Complementation method for meteorological monitoring data missing

Abstract

The invention relates to the technical field of meteorological monitoring data, and discloses a meteorological monitoring data missing complementing method, which comprises the following steps: selecting a monitoring station with data missing as a to-be-complemented whole station, finding an intermediate station which is closest to the monitoring station and has complete data to carry out missing simulation processing, and according to the distance between the intermediate station and the surrounding monitoring station, carrying out data missing complementing on the to-be-complemented whole station; the method comprises the following steps: gradually increasing the number of modeling stations, constructing an observation matrix, calculating a root-mean-square error, determining the number of optimal modeling stations, complementing the data of the whole station to be complemented by using the data of the optimal modeling stations, considering both the time sequence and the spatial distribution characteristics, and having high interpretability and transportability. Meanwhile, the method only depends on the physical characteristics driven by Beidou meteorological data, does not depend on external training data, is simple in calculation, does not have the problems of temporal-spatial resolution and updating period difference between different data sources, can be adaptively adjusted to adapt to different monitoring station intensities, ensures that complemented data approaches to a real value, and improves the accuracy of data complementation. And the stability and integrity of Beidou meteorological monitoring are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of meteorological monitoring data, and particularly to a method for filling in missing meteorological monitoring data. Background Art

[0002] The timeliness, accuracy, and integrity of meteorological monitoring data are crucial for aspects such as disaster warning, emergency response, sustainable development of agriculture and the environment, and national security. The Beidou satellite navigation system, as an advanced technology independently developed in China, not only provides positioning, navigation, and timing services but also can monitor ground meteorological data in real time, demonstrating its great potential in the field of meteorological monitoring.

[0003] However, in practical applications, Beidou meteorological monitoring data often lacks data due to various factors. Given the key role of meteorological data in fields such as climate research, disaster prediction, agricultural production, and public safety, how to effectively fill in these missing data has become a core issue to be solved urgently.

[0004] Traditional methods for filling in missing meteorological data, such as interpolation and regression analysis, are often designed for general meteorological data and lack a dedicated solution for Beidou meteorological monitoring data. At the same time, these methods usually only consider the time characteristics of the data and ignore the temporal and spatial distribution characteristics simultaneously possessed by Beidou meteorological monitoring stations. In recent years, although the multi-source data fusion strategy has become a research hotspot, the methods based on machine learning have achieved certain results, but their model interpretability and portability are poor, and they highly rely on a large amount of training data, with high computational complexity. The differences in spatio-temporal resolution and update period between different data sources also limit the wide application of this method in the meteorological field. Summary of the Invention

[0005] Based on this, it is necessary to address the above problems and propose a method for filling in missing meteorological monitoring data that takes into account both temporal and spatial distribution characteristics, has high interpretability and portability, only relies on the physical characteristics driven by Beidou meteorological data itself, does not rely on external training data, has simple calculations, does not have problems with spatio-temporal resolution and update period differences between different data sources, and can adaptively adjust to different monitoring station densities to ensure that the filled data approaches the true value and effectively improve the stability and integrity of Beidou meteorological monitoring.

[0006] To achieve the above object, in the first aspect, the present invention provides a method for filling in missing meteorological monitoring data, and the method includes: Obtain the meteorological monitoring data of all monitoring stations in the target area within a preset time series, and select one of the monitoring stations with missing meteorological monitoring data as the station to be filled in among all monitoring stations; Take the monitoring station that is closest to the whole station to be supplemented and has no missing meteorological monitoring data as the intermediate station, and use the meteorological monitoring data of the emptied intermediate station as the missing meteorological monitoring data of the intermediate station; Take the n monitoring stations that are closest to the intermediate station as the modeling stations, where n is a positive integer and the initial value of n is 1; Form an observation matrix by columns with the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations, and based on the observation matrix, complete the missing meteorological monitoring data of the intermediate station to obtain the completed meteorological monitoring data of the intermediate station; Determine the root mean square error based on the completed meteorological monitoring data of the intermediate station and the meteorological monitoring data; Let n = n + 1, return to execute the step of taking the n monitoring stations that are closest to the intermediate station as the modeling stations until n is equal to the maximum modeling threshold, obtain multiple root mean square errors, and take the n corresponding to the minimum root mean square error as the target modeling number. Let the target modeling stations be m; Take the m monitoring stations that are closest to the whole station to be supplemented as the modeling stations; Form a to-be-completed observation matrix by columns with the meteorological monitoring data of the whole station to be supplemented and the meteorological monitoring data of the m modeling stations, and based on the to-be-completed observation matrix, complete the meteorological monitoring data of the whole station to be supplemented to obtain the completed meteorological monitoring data of the whole station to be supplemented.

[0007] Optionally, before the step of based on the observation matrix, completing the missing meteorological monitoring data of the intermediate station to obtain the completed meteorological monitoring data of the intermediate station, the method further includes: Determine whether the row vectors of the observation matrix at any observation epoch satisfy non-empty based on the observation matrix; In the case where there is a row vector at any observation epoch of the observation matrix that satisfies non-empty, let n = n + 1, and return to execute the step of taking the n monitoring stations that are closest to the intermediate station as the modeling stations until the row vectors of the observation matrix at any observation epoch do not satisfy non-empty.

[0008] Optionally, the step of based on the observation matrix, completing the missing meteorological monitoring data of the intermediate station to obtain the completed meteorological monitoring data of the intermediate station includes: Determine the covariance matrix based on the observation matrix; Determine the non-missing row vector and the missing row vector at the i-th observation epoch based on the observation matrix, where i is a positive integer and the initial value of i is 1; Determine the non-missing mean estimate value based on the non-missing row vector at the i-th observation epoch, and determine the missing mean estimate value based on the missing row vector at the i-th observation epoch; Determine a non - missing estimation matrix corresponding to the covariance matrix of non - missing row vectors and a pre - cross - estimation matrix corresponding to the cross - covariance matrix between non - missing row vectors and missing row vectors at the \(i\) - th observation epoch according to the covariance matrix; Determine a regression coefficient according to the non - missing estimation matrix and the pre - cross - estimation matrix; Determine a completed estimation row vector at the \(i\) - th observation epoch according to the regression coefficient, the non - missing mean estimate value, the missing mean estimate value, and the non - missing row vectors at the \(i\) - th observation epoch; Complete the row vectors of the observation matrix at the \(i\) - th observation epoch according to the completed estimation row vector at the \(i\) - th observation epoch to obtain an intermediate matrix; Extract the completed filling elements from the intermediate matrix to obtain a completed filling column vector and completed filling column labels; Determine a stagnation tolerance according to the completed filling column vector and the completed filling column labels; Determine whether the intermediate matrix is completed according to the stagnation tolerance; In the case that the intermediate matrix is not completed, determine a missing estimation matrix corresponding to the missing covariance matrix of the missing row vectors and a post - cross - estimation matrix corresponding to the cross - covariance matrix between the missing row vectors and non - missing row vectors at the \(i\) - th observation epoch according to the covariance matrix; Determine a residual covariance matrix according to the regression coefficient, the non - missing estimation matrix, the missing estimation matrix, the pre - cross - estimation matrix, and the post - cross - estimation matrix; Determine an intermediate covariance matrix according to the residual covariance matrix and the covariance matrix; Take the intermediate covariance matrix as the covariance matrix, let \(i = i + 1\), and return to execute the step of determining non - missing row vectors and missing row vectors at the \(i\) - th observation epoch according to the observation matrix until the intermediate matrix is completed; Take the completed intermediate matrix as the target observation matrix; Complete the missing meteorological monitoring data of the intermediate station according to the target observation matrix to obtain the completed meteorological monitoring data of the intermediate station.

