency test based on inverse distance weighting can be performed on the ionospheric delay observations from all stations, following step S102: S1021, Spatial consistency verification is performed with each station as the target station; S1022, determine the preset range based on a preset radius with the target station as the center, and determine the adjacent stations that fall within the preset range.

[0036] Specifically, the size of the selected preset range can be adjusted according to the state of the ionosphere and the distribution density of the stations. The sparser the station distribution, the larger the preset radius of the preset range can be set. This application embodiment does not limit this.

[0037] S1023, calculate the geodetic distance between each adjacent station and the target station, including: If there are n adjacent stations, the latitude and longitude differences between the i-th adjacent station and the target station can be calculated using the following formula: , ; application Harversine The function can calculate the geodetic distance (the shortest path length between two points on the Earth's surface) between the i-th adjacent station and the target station, expressed by the formula: ; ; ; in, Indicates the latitude of the target station. Indicates the longitude of the target station; Indicates the latitude of the i-th adjacent station. This represents the longitude of the i-th adjacent station. This represents the latitude difference between the i-th adjacent station and the target station. This represents the longitude difference between the i-th adjacent station and the target station; This represents the geodetic distance between the i-th adjacent station and the target station. These are the process parameters used in the calculation.

[0038] S1024, based on the numerical value of the geodetic distance, determines the weighted interpolation weights of the observations from adjacent stations, using the following formula: ; in, This represents the weighted interpolation weight of the observations from the i-th adjacent station; the subscript j indicates the sequence number of the adjacent station. Represents the geodetic distance between n adjacent stations The sum of .

[0039] S1025, based on the weighted interpolation weights, performs weighted interpolation calculations on the observations of each adjacent station to obtain the interpolation result, expressed by the formula: ; in, This represents the observed value of the ionospheric delay at the i-th adjacent station. This represents the interpolation result.

[0040] S1026, the first residual is calculated based on the absolute value of the difference between the interpolation result and the observation value of the target station, expressed by the formula: ; in, The observed value representing the ionospheric delay at the target station. This represents the first residual.

[0041] S1027, Calculate the ratio of the first residual to the first standard deviation of the observations at each adjacent station within the preset range. If the following conditions are met: First preset threshold; ; in, The first standard deviation of the observations from each adjacent station within the preset range. This is the average of the observations from each adjacent station within a preset range. The first preset threshold can be set to 3.

[0042] That is, ratio If the value is greater than the first preset threshold, it indicates that the observation value of the target station at the corresponding time is greater than the first preset threshold. The first anomalous observation is the one with spatial dimensional anomalies; remove the first anomalous observation.

[0043] Perform steps S1021-S1027 above for each target station to remove all first-abnormal observations.

[0044] Next, after removing all first outlier observations in step S102, a time consistency check is performed, and step S103 is executed, including: First, execute S1031 to fit a time series model based on the observations at the target station at each time step. That is, fit a curve of the observations changing along the time axis based on the relationship between each time step and the observations, and establish a quadratic function model between the observation Z and time t, which can be expressed as the following formula: ; Where t represents time (time variable) , A time series model representing the variation of the observed value Z with time t. , , This represents the fitting coefficient.

[0045] The fitting coefficients can be obtained by minimizing the sum of squares of the residuals using the least squares method, as expressed by the formula: ; For example, select a time window of preset length K, and extract the time when the target stands within that time window. Observations Used to solve for the fitting coefficients. .

[0046] S1032, Extract the observation values ​​of the target station at each moment within a preset time window. Based on the time series model, the predicted value for each moment within a preset time window is calculated. .

[0047] S1033, calculate the absolute value of the difference between each observed value and the predicted value at the corresponding time, and obtain the second residual, expressed by the formula: ; in, This represents the second residual between the observed value at time k and the predicted value at the corresponding time.

