RU2518013C1 - Method of estimating angular parameters of ionospheric signals - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: circular antenna system located on the surface of the earth is further provided with a linear dipole system lying along the vertical to the surface of the earth. The formed antenna system (three-dimensional antenna system), a multichannel receiver, a multichannel analogue-to-digital converter (ADC) and time Fourier transform are used to generate a space-time array of complex data $${\stackrel{\wedge }{E}}_{n,m},$$

which displays field strength values at n points of three-dimensional space (n is the of the dipole) and at the m-th moment in time, with intervals of 1-2 s (index m defines the number of the time sample of data at n dipoles m=1-M+1). The number of time samples of data is one greater than the number of beams M. The method further includes corresponding mathematical processing, filtering single-beam fields from a plurality of fields of the ionospheric signal, forming a beam pattern for each selected field, scanning the beam pattern in the range of estimate maxima and elevation angles and estimating azimuths, elevation angles and amplitudes from the maximum of the beam pattern from M beams of the ionospheric signal.

EFFECT: broader functional capabilities of direction-finding, shorter time for calculating angular parameters of a multi-beam ionospheric signal.

6 dwg

Description

The invention relates to radio engineering, and in particular to the field of direction finding, and can be used to measure azimuths and elevation angles of ionospheric signals under conditions of receiving several interfering rays, including at low elevation angles. When receiving ionospheric signals, as a rule, several rays (1 ÷ 4), reflected from different layers of the ionosphere, come with the azimuths located in the region of the main lobe of the radiation pattern (Δα ~ 5 ÷ 10 degrees). Due to interference, the total main lobe of the antenna system's radiation pattern, consisting of the sum of the radiation patterns of individual beams, changes significantly, often creating false azimuths (bearings) that differ from true azimuths (bearings) by tens of degrees. As a result, the reliability of estimates of azimuths, as well as elevation angles of ionospheric signals is low. In addition, in the direction finding of ionospheric signals there is a problem of small elevation angles. When receiving ionospheric signals at distances of more than 2000 km, the elevation angle β is in the range from 0 ° to 15 ÷ 20 °. Under these conditions, the spatial base for determining the elevation angle L = Rsin (β) becomes small and the variance of the measured elevation angles increases significantly. The task of direction finding of ionospheric signals is to determine the coordinates of the radiation source. In this regard, in the direction finding method, it is necessary to solve the problem of isolating the beam structure of the signal and determining, according to the measured beam structure, the coordinates of the emitter. In this case, information on both azimuths and elevation angles of the multipath ionospheric signal is important.

. В условиях приема двух или нескольких близких по азимуту лучей фазовые способы оценки азимута и угла места являются неустойчивыми. При разности фаз между лучами ~180° они дают отклонения азимута на десятки градусов (ложные пеленги), что значительно снижает достоверность оценок азимутов и углов места ионосферных сигналов. Разработанные к настоящему времени фазовые методы оценки азимутов и углов места (пеленгации) предназначены для оценок этих параметров для одного луча на заданной частоте. Антенная система, расположенная в плоскости земной поверхности, не может решить проблему малых углов в оценке азимутов и углов места ионосферных сигналов.Known phase methods for measuring the azimuth and elevation (direction finding), carried out by measuring the phase difference between the vibrators of the antenna system and the assessment of these measurements of azimuth and elevation (Patent RU No. 2263327, published October 27, 2005; Patent RU No. 2365931, published August 27 .2009; Patent RU No. 2429500, published September 20, 2011; Patent RU No. 2450283, published May 10, 2012; Application for invention RU No. 20143935, published May 10, 2012; Application RU No. 2003108306 of March 25, 2003 ., G01S 3/14, published October 10, 2004). The disadvantage of the above methods is that only phase information is used. Unambiguous determination of the phase of the wave on the vibrators is possible in the interval 0 ÷ 360 °. This requires a small, in comparison with the wavelength, spatial separation of the vibrators $$|\; |\; |{\overline{R}}_{n+\mathrm{one}}-{\overline{R}}_n|\; |\; |<\frac{\lambda }{2}$$

. Under conditions of receiving two or more rays close in azimuth, the phase methods for estimating the azimuth and elevation are unstable. When the phase difference between the rays is ~ 180 °, they give azimuth deviations of tens of degrees (false bearings), which significantly reduces the reliability of estimates of azimuths and elevation angles of ionospheric signals. Currently developed phase methods for estimating azimuths and elevation angles (direction finding) are intended for estimating these parameters for a single beam at a given frequency. An antenna system located in the plane of the earth's surface cannot solve the problem of small angles in the estimation of azimuths and elevation angles of ionospheric signals.

Known methods for direction finding to the maximum radiation pattern of the antenna system (Patent RU No. 2144200, published January 10, 2000; Patent RU No. 2258241, published August 10, 2005; Patent RU No. 2419805, published May 27, 2011; Patent RU No. 2201599 , published March 27, 2003; Patent RU No. 2004100714, published June 20, 2005). In this case, the temporary Fourier transform is used to frequency isolate the signal from individual vibrators of the antenna system and various forms of spatial data processing (beamforming). The radiation pattern is best formed using the spatial Fourier transform. The result is a two-dimensional complex angular spectrum (radiation pattern of the antenna system). When using the spatial Fourier transform, the radiation pattern is formed by the expression (complex view):

$$\stackrel{\wedge }{U}({\alpha }_{}^{\text{'}\text{'}},{\beta }_{}^{\text{'}\text{'}})=\frac{\mathrm{one}}{N}{\displaystyle \sum _{n=\mathrm{one}}^N{\stackrel{\wedge }{E}}_n{e}^{-i\overline{K}(\alpha \text{'}\text{'},\beta \text{'}\text{'}){\overline{R}}_n}}(\mathrm{one})$$

Where:

- комплексная амплитуда в n-точке пространства с радиус-вектором $${\overline{R}}_n$$

, $${\stackrel{\wedge }{E}}_n$$

is the complex amplitude at the n-point of space with a radius vector $${\overline{R}}_n$$

,

- оценочный волновой вектор ионосферного сигнала, $$\overline{K}(\alpha \text{'}\text{'},\beta \text{'}\text{'})$$

- estimated wave vector of the ionospheric signal,

, $$\beta \text{'}$$

' - оценочные значения азимута и угла места ионосферного сигнала.

, $$\beta \text{'}\text{'}$$

'- estimated azimuth and elevation angle of the ionospheric signal.

The square of the module of the normalized radiation pattern (design form) is determined by the expression

$$U^2(a\text{'}\text{'},\beta \text{'}\text{'})=\frac{{\overline{E_n\cos ({\psi }_n-\overline{K}(\alpha \text{'}\text{'},\beta \text{'}\text{'}){\overline{R}}_n)}}^2+{\overline{E_n\sin ({\psi }_n-\overline{K}(\alpha \text{'}\text{'},\beta \text{'}\text{'}){\overline{R}}_n)}}^2}{{\overline{E}}_n^2},\text{(2)}$$

where the bar above means summation over the index "n".

