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Electron Density Profile Recovery Accuracy and Application of Polynomial Approximations in the Frequency-And-Angular Sounding of the Ionosphere

*Radio Physics and Radio Astronomy*, Vol. 24, #3, pp.184-194

**(2019)**(in Russian)

### V.G. Galushko

Purpose: Analysis of the error in recovering the height profile of the electron density of the ionosphere by the frequency-andangular sounding technique in dependence on the accuracy of measuring vertical plane angles of arrival of the probe signals and inexactness of specifying the propagation path length.
Development of algorithms for ionospheric diagnostics in the case of a limited number of the sounding frequencies on the basis of polynomial approximations of the sought for electron density profile or measured frequency-and-angular characteristic of the probe signals.
Design/methodology/approach: To treat the inverse problem of recovering the ionospheric electron density profile, the standard method is applied for solving an Abel integral equation, relating the sought for profile to frequency dependences of arrival angles of the probe signals propagating along oblique radio paths. The accuracy of the developed algorithm is analyzed with
the use of the statistical theory of measurement error estimation.
Findings: The error of recovering the electron density profile of the ionosphere by the frequency-and-angular sounding technique has been estimated in dependence on the accuracy of measuring the arrival angles of the probe signals and inexactness of specifying the propagation path length. Algorithms have been developed for ionospheric diagnostics in the case of a limited
number of sounding frequencies, based on polynomial approximations of either the sought for electron density profile or the frequency dependence of the arrival angles of the probe signals.
Conclusions: The ray optics technique is used within the isotropic plasma approximation to solve the inverse problem of oblique sounding of a plane stratified ionosphere in the integral formulation. The measured parameters are frequency dependences of the vertical plane angles of arrival of HF signals propagating along single-hop radio paths of moderate lengths (up to
1000 km). It is shown that to provide the accuracy of electron density profile recovering, comparable to the characteristics of modern ionosondes, the error in measuring the frequencyand-angular characteristics of the probe signals should not exceed 0.5 degree for path lengths 300 to 1000 km.
The error of the method associated with inaccurate knowledge of the propagation path length is determined by the relative error of its specification. This fact makes it possible to use non-dedicated signals for frequency-and-angular sounding of the ionosphere, for example, emissions of modern HF broadcasting
stations which, as a rule, are equipped by several transmitters (some of them by dozens) being located on areas of units of kilometers in size and radiate simultaneously at several carrier frequencies. For diagnostic links of several hundreds of kilometers in length it can be supposed that all transmitters
of a given broadcast center are located at a single place. The error of recovering the electron density profile in this case will make a few tenths of a percent.
For ionospheric diagnostics in the case of a limited number of sounding frequencies, algorithms for recovering the electron density height distribution have been developed on the basis of polynomial approximations of either the sought for profile or the measured function.
Key words: ionosphere, electron density profile, oblique sounding, probe signal angles of arrival, polynomial approximation

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