RU2516688C1 - Method of finding direction of ionospheric signals in beam interference conditions - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: circular antenna system, multichannel receiver, multichannel analogue-to-digital converter (ADC) and temporary Fourier transform are used to generate a space-time array of complex data E_n,k, displaying field strength values at n points in space (n is the number of the dipole) and at k moments in time with measurement intervals of 1-2 s. A correlation matrix is formed, whose dimension is equal to the number of beams, elements of which are averaged across space. Azimuth and elevation angle estimates are given and beam parameters are estimated based on the maxima of a likelihood composite function in the two-dimensional space of azimuths and elevation angles.

EFFECT: faster and more accurate determination of angular parameters of a multi-beam ionospheric signal.

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Description

The invention relates to radio engineering, namely, to the field of direction finding, and can be used for direction finding (measuring azimuths) and measuring elevation angles of ionospheric signals under conditions of receiving several interfering rays in a wide frequency range. When receiving ionospheric signals, as a rule, several rays (1 ÷ 4 or more), reflected from different layers of the ionosphere, come with the azimuths located in the main lobe of the radiation pattern (~ 5 ÷ 10 degrees). Due to interference, the total main lobe of the antenna system’s radiation pattern changes significantly, creating false bearings that differ from true bearings by tens of degrees.

Known phase direction finding methods, carried out by measuring the phase difference between the vibrators of the antenna system and evaluating these measurements of azimuths and elevation angles (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 dated March 25, 2003, G01S 3/14, published October 10, 2004). The disadvantage of the above methods is that only phase information is used. This requires, for the sake of uniqueness, the measurement of phases on the vibrators of small, compared with the wavelength, spatial diversity of the vibrators

, $$R_{n+\mathrm{one}}-R_n<\frac{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000058.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}{2}$$

,

Under conditions of receiving two (or several) rays close in azimuth, phase direction finding methods are unstable. When the phase difference between the rays is ~ 180 °, they give bearing deviations of tens of degrees (false bearings).

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. 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):

$$\hat{U}\left({\alpha }^{\prime },{\beta }^{\prime }\right)=\frac{\mathrm{one}}{N}{\displaystyle \sum _{n=\mathrm{one}}^N{\hat{E}}_n{e}^{-i\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right){\overline{R}}_n}},(\mathrm{one})$$

,where Ê = E _{0, n} exp (iψ _n ) is the complex amplitude of the field strength of the ionospheric signal at the n-point of space with a radius vector $${\overline{R}}_n$$

,

E _{0, n} , ψ _n is the amplitude and phase of the signal field strength on the n-vibrator.

- оценочный волновой вектор ионосферного сигнала, $$\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right)$$

- estimated wave vector of the ionospheric signal,

α ', β' - 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

$$U^2\left({\alpha }^{\prime },{\beta }^{\prime }\right)=\frac{{\overline{E_n\cos \left({\psi }_n-\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right){\overline{R}}_n\right)}}^2+{\overline{E_n\sin \left({\psi }_n-\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right){\overline{R}}_n\right)}}^2}{{\overline{E}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="00000058.png"\; state="\{\{state\}\}">n</figure-callout>}}^2},(2)$$

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

The disadvantage of the above methods associated with the spatial Fourier transform is the instability of the solution in the presence of a lot of beam interference with a phase difference between the rays of ~ 180 °. When two 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 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.

Known methods of direction finding, the antenna system in which 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 is low noise immunity, due to the lack of statistical data processing, and the presence of false bearings when receiving two close in azimuth rays of the ionospheric signal.

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

According to this method of direction finding (prototype), the sequence of actions is as follows. Using an antenna array consisting of N vibrators located uniformly around a circle of radius R (spatial base of the signal) 1) receive ionospheric signals, 2) convert them in frequency and 3) amplify through a multi-channel receiver. From the outputs of the receiver, the analog signals in each channel (from each vibrator) 4) are converted into digital form using a multi-channel analog-to-digital converter (ADC), 5) the amplitudes E _{0, n} and phase ψ _{n of the} received ionospheric signal in each channel (from each vibrator) using the temporary Fourier transform and 6) form the total four-dimensional (for two rays) radiation pattern taking into account the correlation coefficient between the rays according to the expressions

$$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}},\right)=\frac{\hat{U}\overline{E_n^{*}\exp \left(-i\overline{k}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}\right){\overline{R}}_n\right)}+\hat{U}\overline{E_n^{*}\exp \left(-i\overline{k}\left({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right){\overline{R}}_n\right)}}{\overline{{\hat{E}}_n{\hat{E}}_n^{*}}},(3)$$