The disadvantage of the above methods associated with estimating elevation angles from the maximum radiation pattern of the antenna system is the instability of the solution in the presence of multipath interference with a phase difference between the rays of ~ 180 °. When two or more interfering rays of the ionospheric signal are received (the difference in azimuths is less than the width of the radiation pattern), the total radiation pattern due to a change in the phase difference between the rays (in the region of ~ 180 degrees) is largely suppressed. The side or back lobes of the total radiation pattern in these conditions become larger in magnitude than the main lobe of the radiation pattern. As a result, the azimuth (bearing) in the amplitude direction finding method is determined by the maximum lateral or rear lobe of the antenna system radiation pattern. Azimuth deviations (false bearings) reach tens of degrees. As a result, the reliability of estimates of azimuths and elevation angles of ionospheric signals is low. In addition, it is impossible to ensure the operability of the direction finder in a wide frequency range of 2–30 MHz. The accuracy requirements for bearing measurement in the low-frequency part of the range (3 ÷ 4 MHz) determine the base of the antenna system 2R≥150 m. However, when the number of vibrators is ~ 16 in the high-frequency part of the range (20 ÷ 30 MHz), the radiation pattern is not formed due to the large spatial separation of the vibrators compared to the wavelength, which limits the frequency range from above. The location of the antenna system vibrators on the surface of the earth (on the plane) cannot solve the problem of small angles during direction finding of ionospheric signals.

Known methods for determining the azimuth and elevation (direction finding), the antenna system in which consists of two mutually perpendicular linear equidistant antenna arrays (Patent RU No. 2192651, published 05.10.2000). The method includes receiving a signal using an antenna system, a multi-channel receiver, converting the analog signals in each channel to digital form, using a two-dimensional angular Fourier transform, which creates a radiation pattern of the antenna system. The maximum radiation pattern allows you to evaluate the azimuth (bearing) and elevation. The disadvantage of this method of direction finding is the dependence of the accuracy of the bearing measurement on the relative orientation of the antenna system and the bearing. During direction finding of ionospheric signals under conditions of receiving two or more interfering rays, false bearings may occur, which significantly reduces the reliability of estimates of azimuths and elevation angles of ionospheric signals. The location of the antenna system vibrators on the surface of the earth (in the plane) cannot solve the problem of small angles during direction finding of ionospheric signals by this direction finding method.

Known methods for evaluating azimuths and elevation angles (direction finding), in which the antenna system consists of a limited number of vibrators (3 ÷ 5 vibrators) (Patent RU No. 2262119, published October 10, 2005; Patent RU No. 2253877, published June 10, 2005 ) The disadvantages of this method of direction finding are low noise immunity, due to the lack of statistical processing of data, the presence of false bearings when receiving two or more close in azimuth rays of the ionospheric signal, the inability to solve the problem of small elevation angles.

The closest (prototype) to the proposed method for evaluating the angular parameters when receiving multipath ionospheric signals is the "Direction finding method taking into account the correlation between the rays", patent RU No. 2305294, IPC G01S 3/16, published on 08.27.2007

между лучами по выражениямAccording to this method of direction finding (prototype), the sequence of actions is as follows. Using an antenna system consisting of N-vibrators arranged uniformly around a circle of radius R (spatial base of the signal) 1) receive ionospheric signals, 2) convert them in frequency, 3) amplify through a multi-channel receiver. The analog signals at the outputs of the multi-channel receiver in each channel (from each vibrator) 4) are converted to digital form using a multi-channel analog-to-digital converter (ADC). 5) The amplitudes E _n and phases ψ _{n of the} received ionospheric signal in each channel (from each vibrator) are determined using the time Fourier transform. 6) Form the total four-dimensional (for two rays) radiation pattern taking into account the correlation coefficient $$\stackrel{\wedge }{A}\mathrm{one}$$

between rays by expressions

$$\stackrel{\wedge }{U}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}})=\frac{{\stackrel{\wedge }{U}}_{\mathrm{one}}\overline{E_n^{*}\exp (-i\overline{k_{\mathrm{one}}}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}){\overline{R}}_n)}+{\stackrel{\wedge }{U}}_2\overline{E_n^{*}\exp (-i\overline{k_2}({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}){\overline{R}}_n)}}{\overline{{\stackrel{\wedge }{E}}_n{\stackrel{\wedge }{E}}_n^{*}}}\text{(3)}$$

Where

$${\stackrel{\wedge }{U}}_{\mathrm{one}}=\frac{\overline{E_n^{}\exp (i\overline{k_{\mathrm{one}}}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}){\overline{R}}_n)}+\overline{E_n^{}\exp (i\overline{k_2}({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}){\overline{R}}_n)}\stackrel{\wedge }{A}\mathrm{one}}{\overline{\mathrm{one}-\stackrel{\wedge }{A}\mathrm{one}\stackrel{\wedge }{A}{\mathrm{one}}_{}^{*}}}$$

$${\stackrel{\wedge }{U}}_2=\frac{\overline{E_n^{}\exp (i\overline{k_2}({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}){\overline{R}}_n)}+\overline{E_n^{}\exp (i\overline{k_{\mathrm{one}}}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}){\overline{R}}_n)}\stackrel{\wedge }{A}{\mathrm{one}}^{*}}{\overline{\mathrm{one}-\stackrel{\wedge }{A}\mathrm{one}\stackrel{\wedge }{A}{\mathrm{one}}_{}^{*}}}$$

$$\stackrel{\wedge }{A}\mathrm{one}=\overline{\exp (i({\overline{k}}_2({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}})-{\overline{k}}_{\mathrm{one}}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}})){\overline{R}}_n}$$

- комплексная амплитуда сигнала, измеренная на n вибраторе, $${\stackrel{\wedge }{E}}_n$$

- the complex amplitude of the signal, measured on n vibrator,

- радиус-вектор, определяющий местоположение n вибратора, $${\overline{R}}_n$$

- radius vector that determines the location n of the vibrator,

, $${\overline{k}}_2({\alpha }_2^{\text{'}},{\beta }_2^{\text{'}})$$

- волновые векторы первого и второго лучей ионосферного сигнала, зависящие от оценочных азимутов $${\alpha }_1^{\text{'}}$$

, $${\alpha }_2^{\text{'}}$$

и углов места $${\beta }_1^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

, $${\overline{k}}_{\mathrm{one}}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}})$$

, $${\overline{k}}_2({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}})$$

- wave vectors of the first and second rays of the ionospheric signal, depending on estimated azimuths $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\alpha }_2^{\text{'}\text{'}}$$

and elevation $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

,

- коэффициент корреляции между лучами. $$\stackrel{\wedge }{A}\mathrm{one}$$

- the correlation coefficient between the rays.

The bar above means summation over index n.

The * sign means complex conjugation,

The sign ∧ means a complex quantity.