[0048] S1034, calculate the ratio of the second residual to the second standard deviation of the observations at each time point within a preset time window, if the following conditions are met: Second preset threshold; ; in, The second standard deviation, This is the average of the observations at each moment within a preset time window. The second preset threshold can be set to 3.

[0049] That is, ratio If the value is greater than the second preset threshold, it indicates that the target station is at time [time value missing]. Observations The second abnormal observation is the one that is abnormal in the time dimension. The second abnormal observation is removed.

[0050] Perform steps S1031-S1034 above for each target station to remove all second abnormal observations.

[0051] Next, after removing all second outlier observations in step S103, the spatiotemporal rearrangement test continues, executing steps S104 and thereafter, including: In S104, the first step is to establish a spatiotemporal neighborhood, which includes the following steps: S1041, construct a spherical Delaunay triangulation with the puncture point corresponding to the target station and the puncture points corresponding to any two other stations as vertices, such that there are no puncture points outside the vertices of the spherical triangles within the circumscribed circle of each spherical triangle in the spherical Delaunay triangulation.

[0052] Specifically, an extended Bowyer-Watson algorithm can be used to construct a spherical Delaunay triangulation to achieve spatial neighborhood partitioning of spherical nodes. The construction process can be referred to... Figure 2 The provided diagrams specifically include: (1) Using a regular octahedron as the initial structure: The six vertices of the regular octahedron are evenly distributed on the target sphere (i.e., the sphere of the ionosphere) where the puncture point of the station is located, forming eight spherical triangles. This initial triangulation satisfies Delaunay's empty circle criterion—the interior of the circumscribed sphere of each triangle (referring to the smaller area enclosed by the circle on the sphere) does not contain any other nodes to be processed except for its own three vertices, thus forming the initial Delaunay triangulation.

[0053] (2) Add a new node to the initial Delaunay triangulation, denoted as point P (e.g., ...). Figure 2 (As shown in red), cavity detection is performed using the circumscribed sphere of a triangle: traverse all triangles in the current triangulation network. If the distance from point P to the circumscribed sphere of a triangle is less than the radius of that circle (indicating that P is inside the circle), then the spherical triangle corresponding to the circumscribed sphere of that triangle violates the empty circle criterion. All triangles that violate the criterion together constitute a cavity.

[0054] For example, such as Figure 2 As shown, after adding the red point P, a cavity was detected, and the non-common edges of the cavity were marked in yellow.

[0055] (3) Reconstruct the cavity: Delete the common edges of all spherical triangles within the cavity to form a closed spherical polygon boundary; connect point P to all vertices of the boundary in sequence to generate new spherical triangles—these new triangles all satisfy the empty circle criterion, forming the Delaunay triangulation after inserting P, such as Figure 2 The rightmost sub-figure is shown below.

[0056] The above description of (1)-(3) is repeated until all the puncture points corresponding to the stations are inserted. Then, the 6 vertices of the initial regular octahedron and their associated edges are deleted to obtain the final spherical Delaunay triangulation containing only the original spherical nodes, i.e. the spherical Delaunay triangulation constructed by S1041.

[0057] S1042, extract each spherical triangle from the constructed triangular network, determine the first-order neighboring stations directly connected to the target station based on the vertices of the spherical triangles, and construct a spatial neighborhood containing the target station and the first-order neighboring stations.

[0058] For example, such as Figure 3 As shown, there are golden dots. The spatial neighborhood diagram makes it easy to identify the green points in the diagram as points [intercepting / intercepting]. Directly connected first-order neighboring points, point Spatial neighborhood includes points The sampled observations and their relationship with the points The observations obtained at the same sampling time for each directly connected first-order neighbor.

[0059] S1043 expands the spatial neighborhood into a spatiotemporal neighborhood by using a sliding time window as a time constraint.

[0060] Specifically, a sliding time window can be constructed using three adjacent sampling moments on the time axis, i.e., sampling moments. Sampling time and sampling time .