[0009] Optionally, the determining a regression coefficient according to the non - missing estimation matrix and the pre - cross - estimation matrix includes: Use the formula to determine the regression coefficient; where is the regression coefficient, is the diagonal matrix of the non - missing estimation matrix, is the non - missing estimation matrix, is the ridge parameter of ridge regression, is the identity matrix, is the forward cross - estimation matrix.

[0010] Optionally, determining the completed estimation row vector at the i - th observation epoch according to the regression coefficient, the non - missing mean estimation value, the missing mean estimation value, and the non - missing row vector at the i - th observation epoch includes: Using the formula to determine the completed estimation row vector at the i - th observation epoch; where, is the completed estimation row vector at the i - th observation epoch, is the missing mean estimation value, is the non - missing row vector at the i - th observation epoch, is the non - missing mean estimation value, is the regression coefficient.

[0011] Optionally, determining the residual covariance matrix according to the regression coefficient, the non - missing estimation matrix, the missing estimation matrix, the forward cross - estimation matrix, and the backward cross - estimation matrix includes: Using the formula to determine the residual covariance matrix; where, is the residual covariance matrix, is the missing estimation matrix, is the regression coefficient, is the transpose symbol, is the non - missing estimation matrix, is the forward cross - estimation matrix, is the backward cross - estimation matrix.

[0012] Optionally, determining the covariance matrix according to the observation matrix includes: Determining the column mean row vector according to the observation matrix; Determining the centering matrix according to the column mean row vector and the observation matrix; Determining the covariance matrix according to the centering matrix; The determining the non - missing row vector and the missing row vector at the i - th observation epoch according to the observation matrix includes: Determining the non - missing row vector and the missing row vector at the i - th observation epoch according to the centering matrix; Completing the row vector of the observation matrix at the $i$-th observation epoch according to the completed estimation row vector, to obtain an intermediate matrix, includes: Completing the row vector of the centralized matrix at the $i$-th observation epoch according to the completed estimation row vector, to obtain the intermediate matrix; Determining the stagnation tolerance according to the completed filling column vector and the completed filling column label, includes: Determining the filling label mean row vector according to the completed filling column label and the column mean row vector; Determining the stagnation tolerance according to the filling label mean row vector and the completed filling column vector; Taking the completed intermediate matrix as the target observation matrix, includes: Determining an intermediate observation matrix according to the completed intermediate matrix and the column mean row vector; Taking the intermediate observation matrix as the target observation matrix.

[0013] Optionally, determining the stagnation tolerance according to the filling label mean row vector and the completed filling column vector, includes: Using the formula to determine the stagnation tolerance; where is the matrix norm function, is the filling column vector, is the total number of missing elements of the observation matrix or the centralized matrix, is the filling mean row vector, is the transpose symbol, is the stagnation tolerance.

[0014] Optionally, determining whether the intermediate matrix is completed according to the stagnation tolerance, includes: When the stagnation tolerance is greater than or equal to the stagnation tolerance threshold, determining that the intermediate matrix is not completed; When the stagnation tolerance is less than the stagnation tolerance threshold, determining that the intermediate matrix is completed.

[0015] Optionally, completing the meteorological monitoring data of the station to be completed according to the observation matrix to be completed, to obtain the completed meteorological monitoring data of the station to be completed, includes: Taking the observation matrix to be completed as the observation matrix, returning to execute the step of determining the covariance matrix according to the observation matrix, to obtain the target observation matrix, and taking the target observation matrix as the target completed observation matrix; Complete the observation matrix according to the target, and complete the meteorological monitoring data of the station to be supplemented to obtain the completed meteorological monitoring data of the station to be supplemented.

[0016] To achieve the above object, the present invention provides a device for completing missing meteorological monitoring data in a second aspect. The device includes: An acquisition and selection module, configured to acquire the meteorological monitoring data of all monitoring stations in a target area within a preset time series, and select one of the monitoring stations with missing meteorological monitoring data as the station to be supplemented among all the monitoring stations; A determination and nulling module, configured to use a monitoring station that is closest to the station to be supplemented and has no missing meteorological monitoring data as an intermediate station, and use the meteorological monitoring data of the nulled intermediate station as the missing meteorological monitoring data of the intermediate station; An iterative initial module, configured to use the n monitoring stations closest to the intermediate station as modeling stations, where n is a positive integer and the initial value of n is 1; A first composition and completion module, configured to form an observation matrix by columns with the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations, and complete the missing meteorological monitoring data of the intermediate station according to the observation matrix to obtain the completed meteorological monitoring data of the intermediate station; A root mean square error determination module, configured to determine the root mean square error according to the completed meteorological monitoring data and the meteorological monitoring data of the intermediate station; An iteration module, configured to make n=n+1, and return to execute the step of using the n monitoring stations closest to the intermediate station as modeling stations until n is equal to the maximum modeling threshold, obtaining multiple root mean square errors, and using the n corresponding to the minimum root mean square error as the target modeling number. Let the target modeling stations be m; A modeling determination module, configured to use the m monitoring stations closest to the station to be supplemented as modeling stations; A second composition and completion module, configured to form a to-be-completed observation matrix by columns with the meteorological monitoring data of the station to be supplemented and the meteorological monitoring data of the m modeling stations, and complete the meteorological monitoring data of the station to be supplemented according to the to-be-completed observation matrix to obtain the completed meteorological monitoring data of the station to be supplemented.

[0017] To achieve the above object, the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor is caused to execute the method according to any one of the first aspect.

[0018] To achieve the above object, the present invention provides a computer device in a fourth aspect, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor is caused to execute the method described in any one of the first aspect.

[0019] By adopting the embodiment of the present invention, the following beneficial effects are achieved: By obtaining the meteorological monitoring data of all monitoring stations in the target area within a preset time series, and among all the monitoring stations, selecting one monitoring station with missing meteorological monitoring data as the station to be completely supplemented; Selecting a monitoring station that is closest to the station to be completely supplemented and has no missing meteorological monitoring data as the intermediate station, and using the meteorological monitoring data of the intermediate station after being set to null as the missing meteorological monitoring data of the intermediate station; Considering all monitoring stations that are closest to the intermediate station as modeling stations, where n is a positive integer and the initial value of n is 1; Composing an observation matrix by columns with the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations, and based on the observation matrix, complementing the missing meteorological monitoring data of the intermediate station to obtain the complemented meteorological monitoring data of the intermediate station; Determining the root mean square error based on the complemented meteorological monitoring data of the intermediate station and the meteorological monitoring data; Letting n = n + 1, and returning to execute the step of considering all monitoring stations that are closest to the intermediate station as modeling stations until n is equal to the maximum modeling threshold, obtaining multiple root mean square errors, and taking the n corresponding to the minimum root mean square error as the target modeling number, and setting the target modeling stations as m; Considering all m monitoring stations that are closest to the station to be completely supplemented as modeling stations; Composing a to-be-complemented observation matrix by columns with the meteorological monitoring data of the station to be completely supplemented and the meteorological monitoring data of the m modeling stations, and based on the to-be-complemented observation matrix, complementing the meteorological monitoring data of the station to be completely supplemented to obtain the complemented meteorological monitoring data of the station to be completely supplemented. That is, by selecting the monitoring station with missing data as the station to be completely supplemented, finding the closest intermediate station with complete data for simulating the missing data, then gradually increasing the number of modeling stations according to the distance between the intermediate station and the surrounding monitoring stations, determining the optimal number of modeling stations by constructing an observation matrix and calculating the root mean square error, and finally using the data of the optimal modeling stations to complement the data of the station to be completely supplemented. This method not only considers the time series but also takes into account the spatial distribution characteristics, and has high interpretability and portability. At the same time, this method only relies on the physical characteristics driven by the Beidou meteorological data itself, does not rely on external training data, has simple calculations, does not have the problem of differences in spatio-temporal resolution and update cycle between different data sources, and can adaptively adjust to different monitoring station densities to ensure that the complemented data approaches the true value, effectively improving the stability and integrity of Beidou meteorological monitoring. Description of the Drawings