, $${\alpha }_2^{\text{'}}$$

и $${\beta }_1^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

в указанных угловых диапазонах с определенным шагом и запоминая значения параметров $${\alpha }_1^{\text{'}}$$

, $${\alpha }_2^{\text{'}}$$

, $${\beta }_1^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

, $${\stackrel{\wedge }{U}}_1$$

, $${\stackrel{\wedge }{U}}_2$$

, $$\stackrel{\wedge }{U}({\alpha }_1^{\text{'}},{\beta }_1^{\text{'}},{\alpha }_2^{\text{'}},{\beta }_2^{\text{'}})$$

. Азимут и угол места каждого луча определяются по максимуму четырехмерной диаграммы направленности.7) Perform scanning with a radiation pattern in four-dimensional space by changing the estimated azimuths and elevation angles $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\alpha }_2^{\text{'}\text{'}}$$

and $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

in the specified angular ranges with a certain step and remembering the values of the parameters $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\alpha }_2^{\text{'}\text{'}}$$

, $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

, $${\stackrel{\wedge }{U}}_{\mathrm{one}}$$

, $${\stackrel{\wedge }{U}}_2$$

, $$\stackrel{\wedge }{U}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}})$$

. The azimuth and elevation of each beam are determined by the maximum of the four-dimensional radiation pattern.

, $${\beta }_1^{\text{'}}$$

и $${\alpha }_2^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

) с шагом по азимуту Δα≤0.5° в диапазоне 0÷360 градусов и с шагом по углу места Δβ≤0.5° в диапазоне 0÷90 градусов в четырехмерном пространстве азимутов и углов места. При увеличении количества лучей в этом способе пеленгации время, требуемое для расчета параметров, увеличивается экспоненциально с увеличением количества лучей. Если Т - необходимое время расчета параметров одного луча в одной точке области определения и М - количество точек, то для N лучей требуется время Т_Т=Т*M^2N. Третьим недостатком является наличие проблемы малых углов места при данном способе пеленгации ионосферных сигналов, обусловленное плоской (двумерной) антенной системой.The disadvantage of the direction finding method, taking into account the correlation between the rays (prototype), is its limitation associated with the reception of only one or two rays of the ionospheric signal, while in the ionospheric signal the number of rays can reach four or more. The second disadvantage of this method is the great complexity associated with the need to sort (scan the radiation pattern) of two azimuths and two elevation angles ( $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

and $${\alpha }_2^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

) with a step in azimuth Δα≤0.5 ° in a range of 0 ÷ 360 degrees and with a step in elevation Δβ≤0.5 ° in a range of 0 ÷ 90 degrees in four-dimensional space of azimuths and elevation angles. With an increase in the number of rays in this direction finding method, the time required to calculate the parameters increases exponentially with an increase in the number of rays. If T is the necessary time to calculate the parameters of one beam at one point in the domain of definition and M is the number of points, then for N rays, the time T _T = T * M ^2N is required. The third disadvantage is the presence of a problem of small elevation angles with this method of direction finding of ionospheric signals due to a planar (two-dimensional) antenna system.

The block diagram of the technical implementation of this method of direction finding (prototype) is presented in figure 1. According to the direction finding method, taking into account the correlation between the rays, the sequence of actions is as follows.

1. Receive signals using a circular antenna system,

, расположенных на поверхности земли равномерно по окружности радиуса R $$(R\ge \frac{2\pi }{3\left|\overline{k}({\alpha }_{01},{\beta }_{01})-{\overline{k}}_2({\alpha }_{02},{\beta }_{02})\right|})$$

(блок 1). Количество вибраторов определяется количеством параметров ионосферного сигнала и заданным значением отношения сигнал/шум. Радиус антенной системы определяется размером пространственных интерференционных максимумов на поверхности земли.consisting of N vibrators $$(N\ge N\mathrm{one}+\frac{\mathrm{one}}{(\mathrm{one}-{|\; |\; |\stackrel{\wedge }{A}\mathrm{one}|\; |\; |}^2)},N\mathrm{one}=8)$$

located on the surface of the earth evenly around a circle of radius R $$(R\ge \frac{2\pi }{3|\; |\; |\overline{k}({\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000130.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01},{\beta }_{01})-{\overline{k}}_2({\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000130.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02},{\beta }_{02})|\; |\; |})$$

(block 1). The number of vibrators is determined by the number of parameters of the ionospheric signal and a given value of the signal-to-noise ratio. The radius of the antenna system is determined by the size of the spatial interference maxima on the earth's surface.

2. Using a multi-channel receiver, the signals from each antenna (in each channel) are converted in frequency, amplified and filtered (block 2).

3. Convert the analog signals at the outputs of the multi-channel receiver from each vibrator into digital form using a multi-channel analog-to-digital converter (ADC) (block 3).

4. Determine the amplitudes E _n and phase ψ _{n of the} signals from each

a vibrator (in each channel), for example, using a temporary Fourier transform (block 4).

, $${\alpha }_2^{\text{'}}$$

и углов места $${\beta }_1^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

и определяют согласно (3) четырехмерную диаграмму направленности $$\stackrel{\wedge }{U}({\alpha }_1^{\text{'}},{\beta }_1^{\text{'}},{\alpha }_2^{\text{'}},{\beta }_2^{\text{'}})$$

в заданной точке по выборке данных $${\stackrel{\wedge }{E}}_n$$

и запоминают ее значения и значения переменных $${\stackrel{\wedge }{U}}_1,{\stackrel{\wedge }{U}}_2$$

(Блок 5).5. Set a point in the space of estimated azimuths $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\alpha }_2^{\text{'}\text{'}}$$

and elevation $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

and determine according to (3) a four-dimensional radiation pattern $$\stackrel{\wedge }{U}({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}})$$

at a given point on data sampling $${\stackrel{\wedge }{E}}_n$$

and remember its values and the values of variables $${\stackrel{\wedge }{U}}_{\mathrm{one}},{\stackrel{\wedge }{U}}_2$$

(Block 5).

, $${\alpha }_2^{\text{'}}$$

и $${\beta }_1^{\text{'}}$$

, $${\beta }_2^{\text{'}}$$

(из области их определения) с шагом по азимуту Δα≤0.5° в диапазоне 0÷360 градусов и с шагом по углу места Δβ≤0.5° в диапазоне 0÷90 градусов и создают поверхность в четырехмерном пространстве азимутов и углов места (четырехмерную диаграмму направленности) (блок 6).6. Repeat steps (5) with other parameter values $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\alpha }_2^{\text{'}\text{'}}$$

and $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}$$

, $${\beta }_2^{\text{'}\text{'}}$$

(from the field of their definition) with a step in azimuth Δα≤0.5 ° in the range 0 ÷ 360 degrees and with a step in elevation Δβ≤0.5 ° in the range 0 ÷ 90 degrees and create a surface in four-dimensional space of azimuths and elevation angles (four-dimensional radiation pattern ) (block 6).