[0061] The puncture point of each target station and each first-order neighbor station in the spatial neighborhood is determined at each sampling time of the sliding time window, thereby expanding the spatial neighborhood of a single moment to a spatiotemporal neighborhood of three moments within the sliding time window.

[0062] The puncture point at the sampling time in the middle of the three sampling times of the target station is taken as the puncture point to be inspected, and the observation value at the puncture point to be inspected is taken as the observation value to be inspected. The constructed spatiotemporal neighborhood is marked as the spatiotemporal neighborhood of the observation value to be inspected.

[0063] For example, such as Figure 4 The image shows a golden dot. The corresponding spatiotemporal neighborhood of the observed value to be inspected, the golden yellow dot. The puncture point to be examined for the observed value is a golden yellow dot. The corresponding spatiotemporal neighborhood includes the spatial neighborhood at sampling time t and the sampling time. Spatial neighborhood and sampling time The spatial neighborhood.

[0064] Understandably, the spatiotemporal neighborhood corresponding to an observation to be inspected includes the target station corresponding to the observation to be inspected and the observations of all first-order neighboring stations of the target station at each sampling time in the sliding time window, which can be represented as a set TPG(Q), where Q represents the puncture point to be inspected for the observation to be inspected.

[0065] In some embodiments, S105 specifically includes: S1051, calculate the initial local variance of all observations in each spatiotemporal neighborhood, as expressed by the formula: ; in, Represents an observation in the spatiotemporal neighborhood. Represents a puncture point in the spatiotemporal neighborhood. It represents the average value of observations within a spatiotemporal neighborhood. Indicates the observation value to be tested. Let be the initial local variance of the spatiotemporal neighborhood corresponding to the puncture point Q to be inspected.

[0066] For each puncture point to be examined, the initial local variance of the corresponding spatiotemporal neighborhood can be calculated. The spatiotemporal neighborhood of all puncture points to be examined can be represented as a spatiotemporal dataset. The set of initial local variances obtained by calculation can be represented as G represents the total number of puncture sites to be examined. It represents the spatiotemporal neighborhood corresponding to the g-th puncture point to be examined.

[0067] It should be noted that the smaller the local variance, the more similar the ionospheric delay of the puncture point to the ionospheric delay of the surrounding points is. Conversely, the larger the variance, the greater the difference between the point and the surrounding points, indicating that the ionospheric delay of the point is more likely to be an anomalous observation.

[0068] S1052 performs a preset number of random rearrangements on the mapping relationship between all observations and stations within each spatiotemporal neighborhood, and calculates the local variance of the rearrangement.

[0069] It should be noted that during random rearrangement, the time and spatial dimensions of each puncture point and station remain unchanged. However, the observations corresponding to each puncture point are shuffled. For example, if we set puncture point 1, puncture point 2, and puncture point 3, before random rearrangement, puncture point 1 corresponds to observation 1, puncture point 2 corresponds to observation 2, and puncture point 3 corresponds to observation 3. After random rearrangement, we may establish a mapping relationship between observation 1 and puncture point 2, and between observation 2 and puncture point 3. This is only an example of random rearrangement.

[0070] The process of calculating the rearranged local variance is the same as the process of calculating the initial local variance in S1051, and will not be repeated here.

[0071] Next, based on the comparison results between the initial local variance and the rearranged local variance, the determination is made. To determine whether the observed value at the corresponding puncture point is the third abnormal observed value, execute S106, including: S1061, compare the rearranged local variance after each random rearrangement with the initial local variance, and accumulate the total number of times the rearranged local variance is less than or equal to the initial local variance, as expressed by the formula: ; The local variance of the rearrangement generated by the y-th rearrangement If the count is incremented by 1, the total number of times is accumulated; m represents the total number of random rearrangements.

[0072] S1062, Calculate the significance test statistic based on the total number of times, expressed by the formula: ; If the significance test quantile If the value is greater than the significance level R, then the puncture point to be detected in the current spatiotemporal neighborhood is determined. The observed value to be checked is the third outlier, and all third outlier observed values ​​are deleted. The significance level R can be set to 0.05.