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0021] Wherein: Figure 1 It is a schematic diagram of a method for completing missing meteorological monitoring data in an embodiment of the present application; Figure 2 It is a schematic diagram of a device for completing missing meteorological monitoring data in an embodiment of the present application; Figure 3 It is the internal structure diagram of a computer device in some embodiments. Detailed implementation manners

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0023] The timeliness, accuracy, and integrity of meteorological monitoring data are crucial for aspects such as disaster warning, emergency response, sustainable development of agriculture and the environment, and national security. The Beidou satellite navigation system, as an advanced technology independently developed in China, not only provides positioning, navigation, and timing services but also can monitor ground meteorological data in real time, demonstrating its great potential in the field of meteorological monitoring.

[0024] However, in practical applications, Beidou meteorological monitoring data often lacks data due to various factors. Given the key role of meteorological data in fields such as climate research, disaster prediction, agricultural production, and public safety, how to effectively complete these missing data has become a core issue to be solved urgently.

[0025] Traditional methods for completing missing meteorological data, such as interpolation and regression analysis, are often designed for general meteorological data and lack a dedicated solution for Beidou meteorological monitoring data. At the same time, these methods usually only consider the time characteristics of the data and ignore the temporal and spatial distribution characteristics that Beidou meteorological monitoring stations possess simultaneously. In recent years, although the multi-source data fusion strategy has become a research hotspot, the methods based on machine learning have achieved certain results, but their model interpretability and portability are poor, and they highly rely on a large amount of training data, with high computational complexity. The differences in spatio-temporal resolution and update period between different data sources also limit the wide application of this method in the meteorological field.

[0026] In view of the above problems, the present application proposes a method for filling in missing meteorological monitoring data, which takes into account both temporal sequence and spatial distribution characteristics, has high interpretability and portability, and only relies on the physical characteristics driven by Beidou meteorological data itself without relying on external training data. It has simple calculations, does not have the problem of differences in spatio-temporal resolution and update cycle between different data sources, and can adaptively adjust to different monitoring station densities to ensure that the filled data approaches the true value, effectively improving the stability and integrity of Beidou meteorological monitoring. The specific implementation principle will be described in detail in the following embodiments.

[0027] The present application provides a method for filling in missing meteorological monitoring data in a first aspect.

[0028] Please refer to Figure 1 , which is a schematic diagram of a method for filling in missing meteorological monitoring data in an embodiment of the present application. The method includes: Step 110: Obtain the meteorological monitoring data of all monitoring stations in the target area within a preset time series, and select one of the monitoring stations with missing meteorological monitoring data as the station to be filled in among all monitoring stations.

[0029] Among them, both the target area and the preset time series can be set by the operator based on a large amount of experience, experiments or statistics. Of course, they can also be set by the operator according to actual needs.

[0030] In some embodiments, the target area can be a research area determined by the operator; the preset time series can be a complete observation time series determined by the operator based on a large amount of experience, experiments or statistics.

[0031] Step 120: Select a monitoring station that is closest to the station to be filled in and has no missing meteorological monitoring data as the intermediate station, and use the meteorological monitoring data of the emptied intermediate station as the missing meteorological monitoring data of the intermediate station.

[0032] It should be noted that, in order to determine the optimal number of modeling stations for filling in data for the station to be filled in, the present application first selects a monitoring station that is closest to the station to be filled in and has no missing meteorological monitoring data as the intermediate station for modeling simulation, and then determines the optimal number of modeling.

[0033] It can be understood that since the intermediate station is close to the station to be filled in, it can be regarded as having similar meteorological conditions. Therefore, there is a strong spatio-temporal correlation between the meteorological monitoring data of the intermediate station and the station to be filled in.

[0034] Step 130: Select the n monitoring stations closest to the intermediate station as modeling stations, where n is a positive integer and the initial value of n is 1.

[0035] It should be noted that, in order to comprehensively consider the temporal and spatial characteristics of meteorological monitoring data, this application takes the n monitoring stations closest to the intermediate station as modeling stations and performs iteration, aiming to simulate the most suitable number of modeling stations for the station to be supplemented.

[0036] It can be understood that there is a strong spatio-temporal correlation between the meteorological monitoring data between the intermediate station and the station to be supplemented, and there is also a strong spatio-temporal correlation between the meteorological monitoring data of the n monitoring stations and the intermediate station. Moreover, the terrain, meteorological data, monitoring station density, and missing degree in different regions are different, and the most suitable number of modeling stations is also different. Therefore, in order to determine the most suitable number of modeling stations for the station to be supplemented, this application uses spatio-temporal correlation to simulate the most suitable number of modeling stations for the station to be supplemented.

[0037] In some embodiments, the n monitoring stations closest to the intermediate station may or may not include the station to be supplemented; it can be understood that since the station to be supplemented is a monitoring station with missing meteorological monitoring data and subsequent iteration is required to determine the root mean square error and determine the optimal number of modeling stations through the root mean square error, whether the n monitoring stations closest to the intermediate station include the station to be supplemented will not affect the optimal number of modeling stations.

[0038] Step 140: Compose the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations into an observation matrix by columns, and according to the observation matrix, complete the missing meteorological monitoring data of the intermediate station to obtain the completed meteorological monitoring data of the intermediate station.

[0039] In some embodiments, the data of the intermediate station and the n modeling stations can be composed according to one column of data for each station to obtain an observation matrix; for example, when the data of each station in the preset time series is 100 data, the observation matrix is a matrix with 100 rows and n + 1 columns.

[0040] In some embodiments, a matrix completion algorithm (such as singular value decomposition or iterative optimization) can be used to complete the missing meteorological monitoring data of the intermediate station according to the observation matrix to obtain the completed meteorological monitoring data of the intermediate station.

[0041] Step 150: Determine the root mean square error according to the completed meteorological monitoring data of the intermediate station and the meteorological monitoring data.

[0042] In some embodiments, the formula can be used to determine the root mean square error; where is the root mean square error, is the total number of data of the completed meteorological monitoring data or the meteorological monitoring data of the intermediate station, is the r-th data in the supplemented meteorological monitoring data of the intermediate station, is the r-th data in the meteorological monitoring data of the intermediate station.

