CN113960634B - Real-time ionosphere TEC modeling method based on empirical orthogonal function - Google Patents
Real-time ionosphere TEC modeling method based on empirical orthogonal function Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
- G01S19/07—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing data for correcting measured positioning data, e.g. DGPS [differential GPS] or ionosphere corrections
- G01S19/072—Ionosphere corrections
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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Abstract
The invention discloses a real-time ionosphere TEC modeling method based on an empirical orthogonal function in the technical field of space. The technical scheme is that based on historical TEC data, the historical TEC data is divided into four dimensions according to the annual product day, the world time, the longitude and the latitude, an average value is obtained according to the annual product day, and the historical TEC data is flattened; performing experience orthogonal decomposition on historical TEC data after distance flattening, and decomposing into a part reflecting the daily change coefficient of the annual product and a basic function part reflecting the world time, longitude and latitude; acquiring a basis function corresponding to real-time observation data by utilizing real-time observation TEC data through basis function interpolation, and fitting with the real-time TEC data to acquire a real-time coefficient; and finally, constructing a real-time ionosphere TEC model through the acquired real-time coefficient and the historical basis function. The method has the beneficial effects that through statistical analysis of historical TEC data and real-time TEC data driving, the constructed ionosphere TEC model has the characteristics of high convergence rate, good instantaneity and high accuracy, provides important technical support for monitoring space weather events, and has important value in ionosphere theoretical research and satellite navigation positioning correction application research.
Description
Technical Field
The invention provides a real-time ionosphere TEC modeling method based on an empirical orthogonal function, which is suitable for the field of ionosphere TEC modeling design.
Background
The total electronic content (Total Electron Content, TEC) of the ionosphere is one of the important parameters describing the changes, states and structures of the ionosphere, and is receiving a great deal of attention in the fields of ionosphere physical basic research and satellite navigation positioning application research. The space-time variation rule of the ionized layer TEC is researched, and the establishment of the high-precision ionized layer TEC model has important value in the aspects of scientific research and engineering application.
The ionized layer TEC model can be divided into a theoretical model and an empirical model according to the basis established by the forecasting method. The empirical models mainly include a Klobuchar model, a NeQuick model, an international reference ionosphere (International Reference Ionosphere, IRI) model, and the like. The Klobuchar mode is an ionospheric delay correction mode widely used by users of a global positioning system (Global Positioning System, GPS) single-frequency receiver, the NeQuick model is an ionospheric correction model adopted by the broadcast ephemeris of the Galileo system, and the correction precision of the two models is about 50-70%. The IRI model is an ionospheric experience model established by the international radio science union by utilizing a large amount of ground related observation data and combining with the long-term accumulated ionospheric research results, and is one of the most widely applied ionospheric simulation methods. As IRI is a statistical prediction mode, the average state of the ionosphere is mainly reflected, the instantaneous change of the ionosphere is difficult to reflect in actual prediction, and certain error still exists in the ionosphere TEC calculated by using the IRI model. In order to improve the instantaneity and accuracy of an ionosphere TEC empirical model, a real-time ionosphere TEC modeling method based on an empirical orthogonal function is provided, and the method is driven by using real-time TEC data through statistical analysis of historical TEC data, so that the method has the characteristics of high convergence speed, good instantaneity and high accuracy, provides important technical support for monitoring of space weather events, and simultaneously provides reliable data guarantee for subsequent ionosphere scientific research and satellite navigation positioning correction.
Disclosure of Invention
Aiming at the defects existing in the conventional ionosphere TEC empirical model, the invention provides a real-time ionosphere TEC modeling method based on an empirical orthogonal function, which is characterized by comprising the following steps of:
step 1: dividing historical TEC data into four dimensions according to the annual product day, the world time, the longitude and the latitude, taking an average value according to the annual product day, and flattening the historical TEC data;
step 2: performing experience orthogonal decomposition on historical TEC data after distance flattening, and decomposing into a part reflecting the daily change coefficient of the annual product and a basic function part reflecting the world time, longitude and latitude;
step 3: acquiring a basis function corresponding to real-time observation data by utilizing real-time observation TEC data through basis function interpolation, and fitting with the real-time TEC data to acquire a real-time coefficient;
step 4: and (3) constructing a real-time ionosphere TEC model by combining the real-time coefficient obtained in the step (3) with the historical basis function.