[0073] It should be noted that when judging outliers based on the significance test, an assumption was first made for each puncture point to be tested, that is, it is assumed that the observation value of each tropospheric delay in the spatiotemporal neighborhood corresponding to the puncture point does not belong to the homogeneous dataset. In other words, it is assumed that the homogeneity of the spatiotemporal neighborhood corresponding to the puncture point is a coincidence, and the observation value of the puncture point is an outlier.

[0074] If, after rearrangement and scrambling, the calculated local variance of the rearranged specimens is greater than the initial local variance before the scrambling, and the significance test value decreases accordingly, then it indicates that the puncture site before scrambling was not scrambled. The homogeneity is not accidental, thus refuting the hypothesis. Conversely, if the rearranged local variance calculated from multiple rearrangements is less than or equal to the initial local variance before the interruption, it indicates that after the rearrangement, the original local variance of the puncture point before the interruption remains unchanged. The variance at the point actually decreased (the similarity of the ionospheric delay increased), and the significance test value increased accordingly. At this point, the hypothesis was accepted, and the previous puncture point was determined to be disrupted. The homogeneity at a given location is accidental, and the corresponding observed value to be tested should be an outlier.

[0075] In some embodiments, after outputting ionospheric delay data from which all outlier observations have been removed, the method further includes: The vertical total electron content at the puncture point corresponding to each station is calculated based on the ionospheric delay after removing all outlier observations. The calculation formula is as follows: ; in, This represents the vertical total electron content, where f represents the signal frequency. This indicates that the ionospheric delay at the current station has been adjusted to exclude all outlier observations; The total vertical electron content of each neighboring station is selected based on the user's real-time location. The total vertical electron content is then interpolated based on the distance between the user and each neighboring station to obtain the total vertical electron content at the user's location.

[0076] The following are apparatus embodiments of this application, which can be used to execute the method embodiments of this application. For details not disclosed in the apparatus embodiments of this application, please refer to the method embodiments of this application.

[0077] Please see below. Figure 5 The image below is a schematic diagram of a crowdsourced ionospheric delay data processing device based on spatiotemporal rearrangement verification, provided as an exemplary embodiment of this application. The device includes: The crowdsourced data acquisition unit is used to acquire observations of ionospheric delay from multiple stations at each time point; The outlier detection unit is used to take each station as the target station and detect and remove the first outlier observation value of the target station based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station. The outlier detection unit is also used to fit a time series model based on the observations of the target station at each time moment, and to detect and remove the second outlier observations of the target station based on the second residual between the predicted value and the observed value at each time moment obtained based on the time series model. The outlier detection unit is also used to determine the spatial neighborhood formed by the target station and its first-order neighboring stations using a spherical Delaunay triangulation, and to construct a spatiotemporal neighborhood by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. The outlier detection unit is also used to calculate the initial local variance of all observations in each spatiotemporal neighborhood; it is also used to randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance. The outlier detection unit is also used to detect and remove the third outlier observation of the target station based on the comparison results of the rearranged local variance after each random rearrangement and the initial local variance. The crowdsourced ionospheric delay data output unit is used to output ionospheric delay data after removing all outlier observations.

[0078] It should be noted that the apparatus provided in the above embodiments, when executing a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification, is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. Furthermore, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and their implementation process is detailed in the method embodiments, which will not be repeated here.

[0079] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

[0080] Please see Figure 6 This is a structural block diagram of an electronic device provided in an embodiment of this application.

[0081] like Figure 6 As shown, the electronic device includes a processor and a memory.

[0082] In this embodiment, the processor is the control center of the computer system, and can be a processor of a physical machine or a processor of a virtual machine. The processor may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor can be implemented using at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), or PLA (Programmable Logic Array).

[0083] A processor can also include a main processor and a coprocessor. The main processor is used to process data in the wake-up state and is also called the CPU (Central Processing Unit). The coprocessor is a low-power processor used to process data in the standby state.