[0043] Step 160: Let n = n + 1, and return to execute the step of taking the n monitoring stations closest to the intermediate station as modeling stations until n is equal to the maximum modeling threshold, obtaining multiple root mean square errors, and taking the n corresponding to the minimum root mean square error as the target modeling number. Let the target modeling stations be m.

[0044] Among them, the maximum modeling threshold can be set by the operator based on a large amount of experience, experiments or statistics. Of course, it can also be set by the operator according to actual needs.

[0045] It should be noted that the target modeling number is the number of models most suitable for the station to be supplemented simulated by this application by utilizing spatio-temporal correlation.

[0046] Step 170: Take the m monitoring stations closest to the station to be supplemented as modeling stations.

[0047] In some embodiments, the m monitoring stations closest to the station to be supplemented may include the intermediate station.

[0048] Step 180: Compose the meteorological monitoring data of the station to be supplemented and the meteorological monitoring data of the m modeling stations into a to-be-supplemented observation matrix column by column, and based on the to-be-supplemented observation matrix, supplement the meteorological monitoring data of the station to be supplemented to obtain the supplemented meteorological monitoring data of the station to be supplemented.

[0049] For the detailed description of this embodiment, reference can be made to the relevant content of Step 140 above, and details will not be elaborated here.

[0050] In the embodiments of this application, by selecting the monitoring station with missing data as the station to be supplemented, finding the closest intermediate station with complete data for missing data simulation, then gradually increasing the number of modeling stations according to the distance between the intermediate station and surrounding monitoring stations, determining the optimal number of modeling stations by constructing an observation matrix and calculating the root mean square error, and finally using the data of the optimal modeling stations to supplement the data of the station to be supplemented. This method takes into account both the time series and the spatial distribution characteristics, and has high interpretability and portability. At the same time, this method only depends on the physical characteristics driven by the Beidou meteorological data itself, does not depend on external training data, is simple to calculate, does not have the problem of differences in spatio-temporal resolution and update cycle between different data sources, and can adaptively adjust to different monitoring station densities to ensure that the supplemented data approaches the true value, effectively improving the stability and integrity of Beidou meteorological monitoring.

[0051] In a feasible implementation manner, before step 140 in the above embodiment, where the missing meteorological monitoring data of the intermediate station is completed according to the observation matrix to obtain the completed meteorological monitoring data of the intermediate station, the method further includes: determining whether the row vectors of the observation matrix at any observation epoch satisfy non-emptiness according to the observation matrix; in the case where there is a row vector at any observation epoch of the observation matrix that satisfies non-emptiness, let n = n + 1, and return to execute the step of taking the n monitoring stations closest to the intermediate station as the modeling stations until the row vectors of the observation matrix at any observation epoch do not satisfy non-emptiness.

[0052] For meteorological monitoring data, the observation epoch refers to the time points in the preset time series, and for the observation matrix, the observation epoch refers to the row labels in the observation matrix.

[0053] It should be noted that in the case where there is a row vector at any observation epoch of the observation matrix that satisfies non-emptiness, there will be a situation where it cannot be completely completed. At this time, the root mean square error determined by iteration must be relatively large. Therefore, the n in this iteration is definitely not the optimal number of modeling stations. In order to reduce the calculation amount and improve the calculation efficiency, the present application needs to perform an iterative judgment of non-emptiness before the above step 140.

[0054] In the embodiments of the present application, by iteratively detecting and judging the non-emptiness of the observation matrix in advance, the modeling process is optimized, the calculation efficiency is improved, the feasibility and accuracy of the completion are ensured, and at the same time, the robustness of the method is enhanced, which has important practical significance and application value for the completion work of missing meteorological monitoring data.

[0055] In a feasible implementation manner, step 140 in the above embodiment, based on the observation matrix, fills in the missing meteorological monitoring data of the intermediate station to obtain the filled meteorological monitoring data of the intermediate station, including: determining the covariance matrix according to the observation matrix; determining the non-missing row vector and the missing row vector at the i-th observation epoch according to the observation matrix, where i is a positive integer and the initial value of i is 1; determining the non-missing mean estimate value according to the non-missing row vector at the i-th observation epoch, and determining the missing mean estimate value according to the missing row vector at the i-th observation epoch; determining the non-missing estimation matrix corresponding to the covariance matrix of the non-missing row vector at the i-th observation epoch according to the covariance matrix, and the pre-cross estimation matrix corresponding to the cross-covariance matrix between the non-missing row vector and the missing row vector at the i-th observation epoch; determining the regression coefficient according to the non-missing estimation matrix and the pre-cross estimation matrix; determining the filled estimation row vector at the i-th observation epoch according to the regression coefficient, the non-missing mean estimate value, the missing mean estimate value, and the non-missing row vector at the i-th observation epoch; filling in the row vector of the observation matrix at the i-th observation epoch according to the filled estimation row vector at the i-th observation epoch to obtain an intermediate matrix; extracting the completed filling elements from the intermediate matrix to obtain the completed filling column vector and the completed filling column label; determining the stagnation tolerance according to the completed filling column vector and the completed filling column label; determining whether the intermediate matrix is filled according to the stagnation tolerance; in the case where the intermediate matrix is not filled, determining the missing estimation matrix corresponding to the missing covariance matrix of the missing row vector at the i-th observation epoch according to the covariance matrix, and the post-cross estimation matrix corresponding to the cross-covariance matrix between the missing row vector and the non-missing row vector at the i-th observation epoch; determining the residual covariance matrix according to the regression coefficient, the non-missing estimation matrix, the missing estimation matrix, the pre-cross estimation matrix, and the post-cross estimation matrix; determining the intermediate covariance matrix according to the residual covariance matrix and the covariance matrix; taking the intermediate covariance matrix as the covariance matrix, setting i = i + 1, and returning to execute the step of determining the non-missing row vector and the missing row vector at the i-th observation epoch according to the observation matrix until the intermediate matrix is filled; taking the filled intermediate matrix as the target observation matrix; and filling in the missing meteorological monitoring data of the intermediate station according to the target observation matrix to obtain the filled meteorological monitoring data of the intermediate station.

[0056] In determining the covariance matrix according to the observation matrix, in some embodiments, it is also necessary to set the missing elements in the observation matrix to zero; it can be understood that since the missing elements are missing values and the observation matrix cannot be calculated, it is necessary to set the missing elements in the observation matrix to zero.

[0057] For the determination method of non-missing row vectors and missing row vectors at the i-th observation epoch, in some embodiments, the row vectors at the i-th observation epoch can be first determined according to the observation matrix, and then the row vectors at the i-th observation epoch are separated into missing and non-missing ones to obtain the non-missing row vectors and missing row vectors at the i-th observation epoch; for example, when the row vector at the i-th observation epoch is [0, 4.01, 3.99, 0, 4.03], after separating it into missing and non-missing ones, the non-missing row vector at the i-th observation epoch obtained is [4.01, 3.99, 4.03], and the missing row vector at the i-th observation epoch is [0, 0].

[0058] For the determination method of the mean estimated value and the covariance matrix, the existing method can be used for calculation, which will not be elaborated here.

[0059] For the determination method of whether to complete the intermediate matrix, in some embodiments, it can be determined whether to complete the intermediate matrix according to the comparison result between the stagnation tolerance and the threshold value.

