Anomaly detection device, method and program

Abstract

To improve prediction accuracy of regression model upon determining abnormality of a TEC value.SOLUTION: A process executed by an abnormality detector comprises: a step (S910) of obtaining respective observation values of a plurality of observation stations for observing the number of electrons in the ionosphere; steps (S920, S930) of selecting a central observation station from among the plurality of observation stations and selecting a plurality of peripheral observation stations from among the plurality of observation stations based on distances from the central observation station; a step (S940) of calculating a predicted observed value of the central observation station based on the respective observed values of the plurality of peripheral observation stations; a step (S950) of calculating an estimated error between the predicted observed value and an actually measured value of the central observation station; and steps (S960, S970) of determining whether or not the measured value of the central observation station is abnormal based on the estimation error.SELECTED DRAWING: Figure 9

Description

[Technical field]

[0001] The present disclosure relates to anomaly detection devices, and more particularly, to techniques for detecting anomalies in the ionosphere. [Background technology]

[0002] Free electrons that have been repelled from atmospheric molecules by solar radiation float in the ionosphere (layer of the atmosphere). Anomalies in the ionosphere can occur before an earthquake occurs, and it is hoped that detecting electromagnetic anomalies in the ionosphere can be useful, for example, in predicting the occurrence of earthquakes.

[0003] Today, in addition to various seismometers, a dense network of Global Navigation Satellite System (GNSS) receiving stations (hereafter referred to as "observation stations") has been constructed in the Japanese archipelago to measure crustal movements. These observation stations can observe the total electron content (TEC value) in the ionosphere by communicating with GNSS satellites.

[0004] Regarding detection of electromagnetic anomalies in the ionosphere, for example, WO 2018 / 097272 (Patent Document 1) discloses a computer that "based on observation data of a signal received by a ground observation station from a satellite, a computer calculates the amount of change in the total electron number in the ionosphere between the observation station and the satellite from the start of observation. The computer estimates the amount of change in the total electron number to be calculated next based on the time change in the amount of change in the total electron number in the ionosphere from the start of observation, and calculates the difference (estimation error) between the estimated amount of change in the total electron number and the actually calculated amount of change in the total electron number. The computer calculates a correlation value between the estimation error calculated for each observation station and the estimation error calculated for a predetermined number of observation stations in the vicinity of each observation station. If the correlation value calculated for each observation station is equal to or greater than a predetermined threshold, and if the correlation values ​​for a predetermined number of observation stations in the vicinity of this observation station are also equal to or greater than the predetermined threshold, the computer determines that an anomaly has occurred in the ionosphere between this observation station and the satellite" (see [Abstract]). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] International Publication No. 2018 / 097272 Summary of the Invention [Problem to be solved by the invention]

[0006] According to the technology disclosed in Patent Document 1, the prediction of the regression model at each observation station may not correctly determine anomalies in the TEC value. Therefore, there is a need for a technology to improve the prediction accuracy of the regression model at each observation station in determining anomalies in the TEC value.

[0007] The present disclosure has been made in consideration of the above-described background, and an object of the present disclosure in one aspect is to provide a technique for improving the prediction accuracy of a regression model at each observation station when determining anomalies in TEC values. [Means for solving the problem]

[0008] According to one embodiment, there is provided an anomaly detection device. The anomaly detection device includes an input unit that acquires observation values ​​of each of a plurality of observation stations for observing the number of electrons in the ionosphere, and a control unit that determines whether the observation values ​​are abnormal. The control unit selects a central observation station from the plurality of observation stations, selects a plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station, calculates a predicted observation value of the central observation station based on the observation values ​​of each of the plurality of peripheral observation stations, calculates an estimated error between the predicted observation value and an actual measurement value of the central observation station, and determines whether the actual measurement value of the central observation station is abnormal based on the estimated error.

[0009] In one aspect, the anomaly detection device further includes a storage unit that stores information on the first distance and information on the second distance. Selecting the multiple peripheral observation stations from the multiple observation stations based on the distance from the central observation station includes selecting the multiple peripheral observation stations from an area whose distance from the central observation station is equal to or greater than the first distance and equal to or less than the second distance.

[0010] In one aspect, the storage unit further stores information on a third distance. Selecting a plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station includes determining each of the peripheral observation stations to be a virtual weight, calculating a position of a center of gravity of the weight of the selected plurality of peripheral observation stations, and selecting the plurality of peripheral observation stations such that a distance from the central observation station to the center of gravity is equal to or less than the third distance.

[0011] In one aspect, calculating a predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes calculating a predicted observation value of the central observation station based on an average value of the observation values ​​of each of the multiple surrounding observation stations.

[0012] In one aspect, calculating a predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes calculating a predicted observation value of the central observation station based on a median of the observation values ​​of each of the multiple surrounding observation stations.

[0013] In one aspect, selecting the central observation station includes selecting each of the observation stations included in the plurality of observation stations as the central observation station, and calculating the estimation error includes repeatedly calculating the estimation error when each of the observation stations is selected as the central observation station.

[0014] In one aspect, determining whether the actual measurement value of the central observation station is abnormal based on the estimation error includes calculating a correlation value between the estimation error of the central observation station and the estimation errors of multiple observation stations surrounding the central observation station, and determining that the actual measurement value of the central observation station is abnormal based on the correlation value being greater than or equal to a predetermined threshold.

[0015] In one aspect, determining whether the actual measurement value of the central observation station is abnormal based on the estimated error includes calculating a correlation value between the estimated error of the central observation station and the estimated errors of multiple observation stations surrounding the central observation station, calculating a median and standard deviation of the correlation values ​​of the central observation station, calculating a relative value indicating the degree of difference between the correlation value of the central observation station and the median based on the median and standard deviation, and determining that the actual measurement value of the central observation station is abnormal based on the relative value being greater than or equal to a predetermined threshold.

[0016] In one aspect, the anomaly detection device further includes an output unit that outputs an alert when the actual measurement value of the central monitoring station is determined to be abnormal.

[0017] According to another embodiment, there is provided a method for detecting an anomaly in the number of electrons in the ionosphere, the method including the steps of acquiring an observation value of each of a plurality of observation stations for observing the number of electrons in the ionosphere, selecting a central observation station from among the plurality of observation stations, selecting a plurality of peripheral observation stations from among the plurality of observation stations based on a distance from the central observation station, calculating a predicted observation value of the central observation station based on the observation values ​​of each of the plurality of peripheral observation stations, calculating an estimation error between the predicted observation value and an actual measurement value of the central observation station, and determining whether the actual measurement value of the central observation station is abnormal based on the estimation error.

