Ionized layer spatial correlation modeling method based on Gaussian variation function

Abstract

The invention discloses an ionosphere spatial correlation modeling method based on a Gaussian variation function, and belongs to the technical field of GNSS satellite ionospheres. According to the method, ionosphere observation information is obtained through observation data of uniformly distributed GNSS base stations, regional ionosphere semi-variance information is extracted, a Gaussian variation function is used for fitting ionosphere semi-variance to obtain a Gaussian variation function parameter sequence, a Gaussian variation function parameter prediction model is established by using a harmonic estimation method, and the prediction precision of the region ionosphere is improved. And establishing an ionosphere spatial correlation model. Compared with a traditional ionosphere spatial correlation model, the method has the advantages that the precision is improved, the calculation mode is wider, and the applicability is better.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS satellite ionosphere, and in particular relates to an ionosphere spatial correlation modeling method based on Gaussian variation function. Background Art

[0002] For single-frequency users of the Global Navigation Satellite System (GNSS), accurate correction of ionospheric refraction delay is one of the effective means to improve positioning accuracy. Using a high-precision ionospheric model to obtain the total electron content (TEC) information of the ionosphere, and then calculating the ionospheric delay at the corresponding frequency point through a conversion factor is the main method to achieve ionospheric correction. The ionosphere is affected by factors such as solar activity and geomagnetic activity, showing regular changes in the ionosphere and complex irregular changes. Regular changes occur cyclically, mainly including daily changes, annual changes and changes in the solar activity cycle, which can be modeled with reasonable accuracy. This part is also called the ionospheric deterministic component. Irregular changes are mainly caused by unpredictable ionospheric changes caused by sudden changes in solar radiation, geomagnetic field disturbances and other reasons, also known as ionospheric random term components. Commonly used ionospheric modeling methods often only estimate the deterministic components of the ionosphere, while ignoring the impact of ionospheric random terms. And considering that the ionospheric random term components will produce large deviations in years with high solar activity, they cannot be ignored in high-precision applications.

[0003] The ionosphere is a time-space continuous heterogeneous body with high spatial heterogeneity. Therefore, when modeling ionospheric TEC, the Kriging interpolation method can be used to calculate the ionospheric random component. The Kriging interpolation method mainly considers the spatial correlation of vertical TEC at the ionospheric puncture point. Based on the linear, unbiased and minimum mean square error criteria, a certain weight coefficient is assigned according to the relative distance between different sampling points in the search domain, so as to determine the ionospheric vertical total electron content VTEC information of the grid point to be estimated. Compared with the inverse distance weighting and plane fitting method, Kriging not only considers the distance between the ionospheric puncture point and the grid point, but also considers the relative position relationship between the ionospheric puncture points. Therefore, it has high accuracy and is suitable for describing the change of TEC. It should be pointed out that the interpolation accuracy of the Kriging interpolation method is closely related to the reasonable ionospheric spatial correlation model and covariance function. However, there are obvious differences in the activity level of the ionosphere during the day and night. The empirical fixed covariance function and spatial correlation Kriging interpolation method are difficult to accurately describe the spatiotemporal characteristics of ionospheric TEC. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides an ionospheric spatial correlation modeling method based on Gaussian variation function, utilizes fast Fourier transform to extract the main periodic terms of variation function parameters, utilizes harmonic estimation method to determine the amplitude of each periodic term, establishes ionospheric spatial correlation prediction model based on harmonic estimation method, and comprehensively establishes time-varying ionospheric spatial correlation model, which can timely reflect the changes of ionospheric spatial correlation.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows: A method for modeling ionospheric spatial correlation based on Gaussian variogram, the method comprising: Step S1, extracting the ionospheric tilt total electron content STEC at the regional ionospheric puncture point, and converting it to the ionospheric vertical total electron content VTEC using a projection function; Step S2, retrieving the regional ionospheric vertical total electron content VTEC information, and calculating the regional ionospheric semi-variance at each distance; Step S3, based on the obtained ionospheric semi-variance information at different distances, a Gaussian variation function is used for fitting to obtain a Gaussian variation function parameter sequence; Step S4, establishing a Gaussian variogram parameter prediction model based on a harmonic estimation method; Step S5: using the Gaussian variation function parameter prediction model to establish an ionospheric spatial correlation model.

[0006] The beneficial effects of the present invention are: The ionospheric spatial correlation modeling method of the present invention supports adaptive calculation of data in different regions without manual parameter change. In addition, compared with the traditional ionospheric spatial correlation model, the method has improved accuracy, a wider calculation method and better applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 The present invention is a flow chart of a method for modeling ionospheric spatial correlation based on Gaussian variogram; Figure 2 This is a curve chart of the number and form of periodic terms in the Gaussian variogram parameter prediction model. DETAILED DESCRIPTION

[0008] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0009] The present invention provides an ionospheric spatial correlation modeling method based on Gaussian variogram, which obtains ionospheric observation information through uniformly distributed GNSS reference station observation data, constructs a regional ionospheric spatial correlation model through Gaussian variogram, and obtains variogram parameters; establishes a variogram parameter prediction model using a harmonic estimation method, and establishes an ionospheric spatial correlation model based on the above model; it can be seen that the present invention establishes a time-varying Gaussian variogram through the harmonic estimation method, improves the accuracy of the ionospheric spatial correlation model, and further improves the accuracy of the ionospheric total electron content model.