, $${\beta }_1^{\text{'}}={\beta }_{01}$$

, $${\alpha }_2^{\text{'}}={\alpha }_{02}$$

, $${\beta }_2^{\text{'}}={\beta }_{02}$$

, а также $${\stackrel{\wedge }{U}}_1={\stackrel{\wedge }{U}}_{01}$$

, $${\stackrel{\wedge }{U}}_2={\stackrel{\wedge }{U}}_{02}$$

(блок 7).7. Determine the maximum value of the four-dimensional radiation pattern and fix the parameters $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000130.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01}$$

, $${\beta }_{\mathrm{one}}^{\text{'}\text{'}}={\beta }_{01}$$

, $${\alpha }_2^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000130.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02}$$

, $${\beta }_2^{\text{'}\text{'}}={\beta }_{02}$$

, as well as $${\stackrel{\wedge }{U}}_{\mathrm{one}}={\stackrel{\wedge }{U}}_{01}$$

, $${\stackrel{\wedge }{U}}_2={\stackrel{\wedge }{U}}_{02}$$

(block 7).

8. The field rank (single-beam or double-beam) is determined by the condition U ₀₁ / U ₀₂ ≥3 and the solutions that satisfy this condition are left (block 8).

The aim of the invention “Method for assessing the angular parameters of ionospheric signals” (technical result) is:

- expanding the capabilities of the "Method of direction finding taking into account the correlation relationship" in the case of receiving M rays (M = 1 ÷ 4 or more),

- solving the problem of small elevation angles during direction finding of ionospheric signals,

- reducing the calculation time of the angular parameters of the multipath ionospheric signal.

, отображающий значения напряженности поля в n точках трехмерного пространства (n - номер вибратора на поверхности земли и вдоль вертикальной линейки вибраторов) и в m моменты времени, с интервалами 1-2 секунды (индекс m определяет номер временного среза данных на n вибраторах, m=1÷М+1). Количество временных срезов данных берется на единицу больше, чем количество лучей М. Формируют корреляционную матрицу $$\stackrel{\wedge }{A}$$

, размерностью, равной количеству лучей ((М)*(М)), и правый вектор-столбец данных $$\overline{b}={(b_1÷b_{м})}^T$$

, элементы которых усредняются по индексу n (по вибраторам, по пространству), решая векторное уравнение (4), определяют неопределенные коэффициенты $${\stackrel{\wedge }{\alpha }}_1÷{\stackrel{\wedge }{\alpha }}_{м}$$

,The technical result is achieved by the fact that the circular antenna system located on the surface of the earth is supplemented by a linear system of vibrators located along the vertical to the surface of the earth (for example, 5 vibrators with an interval between the vibrators of 10 m). Using the thus formed antenna system (three-dimensional antenna system), a multi-channel receiver, a multi-channel analog-to-digital converter (ADC) and a temporary Fourier transform, a spatio-temporal array of complex data is formed $${\stackrel{\wedge }{E}}_{n,m}$$

that displays the field strengths at n points of three-dimensional space (n is the number of the vibrator on the surface of the earth and along the vertical line of vibrators) and at m time instants, at intervals of 1-2 seconds (index m determines the number of time slice data on n vibrators, m = 1 ÷ M + 1). The number of time slices of data is taken by one more than the number of rays M. Form a correlation matrix $$\stackrel{\wedge }{A}$$

, dimension equal to the number of rays ((M) * (M)), and the right column data vector $$\overline{b}={(b_{\mathrm{one}}÷b_m)}^T$$

whose elements are averaged over the index n (over vibrators, over space), solving the vector equation (4), determine the indefinite coefficients $${\stackrel{\wedge }{\alpha }}_{\mathrm{one}}÷{\stackrel{\wedge }{\alpha }}_m$$

,

$$\stackrel{\wedge }{A}\overline{\alpha }=\overline{b},\text{(four)}$$

Where

,A - correlation matrix with elements $$\overline{{\stackrel{\wedge }{E}}_{n,k}{\stackrel{\wedge }{E}}_{n,p}^{*}}$$

,

- вектор-столбец с координатами $$b_m=\overline{{\stackrel{\wedge }{E}}_{n,M+1}{\stackrel{\wedge }{E}}_{n,m}^{*}}$$

(черта сверху определяет суммирование по индексу n, по вибраторам, m=1÷M).m = 1 ÷ M, p = 1 ÷ M, n = 1 ÷ N, the bar above means summation over the index n. $$\overline{b}={(b_{\mathrm{one}}÷b_M)}^T$$

- column vector with coordinates $$b_m=\overline{{\stackrel{\wedge }{E}}_{n,M+\mathrm{one}}{\stackrel{\wedge }{E}}_{n,m}^{*}}$$

(the bar above determines the summation over index n, over vibrators, m = 1 ÷ M).

- вектор-столбец неопределенных коэффициентов. $$\overline{\alpha }={({\alpha }_{\mathrm{one}}÷{\alpha }_M)}^T$$

is a column vector of undefined coefficients.

(5), частотная зависимость которого позволяет оценить значения доплеровских сдвигов частот ω_m лучей ионосферного сигнала по М минимумам полинома.Form a polynomial $$\stackrel{\wedge }{Y}(\omega )$$

(5), the frequency dependence of which allows us to estimate the values of the Doppler frequency shifts ω _{m of the} rays of the ionospheric signal from the M minima of the polynomial.

$$\stackrel{\wedge }{Y}(\omega )={\stackrel{\wedge }{x}}^M+{\stackrel{\wedge }{\alpha }}_{{}_M}{\stackrel{\wedge }{x}}^{M-\mathrm{one}}+{\stackrel{\wedge }{\alpha }}_{{}_{M-\mathrm{one}}}{\stackrel{\wedge }{x}}^{M-2}+......{\stackrel{\wedge }{\alpha }}_{{}_2}\stackrel{\wedge }{x}+{\stackrel{\wedge }{\alpha }}_{{}_{\mathrm{one}}}=0(5)$$

.Where $$\stackrel{\wedge }{x}=\exp (i\omega \Delta t)$$

.

.The elements of the pulse sequences of the M filters are determined to highlight individual single-beam fields $${\stackrel{\wedge }{E}}_n^{(m)}$$

.

, $${\stackrel{\wedge }{C}}_2^{(m)}={\stackrel{\wedge }{\alpha }}_2^{(m)}+{\stackrel{\wedge }{C}}_1^{(m)}){\stackrel{\wedge }{x}}^{*}$$

, $$\dots \dots$$

, $${\stackrel{\wedge }{C}}_m^{(m)}={\stackrel{\wedge }{\alpha }}_m^{(m)}+{\stackrel{\wedge }{C}}_{m-1}^{(m)}){\stackrel{\wedge }{x}}^{*}$$

, $$\dots \dots$$

, $${\stackrel{\wedge }{C}}_M^{(m)}=1$$

$${\stackrel{\wedge }{C}}_m^{(m)}={\stackrel{\wedge }{\alpha }}_{\mathrm{one}}^{(m)}{\stackrel{\wedge }{x}}_{}^{*}$$

, $${\stackrel{\wedge }{C}}_2^{(m)}={\stackrel{\wedge }{\alpha }}_2^{(m)}+{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(m)}){\stackrel{\wedge }{x}}^{*}$$

, $$......$$

, $${\stackrel{\wedge }{C}}_m^{(m)}={\stackrel{\wedge }{\alpha }}_m^{(m)}+{\stackrel{\wedge }{C}}_{m-\mathrm{one}}^{(m)}){\stackrel{\wedge }{x}}^{*}$$