Where

$${\hat{U}}_{{}_{\mathrm{one}}}=\frac{\overline{{\hat{E}}_n\exp \left(i{\overline{k}}_{\mathrm{one}}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}\right){\overline{R}}_n\right)}+\overline{E_n\exp \left(i{\overline{k}}_2\left({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right){\overline{R}}_n\right)}\hat{A}}{\mathrm{one}-\hat{A}{\hat{A}}^{*}}$$

$${\hat{U}}_{{}_2}=\frac{\overline{{\hat{E}}_n\exp \left(i{\overline{k}}_2\left({\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right){\overline{R}}_n\right)}+\overline{{\hat{E}}_n\exp \left(i{\overline{k}}_{\mathrm{one}}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}\right){\overline{R}}_n\right)}\widehat{A^{*}}}{\mathrm{one}-\hat{A}{\hat{A}}^{*}}$$

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

Ê _n is the complex amplitude of the signal, measured on an n-vibrator,

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

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

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

- волновые векторы первого и второго лучей ионосферного сигнала, зависящие от оценочных азимутов $${\alpha }_1^{\text{'}},{\alpha }_2^{\text{'}}$$

и углов места $${\beta }_1^{\text{'}},{\beta }_2^{\text{'}}$$

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

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

- 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 $${\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}$$

.

Â1 - correlation coefficient between the rays,

a dash means summation over index n.

The * sign means complex conjugation,

the sign ^ means a complex quantity.

и $${\beta }_1^{\text{'}},{\beta }_2^{\text{'}}$$

в указанных угловых диапазонах с определенным шагом, запоминая значения параметров $${\alpha }_1^{\text{'}},{\alpha }_2^{\text{'}}$$

, $${\beta }_1^{\text{'}},{\beta }_2^{\text{'}}$$

, $${\hat{U}}_1,{\hat{U}}_2$$

, $$\hat{U}\left({\alpha }_1^{\text{'}},{\beta }_1^{\text{'}},{\alpha }_2^{\text{'}},{\beta }_2^{\text{'}}\right)$$

.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, remembering the values of the parameters $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}}$$

, $${\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}$$

, $${\hat{U}}_{\mathrm{one}},{\hat{U}}_2$$

, $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

.

 The azimuth and elevation of each beam 8) is determined by the maximum of the four-dimensional radiation pattern.

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. Если T необходимое время расчета параметров одного луча в одной точке области определения и M количество точек, то для N лучей требуется время T_N=T*M^2N.The disadvantage of this method is its limitations 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 high complexity associated with the need to sort (scan by radiation pattern) of two azimuths and two elevation angles $$\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},\mathrm{and}{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

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 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. If T is the necessary time for calculating the parameters of one ray at one point in the domain of definition and M is the number of points, then for N rays the time T _N = T * M ^2N is required.

The block diagram 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 consisting of N vibrators

$$\left(N\ge N\mathrm{one}+\frac{\mathrm{one}}{(\mathrm{one}-{|\; |\; |\hat{A}\mathrm{one}|\; |\; |}^2},N\mathrm{one}=8\right)$$

located on the surface of the earth evenly around a circle of radius R

(блок 1) $$\left(R\ge \frac{2\mathrm{<figure-callout\; id="3"\; label="\pi "\; filenames="00000058.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{3|\; |\; |{\overline{k}}_{\mathrm{one}}\left({\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000057.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01},{\beta }_{01}\right)-\overline{k}\left({\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000057.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02},{\beta }_{02}\right)|\; |\; |}\right)$$

(block 1)

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

3. Convert the analog signals 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 vibrator (in each channel), for example using a temporary Fourier transform (block 4).