[0060] For the determination method of the estimated matrix, in some embodiments, the matrix block division method can be used for calculation, that is, by performing block processing on the covariance matrix to obtain a non-missing estimated matrix, a pre-cross estimated matrix, a missing estimated matrix, and a post-cross estimated matrix.

[0061] For the determination method of the regression coefficient and the residual covariance matrix, in some embodiments, the ridge regression algorithm can be used for calculation.

[0062] For the determination method of the intermediate covariance matrix, in some embodiments, the sum matrix between the residual covariance matrix and the covariance matrix is used as the intermediate covariance matrix.

[0063] For the determination method of the complemented meteorological monitoring data of the intermediate station, in some embodiments, the elements of the column corresponding to the intermediate station in the target observation matrix can be used as the complemented meteorological monitoring data of the intermediate station.

[0064] In the embodiments of the present application, by comprehensively considering strategies such as temporal and spatial characteristics, iterative optimization and dynamic adjustment, self-driven completion based on physical properties, high interpretability and portability, and computational efficiency and optimization, the efficient and accurate completion of the missing Beidou meteorological monitoring data is realized, which is of great significance and application value for improving the stability and integrity of meteorological monitoring, supporting fields such as climate research, disaster prediction, agricultural production, and public safety.

[0065] It is understandable that by comprehensively considering temporal and spatial features: by constructing an observation matrix and combining the calculation of the covariance matrix, this method not only takes into account the temporality of meteorological monitoring data but also fully utilizes the spatial correlation between monitoring stations. This comprehensive consideration makes the completion result closer to the real meteorological conditions and improves the accuracy of completion; iterative optimization and dynamic adjustment: an iterative optimization strategy is adopted in this method. By gradually increasing the number of modeling stations and calculating the root mean square error, the optimal number of modeling stations is determined. This dynamic adjustment process can adaptively adapt to the density and missing degree of different monitoring stations, ensuring the flexibility and robustness of the completion method; self-driven completion based on physical characteristics: this method only relies on the physical characteristics driven by Beidou meteorological data itself and does not rely on external training data. This avoids the problems of possible differences in spatio-temporal resolution and update cycle between different data sources, making the completion result more reliable and consistent; high interpretability and portability: each step and algorithm design in this method are based on clear mathematical principles and statistical methods, with high interpretability. At the same time, since it does not rely on specific external data or models, this method is easy to be transplanted and applied in different regions and meteorological monitoring systems; computational efficiency and optimization: by detecting and judging the non-emptiness of the observation matrix in advance through iteration, the modeling process is optimized, reducing unnecessary computational workload. At the same time, algorithms such as matrix block division and ridge regression are used for calculation, further improving computational efficiency and accuracy.

[0066] In a feasible implementation manner, determining the regression coefficient according to the non-missing estimation matrix and the pre-cross estimation matrix in the above embodiment includes: Using the formula To determine the regression coefficient; Wherein, Is the regression coefficient, Is the diagonal matrix of the non-missing estimation matrix, Is the non-missing estimation matrix, Is the ridge parameter of ridge regression, Is the identity matrix, Is the pre-cross estimation matrix.

[0067] It should be noted that Is the ridge parameter in the ridge regression algorithm and can be preset by the operator.

[0068] In the embodiments of the present application, by using the formula to determine the regression coefficient, it has the advantages of improving the accuracy of completion, enhancing stability, having clear mathematical principles and interpretability, strong adaptability, and high computational efficiency in the missing data completion of meteorological monitoring data, making this method have broad application prospects and practical value in the field of meteorological monitoring.

[0069] It is understandable that improving the accuracy of completion: determining the regression coefficient through the ridge regression algorithm can more accurately reflect the relationship between non-missing data and missing data. Ridge regression performs well in dealing with multicollinearity and data instability, which helps to provide more robust estimates in missing data completion for meteorological monitoring; enhancing stability: ridge regression can control its complexity to a certain extent and prevent overfitting by introducing ridge parameters. In meteorological monitoring data, since the data may contain noise and outliers, this feature of ridge regression helps to enhance stability and make the completion results more reliable; clear mathematical principles and interpretability: using formulas to determine regression coefficients, based on clear mathematical principles and statistical methods, with high interpretability, which makes the design and implementation of the method more transparent, easy to understand and verify; strong adaptability: the ridge regression algorithm is applicable to various types of data sets, including meteorological monitoring data, which may have temporal and spatial correlation. By adjusting the ridge parameters, it can adapt to different data characteristics and missing situations and provide flexible completion solutions; high computational efficiency: formulated methods usually have high computational efficiency because they can directly obtain results through mathematical operations without complex iterations or search processes. This efficiency advantage is particularly important in the missing completion of meteorological monitoring data because of the need to process large amounts of data and real-time monitoring needs.

[0070] In a feasible implementation, the above embodiment determines the completed estimated row vector at the i-th observation epoch according to the regression coefficient, the non-missing mean estimate and the missing mean estimate, and the non-missing row vector at the i-th observation epoch, including: Using the formula Determine the row vector of the completed estimate at the i-th observation epoch; in, is the row vector of the completed estimate at the i-th observation epoch, is the missing mean estimate, is the non-missing row vector at the i-th observation epoch, is the non-missing mean estimate, is the regression coefficient.

[0071] In the embodiment of the present application, by using the formula to determine the completed estimated row vector at the i-th observation epoch, not only the accuracy and stability of the completion are improved, but also the interpretability and adaptability of the method are enhanced, while the computational efficiency is improved. These advantages make this method have broad application prospects and practical value in the field of missing completion of meteorological monitoring data.

[0072] In a feasible implementation, the residual covariance matrix is ​​determined according to the regression coefficient, the non-missing estimation matrix, the missing estimation matrix, the front cross estimation matrix and the back cross estimation matrix in the above embodiment, including: Using the formula Determine the residual covariance matrix; in, is the residual covariance matrix, is the missing estimate matrix, is the regression coefficient, is the transpose symbol, is the non-missing estimation matrix, is the forward cross estimation matrix, is the post-crossover estimation matrix.

[0073] In the embodiments of the present application, the residual covariance matrix is ​​determined by using a formula, which plays an important role in completing missing meteorological monitoring data. It not only improves the accuracy and stability of the completion, but also enhances the interpretability and adaptability of the method, providing strong support for the accurate and complete acquisition of meteorological monitoring data.

[0074] It can be understood that improving the completion accuracy: the calculation of the residual covariance matrix takes into account the complex relationship between missing data and non-missing data. Quantifying this relationship through precise mathematical formulas helps to more accurately estimate missing values ​​in the iterative process, thereby improving the accuracy of the completed data; enhancing robustness: in meteorological monitoring data, due to the influence of various factors (such as equipment failure, weather interference, etc.), the data may contain noise and outliers. By formulaically calculating the residual covariance matrix, the influence of these outliers on the completion results can be suppressed to a certain extent, thereby enhancing the robustness of the method; supporting iterative optimization: the residual covariance matrix is ​​a key input in the iterative optimization process, providing information about the difference between the current estimate and the true value. By continuously updating the residual covariance matrix, the iterative process can be guided to converge to a better solution; clear mathematical principles and interpretability: the residual covariance matrix is ​​determined by formulas, which is based on clear mathematical principles and statistical methods and has high interpretability, which makes the design and implementation of the method more transparent and easy to understand and verify.