[0018] In one aspect, the step of selecting multiple peripheral observation stations from among the multiple observation stations based on their distance from the central observation station includes a step of selecting multiple peripheral observation stations from an area whose distance from the central observation station is greater than or equal to a first distance and less than or equal to a second distance.

[0019] In one aspect, the step of selecting a number of peripheral observation stations from among the number of observation stations based on their distance from a central observation station includes the steps of determining that each of the peripheral observation stations is a virtual weight, calculating the position of the center of gravity of the weights of the selected number of peripheral observation stations, and selecting the number of peripheral observation stations such that the distance from the central observation station to the center of gravity is less than or equal to a third distance.

[0020] In one aspect, the step of calculating a predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes a step of calculating a predicted observation value of the central observation station based on an average value of the observation values ​​of each of the multiple surrounding observation stations.

[0021] In one aspect, the step of calculating a predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes a step of calculating a predicted observation value of the central observation station based on a median of the observation values ​​of each of the multiple surrounding observation stations.

[0022] In one aspect, the step of selecting a central observation station includes a step of selecting each of the observation stations included in the multiple observation stations as the central observation station, and the step of calculating the estimated error includes a step of repeatedly calculating the estimated error when each of the observation stations is selected as the central observation station.

[0023] In one aspect, the step of determining whether the actual measurement value of the central observation station is abnormal based on the estimation error includes a step of calculating a correlation value between the estimation error of the central observation station and the estimation errors of multiple observation stations surrounding the central observation station, and a step of determining that the actual measurement value of the central observation station is abnormal based on the correlation value being greater than or equal to a predetermined threshold.

[0024] In one aspect, the step of determining whether the actual measurement value of the central observation station is abnormal based on the estimated error includes the steps of calculating a correlation value between the estimated error of the central observation station and the estimated errors of a plurality of observation stations surrounding the central observation station, calculating a median and standard deviation of the correlation values ​​of the central observation station, calculating a relative value indicating the degree of difference between the correlation value of the central observation station and the median based on the median and standard deviation, and determining that the actual measurement value of the central observation station is abnormal based on the relative value being greater than or equal to a predetermined threshold.

[0025] In one aspect, the method further includes outputting an alert based on the actual measurement value of the central monitoring station being determined to be abnormal.

[0026] According to another embodiment, a program for causing a computer to execute the above method is provided. Effect of the Invention

[0027] According to an embodiment, it is possible to improve the prediction accuracy of the regression model at each observation station in determining anomalies in the TEC value.

[0028] The above and other objects, features, aspects and advantages of the present disclosure will become apparent from the following detailed description of the disclosure taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0029] [Figure 1] FIG. 1 is a diagram showing an example of an overall view of a TEC value observation system according to an embodiment. [Diagram 2] FIG. 2 is a diagram showing an example of an observation procedure of a TEC value observation system. [Diagram 3] FIG. 1 illustrates an example of a configuration of an anomaly detection system 300 according to an embodiment. [Figure 4] 2 shows an example of a functional configuration of the anomaly detection device 320. [Diagram 5] FIG. 3 illustrates an example of the configuration of an anomaly detection device 320. [Figure 6] FIG. 11 is a diagram showing an example of a process for creating a regression model of the TEC value by the TEC value estimation unit 440. [Figure 7] FIG. 13 is a diagram showing an example of detailed procedures for creating a regression model of a central observation station. [Figure 8] FIG. 11 is a diagram showing an example of a procedure for calculating an estimated error (difference) between a predicted value at a central observation station and an actual measured value. [Figure 9] 11 is a diagram showing an example of a flow of a process performed by an abnormality detection device 320 to determine whether or not a TEC value is abnormal. FIG. [Figure 10] FIG. 13 is a diagram showing an example of conditions for a simulation of the TEC value anomaly detection process performed by the anomaly detection device 320. [Figure 11] 13A and 13B are diagrams illustrating examples of results of simulations of the anomaly detection device 320 and a conventional device. [Figure 12] FIG. 13 is a diagram illustrating an example of an analysis result of a simulation execution result. [Figure 13] FIG. 13 is a diagram showing an example of the sampling periods of an anomaly detection device 320 and a conventional device. [Figure 14] FIG. 11 is a diagram showing a first example of a comparison between an alert output by an anomaly detection device 320 and an alert output by a conventional device. [Figure 15] FIG. 11 is a diagram showing a second example of a comparison between an alert output by the anomaly detection device 320 and an alert output by a conventional device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] Hereinafter, an embodiment of the technical idea according to the present disclosure will be described with reference to the drawings. In the following description, the same components are given the same reference numerals. Their names and functions are also the same. Therefore, detailed description thereof will not be repeated. In the following description, when referring to multiple identical configurations, they may be expressed as configurations 123A, 123B, etc. When referring to them collectively, they will be expressed as configuration 123.

[0031] Fig. 1 is a diagram showing an example of an overall view of a TEC value observation system according to the present embodiment. The system includes a GNSS satellite 100 and an observation station 110. In the example shown in Fig. 1, observation stations 110A, 110B, and 110C are shown, but this is just an example, and in reality, more observation stations 110 may be deployed.

[0032] The ionosphere 120, a region in which molecules and atoms are ionized by sunlight, exists in the upper atmosphere surrounding the Earth. The total electron content (TEC value) of the ionosphere 120 is known to vary significantly due to space weather such as solar flares, in addition to its natural characteristics of day and night and seasonal changes. These changes (especially solar flares) are known to cause radio interference on the ground. Recent research has reported that the TEC value in the atmosphere above the epicenter increases before the occurrence of a large earthquake, and it is hoped that the TEC value observation technology can be applied to earthquake prediction.

[0033] The TEC value analysis method according to this embodiment predicts anomalies in the ionosphere 120, and utilizes the observation results obtained by a TEC value observation system. The TEC value observation system observes the TEC value of the ionosphere 120 using radio wave communication between a GNSS satellite 100 and an observation station 110. The GNSS satellite communicates with each of the multiple observation stations 110 installed on the Earth's surface using radio waves of two frequencies. The TEC value on the radio wave path is obtained by calculating the phase difference in the ionosphere 120 between the radio waves of the two frequencies. The obtained TEC value is stored in a server (not shown) provided in the TEC value observation system.

[0034] Fig. 2 is a diagram showing an example of an observation procedure of the TEC value observation system. A method of calculating the TEC value for each location in the TEC value observation system will be described with reference to Fig. 2. The point where the line (communication path) connecting the GNSS satellite 100 and the terrestrial observation station 110 intersects with the surface of the ionosphere 120 is called an IPP (Ionospheric Penetration Point) 210. The position where the IPP 210 is projected onto the ground is called a SIP (Sub Ionosphere Point) 220.