и углов места $${\beta }_1^{\text{'}},{\beta }_2^{\text{'}}$$

и вычисляют согласно (3) четырехмерную диаграмму направленности $$\hat{U}\left({\alpha }_1^{\text{'}},{\beta }_1^{\text{'}},{\alpha }_2^{\text{'}},{\beta }_2^{\text{'}}\right)$$

в заданной точке по выборке данных Ê_n и запоминают ее значения и значений переменных Û₁, Û₂, $${\alpha }_1^{\text{'}},{\beta }_1^{\text{'}},{\alpha }_2^{\text{'}},{\beta }_2^{\text{'}}$$

(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 calculate according to (3) a four-dimensional radiation pattern $$\hat{U}\left({\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}\right)$$

at a given point in the data sample Ê _n and remember its values and the values of the variables Û ₁ , Û ₂ , $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}},{\beta }_{\mathrm{one}}^{\text{'}\text{'}},{\alpha }_2^{\text{'}\text{'}},{\beta }_2^{\text{'}\text{'}}$$

(block 5).

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 the actions of block 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).

, а также Û₁=Û₀₁, Û₂=Û₀₂ (блок 7).7. Determine the maximum value of the four-dimensional radiation pattern and fix the parameters $${\alpha }_{\mathrm{one}}^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="01"\; label="\alpha "\; filenames="00000057.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{01},{\beta }_{\mathrm{one}}^{\text{'}\text{'}}={\beta }_{01},{\alpha }_2^{\text{'}\text{'}}={\mathrm{<figure-callout\; id="02"\; label="\alpha "\; filenames="00000057.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{02},{\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="00000058.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_2^{\mathrm{one}}={\mathrm{<figure-callout\; id="02"\; label="\beta "\; filenames="00000057.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_{02}$$

, as well as Û ₁ = Û ₀₁ , Û ₂ = Û 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 purpose of this invention (technical result) is to expand the capabilities of the “Direction finding method taking into account the correlation relationship” in the case of receiving K rays (K = 1 ÷ 4 or more) and reducing the time of calculating the angular parameters of a multipath ionospheric signal.

The technical result is achieved by the fact that using a circular 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 Ê _{n, k} is displayed that displays the field strengths at n points of space (n - vibrator number) and at k time instants with intervals of 1-2 seconds (the index k determines the number of time slice data on n vibrators, k = 1 ÷ k). A correlation matrix  is formed with a dimension equal to the number of rays (K * K), the elements of which are averaged over the index n (over vibrators, over space), the estimated azimuth values α 'and elevation angle β' are determined from the domain of their determination and according to the matrix expression (4 ) undetermined coefficients â ₁ ÷ â ₄ ,

$$\hat{A}\overline{a}=\overline{b},gde(\mathrm{four})$$

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

,

k = 1 ÷ K, p = 1 ÷ K, n = 1 ÷ N, the bar above means summation over the index n,

- вектор-столбец с координатами $${\hat{b}}_k=\overline{\exp \left(-i\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right){\overline{R}}_n\right)E_{n,k}^{*}}$$

(черта сверху определяет суммирование по индексу n, по вибраторам). $$\overline{b}={\left({\hat{b}}_{\mathrm{one}}÷{\hat{b}}_K\right)}^T$$

- column vector with coordinates $${\hat{b}}_k=\overline{\exp \left(-i\overline{K}\left({\alpha }^{\prime },{\beta }^{\prime }\right){\overline{R}}_n\right)E_{n,k}^{*}}$$

(the bar above determines the summation over index n, over vibrators).

ā = (â ₁ ÷ â _K ) ^T is the column vector of the indefinite coefficients.

Estimation of uncertain coefficients allows to obtain a value

normalized likelihood functional Δ (α ', β') according to expression (5).

$$\Delta \left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)=\frac{\mathrm{one}}{\mathrm{one}-{\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{k=\mathrm{one}}^K|\; |\; |{\hat{a}}_k{\hat{E}}_{{}_{n,k}}\exp \left(i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)|\; |\; |}}}(5)$$

By searching in azimuth α 'and elevation angle β', a complete functional surface is created in the two-dimensional space of angles (0 ÷ 360 ° in azimuth and 0 ÷ 90 ° in elevation). Using the threshold value U ₀ = 20, K maxima of this surface are extracted, from which the estimated azimuths and elevation angles K of the rays of the ionospheric signal are determined.

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

- 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 (data slices) and the most optimal joint spatio-temporal data processing is carried out.