[0075] In a feasible implementation, determining the covariance matrix based on the observation matrix in the above embodiment includes: determining the column mean row vector based on the observation matrix; determining the centering matrix based on the column mean row vector and the observation matrix; and determining the covariance matrix based on the centering matrix.

[0076] Determining the non-missing row vectors and the missing row vectors at the i-th observation epoch according to the observation matrix in the above embodiment includes: determining the non-missing row vectors and the missing row vectors at the i-th observation epoch according to the centering matrix.

[0077] Completing the row vectors of the observation matrix at the \(i\)-th observation epoch according to the completed estimation row vector in the above embodiments to obtain an intermediate matrix, including: completing the row vectors of the centralized matrix at the \(i\)-th observation epoch according to the completed estimation row vector in the \(i\)-th observation epoch to obtain an intermediate matrix.

[0078] Determining the stagnation tolerance according to the completed filling column vector and the completed filling column label in the above embodiments, including: determining the filling label mean row vector according to the completed filling column label and the column mean row vector; determining the stagnation tolerance according to the filling label mean row vector and the completed filling column vector.

[0079] Taking the completed intermediate matrix as the target observation matrix in the above embodiments, including: determining the intermediate observation matrix according to the completed intermediate matrix and the column mean row vector; taking the intermediate observation matrix as the target observation matrix.

[0080] In determining the covariance matrix according to the observation matrix, in some embodiments, before determining the covariance matrix according to the centralized matrix, it is also necessary to set the missing elements in the centralized matrix to zero.

[0081] For the determination method of the column mean row vector, in some embodiments, its missing elements can be ignored to determine the column mean row vector according to the valid value matrix of the observation matrix.

[0082] For the determination method of the centralized matrix, in some embodiments, the difference matrix between the observation matrix and the column mean row vector can be used as the centralized matrix.

[0083] For the determination method of the covariance matrix, in some embodiments, the formula can be used to determine the covariance matrix; where is the covariance matrix, is the centralized matrix, is the transpose symbol, is the total number of rows of the centralized matrix.

[0084] For the determination method of the non-missing row vector and the missing row vector at the \(i\)-th observation epoch, in some embodiments, the row vector at the \(i\)-th observation epoch can be first determined according to the centralized matrix, and then the missing and non-missing separation of the row vector at the \(i\)-th observation epoch can be performed to obtain the non-missing row vector and the missing row vector at the \(i\)-th observation epoch.

[0085] For the determination method of the filling label mean row vector, in some embodiments, according to the completed filling column label, the elements with the same column label as the completed filling column label can be extracted from the column mean row vector, and then these are combined into a row vector, and this row vector is used as the filling label mean row vector.

[0086] For the determination method of the intermediate observation matrix, in some embodiments, the sum matrix between the completed intermediate matrix and the column mean row vector can be used as the intermediate observation matrix.

[0087] In the embodiments of the present application, by introducing centering and refining the relevant steps, remarkable effects have been achieved in the missing data completion of meteorological monitoring data, improving the accuracy, robustness, computational efficiency, interpretability, and portability of the completion. At the same time, considering the temporal and spatial characteristics comprehensively, it provides strong support for the accurate and complete acquisition of meteorological monitoring data.

[0088] It can be understood that improving the completion accuracy: by calculating the column mean row vector and centering the observation matrix, the mean shift in the data is eliminated, making the subsequent calculations more accurate. The use of the centering matrix makes the calculation of the covariance matrix more precise, reflecting the true correlation between the data. During the completion process, the centering matrix is used to determine the non-missing and missing row vectors, and calculate the completion estimated row vectors, improving the accuracy of the completed data; enhancing robustness: setting the missing elements in the centering matrix to zero to avoid the interference of missing values on the calculation, enhancing the robustness of the method; through iterative optimization and dynamic adjustment strategies, combined with the judgment of the stagnation tolerance, ensuring the stability and convergence of the completion process; improving computational efficiency: by pre-calculating the column mean row vector and the centering matrix, the subsequent calculation steps are simplified, improving the computational efficiency; using matrix operations and formula-based methods, such as the calculation of the covariance matrix and the determination of regression coefficients, further improving the calculation speed; enhancing interpretability and portability: each step and algorithm design in the method are based on clear mathematical principles and statistical methods, with high interpretability. Since it does not depend on specific external data or models, the method is easy to be transplanted and applied in different regions and meteorological monitoring systems; comprehensively considering the temporal and spatial characteristics: by constructing the observation matrix and the centering matrix, and combining the calculation of the covariance matrix, the method not only considers the temporality of meteorological monitoring data, but also makes full use of the spatial correlation between monitoring stations.

[0089] In a feasible implementation manner, determining the stagnation tolerance according to the filled label mean row vector and the completed filled column vector in the above embodiments includes: Using the formula to determine the stagnation tolerance; where is the matrix norm function, is the filled column vector, is the total number of missing elements in the observation matrix or the centering matrix, is the filled mean row vector, is the transpose symbol, is the stagnation tolerance.

[0090] In the embodiments of the present application, determining the stagnation tolerance by using a formula has significant advantages in the missing data completion of meteorological monitoring data. It not only improves the accuracy and robustness of judgment, but also supports the iterative optimization process, improves the calculation efficiency, and enhances the interpretability and portability of the method. These advantages make the method have broad application prospects and practical value in the field of meteorological monitoring.

[0091] It can be understood that improving the judgment accuracy: calculating the difference between the filled column vector and the filled mean row vector through the matrix norm function can quantify the degree of change in the filling process. This quantification method is more accurate than simple comparison or counting methods because it considers the overall differences of all elements; enhancing the robustness: the calculation of the stagnation tolerance takes into account the completion of all missing elements, rather than relying solely on the changes of individual elements. This makes the method more robust to outliers or noise because large changes in individual elements will not overly affect the overall stagnation judgment; supporting iterative optimization: the stagnation tolerance is an important indicator in the iterative optimization process, used to determine whether the filling process has converged or reached a stable state. By calculating the stagnation tolerance in a formulaic way, the progress of the iterative process can be more objectively evaluated, thereby guiding the termination or continuation of the iterative process; improving the calculation efficiency: the calculation of the matrix norm function usually has high efficiency, especially with the support of modern computers and numerical calculation libraries. This makes the calculation of the stagnation tolerance not become the bottleneck of the entire filling process, thus ensuring the calculation efficiency of the overall method; enhancing the interpretability and portability: using a formula to determine the stagnation tolerance is based on clear mathematical principles and statistical methods, with high interpretability. This method does not rely on specific external data or models and is easy to be transplanted and applied in different regions and meteorological monitoring systems.

[0092] In a feasible implementation manner, determining whether the intermediate matrix is completed according to the stagnation tolerance in the above embodiments includes: when the stagnation tolerance is greater than or equal to the stagnation tolerance threshold, determining that the intermediate matrix is not completed; when the stagnation tolerance is less than the stagnation tolerance threshold, determining that the intermediate matrix is completed.

[0093] Among them, the stagnation tolerance threshold can be set by the operator based on a large amount of experience, experiments or statistics. Of course, it can also be set by the operator according to actual needs.

[0094] In the embodiments of the present application, by using the stagnation tolerance and threshold to determine whether the intermediate matrix is completed, it has significant advantages in the missing data completion of meteorological monitoring data. It not only improves the objectivity, robustness, and computational efficiency of the determination, but also supports the iterative optimization process, enhances the interpretability and portability of the method. These advantages make the method have broad application prospects and practical value in the field of meteorological monitoring.