[0035] 2, the TEC value calculated by communication between the GNSS 100 and the observation station 110 is the TEC value above the SIP 220. The SIP 220 can be calculated based on the respective positions of the GNSS satellite 100 and the observation station 110, the IPP 210, the radius of the Earth, and altitude information to the ionosphere 120, etc. In one aspect, the altitude of the ionosphere 120 may be set to, for example, about 300 km.

[0036] The TEC values ​​obtained by the TEC observation system are easily affected by various natural phenomena such as solar flares, so in order to correctly detect increases and decreases in the TEC value, it is important to eliminate the effects of these natural phenomena as much as possible.

[0037] 3 is a diagram showing an example of the configuration of an anomaly detection system 300 according to the present embodiment. The anomaly detection system 300 acquires and analyzes the TEC values ​​obtained by the TEC value observation system, and can detect or predict anomalies in the TEC values ​​in various locations (SIPs 220).

[0038] The anomaly detection system 300 includes a plurality of observation stations 110, an observation data DB (DataBase) 310, an anomaly detection device 320, a service provider 330, and a user terminal 340. The plurality of observation stations 110, the observation data DB 310, the anomaly detection device 320, and the service provider 330 are configured to be able to communicate with each other via a network 350.

[0039] In one aspect, the anomaly detection system 300 may include only the anomaly detection device 320. In that case, the anomaly detection system 300 may cooperate with a plurality of observation stations 110, an observation data DB 310, the anomaly detection device 320, a service provider 330, and a user terminal 340, which are external devices or services.

[0040] The observation station 110 observes the TEC value at each SIP 220 by communicating with the GNSS satellite 100. The observation station 110 transmits the acquired observation value to the observation data DB 310. A large number of observation stations 110 may be placed in an area where the TEC value in the sky is observed.

[0041] The observation data DB 310 acquires and stores observation values ​​from a plurality of observation stations 110. The observation data DB 310 may be disposed in any device such as a server. In one aspect, the observation value may be a TEC value. In that case, the server including the observation data DB 310 stores the observation value as a TEC value in the observation data DB 310. In another aspect, the observation value may include delay information of communication between the GNSS satellite 100 and the observation station 110, position information of the GNSS satellite 100, and position information of the observation station 110, etc. In that case, the server including the observation data DB 310 may calculate a TEC value from information included in the observation value and store the TEC value in the observation data DB 310.

[0042] In another aspect, the observation data DB 310 may be represented as a table of a relational database, or may be represented in any other data format such as JSON (JavaScript (registered trademark) Object Notation). In another aspect, the observation station 110, the observation data DB 310, and the GNSS satellite 100 may configure a TEC value observation system.

[0043] Observation data of the TEC value of the observation station 110 is acquired from the observation data DB 310. In one aspect, the anomaly detection device 320 may calculate an observation result of the TEC value based on the observation data of the observation station 110. The anomaly detection device 320 detects or predicts a magnetic anomaly in the ionosphere from the acquired TEC value, and delivers an alert to the user terminal 340 as necessary. In one aspect, the anomaly detection device 320 may provide an alert to the service provider 330. In another aspect, the anomaly detection device 320 may be realized as a PC (Personal Computer), a server, or a cloud service.

[0044] Service provider 330 may provide various forecasts or value-added services utilizing the forecasts to user terminal 340 based on the information acquired from anomaly detection device 320. In one aspect, service provider 330 may be realized as a server or a cloud service. In another aspect, the function of service provider 330 may be included in anomaly detection device 320.

[0045] The user terminal 340 may receive an alert from the anomaly detection device 320 or the service provider 330 and display the contents of the alert on a display. In one aspect, the user terminal 340 may be a PC, a smartphone, a tablet, a wearable device, a television, a radio, or any other device.

[0046] Fig. 4 illustrates an example of a functional configuration of the anomaly detection device 320. In one aspect, the configuration illustrated in Fig. 4 may be realized as software, in which case these configurations may be executed by the hardware illustrated in Fig. 5.

[0047] Anomaly detection device 320 includes an observation station position data DB 410, an observation station distance calculation unit 420, an observation station distance data DB 430, a TEC value estimator 440, an estimated error calculation unit 450, a correlation value calculation unit 460, anomaly determination unit 470, and a reporting unit 480. In one aspect, the observation station position data DB 410 and the observation station distance data DB 430 may be represented as a table of a relational database, or may be represented in any other data format such as JSON.

[0048] The observation station position data DB 410 stores position information of each observation station 110. In one aspect, the position information may be information indicating latitude or longitude. In another aspect, the position information may be information indicating each area when the observation target area (such as the Japanese archipelago) is divided into any areas such as a grid.

[0049] The inter-observation station distance calculation unit 420 calculates the distance between each of the observation stations 110. In one aspect, the inter-observation station distance calculation unit 420 may calculate the distance between the observation stations 110 based on the difference between the latitude and longitude of the two observation stations 110. In another aspect, the inter-observation station distance calculation unit 420 may calculate the distance between the two observation stations 110 based on how many squares the two observation stations 110 are separated from each other on the grid. In this case, the inter-observation station distance calculation unit 420 may calculate the distance between the two observation stations 110 by multiplying the number of squares between the two observation stations 110 by the distance per square.

[0050] The inter-observation station distance data DB 430 stores distance data between each of the observation stations 110. In one aspect, the inter-observation station distance data DB 430 may store an identifier of each of two observation stations 110 in association with the distance between the two observation stations 110. In another aspect, the unit of distance may be any unit such as meters or kilometers.

[0051] The TEC value estimation unit 440 selects one observation station 110 from the multiple observation stations 110 as a central observation station, and creates a regression model of the TEC value at the central observation station. The regression model of the TEC value at the central observation station is created based on the observation results of multiple peripheral observation stations located around the central observation station. The regression model at the central observation station refers to an approximation of the TEC value predicted to be observed by the central observation station (a regression model based on the observation results of the peripheral observation stations) when no magnetic anomaly occurs in the ionosphere. Details of the processing by the TEC value estimation unit 440 will be described with reference to Figs. 6 and 7.