- Instead of evaluating the parameters of the rays by the maximum of the four-dimensional radiation pattern in the prototype, the proposed method estimates the parameters of the rays by the maxima of the likelihood functional (the number of maxima coincides with the number of rays) in the two-dimensional space of azimuths and elevation angles.

The rationale for the method of direction finding of the ionospheric signal under the conditions of ray interference is as follows.

We write the signal on the n-vibrator and at the k-point in time Ê _{n, k} in a complex form in the form

$${\hat{E}}_{n,k}={\displaystyle \sum _m^M{\hat{U}}_{{}_m}{e}^{i\left({\omega }_m{t}_k-{\overline{K}}_m\left({\alpha }_{0m},{\beta }_{0m}\right){\overline{R}}_n\right)}}(6)$$

where Û _m is the complex amplitude of the m-beam of the ionospheric signal,

- волновой вектор m-луча ионосферного сигнала, $${\overline{K}}_m\left({\alpha }_{0m},{\beta }_{0m}\right)$$

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

α _{0, m} , β _{0, m} - azimuth and elevation angle of the m-beam of the ionospheric signal,

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

- location of the n-vibrator,

t _k is the time of reading the field strength (k varies from 1 to K, K = M is the number of rays in the ionospheric signal,

ω _m is the circular frequency of the m-beam of the ionospheric signal.

Using the time sequence of data, we exclude variables that describe the field M-1 of the beam

. $$\left({\hat{U}}_{{}_m},{\overline{K}}_m\left({\alpha }_{0m},{\beta }_{0m}\right),{\omega }_m\right)$$

.

As a result, we obtain expression (7) with undetermined coefficients â ₁ ÷ â _K , the expression on the right side of which describes the field of only one wave with unit amplitude (the index m of the variables is removed).

$${\displaystyle \sum _{k=\mathrm{one}}^K{\hat{a}}_k{\hat{E}}_{n,k}=e^{-i\overline{K}\left({\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="00000062.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_0,{\beta }_0\right){\overline{R}}_n}}(7)$$

Undetermined coefficients â ₁ ÷ â _K do not depend on the number of the vibrator n. They depend only on the time interval Δt. Therefore, they are the same for expression (7) for different values of the index n. Based on this, it is possible to carry out statistical processing of spatial data using the maximum likelihood method to find the values of uncertain coefficients. To do this, we write functional (8).

$$\Delta \mathrm{one}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)={{\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{k=\mathrm{one}}^K|\; |\; |{\hat{a}}_k{\hat{E}}_{n,k}-e^{-i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n}|\; |\; |}}}^2(8)$$

In this expression, primes indicate the estimated azimuth and elevation. Differentiating expression (8) with respect to the indefinite coefficients â ₁ ÷ â _K and equating the differentials to zero, we obtain the matrix equation (4).

$$\hat{A}*\overline{a}=\overline{b}$$

.where  is the correlation matrix, the elements of which are determined by the field values on the vibrators $$\overline{{\hat{E}}_{n,k}{\hat{E}}_{n,p}^{*}}$$

.

Summation is performed on index n (the bar is above), the indices k = 1 ÷ K, p = 1 ÷ K determine the dimension of the matrix.

ā = (â ₁ ÷ â _K ) ^T - vector column column of uncertain coefficients.

- вектор столбец, коэффициентами которого являются выражения $$\overline{b}={\left(b_{\mathrm{one}}÷b_K\right)}^T$$

is a column vector whose coefficients are expressions

$$b_K=\overline{\exp -(-i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n{\hat{E}}_{n,k}^{*}}$$

By setting the estimated values of α ', β' from the domain of determination (0-360 ° in azimuth and 0 ÷ 90 ° in elevation), it is possible to solve matrix equation (4) and determine the uncertain coefficients â ₁ ÷ â _K. Substituting them into the likelihood functional (8), we can obtain a surface point of this functional. Going through all the values of the estimated angles α ', β' from the domain of their determination, and repeating the calculation of the coefficients â ₁ ÷ â _K and functional (8), we can obtain the entire surface of the functional. The minima of this surface determine the solutions. For convenience, the functional Δ1 (α ', β') (8) can be transformed into a normalized functional (5).