[0095] In a feasible implementation manner, for step 180 in the above embodiments, according to the observation matrix to be completed, the meteorological monitoring data of the station to be completed is completed to obtain the completed meteorological monitoring data of the station to be completed, including: taking the observation matrix to be completed as the observation matrix, and returning to execute the step of determining the covariance matrix according to the observation matrix to obtain the target observation matrix, and taking the target observation matrix as the target completed observation matrix; according to the target completed observation matrix, the meteorological monitoring data of the station to be completed is completed to obtain the completed meteorological monitoring data of the station to be completed.

[0096] For the determination method of the completed meteorological monitoring data of the station to be completed, in some embodiments, the column elements corresponding to the station to be completed in the target completed observation matrix can be used as the completed meteorological monitoring data of the station to be completed.

[0097] In the embodiments of the present application, by reprocessing the observation matrix to be completed based on the most appropriate number of models, and completing the meteorological monitoring data of the station to be completed according to the target completed observation matrix, this method shows significant advantages in the missing data completion of meteorological monitoring data, including improving the completion accuracy, enhancing the robustness, supporting dynamic adjustment, improving the computational efficiency, and maintaining the consistency and portability of the method. These advantages make the method have broad application prospects and practical value in the field of meteorological monitoring.

[0098] The present application provides a device for completing missing meteorological monitoring data in a second aspect.

[0099] Please refer to Figure 2 , which is a schematic diagram of a device for completing missing meteorological monitoring data in the embodiments of the present application. The device 210 includes: An acquisition and selection module 211, configured to acquire the meteorological monitoring data of all monitoring stations in the target area within a preset time series, and select one of the monitoring stations with missing meteorological monitoring data as the station to be completed among all monitoring stations; A determination and nulling module 212, configured to use the monitoring station closest to the station to be completed and without missing meteorological monitoring data as the intermediate station, and use the meteorological monitoring data of the nulled intermediate station as the missing meteorological monitoring data of the intermediate station; The iterative initial module 213 is used to take the n monitoring stations closest to the intermediate station as modeling stations, where n is a positive integer and the initial value of n is 1; The first component completion module 214 is used to form an observation matrix by column with the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations, and based on the observation matrix, complete the missing meteorological monitoring data of the intermediate station to obtain the completed meteorological monitoring data of the intermediate station; The root mean square error determination module 215 is used to determine the root mean square error according to the completed meteorological monitoring data of the intermediate station and the meteorological monitoring data; The iterative module 216 is used to set n = n + 1, and return to execute the step of taking the n monitoring stations closest to the intermediate station as modeling stations until n is equal to the maximum modeling threshold, obtaining multiple root mean square errors, and taking the n corresponding to the minimum root mean square error as the target modeling number, and setting the target modeling stations as m; The modeling determination module 217 is used to take the m monitoring stations closest to the station to be completed as modeling stations; The second component completion module 218 is used to form a to-be-completed observation matrix by column with the meteorological monitoring data of the station to be completed and the meteorological monitoring data of the m modeling stations, and based on the to-be-completed observation matrix, complete the meteorological monitoring data of the station to be completed to obtain the completed meteorological monitoring data of the station to be completed.

[0100] In the embodiment of the present application, the relevant content of the above-mentioned acquisition and selection module 211, determination and blanking module 212, iterative initial module 213, first component completion module 214, root mean square error determination module 215, iterative module 216, modeling determination module 217 and second component completion module 218 can refer to Figure 1 the content in the shown embodiment, which will not be elaborated here.

[0101] It should be noted that the device 210 of the present application further includes some other modules. It can be understood that there is a one-to-one correspondence between the method of the present application and the device 210. Therefore, some other modules of the device 210 of the present application are the corresponding content of the method of the present application in the above embodiment.

[0102] In the embodiments of the present application, by selecting a monitoring station with missing data as the station to be supplemented, finding an intermediate station with the closest distance and complete data for simulated missing processing, then gradually increasing the number of modeling stations according to the distances between the intermediate station and surrounding monitoring stations, determining the optimal number of modeling stations by constructing an observation matrix and calculating the root mean square error, and finally using the data of the optimal modeling stations to complete the data of the station to be supplemented. This method takes into account both the temporal sequence and the spatial distribution characteristics, and has high interpretability and portability. At the same time, this method only relies on the physical characteristics driven by Beidou meteorological data itself, does not rely on external training data, has simple calculations, does not have the problem of differences in spatio-temporal resolution and update cycle between different data sources, and can adaptively adjust to different monitoring station densities to ensure that the supplemented data approaches the true value, effectively improving the stability and integrity of Beidou meteorological monitoring.

[0103] In a third aspect, the present application also provides a computer-readable storage medium storing a computer program, which when executed by a processor causes the processor to execute a method for completing missing meteorological monitoring data in the above method embodiments.

[0104] In a fourth aspect, the present application also provides a computer device including a memory and a processor, where the memory stores a computer program, which when executed by the processor causes the processor to execute a method for completing missing meteorological monitoring data in the above method embodiments.

[0105] Figure 3 The internal structure diagram of the computer device in some embodiments is shown. The computer device can specifically be a terminal, a server, or a gateway. As Figure 3 shown, the computer device includes a processor, a memory, and a network interface connected through a system bus.

[0106] Among them, the memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium of the computer device stores an operating system and can also store a computer program, which when executed by the processor can cause the processor to implement each step in the above method embodiments. The internal memory can also store a computer program, which when executed by the processor can cause the processor to execute each step in the above method embodiments. Those skilled in the art can understand that Figure 3 the structure shown in

[0107] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods.

[0108] Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0109] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0110] The above-described embodiments only represent several implementation manners of the present application. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for completing missing meteorological monitoring data, characterized in that, The method includes: Obtaining meteorological monitoring data of all monitoring stations within a target area in a preset time series, and selecting, from all the monitoring stations, one monitoring station with missing meteorological monitoring data as the station to be supplemented; Taking the monitoring station that is closest to the station to be supplemented and has no missing meteorological monitoring data as the intermediate station, and taking the meteorological monitoring data of the intermediate station after being emptied as the missing meteorological monitoring data of the intermediate station; Taking the n monitoring stations closest to the intermediate station as the modeling stations, where n is a positive integer and the initial value of n is 1; Composing an observation matrix by columns with the missing meteorological monitoring data of the intermediate station and the meteorological monitoring data of the n modeling stations, and complementing the missing meteorological monitoring data of the intermediate station according to the observation matrix to obtain the complemented meteorological monitoring data of the intermediate station; Determining the root mean square error according to the complemented meteorological monitoring data of the intermediate station and the meteorological monitoring data; Let n = n + 1, and return to execute the step of taking the n monitoring stations closest to the intermediate station as the modeling stations until n is equal to the maximum modeling threshold, obtaining multiple root mean square errors, and taking the n corresponding to the minimum root mean square error as the target modeling number, and setting the target modeling stations as m; Taking the m monitoring stations closest to the station to be supplemented as the modeling stations; Composing a to-be-complemented observation matrix by columns with the meteorological monitoring data of the station to be supplemented and the meteorological monitoring data of the m modeling stations, and complementing the meteorological monitoring data of the station to be supplemented according to the to-be-complemented observation matrix to obtain the complemented meteorological monitoring data of the station to be supplemented.