[0052] The estimated error calculation unit 450 compares a value (predicted value) at a certain time t obtained from the regression model of the central observation station with an actual measurement value of the central observation station at a certain time t, and calculates the estimated error (the difference between the actual measurement value and the predicted value). In this case, the anomaly detection device 320 may obtain the actual measurement value of the central observation station at a certain time t from the observation data DB 310. Details of the processing of the estimated error calculation unit 450 will be described with reference to FIG. 8. The TEC value estimation unit 440 and the estimated error calculation unit 450 select each of all observation stations 110 in turn as a central observation station, and repeatedly execute the above processing.

[0053] The correlation value calculation unit 460 executes processing based on the estimated error of each observation station 110 output by the estimated error calculation unit 450. The correlation value calculation unit 460 selects one observation station as a central observation station, and selects multiple surrounding observation stations as peripheral observation stations. In a certain situation, the correlation value calculation unit 460 may select any number of peripheral observation stations from the observation stations 110 that are within a predetermined distance from the central observation station.

[0054] Next, the correlation value calculation unit 460 calculates a correlation value between the estimation error at the central observation station at a certain time t and the estimation error of each of the peripheral observation stations at the certain time t. The estimation error at the central observation station and the estimation error of each of the peripheral observation stations are calculated based on the observation value (TEC value) at the same time t. The correlation value calculation unit 460 selects each of all observation stations 110 in turn as the central observation station and repeatedly executes the above correlation value calculation process. In a certain aspect, the correlation value calculation unit 460 may calculate the correlation value of the central observation station using a known technique. For example, the correlation value calculation unit 460 may execute the correlation value calculation shown in Patent Document 1.

[0055] Furthermore, the correlation value calculation unit 460 calculates a relative value based on the correlation value in each observation station 110 at a certain time t. The correlation value calculation unit 460 calculates a median and a standard deviation of the correlation values ​​in each observation station 110 at a certain time t. Then, the correlation value calculation unit 460 calculates a relative value indicating how much the correlation value of each observation station 110 differs from the median of the correlation values ​​based on the calculated median and standard deviation of the correlation values. The correlation value calculation unit 460 repeatedly executes the above-mentioned calculation process of the relative value for each correlation value of all the observation stations 110. The correlation value calculation unit 460 may calculate the relative value of each observation station 110 using a known technique. For example, the correlation value calculation unit 460 may execute the relative value calculation shown in Patent Document 1.

[0056] The abnormality determination unit 470 determines whether or not the relative values ​​of all the observation stations 110 at a certain time are equal to or greater than a predetermined threshold. For example, the abnormality determination unit 470 may determine that the observation value (TEC value) of the observation station 110A is abnormal based on the fact that the relative value of the observation station 110A is equal to or greater than a predetermined threshold. In a certain aspect, the abnormality determination unit 470 may determine whether or not the observation value (TEC value) of the observation station 110A is abnormal by determining whether or not the correlation value is equal to or greater than a predetermined threshold without calculating the relative value. In that case, the abnormality determination unit 470 may determine that the observation value (TEC value) of the observation station 110A is abnormal based on the fact that the correlation value is equal to or greater than a predetermined threshold.

[0057] The notification unit 480 outputs an alert when the abnormality determination unit 470 determines that the observation value of a certain observation station 110 is abnormal. In one aspect, the notification unit 480 may output a notice that the observation value is not abnormal even if the abnormality determination unit 470 does not detect an abnormality. In another aspect, the alert may include intensity information. For example, the intensity information may be determined based on how much larger the correlation value or relative value of the observation station 110 is than a predetermined threshold value.

[0058] 5 is a diagram showing an example of the configuration of the anomaly detection device 320. The anomaly detection device 320 includes a CPU (Central Processing Unit) 501, a primary storage device 502, a secondary storage device 503, an external device interface 504, an input interface 505, an output interface 506, and a communication interface 507.

[0059] The CPU 501 may execute programs for implementing various functions of the anomaly detection device 320. The CPU 501 may be configured, for example, by at least one integrated circuit. The integrated circuit may be configured, for example, by at least one CPU, at least one FPGA (Field Programmable Gate Array), or a combination thereof.

[0060] Primary storage device 502 stores programs executed by CPU 501 and data referenced by CPU 501. In one aspect, primary storage device 502 may be realized by a dynamic random access memory (DRAM), a static random access memory (SRAM), or the like.

[0061] Secondary storage device 503 is a non-volatile memory, and may store programs executed by CPU 501 and data referenced by CPU 501. In this case, CPU 501 executes programs read from secondary storage device 503 to primary storage device 502, and references data read from secondary storage device 503 to primary storage device 502. In one aspect, secondary storage device 503 may be realized by a hard disk drive (HDD), a solid state drive (SSD), an erasable programmable read only memory (EPROM), an electrically erasable programmable read only memory (EEPROM), a flash memory, or the like.

[0062] The external device interface 504 can be connected to any external device such as a printer, a scanner, an external HDD, etc. In one aspect, the external device interface 504 may be realized by a USB (Universal Serial Bus) terminal or the like.

[0063] The input interface 505 may be connected to any input device such as a keyboard, a mouse, a touchpad, or a gamepad. In one aspect, the input interface 505 may be realized by a USB terminal, a PS / 2 terminal, a Bluetooth (registered trademark) module, or the like.

[0064] Output interface 506 can be connected to any output device such as a cathode ray tube display, a liquid crystal display, an organic EL (Electro-Luminescence) display, etc. In one aspect, output interface 506 may be realized by a USB terminal, a D-sub terminal, a DVI (Digital Visual Interface) terminal, an HDMI (High-Definition Multimedia Interface) terminal, etc.

[0065] The communication interface 507 is connected to a wired or wireless network device. In one aspect, the communication interface 507 may be realized by a wired LAN (Local Area Network) port, a Wi-Fi (Wireless Fidelity) (registered trademark) module, or the like. In another aspect, the communication interface 507 may transmit and receive data using a communication protocol such as TCP / IP (Transmission Control Protocol / Internet Protocol) or UDP (User Datagram Protocol).

[0066] 6 is a diagram showing an example of the process of creating a regression model of the TEC value by the TEC value estimation unit 440. First, the TEC value estimation unit 440 selects one of the observation stations 110 as a "central observation station." As an example, it is assumed that the observation station 110A is selected as the central observation station.