$$\Delta \left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)=\frac{\mathrm{one}}{\mathrm{one}-{\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{k=\mathrm{one}}^K|\; |\; |{\hat{a}}_k{\hat{E}}_{n,k}\exp \left(i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)|\; |\; |}}}$$

In this solution functional, its maxima are determined, the values of which vary from 1 to infinity depending on the noise variance. Provided that the signal-to-noise ratio is 20 dB, the threshold value U ₀ separating the maximum values from the noise maximums is U ₀ = 20. Thus, the maxima exceeding the threshold value U ₀ determine K solutions:

$${\alpha }_k^{\text{'}\text{'}}={\alpha }_{0k},{\beta }_k^{\text{'}\text{'}}={\beta }_{0k}$$

If the number of rays in the received ionospheric signal is less than the expected, then for extra rays the maximum of the functional will be at the level of noise maximums and due to the set threshold they are excluded.

The essence of the proposed method for direction finding of ionospheric signals in the conditions of interference of rays is illustrated by the following drawings.

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 of direction finding is implemented. Compared with the prototype, the first four blocks are identical, instead of 5–8 blocks of the prototype, the actions of the new 5–10 blocks are proposed. Using these blocks, a spatio-temporal array is formed, which is transformed using uncertain coefficients (7), and the angular parameters of the multipath ionosphere signal are estimated by the maximum likelihood method.

Figure 3 shows the location of the antennas on the earth's surface, constituting a circular antenna system. The number of vibrators is 16, the radius of the antenna system is 65 m.

Figure 4 shows a schematic spatial-temporal array obtained in block 5. The number of vibrators N, the number of time slices of data K, obtained after a time interval Δt = 1 ÷ 2 s.

Figure 5 shows the surface of the likelihood functional Δ (α ', β') (Delta) depending on the azimuth α '(Alfa) and elevation angle β' (Beta). The four maximums of the functional surface determine the azimuths and elevation angles of the four rays of the ionospheric signal. The surface of the likelihood functional was obtained using model calculations in which the number of rays K = 4 with the angular parameters of the rays presented in Table 1 (the upper two rows) is taken. The bottom two rows of the table determine the likelihood functional, azimuths and elevation angles of four rays found using the maxima of the surface.

Table 1 αβ ° No. 1 Number 2 Number 3 Number 4 α, ° 70 68 66 64 β, ° 40 13 25 thirty α ', ° 70.12 68.12 67.12 64.12 β ', ° 40 12 twenty thirty

The values obtained using the proposed method for direction finding azimuths and elevation angles of four rays are consistent with their model values.

In Fig.6. shows the surface of the likelihood functional obtained using model calculations under the following conditions. The model contains an ionospheric signal with two beams. The calculation of the functional surface was carried out by a four-beam algorithm. The maxima of the two extra rays do not exceed the level of noise maxima (not visible in the drawing). Therefore, the proposed location method is fully operational in cases of receiving an ionospheric signal with one, two, three and four beams.

Figure 7 shows the elevation angles of a multipath ionospheric signal obtained using an eight-channel direction finder operating according to the algorithm of the proposed direction finding method. Using the direction finder, signals are received from Moscow station (RVM) at a frequency f = 9.996 MHz for 22 s. 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 proposed method of direction finding of ionospheric signals in the conditions of interference of rays is as follows (figure 2).

1. Receive signals using a circular antenna system consisting of N vibrators located on the earth's surface evenly around a circle of radius R (block 1).

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

3. Convert the analog signals 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 vibrator (in each channel), for example, using a temporary Fourier transform (block 4).

5. Repeating the actions in blocks 1 ÷ 4 K times (K is the number of rays of the ionospheric signal), at time intervals Δt = 1 ÷ 2 s, a spatio-temporal data array E _{n, k} , ψ _{n, k is formed} (k = 1 ÷ K , data slice number on the vibrators) (block 5).

, (k=1÷k, p=1÷k, n=1÷N). Черта сверху определяет суммирование по индексу n (блок 6).6. Form a correlation matrix of data with elements $$\overline{{\hat{E}}_{n,k}{\hat{E}}_{n,p}^{*}}$$

, (k = 1 ÷ k, p = 1 ÷ k, n = 1 ÷ N). The bar above determines the summation over index n (block 6).