, $$......$$

, $${\stackrel{\wedge }{C}}_M^{(m)}=\mathrm{one}$$

из совокупности М полей ионосферного сигнала по выражениям (6). Верхний индекс в скобках в выражении (6) определяет номер однолучевого поля.Single-beam m fields are isolated (filtered) $${\stackrel{\wedge }{E}}_n^{(m)}$$

from a set M of ionospheric signal fields according to expressions (6). The superscript in parentheses in expression (6) determines the number of the single-beam field.

$$\frac{{\stackrel{\wedge }{E}}_{{}_n}^{(\mathrm{one})}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(\mathrm{one})}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(\mathrm{one})}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(\mathrm{one})}=\stackrel{}{{\stackrel{\wedge }{U}}_{\mathrm{one}}\exp (-i{\overline{K}}_{\mathrm{one}}{\overline{R}}_n)}}{{\stackrel{\wedge }{E}}_{{}_n}^{(M)}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(M)}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(M)}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(M)}=\stackrel{\wedge }{{\stackrel{\wedge }{U}}_M\exp (-i{\overline{K}}_M{\overline{R}}_n)}}(6)$$

, $${\beta }_m^{\text{'}}$$

, $${\stackrel{\wedge }{U}}_m^{\text{'}}$$

.The radiation patterns are generated for the extracted M rays of the ionospheric signal using the spatial Fourier transform, they are scanned by azimuth and elevation, and azimuths, elevation angles and amplitudes of the rays of the ionospheric signal are estimated from the maxima of the angular spectrum $${\alpha }_m^{\text{'}\text{'}}$$

, $${\beta }_m^{\text{'}\text{'}}$$

, $${\stackrel{\wedge }{U}}_m^{\text{'}\text{'}}$$

.

Significant differences of the proposed method of direction finding from the prototype are as follows.

- Instead of a flat (two-dimensional) antenna system (prototype), a three-dimensional antenna system is created, with the help of which the problem of small elevation angles during direction finding of ionospheric signals is solved.

- Excludes the operation of creating a four-dimensional radiation pattern and scanning this diagram in four-dimensional space, which significantly increases the calculation time of the parameters of the ionospheric signal and does not allow to implement the method (prototype) with a large number of rays.

- The spatial information obtained using the antenna system is supplemented with the necessary information in time (10 data slices) and the most optimal joint spatio-temporal data processing is carried out.

- Elements of the M pulse filter sequences are determined to extract M single-beam fields from the sum of the fields of the ionospheric signal and single-beam fields of the ionospheric signal are selected (filtered).

- Instead of evaluating the parameters of the rays at the maximum of the four-dimensional radiation pattern in the prototype, in the proposed method of direction finding, the parameters of the rays of the ionospheric signal are estimated from the maxima of the two-dimensional radiation patterns of the selected M fields of the ionospheric signal.

The rationale for the proposed method for estimating the angular parameters of ionospheric signals is as follows.

в комплексной форме в видеWe record the signal on the n vibrator and at the m point in time $${\stackrel{\wedge }{E}}_{n,m}$$

in complex form as

$${\stackrel{\wedge }{E}}_{n,m}={\displaystyle \sum _{p=\mathrm{one}}^M{\stackrel{\wedge }{U}}_p{e}^{i({\omega }_p{t}_m-{\overline{K}}_p({\alpha }_{0p},{\beta }_{0p}){\overline{R}}_n)}}(6)$$

- комплексная амплитуда р луча ионосферного сигнала,Where $${\stackrel{\wedge }{U}}_p$$

- complex amplitude p of the beam of the ionospheric signal,

- волновой вектор р луча ионосферного сигнала, $${}_{{\overline{K}}_p({\alpha }_{0p},{\beta }_{0p})}$$

- wave vector p of the beam of the ionospheric signal,

, $${\beta }_{\mathrm{0,}p}$$

- значения азимута и угла места р луча ионосферного сигнала, $${\alpha }_{0p}$$

, $${\beta }_{0p}$$

- the azimuth and elevation angle p of the beam of the ionospheric signal,

- местоположение n вибратора, $${\overline{R}}_n$$

- location n of the vibrator,

t _m is the time of reading the field strength (m varies from 1 to M + 1, P = M is the number of rays in the ionospheric signal,

ω _p - Doppler frequency shift p of the beam of the ionospheric signal.

Elementary vibrators of the antenna system are located around a circle of radius R and along the vertical to the surface of the earth Z.

, $${\overline{K}}_p({\alpha }_{\mathrm{0,}p},{\beta }_{\mathrm{0,}p}),{\omega }_p)$$

. В результате получим выражение (7) с неопределенными коэффициентами $${\stackrel{\wedge }{C}}_1÷{\stackrel{\wedge }{C}}_M$$

(М=Р), выражение в правой части которого описывает поле лишь одной волны (индекс р у переменных убран).Using the time sequence of data, we exclude the variables that describe the fields of the P-1 rays ( $${\stackrel{\wedge }{U}}_p$$

, $${\overline{K}}_p({\alpha }_{0p},{\beta }_{0p}),{\omega }_p)$$

. As a result, we obtain expression (7) with indefinite coefficients $${\stackrel{\wedge }{C}}_{\mathrm{one}}÷{\stackrel{\wedge }{C}}_M$$

(M = P), the expression on the right side of which describes the field of only one wave (the index p of the variables is removed).

$${\displaystyle \sum _{m=\mathrm{one}}^M{\stackrel{\wedge }{C}}_m{\stackrel{\wedge }{E}}_{n,m}={\stackrel{\wedge }{U}}_p{e}^{i(\omega t_m-\overline{K}({\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="00000132.png,00000134.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0,{\beta }_0){\overline{R}}_n)}}(7)$$

не зависят от номера вибратора n и номера среза данных m. Они зависят лишь от временного интервала Δt. Следовательно, они одинаковы для выражения (7) при разных значениях индекса m. На основании этого запишемUndefined coefficients $${\stackrel{\wedge }{C}}_{\mathrm{one}}÷{\stackrel{\wedge }{C}}_M$$

independent of vibrator number n and data slice number m. They depend only on the time interval Δt. Therefore, they are the same for expression (7) for different values of the index m. Based on this, we write

$${\displaystyle \sum _{m=\mathrm{one}}^M{\stackrel{\wedge }{C}}_m{\stackrel{\wedge }{E}}_{n,m+\mathrm{one}}=\stackrel{\wedge }{U}{e}^{i(\omega t_m-\overline{K}({\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="00000132.png,00000134.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0,{\beta }_0){\overline{R}}_n)}}{e}^{i\omega \Delta t}(8)$$

Combining (7) and (8) and re-designating the coefficients, we obtain

$${\displaystyle \sum _{m=\mathrm{one}}^M{\stackrel{\wedge }{a}}_m{\stackrel{\wedge }{E}}_{n,m}=\stackrel{\wedge }{E}}n,m={\stackrel{\wedge }{E}}_{n,M+\mathrm{one}}(9)$$