[0067] Next, the TEC value estimation unit 440 selects a plurality of "peripheral observation stations" from an area 620 in which the distance from the observation station 110A is, for example, equal to or greater than a first distance (radius) 630 and equal to or less than a second distance (radius) 640. In one aspect, information on the first distance 630 and information on the second distance 640 may be stored in the secondary storage device 503. In that case, the TEC value estimation unit 440 may acquire information on the first distance 630 and information on the second distance 640 from the secondary storage device 503. In another aspect, the TEC value estimation unit 440 may determine each of the peripheral observation stations as a virtual weight and calculate the position of the center of gravity of these weights. In that case, the TEC value estimation unit 440 may select the peripheral observation stations so that the distance from the central observation station to the center of gravity is equal to or less than a predetermined third distance (radius). In this way, the TEC value estimation unit 440 may select the peripheral observation stations without bias as viewed from the central observation station. Furthermore, the information on the third distance may be stored in the secondary storage device 503. The TEC value estimation unit 440 may obtain the information on the third distance from the secondary storage device 503.

[0068] As an example, it is assumed that the TEC value estimation unit 440 selects the observation stations 110B and 110C as the peripheral observation stations. In this case, the regression model of the observation station 110A (central observation station) is generated based on the observation results of the TEC values ​​at the observation stations 110B and 110C (peripheral observation stations). In one aspect, the regression model of the central observation station may be generated based on the average value of the observation results of the TEC values ​​at the peripheral observation stations. In another aspect, the regression model of the central observation station may be generated based on the median value of the observation results of the TEC values ​​at the peripheral observation stations.

[0069] Observation stations 110B and 110C in region 620 are close to observation station 110A (central observation station) in region 610, and therefore are expected to detect similar TEC values ​​under normal circumstances. In addition, even if an earthquake occurs in region 610, for example, the ionosphere above region 620 is expected to be less affected by the earthquake that occurred in region 610, since there is a certain distance between regions 610 and 620.

[0070] Therefore, if an earthquake causes a magnetic anomaly in the ionosphere in region 610, it is expected that a difference will occur between the TEC value observed by observation station 110A in region 610 and the TEC value observed by observation stations 110B and 110C in region 620. In one aspect, first distance 630 and second distance 640 may be distances that are set to be outside the range of influence of a localized natural phenomenon such as an earthquake, based on data of past natural phenomena such as earthquakes.

[0071] The TEC value estimation unit 440 compares a regression model generated based on the TEC values ​​of multiple surrounding observation stations with the actual measured TEC value by the observation station 110A to detect an estimation error. The estimation error is used to detect an anomaly in the ionospheric TEC value, as will be described with reference to Figures 8 and 9.

[0072] Fig. 7 is a diagram showing an example of details of a procedure for creating a regression model of a central observation station. The process shown in Fig. 7 can be executed by the TEC value estimation unit 440. The TEC value estimation unit 440 acquires actual measured values ​​of the TEC values ​​of each of the peripheral observation stations. Then, the TEC value estimation unit 440 generates (estimates) a regression model of the central observation station based on the actual measured values ​​of the TEC values ​​of these peripheral observation stations.

[0073] As an example, a procedure for creating a regression model 720 of a central observation station based on an actual measurement value 710B of a TEC value by an observation station 110B selected from the area 620 and an actual measurement value 710C of a TEC value by an observation station 110C will be described.

[0074] First, the TEC value estimator 440 acquires an actual measurement value 710B at the observation station 110B. Similarly, the TEC value estimator 440 acquires an actual measurement value 710C at the observation station 110C. In one aspect, the actual measurement values ​​710B and 710C may be acquired from the observation data DB 310.

[0075] Next, the TEC value estimation unit 440 generates a regression model 720 for the observation station 110A (central observation station) based on the average or median of the actual measurement value 710B of the observation station 110B and the actual measurement value 710C of the observation station 110C. The value of the regression model 720 at time t indicates a predicted TEC value that the observation station 110A would normally output at time t.

[0076] Fig. 8 is a diagram showing an example of a procedure for calculating an estimated error (difference) between a predicted value and an actual measured value at a central observation station. The process shown in Fig. 8 can be executed by an estimated error calculation unit 450. The estimated error calculation unit 450 compares the value of the regression model 720 of the central observation station at time t (predicted value of the TEC value at the central observation station at time t) with the value of the actual measured value 810 of the central observation station at time t (actual measured value of the TEC value at the central observation station at time t) to calculate an estimated error 820.

[0077] A large estimated error 820 means that the TEC value observed at the central observation station is significantly different from the TEC value predicted to be observed at the central observation station under normal circumstances. In other words, a large estimated error 820 may indicate the possibility that a factor (e.g., a major earthquake) that causes the TEC value to fluctuate near the central observation station has occurred. The anomaly detection device 320 may determine whether the actual measurement value at the central observation station is abnormal based on the calculated estimated error 820. More specifically, the anomaly detection device 320 calculates the correlation value and the relative value of the central observation station based on the estimated error 820. Furthermore, the anomaly detection device 320 may determine that the actual measurement value at the central observation station is abnormal based on whether either the correlation value or the relative value is equal to or greater than a predetermined threshold.

[0078] Usually, the TEC value observed by the observation station 110 may fluctuate due to the influence of various natural phenomena. Therefore, even if only the change in the TEC value of one observation station 110 is observed, it is not possible to determine whether the change is due to the influence of a natural phenomenon in a wide range or a local range. Therefore, the anomaly detection device 320 according to this embodiment generates a regression model of the central observation station based on the observation results of the TEC values ​​of the surrounding observation stations. Since the regression model of the central observation station is generated based on the observation results of the TEC values ​​of the surrounding observation stations, it is not easily affected by local natural phenomena that occur near the central observation station. Therefore, a large estimation error 820 means that the predicted value is not affected by natural phenomena in a wide range, and the actual measured value is affected by natural phenomena in a local range, and may indicate a high possibility that a local natural phenomenon (such as a major earthquake) has occurred.

[0079] Fig. 9 is a diagram showing an example of a process flow for determining an abnormality in a TEC value by anomaly detection device 320. In one aspect, CPU 501 may load a program for performing the process of Fig. 9 from secondary storage device 503 to primary storage device 502 and execute the program. In another aspect, some or all of the process may be realized as a combination of circuit elements configured to perform the process.

[0080] In step S910, CPU 501 acquires a TEC value for each observation station 110. In one aspect, CPU 501 may acquire the TEC value for each observation station 110 via external device interface 504, input interface 505, or communication interface 507. In another aspect, CPU 501 may acquire the TEC value for each observation station 110 from observation data DB 310. In another aspect, CPU 501 may calculate the TEC value for each observation station 110 based on data acquired from observation data DB 310.

[0081] In step S920, CPU 501 calculates the distance between each of observation stations 110. More specifically, CPU 501 refers to observation station position data DB 410 to acquire position information of each of observation stations 110. CPU 501 calculates the distance between each of observation stations 110 based on the acquired position information of each of observation stations 110. CPU 501 stores the calculated distance information in observation station distance data DB 430. In one aspect, observation station position data DB 410 and observation station distance data DB 430 may be arranged in secondary storage device 503.