In step 1, the formula for taking the average value according to the annual product date is:
wherein,,the average value of vertical TEC of all annual accumulation days of the ith moment, the jth geographic longitude and the kth geographic latitude is given, t represents the annual accumulation day, N represents the maximum number of annual accumulation days, and +.>Vertical TEC values at the t-th annual product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude are shown.
The calculation formula of distance flattening:
vertical TEC values after flattening are shown for the t-th annual product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude.
In the step 2, the formula of empirical orthogonal decomposition of TEC data after historical distance flattening:
wherein,,for the flattened vertical TEC, t, i, j and k, the t-th product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude, respectively, l represents the fitted order, M represents the total order>Representing the first order coefficient after empirical orthogonal decomposition, < >>Representing the first order basis functions after empirical orthogonal decomposition.
Step 3: the calculation formula of the fitting coefficient through the real-time data is as follows:
vertical TEC for real-time observation on the p-th annual product day, the i-th moment, the j-th geographical longitude and the k-th geographical latitude, +.>Average value of vertical TEC for all year long for the ith time, jth geographic longitude and kth geographic latitude,/->For the first order basis function interpolated at the i-th moment, the j-th geographical longitude and the k-th geographical latitude,and obtaining a first order coefficient for real-time fitting of the p th annual product day.
Step 4: the calculation formula for constructing the real-time ionized layer TEC model is as follows:
vertical TEC on the p-th annual product day, i-th moment, j-th geographic longitude and k-th geographic latitude obtained by real-time data construction, +.>Mean value of vertical TEC of all year long for ith moment, jth geographic longitude and kth geographic latitude, +.>First order coefficients fitted in real time for the p-th annual product day, +.>Representing the first order basis functions after empirical orthogonal decomposition.
The method has the advantages that the real-time ionosphere TEC modeling method based on the empirical orthogonal function can be driven by using real-time TEC data, has the characteristic of quickly and accurately constructing the regional ionosphere TEC model, and has important application value in the aspects of monitoring of space weather events, ionosphere scientific research, satellite navigation positioning correction and the like.
Drawings
FIG. 1 is an average distribution of historical TEC data calculated by the method provided by the invention at world times 00:00, 06:00 and 12:00.
FIG. 2 is a distribution of 1-4 th order basis functions of historical TEC data calculated by the method provided by the invention at the time of 00:00 in the world.
Fig. 3 is a distribution of historical TEC data coefficients of order 1-4 and solar activity F10.7 index calculated by the method provided by the present invention over the period of 1998-2010.
FIG. 4 is a distribution of ionosphere TEC models constructed using real-time data at world time 02:00 in the method provided by the invention.
Detailed Description
The preferred embodiments are described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary in nature and is in no way intended to limit the scope of the invention or its applications.
Taking ionosphere TEC data of a certain area in 1998-2010 of a certain organization as historical TEC data, and taking GNSS-TEC observed in 2014, 9 and 28 of a certain observation network as real-time observation data, executing the following steps:
step 1: taking the vertical TEC calculation average for all year product days of time 1, longitude 1 and latitude 1 as an example,
where n=4596, calculated8.13.
Taking the vertical TEC at time 1, longitude 1 and latitude 5 years before 1 as an example, the distance flattening results are as follows:
FIG. 1 shows the mean distribution of historical TEC data calculated by the method provided by the invention at world times 00:00, 06:00 and 12:00.
Step 2: taking the vertical TEC at time 1, longitude 1, latitude 1, and product day 2 as an example, empirical orthogonal decomposition is performed from flattened TEC data:
where M is the total order of the empirical orthogonal decomposition, with a value of 4596, taking m=5 as an example,
FIG. 2 shows that the 1-4 order basis functions of the historical TEC data calculated by the method provided by the invention are calculated at the world time of 00: distribution at 00.