и $${\stackrel{\wedge }{a}}_m$$

определяется выражениямиRatio Relationship $${\stackrel{\wedge }{C}}_m$$

and $${\stackrel{\wedge }{a}}_m$$

defined by expressions

$${\stackrel{\wedge }{C}}_{{}_{\mathrm{one}}}={\stackrel{\wedge }{a}}_{{}_{\mathrm{one}}}{\stackrel{\wedge }{x}}^{*},$$

$${\stackrel{\wedge }{C}}_2=({\stackrel{\wedge }{a}}_2+{\stackrel{\wedge }{C}}_{\mathrm{one}}){\stackrel{\wedge }{x}}^{*},......,$$

$${\stackrel{\wedge }{C}}_m=({\stackrel{\wedge }{a}}_m+{\stackrel{\wedge }{Cm-}}_{\mathrm{one}}){\stackrel{\wedge }{x}}^{*},......,$$

$${\stackrel{\wedge }{C}}_M=\stackrel{\wedge }{a}{}_{M+\mathrm{one}}=\mathrm{one,}$$

$${\stackrel{\wedge }{x}}^{*}=\exp (-i\omega \Delta t)(10)$$

Using expression (9), we write the likelihood functional in the form

$$\Delta ({\stackrel{\wedge }{a}}_{\mathrm{one}}...{\stackrel{\wedge }{a}}_M)={\displaystyle \sum _n^N{|\; |\; |{\displaystyle \sum _m^M{\stackrel{\wedge }{a}}_{{}_m}{\stackrel{\wedge }{E}}_{{}_{n,m}}-{\stackrel{\wedge }{E}}_{{}_{n,M+\mathrm{one}}}}|\; |\; |}^2(\mathrm{eleven})}$$

и приравнивая дифференциалы к нулю, можно получить матричное уравнение. В векторной форме оно имеет вид (4)Differentiating expression (11) with respect to the coefficients $${\stackrel{\wedge }{a}}_m$$

and equating the differentials to zero, we can obtain the matrix equation. In vector form, it has the form (4)

$$\stackrel{\wedge }{A}\overline{a}=\overline{b},\text{(four)}$$

Where

- корреляционная матрица с элементами $$\overline{{\stackrel{\wedge }{E}}_{n,k}{\stackrel{\wedge }{E}}_{n,p}^{*}}$$

, $$\stackrel{\wedge }{A}$$

- correlation matrix with elements $$\overline{{\stackrel{\wedge }{E}}_{n,k}{\stackrel{\wedge }{E}}_{n,p}^{*}}$$

,

- вектор-столбец с координатами $$b_m=\overline{{\stackrel{\wedge }{E}}_{n,M+1}{\stackrel{\wedge }{E}}_{n,m}^{*}}$$

(черта сверху определяет суммирование по индексу n, по вибраторам, m=1÷М).m = 1 ÷ M, p = 1 ÷ M, n = 1 ÷ N, the bar above means summation over the index n, $$\overline{b}={(b_{\mathrm{one}}÷b_M)}^T$$

- column vector with coordinates $$b_m=\overline{{\stackrel{\wedge }{E}}_{n,M+\mathrm{one}}{\stackrel{\wedge }{E}}_{n,m}^{*}}$$

(the bar above determines the summation over index n, over vibrators, m = 1 ÷ M).

- вектор-столбец неопределенных коэффициентов. $$\overline{\alpha }={({\alpha }_{\mathrm{one}}÷{\alpha }_M)}^T$$

is a column vector of undefined coefficients.

вектора $$\overline{a}$$

. Используя коэффициенты $$a_1÷a_M$$

, составим полином, зависящий от частоты ω (5).Solving the vector equation (4), we can obtain the values of the coefficients $$a_{\mathrm{one}}÷a_M$$

of vector $$\overline{a}$$

. Using the coefficients $$a_{\mathrm{one}}÷a_M$$

, we compose a polynomial depending on the frequency ω (5).

$$\stackrel{\wedge }{Y}(\omega )={\stackrel{\wedge }{x}}^M+{\stackrel{\wedge }{a}}_{{}_M}{\stackrel{\wedge }{x}}^{M-\mathrm{one}}+{\stackrel{\wedge }{a}}_{{}_{M-\mathrm{one}}}{\stackrel{\wedge }{x}}^{M-2}+......{\stackrel{\wedge }{a}}_{{}_2}\stackrel{\wedge }{x}+{\stackrel{\wedge }{a}}_{{}_{\mathrm{one}}}=0(5)$$

. Следовательно, по выражениям (10) можно определить коэффициенты $${\stackrel{\wedge }{C}}_p^{(m)}$$

, которые представляют собой элементы импульсной последовательности фильтра для выделения однолучевого поля из суммы полей ионосферного сигнала. Используя коэффициенты $${\stackrel{\wedge }{C}}_p^{(m)}$$

, можно выделить (отфильтровать) однолучевые поля $${\stackrel{\wedge }{E}}_n^m$$

(выражения (6)).The roots of a polynomial of degree M give M solutions $${\stackrel{\wedge }{x}}^{(m)}=\exp (i{\omega }_m\Delta t)$$

. Therefore, using expressions (10), we can determine the coefficients $${\stackrel{\wedge }{C}}_p^{(m)}$$

, which are the elements of the pulse sequence of the filter to highlight a single-beam field from the sum of the fields of the ionospheric signal. Using the coefficients $${\stackrel{\wedge }{C}}_p^{(m)}$$

, you can select (filter) single-beam fields $${\stackrel{\wedge }{E}}_n^m$$

(expressions (6)).

$$\frac{{\stackrel{\wedge }{E}}_{{}_n}^{(\mathrm{one})}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(\mathrm{one})}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(\mathrm{one})}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(\mathrm{one})}=\stackrel{}{{\stackrel{\wedge }{U}}_{\mathrm{one}}\exp (-i{\overline{K}}_{\mathrm{one}}{\overline{R}}_n)}}{{\stackrel{\wedge }{E}}_{{}_n}^{(M)}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(M)}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(M)}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(M)}=\stackrel{\wedge }{{\stackrel{\wedge }{U}}_M\exp (-i{\overline{K}}_M{\overline{R}}_n)}}(6)$$

For each single-beam field, by performing the spatial Fourier transform, one can obtain a radiation pattern.

$${\stackrel{\wedge }{U}}_m({\alpha }_m^{\text{'}\text{'}},{\beta }_m^{\text{'}\text{'}})={\displaystyle \sum _n^N{\stackrel{\wedge }{E}}_n^{(m)}\exp (i{\overline{K}}_m({\alpha }_m^{\text{'}\text{'}},{\beta }_m^{\text{'}\text{'}}){\overline{R}}_n)},m=\mathrm{one}÷M(12)$$

, для М лучей ионосферного сигнала.The maximums of the radiation patterns determine the azimuths α _m , elevation angles β _m and amplitudes $${\stackrel{\wedge }{U}}_m$$

, for M rays of the ionospheric signal.