[0082] In step S930, the CPU 501 extracts peripheral observation stations for each observation station 110 (for each central observation station). More specifically, the CPU 501 selects a central observation station and extracts multiple peripheral observation stations for the central observation station. The processing in this step corresponds to the processing described with reference to FIG. 6.

[0083] In step S940, CPU 501 calculates a predicted value of the observation value (TEC value) of the central observation station based on the TEC values ​​of the peripheral observation stations. More specifically, CPU 501 generates a regression model of the TEC value of the central observation station based on the TEC values ​​of the peripheral observation stations extracted in step S930. The TEC value of the regression model at time t becomes the predicted TEC value (predicted value of the TEC value) of the central observation station at time t. The processing of this step corresponds to the processing described with reference to FIG. 7.

[0084] In step S950, the CPU 501 calculates the estimation error 820 for each observation station 110. More specifically, the CPU 501 compares the predicted value indicated by the regression model generated in step S940 with the actual measured TEC value of the central observation station, and calculates the estimation error (the difference between the predicted value and the actual measured value). The processing in this step corresponds to the processing described with reference to FIG. 8.

[0085] In step S960, the CPU 501 calculates a correlation value for each observation station 110. Furthermore, the CPU 501 calculates a relative value for each observation station 110 based on the correlation value. The process of this step corresponds to the process executed by the correlation value calculation unit 460.

[0086] In step S970, CPU 501 executes an alert determination. More specifically, CPU 501 may determine whether or not the correlation value or the relative value calculated in step S960 is equal to or greater than a predetermined threshold. If the correlation value or the relative value calculated in step S960 is equal to or greater than a predetermined threshold, CPU 501 outputs an alert. If not, CPU 501 may not output an alert, or may output a notification indicating that there is no abnormality in the observed TEC value. The process of this step corresponds to the process executed by abnormality determination unit 470 and notification unit 480. The processes from steps S910 to S970 above may be repeatedly executed for each of all observation stations 110.

[0087] Next, referring to Figures 10 to 15, a comparison will be made between the results of detecting abnormalities in TEC values ​​by the anomaly detection device 320 and the results of detecting abnormalities in TEC values ​​by a conventional device (the device described in Patent Document 1) when a simulation of detecting abnormalities in TEC values ​​was performed in Japan under the same conditions.

[0088] Fig. 10 is a diagram showing an example of conditions for a simulation of the TEC value anomaly detection process by the anomaly detection device 320. The conditions shown in Fig. 10 use data from when a major earthquake occurred in the past. The "observation period 1010" is the period from 00:00 UTC until the occurrence of the earthquake. In other words, the observation period 1010 is the period during which the simulation is performed.

[0089] The "target period 1020" is the period from one hour before the occurrence of the earthquake to the occurrence of the earthquake. In other words, the target period 1020 is the period during which there is a high possibility that an abnormality will occur in the TEC value due to the influence of the earthquake.

[0090] The "target space 1030" is a space that includes the epicenter and is within 1 degree of latitude and longitude. In other words, the target space 1030 is a region where an earthquake occurred, and is a space where an abnormality is thought to occur in the TEC value in the sky due to the effects of the earthquake.

[0091] It is desirable for the anomaly detection device 320 and the conventional device to detect an anomaly in the TEC value above the target space 1030 and output an alert during the target period 1020. This is because detecting an anomaly in the TEC value above the target space 1030 during the target period 1020 means detecting a change in the TEC value due to an earthquake.

[0092] In the simulation, the anomaly detection device 320 and the conventional device may use the observation results of the TEC values ​​calculated from all the observation stations 110 and all the satellites in Japan during the observation period. For example, the anomaly detection device 320 and the conventional device may obtain the observation results of the TEC values ​​every 30 seconds consisting of a combination of about 1,300 observation stations 110 and GNSS satellites 100. In reality, each of the multiple observation stations 110 may receive communication from each of the multiple GNSS satellites 100.

[0093] 11 is a diagram showing an example of the results of executing a simulation of anomaly detection device 320 and a conventional device. Experimental result 1100A is the output result of anomaly detection device 320. Experimental result 1100B is the output result of the conventional device.

[0094] Cell S1 of "Target, with alert" indicates the number of times that each device detected an abnormal TEC value in the air above the target space 1030 during the target period 1020 and output an alert. In other words, cell S1 of "Target, with alert" indicates the number of times that each device detected an abnormal TEC value in the air near the epicenter when an earthquake occurred (including immediately before the earthquake occurred) and output an alert. For example, according to cell S1A of "Target, with alert", the anomaly detection device 320 detected an abnormal TEC value in the air above the target space 1030 738 times during the target period 1020 and output an alert. According to cell S1B of "Target, with alert", the conventional device detected an abnormal TEC value in the air above the target space 1030 847 times during the target period 1020 and output an alert.

[0095] Cell S2 of "Target, no alert" indicates the number of times that each device did not detect an abnormality in the TEC value and did not output an alert in the air above the target space 1030 during the target period 1020. In other words, cell S2 of "Target, no alert" indicates the number of times that each device did not detect an abnormality in the TEC value in the air near the epicenter when an earthquake occurred (including immediately before the earthquake occurred).

[0096] Cell S3 "outside target, with alert" indicates the total number of times that each device detected an abnormal TEC value and output an alert during a period outside the target period 1020, and the total number of times that each device detected an abnormal TEC value and output an alert in the air above a location outside the target space 1030 within the target period 1020. In other words, cell S3 "outside target, with alert" indicates the total number of times that each device detected an abnormal TEC value and output an alert during a period when no earthquake occurred, and the total number of times that each device detected an abnormal TEC value and output an alert in the air above an area other than the epicenter when an earthquake occurred (including immediately before the earthquake occurred).

[0097] Cell S4 "Not targeted, no alert" indicates the total number of times that each device did not detect an abnormal TEC value during periods outside the target period 1020, and the total number of times that each device did not detect an abnormal TEC value above a location outside the target space 1030 during the target period 1020.

[0098] 9 (the process of determining an abnormality in the TEC value) during the observation period 1010. Similarly, the sum of the above cells S1B to S4B indicates the number of times that the conventional device repeated the process of determining an abnormality in the TEC value during the observation period 1010.