[0010] like Figure 1 As shown, a method for modeling ionospheric spatial correlation based on Gaussian variogram of the present invention specifically comprises the following steps: S1, extract the ionospheric tilt total electron content STEC at the regional ionospheric puncture point, and convert it to the ionospheric vertical total electron content VTEC using the projection function; It should be noted that through the observation information of GNSS receivers evenly distributed in the region, the carrier phase smoothing pseudorange method is used to obtain the smoothed pseudorange geometry-free combination observation information, the synchronous estimation method is used to extract the receiver differential code bias, and the high-precision satellite differential code bias product is used to obtain the satellite differential code bias, and then the ionospheric STEC information is obtained, and the ionospheric VTEC information is extracted through the projection function.

[0011] Ionospheric VTEC extraction includes cycle slip detection, carrier phase smoothing pseudorange, receiver hardware differential code bias estimation, satellite differential code bias correction, and STEC conversion; Among them, the method of using carrier phase smoothing pseudorange to obtain smoothed pseudorange non-geometric combination observation information includes: (1) In the formula, For the moment Smoothed pseudorange without geometric combination observations, is the ionospheric delay conversion factor, is the first carrier frequency, is the second carrier frequency, For satellite With receiver At the moment STEC, For receiver At the first carrier frequency With the carrier second frequency The receiver-side differential code deviation is For satellite At the first carrier frequency With the carrier second frequency The satellite differential code deviation.

[0012] Extracting the differential code deviation at the receiver using the synchronous estimation method , using satellite differential code bias product correction ,from Get .

[0013] Using the projection function, STEC is converted to VTEC: (2) in, is the ionospheric projection function, For satellite With receiver At the moment VTEC.

[0014] S2, retrieve the regional ionospheric vertical total electron content VTEC information, and calculate the regional ionospheric semi-variance at each distance; The ionospheric semivariance is calculated by ionospheric VTEC. The ionospheric semivariance extraction method in step S2 includes: (3) in, is the distance between the two ionospheric puncture points, and the semivariance of ionospheric VTEC It is defined as all the distances in the region half the variance of the ionospheric VTEC differences between pairs of ionospheric puncture points, To find the expected function, VTEC and The distance between VTEC is .

[0015] It should be noted that in this step, the ionospheric VTEC semivariance at different distances is calculated by distance retrieval. The search range is set to 0 km to 5000 km, and the search step is set to 20 km.

[0016] S3, based on the ionospheric semi-variance information at different distances obtained in the above steps, fitting is performed using a Gaussian variogram to obtain a Gaussian variogram parameter sequence; (4) in, is the Gaussian variogram range, is the Gaussian variation function nugget, that is, the Gaussian variation function value between two points with a distance of 0; is the partial sill of the Gaussian variogram, is the Gaussian variogram base, represents the multiplication operation, and e represents the exponential function.

[0017] S4. Establish a Gaussian variogram parameter prediction model based on the harmonic estimation method; (5) in, is the initial amplitude of the nugget parameter, is the amplitude of the cosine component of each periodic term of the nugget parameter, is the amplitude of the sinusoidal component of each periodic term of the nugget parameter, is the number of nugget parameter period items, Nugget parameter The frequency of the periodic term; is the amplitude of each periodic term of the partial sill parameter, is the amplitude of the cosine component of each periodic term of the partial base parameter, is the amplitude of the sinusoidal component of each periodic term of the partial base parameter, is the number of periodic terms of partial sill parameters, is the partial sill parameter The frequency of the periodic term, is the amplitude of the periodic term of the range parameter, is the amplitude of the cosine component of each periodic term of the range parameter, is the amplitude of the sinusoidal component of each periodic term of the range parameter, is the number of periodic terms of the range parameter, is the range parameter The frequency of the periodic term; The Julian day time for the forecast moment.

[0018] It should be noted that the method for establishing the prediction model of the variogram parameters is a harmonic estimation method, including the extraction of parameter periodic terms and the estimation of the amplitude corresponding to the parameter periodic terms. Among them, when extracting the periodic terms, the power spectrum of the parameters is first extracted by fast Fourier transform, and the main periodic terms are extracted according to the power spectrum analysis. When extracting the main periodic terms of the variogram parameters, the Gaussian variogram nugget is used. It reaches its maximum value between 14:00 and 16:00 local time, tends to be calm at night, and the Gaussian variation function is nugget. It mainly includes two cycles, of which the long cycle for The long period is mainly caused by the changes in the solar zenith angle and solar radiation; the short period for Hours, this short period is mainly affected by the solar diurnal variation. Gaussian variation function range and the partial sill parameter of the Gaussian variogram Both contain long-term and short-term terms, and That is, in this example, if Figure 2 As shown in the figure, the number and form of periodic terms in the constructed Gaussian variogram parameter prediction model are as follows: (6) S5. Use the Gaussian variation function parameter prediction model to establish the ionospheric spatial correlation model.