The azimuth dispersion D _α and the dispersion of elevation angles D _β for a single-beam field (Rao-Cramer dispersion) with a three-dimensional antenna system are determined by the expressions.

$$D_{\alpha }=\frac{2{\sigma }^2}{|\; |\; |\stackrel{\wedge }{E}|\; |\; |{(k_{0}R\cos (\beta ))}^{2}N}$$

$$D_{\beta }=\frac{6{\sigma }^2}{{|\; |\; |\stackrel{\wedge }{E}|\; |\; |}^2{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="00000132.png,00000134.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2({(3R\sin (\beta ))}^{2}N+2{(Z\cos (\beta \text{'}\text{'}))}^{2}M\mathrm{one})}(13)$$

where σ ^{2 is the} dispersion of noise,

- модуль напряженности однолучевого поля, $$|\; |\; |\stackrel{\wedge }{E}|\; |\; |$$

- single-field field strength module,

K ₀ = 2π / λ is the wave number, λ is the wavelength,

R is the radius of the antenna system,

Z is the coordinate perpendicular to the surface of the earth,

N, M1 - the number of vibrators on a circle of radius R and along the coordinate Z.

The azimuth dispersion is determined only by vibrators located on a circle on the ground (N). The dispersion of the elevation angle depends on both the horizontal spatial base and the vertical base of the antenna system. At β = 0, the variance of the elevation angle is determined by the expression

$$D_{\beta |\; |\; |}{}_{b=0}=\frac{3{\sigma }^2}{{|\; |\; |\stackrel{\wedge }{E}|\; |\; |}^2{(k_{0}Z)}^{2}M\mathrm{one}}(\mathrm{fourteen})$$

Thus, the variance of the elevation angle depends on the new spatial base:

$$L=\sqrt{{(R\sin (\beta ))}^{2}N+2{\left(\frac{Z}{3}\cos (\beta \text{'}\text{'})\right)}^{2}M\mathrm{one}}(\mathrm{fourteen})$$

This base does not vanish at a value of β tending to zero. Therefore, the dispersion of the three-dimensional antenna system will not increase as β approaches zero. The problem of small elevation angles during direction finding of ionospheric signals is solved.

The essence of the proposed method for estimating the angular parameters of ionospheric signals is illustrated by the following figures and diagrams.

Figure 1 presents the structural diagram of the device with which the prototype "Method of direction finding taking into account the correlation relationship between the rays" is implemented.

Figure 2 presents the structural diagram of the device with which the proposed method "Method for assessing the angular parameters of the ionospheric signal" is implemented. Compared with the prototype, the second, third, fourth blocks are identical to the blocks of the prototype, instead of 1.5 ÷ 8 blocks of the prototype, the actions of the new blocks of 1.5 ÷ 12 are proposed. Using these blocks, a spatio-temporal array is formed, a correlation matrix and the right column vector of the vector equation are created. When solving the vector equation, the coefficients are found, the polynomial is formed and its roots are found. This makes it possible to determine the elements of the pulse sequence of filters and to select (filter) single-beam fields. The radiation patterns for individual rays are determined, and the amplitudes and angular characteristics are estimated from the maxima of the radiation patterns.

Figure 3 shows the location of the antennas on the surface of the earth that make up a circular antenna system (16 vibrators), supplemented by a vertical line of vibrators (5 vibrators installed over an interval of 10 m) "Circle-Z". The radius of the antenna system is 65 m.

Figure 4 shows the elevation radiation patterns of the Circle-Z antenna system at a frequency of 10 MHz (line 2), at a frequency of 15 MHz (line 1) and the elevation radiation patterns of a flat circular antenna system at a frequency of 10 MHz (line 3). In the region of small elevation angles, the flat antenna system does not have a clearly defined maximum, and therefore, elevation angles are determined with large errors. So, for example, if a plane wave arrives at an elevation angle of 10 °, then the Circle-Z antenna system has a maximum radiation pattern at β = 10 °. At the same time, the directional pattern of a flat antenna system "Circle" has a flat top from 0 ° to 20 °. This leads to the problem of small angles when receiving ionospheric signals.

Figure 5 shows the variance of the elevation angles of the antenna system "Circle-Z" depending on the elevation angles of a plane wave. The solid line represents the calculation of the variance of elevation angles using expression (13). The dots indicate the variances of elevation angles obtained when evaluating it from 50 calculations. Thus, the addition of a line of vibrators to altitudes from 0 to 40 m to a flat antenna of the “Circle” type completely solves the problem of small angles when receiving ionospheric signals.

Figure 6 shows the elevation angles of a multipath ionospheric signal obtained using an eight-channel direction finder, operating according to the algorithm of the proposed method of direction finding. Using the direction finder, signals are received by the BBC radio station (England). f = 6.02 MHz. The presence of both a two-beam structure of the ionospheric signal and a three-beam structure is noted. It is not possible to obtain such estimates of elevation angles using classical direction finding methods.

The structural diagram of the device, which implements a method for estimating the angular parameters of ionospheric signals, is presented in figure 2.

According to the proposed method, the sequence of actions is as follows (figure 2).

1. Receive the ionospheric signal using a circular antenna system, complemented by a vertical line of vibrators with respect to the earth's surface. Create a three-dimensional antenna system (block 1).

2. Convert the signals in each channel (from each vibrator) in frequency, amplify and filter using a multi-channel receiver (block 2).

3. Convert the analog signals at the outputs of the multi-channel receiver into digital form using a multi-channel analog-to-digital converter (ADC) (block 3).

, выделяя максимумы частотных спектров (блок 4).4. Receive the frequency spectrum of the signal in N channels using the Fourier transform. Form a spatial array of complex data $${\stackrel{\wedge }{E}}_n$$

, highlighting the maxima of the frequency spectra (block 4).

, повторяя действия 1÷4 через интервалы 1÷2 с. Количество временных срезов данных на единицу больше (m=1÷M+1), чем количество лучей М (блок 5).5. Form a spatio-temporal data array $${\stackrel{\wedge }{E}}_{n,m}$$

repeating steps 1 ÷ 4 at intervals of 1 ÷ 2 s. The number of time slices of the data is one more (m = 1 ÷ M + 1) than the number of rays M (block 5).

, размерностью, равной количеству лучей ((М)*(М)), и правый вектор-столбец данных $$\overline{b}={(b_1÷b_M)}^T$$

, элементы которых усредняются по индексу n (по вибраторам, по пространству) (блок 6).6. Form a correlation matrix $$\stackrel{\wedge }{A}$$

, dimension equal to the number of rays ((M) * (M)), and the right column data vector $$\overline{b}={(b_{\mathrm{one}}÷b_M)}^T$$

, the elements of which are averaged by index n (by vibrators, by space) (block 6).