[0099] 12 is a diagram showing an example of an analysis result of a simulation execution result. Analysis result 1200A shows the analysis result of experimental result 1100A of anomaly detection device 320. Analysis result 1200B shows the analysis result of experimental result 1100B of a conventional device. Below, S1, S2, S3, and S4 in experimental results 1200A and 1200B respectively indicate the numerical values ​​of cell S1, cell S2, cell S3, and cell S4.

[0100] Recall is the probability of issuing an alert in response to a precursor phenomenon, and the higher the better. In this case, "precursor phenomenon" refers to the change in TEC values ​​that will likely be observed in the air near the epicenter in the period from just before the earthquake occurs until the time of the earthquake. In the case of this simulation, recall is the probability of detecting an abnormality in the TEC values ​​in the air near the epicenter when there is a precursor phenomenon (the occurrence of an earthquake and its precursors). Recall can be calculated as follows: Recall rate=S1 / (S1+S2) Precision is the probability that when an alert is issued, it is based on a precursor phenomenon, and the higher the precision, the better. In this simulation, precision is the probability that an alert is issued based on a certain precursor phenomenon (the occurrence of an earthquake and its precursors). Precision can be calculated as follows: Precision rate=S1 / (S1+S3) Specificity is the probability that an alert will not be issued under normal circumstances, and the higher the probability, the better. In the case of this simulation, specificity is the probability that an alert will not be issued if there are no precursor phenomena (the occurrence of an earthquake and its precursors). Specificity is calculated as follows: Specificity=S4 / (S3+S4) Accuracy indicates the degree to which the judgment is correct overall, and the higher the accuracy, the better. Accuracy is calculated as follows: Accuracy = (S1+S4) / (S1+S2+S3+S4) The F-value indicates the degree of accuracy of the judgment when the degree of imbalance in the data is taken into account; the larger the value, the better. The F-value is calculated as follows: In the case of this simulation, the accuracy and F-value indicate the degree of precision in predicting precursor phenomena (the occurrence of earthquakes and their precursors). F-score = 2 / (1 / recall + 1 / precision) The false negative rate is the probability of missing a precursor phenomenon, and the smaller the rate, the better. In this simulation, the false negative rate is the probability of issuing an alert when a precursor phenomenon (an earthquake occurrence and its precursors) is present. The false negative rate can be calculated as follows: False negative rate=S2 / (S1+S2) The false positive rate is the probability of outputting a false alarm, and the smaller the rate, the better. In the case of this simulation, the false positive rate is the probability of outputting an alert when there are no precursor phenomena (the occurrence of an earthquake and its precursors). The false positive rate can be calculated as follows: False positive rate=S3 / (S3+S4) Referring to the analysis results 1200A and 1200B, anomaly detection device 320 shows better results in terms of precision, specificity, accuracy, F-measure, and false positive rate compared to the conventional device. This shows that anomaly detection device 320 has improved accuracy in determining anomalies in TEC values ​​compared to the conventional device.

[0101] FIG. 13 is a diagram showing an example of the sampling periods of the anomaly detection device 320 and a conventional device. A sampling period is usually required to generate a regression model. The sampling period 1310 of the anomaly detection device 320 is about half the sampling period 1320 of the conventional device. Furthermore, as shown in FIG. 12, even with a sampling period that is about half that of the conventional device (even with a smaller number of samples), the anomaly detection device 320 can detect anomalies in the TEC value with accuracy equal to or higher than that of the conventional technology because the accuracy of the regression model is higher than that of the conventional technology.

[0102] 14 is a diagram showing a first example of a comparison between an alert output by anomaly detection device 320 and an alert output by a conventional device. Display 1410A is a display of an alert output by anomaly detection device 320 during a period in which no earthquakes have occurred in the simulation. Display 1410B is a display of an alert output by a conventional device during a period in which no earthquakes have occurred in the simulation. Triangles plotted on displays 1410A and 1410B indicate the strength of the alert.

[0103] Comparing displays 1410A and 1410B, display 1410B outputs high-intensity alerts in areas 1420B, 1430B, and 1440B. In contrast, display 1410A does not display high-intensity alerts, and it can be seen that anomaly detection device 320 has a more accurate regression model and fewer false alarms than conventional devices.

[0104] 15 is a diagram showing a second example of a comparison between an alert output by anomaly detection device 320 and an alert output by a conventional device. Display 1510A is a display of an alert output by anomaly detection device 320 during the period when an earthquake occurs in the simulation (including immediately before the earthquake occurs). Display 1510B is a display of an alert output by a conventional device during the period when an earthquake occurs in the simulation (including immediately before the earthquake occurs).

[0105] Comparing displays 1510A and 1510B, display 1510B displays high-intensity alerts in three locations, areas 1520B, 1530B, and 1540B, whereas display 1510A displays a single high-intensity alert in area 1520A. In other words, it can be seen that anomaly detection device 320 can detect anomalies in the TEC value with higher accuracy in a narrower range than conventional devices.

[0106] As described above, the anomaly detection device 320 according to this embodiment generates a regression model for the central observation station based on the TEC values ​​of the peripheral observation stations selected from the surroundings of the central observation station. Then, the anomaly detection device 320 compares the predicted value of the regression model with the actual measurement value of the central observation station to calculate an estimation error, and predicts an anomaly in the TEC value based on the estimation error. This allows the anomaly detection device 320 to detect an anomaly in the TEC value with higher accuracy than before (the rate of false alarms in the detection of an anomaly in the TEC value is reduced). It is known that phenomena in the ionosphere have various effects on social infrastructure including communication and wireless. Therefore, the technology for detecting an anomaly in the TEC value according to this embodiment can also be used for ionosphere anomaly observation technology for operating social infrastructure, space weather model construction, and observation of plasma turbulence and changes.

[0107] The embodiments disclosed herein should be considered to be illustrative and not restrictive in all respects. The scope of the present disclosure is indicated by the claims, not by the above description, and is intended to include all modifications within the meaning and scope of the claims. In addition, the disclosure contents described in the embodiments and each modified example are intended to be implemented, as far as possible, either alone or in combination. [Explanation of symbols]

[0108] 100 GNSS satellite, 110 observation station, 120 ionosphere, 300 anomaly detection system, 310 observation data DB, 320 anomaly detection device, 330 service provider, 340 user terminal, 350 network, 410 observation station position data DB, 420 observation station distance calculation unit, 430 observation station distance data DB, 440 value estimation unit, 450 estimation error calculation unit, 460 correlation value calculation unit, 470 anomaly determination unit, 480 reporting unit, 501 CPU, 502 primary storage device, 503 secondary storage device, 504 external device interface, 505 input interface, 506 output interface, 507 communication interface, 610, 620, 1420B, 1430B, 1440B, 1520A, 1520B, 1530B, 1540B area, 630 First distance, 640 Second distance, 710B,710C Actual measurement value, 720 Regression model, 810 Actual measurement value, 820 Estimation error, 1010 Observation period, 1020 Target period, 1030 Target space, 1100A,1100B Experimental results, 1200A,1200B Analysis results, 1310,1320 Sampling period, 1410A,1410B,1510A,1510B Display.