Fig. 3 shows the distribution of the historical TEC data 1-4 coefficients and solar activity F10.7 index calculated by the method provided by the present invention during 1998-2010.
Step 3: taking real-time observation data on world time 1, geographic longitude 12 and geographic latitude 18 of a certain observation network 2014, 9 th month and 28 th day (year product day 271) as an example, the fitted 1 st order coefficient is as follows,
step 4: taking an ionosphere TEC model constructed by a 1 st order coefficient fitted by real-time data on the 1 st world time, the 12 th geographic longitude and the 20 th geographic latitude of the 28 th month of 2014 (the year product day is 271) as an example, the calculation result is as follows:
FIG. 4 shows the distribution of ionosphere TEC models constructed using real-time data at 02:00 world time in the method provided by the invention.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the technical scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (5)
1. The real-time ionosphere TEC modeling method based on the empirical orthogonal function is characterized by comprising the following steps of:
step 1: dividing historical TEC data into four dimensions according to the annual product day, the world time, the longitude and the latitude, taking an average value according to the annual product day, and flattening the historical TEC data;
step 2: performing experience orthogonal decomposition on historical TEC data after distance flattening, and decomposing into a part reflecting the daily change coefficient of the annual product and a basic function part reflecting the world time, longitude and latitude;
step 3: acquiring a basis function corresponding to real-time observation data by utilizing real-time observation TEC data through basis function interpolation, and fitting with the real-time TEC data to acquire a real-time coefficient;
step 4: and (3) constructing a real-time ionosphere TEC model by combining the real-time coefficient obtained in the step (3) with the historical basis function.
2. The method for modeling a real-time ionosphere TEC based on an empirical orthogonal function according to claim 1, wherein in the step 1, the formula for averaging according to the yearly product day is:
wherein,,for the i time, the j geographic longitude and the k geographicAverage value of vertical TEC of all annual holidays of latitude, t represents annual holiday, N represents maximum number of annual holidays, ">Vertical TEC values representing the t-th annual product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude;
the calculation formula of distance flattening:
vertical TEC values after flattening are shown for the t-th annual product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude.
3. The method for modeling a real-time ionosphere TEC based on an empirical orthogonal function according to claim 1, wherein in step 2, the formula of empirical orthogonal decomposition of the TEC data after the history distance flattening is as follows:
wherein,,for the flattened vertical TEC, t, i, j and k, the t-th product day, the i-th time, the j-th geographic longitude and the k-th geographic latitude, respectively, l represents the fitted order, M represents the total order>Representing the first order coefficient after empirical orthogonal decomposition, < >>Representing the first order basis after empirical orthogonal decompositionA function.
4. The method for modeling a real-time ionosphere TEC based on an empirical orthogonal function according to claim 1, wherein in step 3, the calculation formula of the fitting coefficient by real-time data is:
vertical TEC for real-time observation on the p-th annual product day, the i-th moment, the j-th geographical longitude and the k-th geographical latitude, +.>Average value of vertical TEC for all year long for the ith time, jth geographic longitude and kth geographic latitude,/->For the first order basis function interpolated at the i time, the j geographic longitude and the k geographic latitude>And obtaining a first order coefficient for real-time fitting of the p th annual product day.
5. The method for modeling a real-time ionosphere TEC based on an empirical orthogonal function according to claim 1, wherein in step 4, a calculation formula for constructing the real-time ionosphere TEC model is as follows:
to pass through the realityThe p-th annual product day, the i-th moment, the j-th geographic longitude and the vertical TEC on the k-th geographic latitude obtained by time data construction, +.>Average value of vertical TEC for all year long for the ith time, jth geographic longitude and kth geographic latitude,/->First order coefficients fitted in real time for the p-th annual product day, +.>Representing the first order basis functions after empirical orthogonal decomposition.
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