при решении векторного уравнения (4) (блок 7). $$\stackrel{\wedge }{A}\overline{a}=\overline{b}.\text{ (4)}$$

7. Determine the coefficients $$\overline{\alpha }={({\alpha }_{\mathrm{one}}÷{\alpha }_M)}^T$$

when solving the vector equation (4) (block 7). $$\stackrel{\wedge }{A}\overline{a}=\overline{b}.\text{(four)}$$

, степени М для оценки значений доплеровских сдвигов частот ионосферного сигнала по выражению (5) и оценки по минимумам полинома $$\stackrel{\wedge }{Y}(\omega )$$

М доплеровских сдвигов частот ионосферного сигнала ω_m (блок 8).8. Form a polynomial $$\stackrel{\wedge }{Y}(\omega )$$

, degree M for estimating the values of Doppler shifts of the frequencies of the ionospheric signal by expression (5) and estimating the minimums of the polynomial $$\stackrel{\wedge }{Y}(\omega )$$

M Doppler frequency shifts of the ionospheric signal ω _m (block 8).

$$\stackrel{\wedge }{Y}(\omega )={\stackrel{\wedge }{x}}^M+{\stackrel{\wedge }{a}}_{{}_M}{\stackrel{\wedge }{x}}^{M-\mathrm{one}}+{\stackrel{\wedge }{a}}_{{}_{M-\mathrm{one}}}{\stackrel{\wedge }{x}}^{M-2}+......{\stackrel{\wedge }{a}}_{{}_2}\stackrel{\wedge }{x}+{\stackrel{\wedge }{a}}_{{}_{\mathrm{one}}}=0$$

$${\stackrel{\wedge }{x}}_m=\exp (i{\omega }_m\Delta t)(5)$$

$${\stackrel{\wedge }{C}}_m^k=({\stackrel{\wedge }{a}}_m^{}+{\stackrel{\wedge }{C}}_{m-1}^k){\stackrel{\wedge }{x}}_k^{*},$$

$${\stackrel{\wedge }{C}}_m^{(k)}=\mathrm{1,}$$

9. Determine the elements of the pulse sequences of the filters $${\stackrel{\wedge }{C}}_{\mathrm{one}}^{(k)}={\stackrel{\wedge }{a}}_{\mathrm{one}}^{}{\stackrel{\wedge }{x}}_k^{*},$$

$${\stackrel{\wedge }{C}}_m^k=({\stackrel{\wedge }{a}}_m^{}+{\stackrel{\wedge }{C}}_{m-\mathrm{one}}^k){\stackrel{\wedge }{x}}_k^{*},$$

$${\stackrel{\wedge }{C}}_m^{(k)}=\mathrm{one,}$$

k = 1 ÷ M (block 9).

из совокупности полей ионосферного сигнала по выражениям (6) (блок 10).10. Allocate (filter) single-beam fields $${\stackrel{\wedge }{E}}_n^m$$

from the set of ionospheric signal fields according to expressions (6) (block 10).

$$\frac{{\stackrel{\wedge }{E}}_{{}_n}^{(\mathrm{one})}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(\mathrm{one})}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(\mathrm{one})}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(\mathrm{one})}=\stackrel{}{{\stackrel{\wedge }{U}}_{\mathrm{one}}\exp (-i{\overline{K}}_{\mathrm{one}}{\overline{R}}_n)}}{{\stackrel{\wedge }{E}}_{{}_n}^{(M)}={\stackrel{\wedge }{E}}_{{}_{n\mathrm{,one}}}{\stackrel{\wedge }{C}}_{\mathrm{one}}^{(M)}+{\stackrel{\wedge }{E}}_{{}_{n\mathrm{,\; 2}}}{\stackrel{\wedge }{C}}_2^{(M)}+......+{\stackrel{\wedge }{E}}_{{}_{n,M}}{\stackrel{\wedge }{C}}_M^{(M)}=\stackrel{\wedge }{{\stackrel{\wedge }{U}}_M\exp (-i{\overline{K}}_M{\overline{R}}_n)}}(6)$$

диаграммы направленности с помощью пространственного преобразования Фурье по выражению (12) и сканируют этой диаграммой направленности в диапазоне оценочных азимутов α'=0÷360° и углов места β'=0÷90°.11. Form for each selected field $${\stackrel{\wedge }{E}}_n^m$$

radiation patterns using the spatial Fourier transform according to expression (12) and scan this radiation pattern in the range of estimated azimuths α '= 0 ÷ 360 ° and elevation angles β' = 0 ÷ 90 °.

$${\stackrel{\wedge }{U}}_m({\alpha }_m^{\text{'}\text{'}},{\beta }_m^{\text{'}\text{'}})={\displaystyle \sum _n^N{\stackrel{\wedge }{E}}_n^{(m)}\exp (i{\overline{K}}_m({\alpha }_m^{\text{'}\text{'}},{\beta }_m^{\text{'}\text{'}}){\overline{R}}_n)},m=\mathrm{one}÷M(bl\mathrm{about}\mathrm{to}\text{eleven})(12)$$

, углы места $${\beta }_m^{\text{'}}={\beta }_{\mathrm{0,}m}$$

и амплитуды $${\stackrel{\wedge }{U}}_m$$

по максимуму диаграммы направленности для М лучей ионосферного сигнала (блок 12).12. Estimated azimuths $${\alpha }_m^{\text{'}\text{'}}={\alpha }_{0m}$$

elevation angles $${\beta }_m^{\text{'}\text{'}}={\beta }_{0m}$$

and amplitudes $${\stackrel{\wedge }{U}}_m$$

maximum radiation pattern for M rays of the ionospheric signal (block 12).

Claims (1)

A method for evaluating the angular parameters of ionospheric signals, including the reception of an ionospheric signal using a circular antenna system consisting of N vibrators arranged uniformly around a circle of radius R, frequency conversion and amplification of signals from each n vibrator using a multi-channel receiver, conversion of analog signals at the outputs of a multi-channel the receiver in each n channel into digital form using a multi-channel analog-to-digital converter, determining the amplitude E _n and phase ψ _{n of the} received ionospheric the signal in each channel using the time Fourier transform, characterized in that the circular antenna system is supplemented with a vertical line of vibrators with numbers n = N + 1 ÷ N1, creating a three-dimensional antenna system, additionally using the antenna system, multi-channel receiver, multi-channel ADC, conversion unit Fourier form a spatio-temporal data array E _{n, k} , ψ _{n, k} , repeating the measurements through the time interval Δt = 1 ÷ 2 s, where the index n = 1 ÷ N1 determines the number of the vibrator, and the index k = 1 ÷ K determines the number of the temporary data cut x, wherein K = M + 1, is formed by a spatio-temporal correlation matrix of the array data

, dimension equal to the number of rays M, with elements

, where the index p = 1 ÷ K, and the right column vector

, where T means the transposition of the column vector, the elements of which are averaged over the index n (over the vibrators), solving the vector equation $$\widehat{A}\overline{a}=\overline{b},$$

find the values of the M coefficients of the vector

equal to the number of rays, form a polynomial of degree equal to the number of rays m,

where $${\widehat{x}}_m=\exp (i{\omega }_m\Delta t),$$

and find M solutions (

, m = 1 ÷ M) of this polynomial, equal to the number of rays, determine, using the obtained solutions, the elements M of the pulse filter sequences

equal to the number of rays by which M single-beam fields are isolated (filtered)

an ionospheric signal equal to the number of rays from which two-dimensional radiation patterns are formed, azimuths α _m and elevation angles β _m M of the rays of the ionospheric signal are estimated from the maximums of the radiation patterns.

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