Claims

1. an input unit for acquiring observation values ​​from a plurality of observation stations for observing the number of electrons in the ionosphere; A control unit that determines an abnormality in the observed value, The control unit is selecting a central observation station from among the plurality of observation stations; selecting a plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station; calculating a predicted observation value of the central observation station based on the observation values ​​of each of the plurality of peripheral observation stations; Calculating an estimated error between the predicted observation value and the actual measurement value of the central observation station; An anomaly detection device that determines whether the actual measurement value of the central observation station is abnormal based on the estimated error.

2. Further comprising a storage unit for storing information on the first distance and information on the second distance, 2. The anomaly detection device of claim 1, wherein selecting the plurality of peripheral observation stations from the plurality of observation stations based on their distance from the central observation station includes selecting the plurality of peripheral observation stations from an area whose distance from the central observation station is greater than or equal to the first distance and less than or equal to the second distance.

3. The storage unit further stores information on a third distance, selecting the plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station, determining each of the peripheral observation stations as a virtual weight; Calculating the position of the center of gravity of the weights of the selected peripheral observation stations; The anomaly detection device according to claim 2 , further comprising: selecting the plurality of peripheral observation stations such that a distance from the central observation station to the center of gravity is equal to or less than the third distance.

4. An anomaly detection device as described in any one of claims 1 to 3, wherein calculating the predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes calculating the predicted observation value of the central observation station based on an average value of the observation values ​​of each of the multiple surrounding observation stations.

5. An anomaly detection device as described in any one of claims 1 to 3, wherein calculating the predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes calculating the predicted observation value of the central observation station based on a median of the observation values ​​of each of the multiple surrounding observation stations.

6. selecting the central observation station includes selecting each of the observation stations included in the plurality of observation stations as the central observation station; 6. The anomaly detection device according to claim 1, wherein calculating the estimated error includes repeatedly calculating the estimated error when each of the observation stations is selected as the central observation station.

7. Determining whether the actual measurement value of the central observation station is abnormal based on the estimation error calculating a correlation value between the estimated error of the central observation station and the estimated errors of a plurality of observation stations located in the periphery of the central observation station; The anomaly detection device according to claim 6 , further comprising: determining that the actual measurement value of the central monitoring station is abnormal based on the correlation value being equal to or greater than a predetermined threshold value.

8. Determining whether the actual measurement value of the central observation station is abnormal based on the estimation error calculating a correlation value between the estimated error of the central observation station and the estimated errors of a plurality of observation stations located in the periphery of the central observation station; calculating a median and a standard deviation of the correlation values ​​of the central observation station; calculating a relative value indicating a degree of difference between the correlation value and the median value of the central observation station based on the median value and the standard deviation; The anomaly detection device according to claim 6 , further comprising: determining that the actual measurement value of the central monitoring station is abnormal based on the relative value being equal to or greater than a predetermined threshold value.

9. An output unit that outputs an alert is further provided, 9. The anomaly detection device according to claim 1, wherein the output unit outputs an alert when the actual measurement value of the central monitoring station is determined to be abnormal.

10. 1. A method for detecting an anomaly in ionospheric electron content, comprising: acquiring observation values ​​from a plurality of observation stations for observing the number of electrons in the ionosphere; selecting a central observation station from among the plurality of observation stations; selecting a plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station; calculating a predicted observation value of the central observation station based on the observation values ​​of each of the plurality of peripheral observation stations; calculating an estimated error between the predicted observation value and an actual measurement value at the central observation station; and determining whether the actual measurement value of the central observation station is abnormal based on the estimation error.

11. The method according to claim 10, wherein the step of selecting the plurality of peripheral observation stations from the plurality of observation stations based on the distance from the central observation station includes a step of selecting the plurality of peripheral observation stations from an area whose distance from the central observation station is equal to or greater than a first distance and equal to or less than a second distance.

12. The step of selecting the plurality of peripheral observation stations from the plurality of observation stations based on a distance from the central observation station includes: determining that each of the peripheral observation stations is a virtual weight; Calculating the positions of the centers of gravity of the weights of the selected peripheral observation stations; and selecting the plurality of peripheral observation stations such that a distance from the central observation station to the center of gravity is less than or equal to a third distance.

13. A method according to any one of claims 10 to 12, wherein the step of calculating the predicted observation value of the central observation station based on the observation values ​​of each of the multiple surrounding observation stations includes a step of calculating the predicted observation value of the central observation station based on an average value of the observation values ​​of each of the multiple surrounding observation stations.

14. A method according to any one of claims 10 to 12, wherein the step of calculating the predicted observation value of the central observation station based on the observation values ​​of each of the plurality of surrounding observation stations includes a step of calculating the predicted observation value of the central observation station based on a median of the observation values ​​of each of the plurality of surrounding observation stations.

15. the step of selecting the central observation station includes a step of selecting each of the observation stations included in the plurality of observation stations as the central observation station; The method according to any one of claims 10 to 14, wherein the step of calculating the estimated error includes a step of repeatedly calculating the estimated error when each of the observation stations is selected as the central observation station.

16. The step of determining whether the actual measurement value of the central observation station is abnormal based on the estimation error includes: calculating a correlation value between the estimated error of the central observation station and the estimated errors of a plurality of observation stations located in the periphery of the central observation station; The method according to claim 15 , further comprising: determining that the actual measurement value of the central monitoring station is abnormal based on the correlation value being equal to or greater than a predetermined threshold value.

17. The step of determining whether the actual measurement value of the central observation station is abnormal based on the estimation error includes: calculating a correlation value between the estimated error of the central observation station and the estimated errors of a plurality of observation stations located in the periphery of the central observation station; calculating a median and a standard deviation of the correlation values ​​of the central observation stations; calculating a relative value indicating a degree of difference between the correlation value and the median value of the central observation station based on the median value and the standard deviation; and determining that the actual measurement value of the central monitoring station is abnormal based on the relative value being equal to or greater than a predetermined threshold.

18. The method according to any one of claims 10 to 17, further comprising the step of outputting an alert based on the actual measurement value of the central monitoring station being determined to be abnormal.

19. A program for causing a computer to execute the method according to any one of claims 1 to 18.

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