7. A point is set in the domain of determining the estimated angles α ', β' and the indefinite coefficients â ₁ ÷ â ₄ are calculated using the matrix equation (4), with which the likelihood functional (5) is calculated (block 7).

$$\Delta \left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)=\frac{\mathrm{one}}{\mathrm{one}-{\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{k=\mathrm{one}}^K|\; |\; |{\hat{a}}_k{\hat{E}}_{n,k}\exp \left(i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)|\; |\; |}}}$$

8. By searching in azimuth α 'and elevation angle β', repeating the actions in block 7, create a complete functional surface in two-dimensional space of angles (0 ÷ 360 ° in azimuth and 0 ÷ 90 ° in elevation (block 8).

9. Using the threshold level U ₀ = 20 K, the maximums of the likelihood functional Δ (α ', β') ≥U _{0 are} distinguished, thereby determining the number of rays contained in the ionospheric signal.

и углы места $${\beta }_k^{\text{'}}={\beta }_{\mathrm{0,}k}$$

K лучей ионосферного сигнала по выделенным K максимумам функционала правдоподобия.10. Estimated azimuths $${\alpha }_k^{\mathrm{one}}={\alpha }_{0k}$$

and elevation $${\beta }_k^{\text{'}\text{'}}={\beta }_{0k}$$

K rays of the ionospheric signal from the selected K maxima of the likelihood functional.

Claims (1)

A method for detecting ionospheric signals under interference of rays, including receiving a signal reflected from the ionosphere using an antenna system consisting of N vibrators arranged uniformly around a circle of radius R, frequency conversion and amplification of signals from each vibrator using a multi-channel receiver, analog conversion signals in each channel in digital form using a multi-channel analog-to-digital converter, determining the amplitude E _n and phase ψ _{n of the} received signal reflected from the ionosphere , in each channel using the time Fourier transform, characterized in that they additionally form a spatio-temporal data array E _{n, k} , ψ _{n, k} through the measurement time interval Δt = 1 ÷ 2 s, using the antenna system, a multi-channel receiver, a multichannel ADC and a Fourier transform block, then a correlation matrix is formed using a spatio-temporal data array $$\widehat{A}$$

with elements $$\overline{{\widehat{E}}_{n,k}{\widehat{E}}_{n,p}^{*}}$$

averaged over space (index n), after which a point is set in the domain of definition of the estimated angles α ', β' and the uncertain coefficients are determined $${\widehat{a}}_{\mathrm{one}}÷{\widehat{a}}_{\mathrm{four}}$$

according to the matrix equation
$$\widehat{A}\overline{a}=\overline{b}$$

,
Where $$\widehat{A}$$

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

,
k = 1 ÷ K, p = 1 ÷ K, n = 1 ÷ N, the bar above means summation over the index n,
$$\overline{b}={\left({\widehat{b}}_{\mathrm{one}}÷{\widehat{b}}_K\right)}^T$$

- column vector with coordinates $${\widehat{b}}_k=\overline{\exp \left(-i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right){\widehat{E}}_{n,k}^{*}}$$

(the bar above determines the summation over index n, over vibrators),
$$\overline{a}={\left({\widehat{a}}_{\mathrm{one}}÷{\widehat{a}}_K\right)}^T$$

- a column vector of undetermined coefficients with which help determine the value of the likelihood functional
$$\Delta \left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right)=\frac{\mathrm{one}}{\mathrm{one}-{\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{k=\mathrm{one}}^K|\; |\; |{\widehat{a}}_k{\widehat{E}}_{n,k}\exp \left(i\overline{K}\left(\alpha \text{'}\text{'},\beta \text{'}\text{'}\right){\overline{R}}_n\right)|\; |\; |}}}$$

,
then the complete surface of the likelihood functional Δ (α ', β') is formed by sorting the angles α ', β' in the range 0 ÷ 360 ° in the azimuth α 'and 0 ÷ 90 ° in the elevation angle β'; ₀ K maxima of the likelihood functional, after which the azimuths are estimated from the selected maxima $${\alpha }_k^{\text{'}\text{'}}={\alpha }_{0k}$$

and elevation $${\beta }_k^{\text{'}\text{'}}={\beta }_{0k}$$

for K rays of the signal reflected from the ionosphere.

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