2. The method for complementing missing meteorological monitoring data according to claim 1, characterized in that Before the step of complementing the missing meteorological monitoring data of the intermediate station according to the observation matrix to obtain the complemented meteorological monitoring data of the intermediate station, the method further includes: Determining whether the row vectors of the observation matrix at any observation epoch satisfy non-empty according to the observation matrix; In the case where there is a row vector at any observation epoch of the observation matrix that satisfies non-empty, let n = n + 1, and return to execute the step of taking the n monitoring stations closest to the intermediate station as the modeling stations until the row vectors of the observation matrix at any observation epoch do not satisfy non-empty.

3. The method for completing missing meteorological monitoring data according to claim 1, characterized in that, The step of complementing the missing meteorological monitoring data of the intermediate station according to the observation matrix to obtain the complemented meteorological monitoring data of the intermediate station includes: Determining the covariance matrix according to the observation matrix; Determining the non-missing row vector and the missing row vector at the i-th observation epoch according to the observation matrix, where i is a positive integer and the initial value of i is 1; Determining the non-missing mean estimate value according to the non-missing row vector at the i-th observation epoch, and determining the missing mean estimate value according to the missing row vector at the i-th observation epoch; Determining the non-missing estimation matrix corresponding to the covariance matrix of the non-missing row vector at the i-th observation epoch and the pre-cross estimation matrix corresponding to the cross-covariance matrix between the non-missing row vector and the missing row vector at the i-th observation epoch according to the covariance matrix; Determining the regression coefficient according to the non-missing estimation matrix and the pre-cross estimation matrix; Determine a completed estimation row vector at the \(i\)-th observation epoch according to the regression coefficient, the non-missing mean estimation value, the missing mean estimation value, and the non-missing row vector at the \(i\)-th observation epoch; Complete the row vector of the observation matrix at the \(i\)-th observation epoch according to the completed estimation row vector at the \(i\)-th observation epoch to obtain an intermediate matrix; Extract the completed filling elements from the intermediate matrix to obtain a completed filling column vector and completed filling column labels; Determine the stagnation tolerance according to the completed filling column vector and the completed filling column labels; Determine whether the intermediate matrix is completed according to the stagnation tolerance; In the case where the intermediate matrix is not completed, determine a missing estimation matrix corresponding to the missing covariance matrix of the missing row vector at the \(i\)-th observation epoch according to the covariance matrix, and a post-cross estimation matrix corresponding to the cross-covariance matrix between the missing row vector and the non-missing row vector at the \(i\)-th observation epoch; Determine a residual covariance matrix according to the regression coefficient, the non-missing estimation matrix, the missing estimation matrix, the pre-cross estimation matrix, and the post-cross estimation matrix; Determine an intermediate covariance matrix according to the residual covariance matrix and the covariance matrix; Take the intermediate covariance matrix as the covariance matrix, let \(i = i + 1\), and return to execute the step of determining the non-missing row vector and the missing row vector at the \(i\)-th observation epoch according to the observation matrix until the intermediate matrix is completed; Take the completed intermediate matrix as the target observation matrix; Complete the missing meteorological monitoring data of the intermediate station according to the target observation matrix to obtain the completed meteorological monitoring data of the intermediate station.

4. The method for complementing missing meteorological monitoring data according to claim 3, wherein The determining the regression coefficient according to the non-missing estimation matrix and the pre-cross estimation matrix includes: Using the formula to determine the regression coefficient; wherein, is the regression coefficient, is the diagonal matrix of the non-missing estimation matrix, is the non-missing estimation matrix, is the ridge parameter of ridge regression, is the identity matrix, is the forward cross-estimation matrix.

5. The method for completing missing meteorological monitoring data according to claim 3, wherein The determining the completed estimation row vector at the \(i\)-th observation epoch according to the regression coefficient, the non-missing mean estimation value, the missing mean estimation value, and the non-missing row vector at the \(i\)-th observation epoch includes: Using the formula to determine the completed estimation row vector at the i-th observation epoch; wherein, is the completed estimation row vector at the i-th observation epoch, is the missing mean estimation value, is the non-missing row vector at the i-th observation epoch, is the non-missing mean estimation value, is the regression coefficient.

6. The method for complementing missing meteorological monitoring data according to claim 3, wherein The determining the residual covariance matrix according to the regression coefficient, the non-missing estimation matrix, the missing estimation matrix, the pre-cross estimation matrix, and the post-cross estimation matrix includes: Using the formula to determine the residual covariance matrix; Among them, is the residual covariance matrix, is the missing estimation matrix, is the regression coefficient, is the transpose symbol, is the non-missing estimation matrix, is the forward cross-estimation matrix, is the backward cross-estimation matrix.

7. The method for completing missing meteorological monitoring data according to claim 3, wherein The determining the covariance matrix according to the observation matrix includes: Determine a column mean row vector according to the observation matrix; Determine a centering matrix according to the column mean row vector and the observation matrix; Determine the covariance matrix according to the centering matrix; The determining the non-missing row vector and the missing row vector at the \(i\)-th observation epoch according to the observation matrix includes: Determine the non-missing row vector and the missing row vector at the \(i\)-th observation epoch according to the centering matrix; The completing the row vector of the observation matrix at the \(i\)-th observation epoch according to the completed estimation row vector at the \(i\)-th observation epoch to obtain an intermediate matrix includes: Complete the row vector of the centering matrix at the \(i\)-th observation epoch according to the completed estimation row vector at the \(i\)-th observation epoch to obtain the intermediate matrix; Determining the stagnation tolerance according to the completed filling column vector and the completed filling column label includes: Determining the mean row vector of filling labels according to the completed filling column label and the column mean row vector; Determining the stagnation tolerance according to the mean row vector of filling labels and the completed filling column vector; Regarding the completed intermediate matrix as the target observation matrix includes: Determining the intermediate observation matrix according to the completed intermediate matrix and the column mean row vector; Regarding the intermediate observation matrix as the target observation matrix.

8. The method for completing missing meteorological monitoring data according to claim 7, characterized in that Determining the stagnation tolerance according to the mean row vector of filling labels and the completed filling column vector includes: Using the formula to determine the stagnation tolerance; Among them, is the matrix norm function, is the filling column vector, is the total number of missing elements of the observation matrix or the centering matrix, is the filling mean row vector, is the transpose symbol, is the stagnation tolerance.

9. The method for completing missing meteorological monitoring data according to claim 3, characterized in that Determining whether the intermediate matrix is completed according to the stagnation tolerance includes: When the stagnation tolerance is greater than or equal to the stagnation tolerance threshold, determining that the intermediate matrix is not completed; When the stagnation tolerance is less than the stagnation tolerance threshold, determining that the intermediate matrix is completed.

10. The method for completing missing meteorological monitoring data according to any one of claims 3 to 9, characterized in that, Completing the meteorological monitoring data of the station to be filled according to the observation matrix to be filled to obtain the completed meteorological monitoring data of the station to be filled includes: Regarding the observation matrix to be filled as the observation matrix, returning to execute the step of determining the covariance matrix according to the observation matrix to obtain the target observation matrix, and regarding the target observation matrix as the target completed observation matrix; Completing the meteorological monitoring data of the station to be filled according to the target completed observation matrix to obtain the completed meteorological monitoring data of the station to be filled.

Images