[0084] The memory may include one or more computer-readable storage media, which may be non-transitory. The memory may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments of this application, the non-transitory computer-readable storage media in the memory are used to store at least one instruction, which is executed by a processor to implement the methods in the embodiments of this application.

[0085] In some embodiments, the electronic device further includes a peripheral device interface and at least one peripheral device. The processor, memory, and peripheral device interface are connected via a bus or signal line. Each peripheral device is connected to the peripheral device interface via a bus, signal line, or circuit board. Specifically, the peripheral device includes: a display screen, a camera, and audio circuitry. The peripheral device interface can be used to connect at least one I / O (Input / Output) related peripheral device to the processor and memory.

[0086] In some embodiments of this application, the processor, memory, and peripheral device interfaces are integrated on the same chip or circuit board; in other embodiments of this application, any one or two of the processor, memory, and peripheral device interfaces can be implemented on separate chips or circuit boards. This application does not specifically limit the implementation in this regard.

[0087] The electronic device structural block diagrams shown in the embodiments of this application do not constitute a limitation on the electronic device. The electronic device may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0088] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the methods in any of the foregoing embodiments. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0089] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of software products. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification, characterized in that, include: Acquire observations of ionospheric delay from multiple stations at each time step; Each station is taken as the target station. The first abnormal observation value of the target station is detected and removed based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station. A time series model is obtained by fitting the observations of the target station at each time step. The second abnormal observations of the target station are detected and removed based on the second residual between the predicted values ​​and the observed values ​​at each time step obtained from the time series model. The spatial neighborhood formed by the target station and its first-order neighboring stations is determined by using a spherical Delaunay triangulation. The spatiotemporal neighborhood is constructed by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. Calculate the initial local variance of all observations in each spatiotemporal neighborhood; randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance; The third outlier observation of the target station is detected and removed based on the comparison between the rearranged local variance after each random rearrangement and the initial local variance. The output is ionospheric delay data that has been filtered out for all outlier observations.

2. The crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to claim 1, characterized in that, The acquisition of observations of ionospheric delay from multiple stations at each moment includes: For each station, precise single-point positioning observation data of the station at each time moment is acquired, and the oblique path ionospheric delay of the station at the corresponding time moment is calculated based on the precise single-point positioning observation data. Extract the latitude and longitude data of the puncture point corresponding to the precise single-point positioning observation data and the elevation angle of the observation satellite, and convert the oblique path ionospheric delay into the vertical ionospheric delay at the corresponding time. The vertical ionospheric delay is output as the observed value of the ionospheric delay at the corresponding time of the station.

3. The crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to claim 1, characterized in that, The step of detecting and removing the first abnormal observation value of the target station based on the first residual of the observation values ​​of all adjacent stations within a preset range of the target station at the same time includes: The preset range is determined based on a preset radius with the target station as the center, and adjacent stations falling within the preset range are identified. The geodetic distance between each adjacent station and the target station is calculated. Based on the geodetic distance, the weighted interpolation weights of the observations of the corresponding adjacent stations are determined. Based on the weighted interpolation weights, the observations of each adjacent station are weighted and interpolated to obtain the interpolation result. The first residual is calculated based on the absolute value of the difference between the interpolation result and the observation value of the target station; If the ratio of the first residual to the first standard deviation of the observation value of each adjacent station within the preset range is greater than the first preset threshold, then the observation value of the target station at the corresponding time is the first abnormal observation value with spatial dimension anomaly. Remove all first outlier observations.

4. The crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to claim 3, characterized in that, The step of detecting and removing second abnormal observations of the target station based on the second residual between the predicted and observed values ​​obtained from the time series model at each time step includes: Extract the observation values ​​of the target station at each moment within a preset time window, and calculate the predicted values ​​at each moment within the preset time window based on the time series model; The absolute value of the difference between each observed value and the predicted value at the corresponding time is calculated to obtain the second residual; If the ratio of the second residual to the second standard deviation of the observation value at each moment within the preset time window is greater than the second preset threshold, then the observation value of the target station at the corresponding moment is the second abnormal observation value with an abnormal time dimension. Remove all second outlier observations.