[0019] (7) in, is the distance between two ionospheric piercing points, The distance is The spatial covariance between the two ionospheric piercing points is is the semivariance of ionospheric VTEC at infinite distance, The distance is The semivariance of ionospheric VTEC at time , is the Gaussian variogram range, is the Gaussian variation function nugget, that is, the Gaussian variation function value between two points with a distance of 0; is the partial sill of the Gaussian variogram, is the Gaussian variogram base station, and e represents an exponential function. In summary, the present invention improves the traditional fixed empirical ionospheric spatial correlation model into a time-varying ionospheric spatial correlation model based on the Gaussian variogram, extracts the main periodic terms of the ionospheric spatial correlation function parameters based on the Gaussian variogram, obtains the amplitude of the periodic term using the harmonic estimation method, and establishes a time-varying ionospheric spatial correlation model based on the Gaussian variogram; the ionospheric spatial correlation modeling method involved supports adaptive calculation of data from different regions.

[0020] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling ionospheric spatial correlation based on Gaussian variogram, characterized in that: The method comprises: Step S1, extracting the ionospheric tilt total electron content STEC at the regional ionospheric puncture point, and converting it to the ionospheric vertical total electron content VTEC using a projection function; Step S2, retrieving the regional ionospheric vertical total electron content VTEC information, and calculating the regional ionospheric semi-variance at each distance; Step S3, based on the obtained ionospheric semi-variance information at different distances, a Gaussian variation function is used for fitting to obtain a Gaussian variation function parameter sequence; Step S4, establishing a Gaussian variogram parameter prediction model based on a harmonic estimation method; Step S5: using the Gaussian variation function parameter prediction model to establish an ionospheric spatial correlation model.

2. The ionospheric spatial correlation modeling method based on Gaussian variogram according to claim 1, characterized in that: The step S1 comprises: The carrier phase smoothing pseudorange method is used to obtain the smoothed pseudorange geometry-free combination observation information, the receiver-side differential code bias is extracted using the synchronous estimation method, and the satellite differential code bias product is used to correct the satellite differential code bias. Based on the observation information, the receiver-side differential code bias, and the satellite differential code bias, the ionospheric STEC information is obtained, and the ionospheric STEC information is slowly converted into the ionospheric VTEC information through the projection function.

3. The ionospheric spatial correlation modeling method based on Gaussian variogram according to claim 1, characterized in that: The step S2 comprises: The ionospheric semivariance is calculated based on the ionospheric VTEC information: （3） in, is the distance between the two ionospheric piercing points, and the distance is The semivariance of ionospheric VTEC at It is defined as all the distances in the region half the variance of the ionospheric VTEC differences between pairs of ionospheric puncture points, To find the expected function, Respectively represent , ionospheric VTEC.

4. The ionospheric spatial correlation modeling method based on Gaussian variogram according to claim 1, characterized in that: The step S3 includes obtaining the Gaussian variation function parameter sequence by the following formula: （4） in, is the Gaussian variogram range, is the distance between two ionospheric piercing points, Indicates the distance The semivariance of ionospheric VTEC at time , is the Gaussian variogram nugget; is the partial sill of the Gaussian variogram, is the Gaussian variogram base, represents the multiplication operation, and e represents the exponential function.

5. The ionospheric spatial correlation modeling method based on Gaussian variogram according to claim 1, characterized in that: The Gaussian variogram parameter prediction model in step S4 is: （5） in, is the Gaussian variogram range, is the Gaussian variogram nugget; is the partial sill of the Gaussian variogram, is the initial amplitude of the nugget parameter, is the amplitude of the cosine component of each periodic term of the nugget parameter, is the amplitude of the sinusoidal component of each periodic term of the nugget parameter, is the number of nugget parameter period items, Nugget parameter The frequency of the periodic term; is the amplitude of each periodic term of the partial sill parameter, is the amplitude of the cosine component of each periodic term of the partial base parameter, is the amplitude of the sinusoidal component of each periodic term of the partial sill parameter, is the number of periodic terms of partial sill parameters, is the partial sill parameter The frequency of the periodic term, is the amplitude of the periodic term of the range parameter, is the amplitude of the cosine component of each periodic term of the range parameter, is the amplitude of the sinusoidal component of each periodic term of the range parameter, is the number of periodic terms of the range parameter, is the range parameter The frequency of the periodic term; The Julian day time for the forecast moment.

6. The ionospheric spatial correlation modeling method based on Gaussian variogram according to claim 1, characterized in that: The ionospheric spatial correlation model in step S5 is: （7） in, is the distance between two ionospheric piercing points, The distance is The spatial covariance between the two ionospheric piercing points is is the semivariance of ionospheric VTEC at infinite distance, The distance is The semivariance of ionospheric VTEC at time , is the Gaussian variogram range, is the Gaussian variogram nugget; is the partial sill of the Gaussian variogram, is the base of Gaussian variogram, and e represents the exponential function.

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