5. The crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to claim 1, characterized in that, The method of determining the spatial neighborhood of the target station and its first-order neighboring stations using a spherical Delaunay triangulation includes: Construct a spherical Delaunay triangulation with the puncture point corresponding to the target station and the puncture points corresponding to any two other stations as vertices, such that there are no puncture points outside the vertices of the spherical triangles within the circumscribed circle of each spherical triangle in the spherical Delaunay triangulation. Extract each spherical triangle from the constructed triangulation network, determine the first-order neighboring stations directly connected to the target station based on the vertices of the spherical triangles, and construct a spatial neighborhood containing the target station and the first-order neighboring stations. The process of extracting observations from each station within a spatial neighborhood based on a sliding time window to construct a spatiotemporal neighborhood includes: A sliding time window is constructed using three adjacent sampling times on the time axis. The observations of the target station and the first-order neighboring station are extracted at each sampling time. The observation corresponding to the sampling time in the middle of the three sampling times of the target station is used as the observation to be examined, and the corresponding spatiotemporal neighborhood is constructed.

6. The crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to claim 5, characterized in that, The detection and removal of third outlier observations at the target station based on the comparison between the rearranged local variance after each random rearrangement and the initial local variance includes: After each random rearrangement, the size of the rearranged local variance is compared with the initial local variance, and the total number of times the rearranged local variance is less than or equal to the initial local variance is accumulated. The significance test value is calculated based on the total number of times. If the significance test value is greater than the significance level, the observation to be tested in the current spatiotemporal neighborhood is determined to be the third abnormal observation value. Remove all third-anomaly observations in the spatiotemporal neighborhood.

7. A crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification according to any one of claims 1-6, characterized in that, After removing ionospheric delay data from all outlier observations from the output, the method further includes: The vertical total electron content at the puncture point corresponding to each station is calculated based on the ionospheric delay after all outlier observations have been removed. The total vertical electron content of each neighboring station is selected based on the user's real-time location. The total vertical electron content is then interpolated based on the distance between the user and each neighboring station to obtain the total vertical electron content at the user's location.

8. A crowdsourced ionospheric delay data processing device based on spatiotemporal rearrangement verification, characterized in that, include: The crowdsourced data acquisition unit is used to acquire observations of ionospheric delay from multiple stations at each time point; The outlier detection unit is used to take each station as the target station and detect and remove the first outlier observation value of the target station based on the first residual of the observation values ​​of all adjacent stations and the target station at the same time within the preset range of the target station. The outlier detection unit is also used to fit a time series model based on the observations of the target station at each time moment, and to detect and remove the second outlier observations of the target station based on the second residual between the predicted value and the observed value at each time moment obtained based on the time series model. The outlier detection unit is also used to determine the spatial neighborhood formed by the target station and its first-order neighboring stations using a spherical Delaunay triangulation, and to construct a spatiotemporal neighborhood by extracting the observation values ​​of each station in the spatial neighborhood based on a sliding time window. The outlier detection unit is also used to calculate the initial local variance of all observations in each spatiotemporal neighborhood; it is also used to randomly rearrange the mapping relationship between all observations and stations in each spatiotemporal neighborhood a preset number of times, and calculate the rearranged local variance. The outlier detection unit is also used to detect and remove the third outlier observation of the target station based on the comparison results of the rearranged local variance after each random rearrangement and the initial local variance. The crowdsourced ionospheric delay data output unit is used to output ionospheric delay data after removing all outlier observations.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a crowdsourced ionospheric delay data processing method based on spatiotemporal rearrangement verification as described in any one of claims 1 to 7.

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